THE SCIENCE OF LOGIC
THE
SCIENCE OF LOGIC
AN INQUIRY INTO THE PRINCIPLES OF ACCURATE THOUGHT AND SCIENTIFIC METHOD
P. COFFEY, PH.D. (LOUVAIN)
PROFESSOR OF LOGIC AND METAPHYSICS, MAYNOOTH COLLEGE, IRELAND
IN TWO VOLUMES
VOL. II. METHOD, SCIENCE, AND CERTITUDE
NEW YORK
PETER SMITH
1938
FIRST PUBLISHED, 1912
REPRINTED 1938 BY
SPECIAL ARRANGEMENT WITH
LONGMANS, GREEN AND CO., LONDON
FEB 1 6 1948
PRINTED IN THE UNITED STATES OF AMERICA
CONTENTS OF VOLUME II.
PART IV.
METHOD : OR THE APPLICATION or LOGICAL PROCESSES TO THE CERTAIN ATTAINMENT OF TRUTH.
CHAPTER I. GENERAL OUTLINE OF METHOD.
PAGE
200. Transition to Part IV i
201. Logic and Method 2
202. Synthesis and Analysis 7
203. General Rules of Method 10
204. Didactics : Analysis and Synthesis in Teaching 14
205. Scholastic Methods of Exposition and Debate 16
CHAPTER II.
INDUCTION IN ITS VARIOUS SENSES. INTRODUCTORY AND HISTORICAL NOTIONS.
206. The Problem of Induction : Ascent from the Particular to the Universal 23
207. The so-called " Inductive Syllogism " : or " Induction by Simple
Enumeration of Instances" — "Complete" and "Incomplete" . 27
208. Scientific Induction as Treated by Aristotle and the Mediaeval Scholastics 32
209. Lord Bacon's Novum Organon : The Two Ideals of Generalization . . 37
210. Modern Conceptions of Induction : Newton, Whewell, J. S. Mill, Jevons 41
211. Analysis and Illustration of the Process of Scientific Induction . . 44
212. Scientific Induction and Deductive Inference 48
213. Relation of Antecedent to Consequent in Induction and in Deduction:
The Latter Considered as an " Inverse Process " .... 53
CHAPTER III.
PRESUPPOSITIONS OF INDUCTION : CONCEPTS OF " REASON " AND " CAUSE ".
214. Justification of Chapters III. and IV 56
->I5. "Reality" and the " Principle of Sufficient Reason " .... 58
vi TABLE OF CONTENTS
PAGE
216. The "Principle of Causality" in Induction: Aristotle's Classification of
Causes . . 61
217. "Purpose" or "Design": "Final Causes" and "Law" in Physical
Nature 66
218. Contrast between Traditional and Empiricist Conceptions of Efficient
Causality 70
219. The Sensist or Empiricist View of Causality : Mill's Teaching . . 75
220. Causality, Sequence in Time, and Contiguity in Space .... 80
221. "Plurality of Causes": "Reciprocal" and "Non-Reciprocal" Causal
Relation 84
222. Science and the Discovery of " Causes " and " Laws " .... 86
CHAPTER IV.
PRESUPPOSITIONS OF INDUCTION : UNIFORMITY OF NATURE.
223. Interpretations of the Principle of Uniformity in Nature 93
224. Ultimate Rational Grounds ot our Belief in Uniformity : The Scholastic,
Empiricist, and Idealist Views 99
225. Relation of the Principle to Induction and to Deduction . . . .113
CHAPTER V. HYPOTHESIS: ITS NATURE, FUNCTIONS, AND SOURCES.
226. Functions of Scientific Hypothesis 120
227. Scientific Value of Various Kinds of Hypothesis 122
228. Nature and Verification of Causal or Explanatory Hypotheses . . 127
229. The R61e of Analogy in Verification : Ultimate Systematic Conceptions 135
230. Verification by Cumulative Evidence 141
231. " Postulates " and their Justification : " Truth " of Verified Hypotheses . 142
232. Theism as a Verifiable Hypothesis 145
233. Summary of Logical Requirements for a Legitimate Hypothesis . . 148
234. Sources of Scientific Hypotheses : Analogy ... . . 151
235. Worth of .Analogy : Its Function in Verification 155
236. The Argument from " Example " in Aristotle 158
237. "Analogy" as understood by Aristotle 160
CHAPTER VI.
METHOD OF DISCOVERING CAUSAL LAWS BY ANALYSIS OF FACTS : OBSERVATION AND EXPERIMENT.
238. Observation and Selection : Initial Precautions 162
239. Experiment : its Relations to Observation 164
240. The Function of Experiment : Difficulties of Analysis .... 165
241. The "Rules" or "Canons" of Inductive Analysis; "Methods" of
" Agreement " and " Difference " 172
242. Combination of " Agreement " and " Difference " 179
243. Method of " Concomitant Variations ". Measurement. Statistics. . 186
244. Method of" Residues," "Conjunction of Causes," and " Intermixture of
Effects" 193
245. Scope of the " Methods " : Use of Symbols .... . 197
246. Quantitative Determination : Modes of Measurement . . . .201
247. " Empirical Laws " and their Explanation : Transition to Part V. . .205
TABLE OF CONTENTS vii PART V.
THE ATTAINMENT OF SCIENCE AND CERTITUDE.
CHAPTER I. SCIENCE AND DEMONSTRATION.
PAGE
248. Elementary Notions Defined: Truth, Ignorance, Error, Evidence,
Certitude, Opinion, Probability, Doubt 210
249. Three Kinds of Certitude ; Metaphysical, Physical, and Moral . . 214
250. Necessary Truth of Metaphysical Laws ; Contingent Truth of Physical
Laws and Facts 217
251. Aristotle's Ideal of " Scientific " Knowledge 223
252. Nature and Conditions of Demonstration 225
253. Restricted Scope of Aristotelean " Science " 229
254. Principal Kinds of Proof 232
255. Demonstration and Scientific Explanation. " Popular Explanation " . 235
256. Limitations of Scientific Explanation 239
257. An Erroneous View of Explanation 241
258. Discovery and Proof of Truth by Induction and by Deduction . . . 243
259. Moral Certitude in the " Human " Sciences .... . 248
260. Belief on Authority 250
261. Historical Science and Certitude : Its Criteria and Sources . . . 253
CHAPTER II. OPINION AND PROBABILITY.
262. Nature of Probability : Cumulative Evidence : " Practical " Certitude . 260
263. Probable Arguments : The Aristotelean Enthymeme .... 263
264. Estimation of Probability : The Concept of " Chance " . . . .268
265. Conditions for the Mathematical Estimation of Probability . . . 272
266. Rules for Estimating Probability 276
267. Inverse Probability : Bernoulli's Theorem : Elimination of Chance . . 278
268. Application of the Calculus of Probability to Natural and Social
Phenomena 282
269. Function of Statistics and Averages : Their Right and Wrong Interpre
tations 285
CHAPTER III. ERROR AND FALLACIES.
270. Logical Treatment of Error and its Sources 294
271. Error and Fallacy 296
272. Some Attempted " Classifications " of Fallacies : " Formal " and
" Material " Fallacies 298
273. Fallacies Incident to Conception 303
274. Fallacies Incident to Judgment and Immediate Inference . . . 308
275. Fallacies Incident to Method 315
QUESTIONS 338
GENERAL INDEX 343
PART IV.
METHOD ; OR THE APPLICATION OF LOGICAL PRO CESSES TO THE ATTAINMENT OF TRUTH.
CHAPTER I. GENERAL OUTLINE OF METHOD.
200. TRANSITION TO PART IV.— We have now completed our examination of the formal aspect of the reasoning process, and of the rules that guarantee its formal correctness or validity (Part III.). But the object of all reasoning, of all science and philosophy in fact, is to arrive at a certain knowledge of truth ; and, to secure this, it is not enough that our reasoning processes be correct or valid formally : the judgments involved in them must, furthermore, be all both true and certain.
Truth is, as we saw (9, 79), contained in the mental act of judgment, to which the operations both of inference and of conception are thus subsidiary. An analysis of the material or " truth " aspect of inference will therefore, of necessity, direct our attention once more to the judgments of which our inferences are composed, and to the concepts or ideas which enter into our judgments (Parts I. and II.). After having separately examined each of the three mental operations, of conception, judgment, and inference, our next concern is to inquire how we reach true judgments, especially those true universal judgments which constitute scientific knowledge : how, in other words, we are to exercise those three mental operations on the data of knowledge to the best advantage for the acquiring of truth : how we are to regulate and co-ordinate those mental acts, conception, judgment, and reasoning, in exploring the various departments of the knowable universe. This portion of logical doctrine is variously described as applied logic, methodology, or the science of logical method.
VOL. II. I
2 THE SCIENCE OF LOGIC
In all logical inference, our reason for assenting to the conclusion is its evident connexion with premisses to which we have already assented. But how do we come to assent to these latter ? Either because they are self-evident — like the universal axioms involved in all inference (193), — or derived by demonstrative evidence from such self-evident truths, or generalized by induction from observed facts. The general truths of the sciences may, then, be roughly divided into these three classes : (a) self-evident axioms or principles, such, for example, as " The whole is greater than its part " : these are reached by a comparatively simple process of intellectual abstraction and intuition, involving Definition and Division of concepts, and their mutual comparison in judgment ; (£) general truths that are not self-evident, but which have been generalized by Induction from observed facts ; (c) conclusions inferred by Demonstration from truths of classes (a) or (£).
Before the inductive method was developed, attention was largely de voted, in the traditional Aristotelean logic, to definition, division, and demonstration — the tres modi sciendi as they were called.1 Definition, by analysing our concepts of things into the simplest possible notions, gives rise to certain primordial, self-evident relations between these notions. These relations are formulated in judgments and propositions which furnish the foundations of the scientific edifice— the principles of the sciences. While definition thus analyses our concepts, and gives us information about the nature of their objects, it thereby also shows us wherein those objects agree in thought and wherein they differ from one another. The process of differentiation, or classification, or division, is thus the indispensable con comitant of definition.
According as the mind becomes equipped with its elementary ideas and judgments by means of sense observation, and intellectual abstraction and intuition, it has recourse to the third mode of procedure, demonstration : it draws certain and evident conclusions from self-evident principles, and from these conclusions still further conclusions, and so on. The employment of those various functions or factors of science, for the advance of knowledge, is what the Scholastics called METHOD.
The process of (real) definition, understood in the Scholastic sense as an explanation of the nature of a thing, and the concomitant process of (real) division or classification, were always regarded in Aristotelean philosophy as material processes, involving observation and analysis of facts, abstraction, generalization, comparison, and even inference and verification of hypotheses — in a word, all the processes nowadays described as " subsidiary to in duction ". These made up the analytic stage of the Scholastic method, as demonstration constituted its synthetic stage.
20 1. LOGIC AND METHOD. — Before investigating the method
1Cf. ZIGLIARA, Logica, (13), (44).
GENERAL OUTLINE OF METHOD 3
or methods of applying the mental processes we have been mentioning, to the pursuit of truth, it will be useful here to take a glance by anticipation at the main departments of human knowledge which the logician may have in mind, and from which he may draw his illustrations, in investigating such methods.
We have pointed out already, in common with all logicians, that it is not the function of logic to explore the provinces of the special sciences in order to expound the various modes of procedure peculiar to each. This is the function of the special sciences themselves : each has, or ought to have, its own special methodology. Logic ought to confine itself to an exposition of those guiding laws and principles of reasoning and research which are so universal that the mind must conform to them always and in every department of rational investigation.1 In thus limiting its field, logic will not be aiding the study of the special sciences so directly as it will aid the study of philosophy proper ; for philosophy presupposes a general knowledge of all the special sciences and endeavours to synthesize their results ; and in this arduous work it is guided by no other " rules of philo sophizing" than the general canons and laws laid down in logic. Indeed, if there be any science to which logic should serve as a special introduction, it is philosophy, the " general science," and not any of the special sciences.
But it is difficult to carry out in practice what is so simple in theory. Just because philosophy does take up, interpret, collate, and harmonize — as far as possible — the assumptions and conclu sions of all the special sciences — mathematical, physical, natural, anthropological, social, economical, ethical, etc. — it is not easy in practice to say where the work of each special science ceases and that of philosophy begins. And so it is, too, with regard to the scope of logic. This may easily deviate into the investigation of methodological details proper to special sciences ; or — which is a more serious mistake — it may, by losing sight of some depart ments of human experience and falling unduly under the influence of others, set forth, as general canons of philosophical investiga tion, methods that may be valid only within the narrower pre suppositions of some special science or group of sciences. These
1 " Logica tradit communem modum procedendi in omnibus aliis scientiis. Modus autem proprius singularum scientiarum, in scientiis singulis circa principium tradi solet."— ST. THOMAS, In II. Metaph. lect. 5.
I *
4 THE SCIENCE OF LOGIC
are mistakes which writers on inductive logic since the time of Mill have not successfully avoided. Nor is it difficult to one looking back, to see why such mistakes were, humanly speaking, almost unavoidable.
At different epochs men engaged in the investigation of those higher and deeper problems which lie along the confines of philo sophy and the special sciences, have been very differently impressed as to the relative values of these latter in advancing human know ledge. At one time the attention of scholars is drawn more exclusively to one group of sciences, and again to another group : and the logic of each period will be found to reflect faithfully the then prevailing attitude, by its fuller consideration of the methods and data of the dominating group.
Thus we see that, broadly speaking, the Middle Ages wit nessed an exhaustive development of the logic of Deductive Reasoning. This was because men were then more satisfied with their principles of knowledge, and perhaps more religiously-minded ; because they set greater store on a knowledge of man's nature and destiny than on a knowledge of the external universe ; be cause for progress in the former they relied on (deductive) reason ing from great, broad, general principles and truths that were universally accepted at the time — some on the authority of God as being revealed by Him, others as self-evident, others again as sufficiently established partly by their intrinsic evidence and partly by the common assent and authority of the learned of past ages.
Then came the period of the Renaissance, a period of doubt about hitherto received principles, of revolt against authority and rejection of traditional views and methods. On the one hand, the hitherto accepted teachings of philosophy and religion were critically re-examined ; and this new analysis had finally the effect of adding to the traditional logic an extensive discussion on the possibility and grounds of human certitude, and on the ultimate criteria or tests of truth (17). On the other hand, a closer attention to the study of external nature led to a wonder ful progress in the domain of the physical sciences. The cultiva tion of this fertile field of research has been rewarded by rich and useful discoveries ; the physical universe is being eagerly explored and made to yield up its secrets ; and the general laws and con ditions according to which its phenomena unroll themselves are the keys by which its most hidden agencies are brought to light and utilized by human enterprise. Hence the high degree of
GENERAL OUTLINE OF METHOD 5
importance that has been attached to general truths of the physical order — in contrast with these other general truths that have to do with man's religion, natural or supernatural, with his moral conduct in life, with the inner nature of his own mind and soul, with the ultimate purpose of his existence, and with his final destiny.1 Hence, too, the very large and prominent place devoted in modern treatises on logic to an analysis of the method and processes by which general truths about the physical universe can be securely and certainly established : as if these were the only general truths of importance, or, anyhow, of most importance, to man ; as if physical induction were the only or the chief method of reaching a certain knowledge of the weightiest truths to which the human mind can hope to attain.
The modern logician of induction invites us into chemical, physical and physiological laboratories ; he familiarizes us with test-tubes and balances, with boilers and engines and dynamos, with microscopes and telescopes ; he teaches us how to observe and experiment, how to detect analogies between physical phenomena, how to construct hypotheses foreshadowing the laws according to which these phenomena take place ; he lays down canons which will help us to simplify our data by elimination of the unessential, and so to test or establish — or, it may be, to reject or to modify — our hypotheses, until we thus finally discover and generalize some abstract law about the conditions requisite for the occurrence and the recurrence of some physical event.
But the general truths we reach about the external universe, as distinct from man himself, by the application of such methods, constitute only one department of human knowledge— an important one, no doubt, yet by no means the most important. There is, for instance, the wide and fertile, if more difficult, department of human research which has for its object the phenomena of human activity in the individual, in the family, and in the State : the domains of anthropology and psychology, of the social, economic, and political sciences. The methods of discovering and establi shing general truths in these sciences should have no smaller degree of interest for the logician than the method of reaching, say, the law of universal gravitation. Yet the modern logician tells us comparatively little about the former : about statistics and averages and the canons of probability : the various means of reaching another class of general truths or laws which may have immense practical interest for us, even though we can have only moral, and not physical or metaphysical, certitude concerning them.
And what about the innumerable truths, or supposed truths, some of which inform us of particular facts in human history, such as the conquest of Gaul by Caesar, or the crucifixion of Christ ; others of which embody generalizations such as that " Moral excellence in men and nations results from their posses sion of deep and true religious beliefs " ; and all of which are accepted and believed, by nine-tenths of those who do accept and believe them, on the authority of their fellowmen, on the strength of historical evidence? If the
1 C/. JOSEPH, op. cit., pp. 344, sqq.
6 THE SCIENCE OF LOGIC
logician thinks it a part of his duty to teach us how to measure masses and motions of matter by the " method of means," the " method of least squares," 1 etc., may we not reasonably expect from him an equally detailed code of directions in the task, let us say, of estimating the value of the historical evi dence for and against the alleged fact— so momentous in human history — that Christ rose from the dead after His crucifixion ?
The logician is no more debarred from dealing with the methodology of " metaphysical," or "ethical," or "historical" truth, than he is from investi gating the methods of discovering and establishing " physical " truths. Truths and theories, facts and phenomena, whether real or alleged, whether "re ligious " or " scientific," forming, as they all do, the common data of philosophy, fall equally within the sphere of logic. They are all subjects of human investi gation : and it ought to be, therefore, the function of general logic, not to teach us how to explore the hidden recesses of any particular department, but rather to give us a general training in the method of discovering and proving truth : a training which will help us equally well all round, which will aid us in determining whether God exists and has spoken to us through Christ, no less than in determining whether radium cures cancer, or whether alleged " telepathic " phenomena are mere coincidences.
The logician must, of course, ultimately use his own discretion in deter mining whether he ought in a general way to indicate the main methods in use in this or that special department of science ; and it is just here, in judging which departments are worthy of a more detailed attention, that he will be influenced, consciously or unconsciously, by the general trend of intellectual activity in his own time and country. In this way he is exposed to the danger of unduly emphasizing the scope and import of certain special methods of scientific research, or even of setting them up as the only methods of attain ing to scientific truth.
Now, modern inductive logic shows pretty clear evidence of suffering from an undue bias of the sort just outlined : it has concerned itself somewhat too exclusively with the mathematically exact quantitative methods of the physical sciences, and it has thus fostered an unwholesome tendency to conceive and treat all human experience as amenable to the laws and methods of mechanics. It has been more or less obsessed by the rigid determinism of the "mechanical theory of the universe," which was so much in vogue about half a century ago.
There is something one-sided in this tendency to cultivate the positive, physical sciences, on the lines of mechanically exact, quantitative laws, and to develop, in logic, a corresponding methodology of them — to the exclusion of the human sciences, the knowledge of man's nature, origin, and destiny, of his conduct and religion, of his social activity and its history. The intellectu ally cogent evidence of the "exact " sciences — mathematics, whether pure or applied to physics — lends itself, of course, most readily to clear, logical treatment. But the " exact " sciences are not the only sciences, nor is the assent which is given on intellectually cogent evidence the only assent that deserves to be called scientific. Assents that are freely given may be scientific and certain, provided that the evidence is as strong as can be reasonably ex pected in the matter under consideration. And even where these assents do fall
1 Cf. WELTON, Logic, ii., § 158; JOYCE, Logic, p. 368.
GENERAL OUTLINE OF METHOD 7
short of certitude, the general method of weighing the evidence on which they are based forms the proper object of logic.
It must be borne in mind that many of the processes to be hereafter de scribed as subsidiary to induction find their application very extensively outside the merely physical sciences, although they are for the most part illustrated by examples drawn from the domain of these latter.1
202. SYNTHESIS AND ANALYSIS. — Method (peOoSo^ means mode or manner of procedure, and may be defined as the proper arrangement of our mental processes in the discovery and proof of truth. If a truth needs proving, we cannot be said to have fully discovered it until we have proved or established it as a truth ; antecedently to this it is only a postulate or hypothesis. The method which thus leads to science is sometimes called inventive or constructive, to distinguish it from the method of teaching or expounding truths already established, this latter being known as didactic method (204).
In scientific method it is customary to distinguish the influ ence of two great mental functions, analysis and synthesis ; and according to the predominance of either of these over the other in any department of scientific investigation, the latter is desig nated an analytic or a synthetic science.
When a science sets out from a few simple ideas and a few necessary, universal principles, and proceeds to combine these elementary notions and relations, in order to deduce from them other new, less simple, more complex relations, its progress is synthetic (nrvv-riffii/ju). It goes from the simple to the complex, from the more general to the less general. It employs the method of composition, the synthetic method. Such a science is called a rational, deductive, abstract science.
Pure mathematics, for example, sets out from a few neces sary and universal principles (" in materia necessaria "), with which the mind equips itself by the simple abstraction of a few element ary concepts from the data of sense, and by direct intellectual intuition of certain self-evident relations between those concepts. These relations it combines and multiplies successively, thus gradually forming definitions of the various thought-objects with which it deals, divisions of these objects into groups or classes, and demonstrations which show the relations, ever more and more complex, between these objects. It is thus ever and always discovering new abstract objects of thought, com-
1 C/. JOSEPH, Logic, pp. 472 sqq.
8 THE SCIENCE OF LOGIC
pounding, or building uf> its conceptions, so to speak, into more and more complex wholes, synthesizing its gradually acquired truths into a logical, harmonious, and progressive system.
Throughout this whole work of elaboration, the student of the pure deductive sciences has no need to call in the aid of sense experience, of observation or experiment : he might conceivably become the greatest pure mathematician in the world without ever leaving his library. He would, of course, need charts or blackboards to aid his imagination in establishing the complex spatial or numerical relations he might desire to examine between the notions with which he deals. But it is from the primary notions, not from the figures or symbols before him, that he de duces even his remotest and most complex conclusions.
If, however, it is true that such quiet seclusion and abstract speculation can produce a great mathematician, is it not equally true that they can never produce a great physical scientist ? A knowledge of the physical world implies actual, positive contact with Nature and its activities. The discovery of its laws is con ditioned by the observation of its concrete phenomena, and even by experimenting with these latter. It is the result of a long analytic process that has been called Induction : hence the designa tion, physical or positive or inductive sciences.
When a science thus starts with concrete facts, with the data of observation and experiment, and aims at discovering general truths and formulating general laws, about those tacts, its progress is from the complex to the simple, from the particular to the general. This is the analytic method (ava\v(o) ; it finds its place mainly in the experimental sciences.
We have already distinguished the reasoning by which we thus ascend to higher and wider laws, as regressive, in opposition to the progressive reasoning which is characteristic of the deductive sciences (187). Professor Welton * thus illustrates the distinction : " Instead of starting from an axiom of the widest generality, in physical science it more frequently happens that the highest and most general principles are the last to be discovered. ' Certain general propositions are first discovered (e.g. the laws of Kepler) under which the individual facts are syllogistically subsumed. The highest principles are discovered later (e.g. the Newtonian law of Gravitation) from which those general propositions are neces-
1 Logic, i., p. 392.
GENERAL OUTLINE OF METHOD 9
sary deductions ' (Ueberweg, Logic, p. 465). . . . A demonstration of this kind is, therefore, called . . . Analytic".
It is usual to draw a distinction between the two scientific methods : the synthetic, or that of the rational, deductive sciences ; and the analytic, or that of the experimental, inductive sciences. - There is reason for such a distinction : but only in this sense, that synthesis is the predominant feature of the former, and analysis of the latter ; not in the sense that either feature belongs exclusively to either group. No such separation of analysis from synthesis is possible in actual thought. As a matter of fact, the self-evident, a priori axioms of the rational sciences necessarily presuppose the mental analysis of some few elementary observations, by which the mind is equipped with the concepts that form those rational prin ciples. On the other hand, the general laws that are reached by the long and laborious analyses and inductions of the experimental scientist furnish us, in turn, with principles or starting points for synthetic or deductive reasoning processes.
In reality, therefore, there is one and only one scientific method : the analytico-synthetic, or combined inductive and deductive method.1
Whether analysis or synthesis will predominate in any parti cular science, or at any particular stage in the growth of a science, will depend on whether the subject-matter is best approached from the side of the abstract universal, or of the concrete particular. But the two methods are not essentially opposed ; rather they "differ only as the road by which we ascend from a valley to a mountain does from that by which we descend from the mountain into the valley, which is no difference of road, but only a difference in the going".2
This, moreover, is what we should expect when we reflect on the unity of human nature ; and it is confirmed by the findings of psychology. Man derives his abstract ideas from data furnished by his senses. Sense observation must, therefore, be the forerunner of all rational speculation. The formation of abstract concepts from the data of sense experience involves analysis of the latter. These abstract concepts are in turn combined in manifold ways by the activity of the intellect, and are being constantly reapplied to the facts of sense observation. Thus it is that rational speculation is ever returning to those same sense realities which first awake its activity. All science is " of the uni versal and necessary " (to use the language of Aristotle) ; but it is no less true that all science must aim at explaining the contingent, individual facts of our sense experience. It must not only ascend by analysis and abstraction from the particular to the universal, from fact to law, from effect to cause, but it
1 C/. MELLONE, Introd. Text-Book of Logic, pp. 383 sqq.
*Port Royal Logic, p. 314, quoted by Professor Welton, Logic, ii., p. 212.
io THE SCIENCE OF LOGIC
must also, by a regressive movement of thought, apply its abstract principles again to concrete facts, and by means of the former explain the latter. This combined and alternating use of analysis and synthesis will be more fully illustrated in connexion with the treatment of Induction, Demonstration, and Scientific Explanation. It is commonly employed in the physical sciences, and it is the only method by which a reliable philosophy of man and the universe can be constructed.1
There have been, in different ages, philosophers such as Descartes (1576-1650) and Spinoza (1632-1677), who have thought it possible to build up a philosophy by the purely synthetic or deductive method, on the basis of a few self-evident fundamental truths. Such projects are chimerical, for philosophy is expected to offer an intelligible interpretation of universal human experience, and must, therefore, set out from an analysis of this latter.
The method of philosophy, too, like the methods of the sciences, is largely influenced by the prevailing general views and standpoints of each successive period : synthesis predominating in one school or in one epoch of philosophic development, analysis in another : the former, for instance, in Plato and Neo- Platonism, in St. Augustine and the early Middle Ages ; the latter in " scien tific " and " inductive " philosophy since the Renaissance ; and neither, perhaps, asserting undue supremacy in Aristotle, or in Scholasticism among its best accredited representatives, whether mediaeval or modern.
A system of philosophy aims at working out and establishing some definite world-view, some interpretation of human experience as a whole. The method or methods that may be involved in the elaboration of such a thought-system will themselves usually imply assent to certain fundamental judgments, whether these be put forward as axioms or as postulates (203, 231). And hence it is that systems of philosophy are to be judged not only by their explicit positive teaching or contents, but also by their methods, for these too imply doctrines.'2 Indeed, it has been said that metaphysical systems differ merely in the stand points from which they approach the interpretation of experience. This is only an exaggeration of the undoubted truth that every such system is largely in fluenced and characterized by some predominating point of view. Thus, the idea of a process of Development, a tendency towards the realization of an ideal, as pervading not only thought but reality, has always exercised more or less influence on the trend of philosophical speculation. But the scientific discoveries of the last few centuries in regard to organic evolution among the forms of life, have led many to suspect the existence and operation of an all- pervading law of Evolution, and to adopt, in all departments, only methods of research directly based on this postulate. The wisdom of this procedure is questionable. If it is really unsound, results will in due time reveal its deficiencies.
203. GENERAL RULES OF METHOD. — Various rules or canons, of more or less practical utility, have been laid down for observance in the pursuit of truth, under the title of General Rules of Method. They are of the nature of counsels. A full
1 Cf. MERCIF.R, Logique, p. 374 : Pratique de 1'analyse et de la synth&se en philosophic.
2 Cf. DE WULF, Scholasticism Old and New, pp. 190-200.
GENERAL OUTLINE OF METHOD u
discussion of their grounds and significance would not be con venient at the present stage of our investigations. For the purpose of enumeration we may conveniently reduce them to the follow ing:—
I. We should select as starting point the simplest, easiest, most familiar objects of thought. What is simplest and easiest to un derstand, will, however, depend on the amount and kind of knowledge already possessed by the seeker ; and will, therefore, be relative and variable. Each must determine, from his own know ledge, what element or elements of the particular subject-matter under investigation may be most easily grasped by him.
Whether what is simplest in itself is simplest for us, will be largely determined by the nature of the subject-matter in hand. Looked at in itself, the abstract, universal principle or law is simpler, less complex in content, than any concrete fact under it : e.g. the law of gravitation than the fall of an apple ; * but it is not always this simple, abstract aspect of reality that comes first under our notice or is most familiar to us. Of some aspects of reality it is the widest and most general truths that are most easily grasped, as in the case of the axioms of the rational sciences ; and then the method employed will be mainly syn7 thetic. Oftener, however, it is the concrete, complex, many- sided fact of sense with which we are most familiar^ as in the data of the inductive sciences ; and then the method employed will be mainly analytic.
II. We should proceed from the known to the unknown, GRADU ALLY, step by step, in an orderly, logical sequence of thought, and not hastily, irregularly, " PER SALTUM".
To secure this, we must observe carefully all the canons of definition, division, reasoning, demonstration, etc. Failure in the observance of these canons will usually expose us to error, and will inevitably involve inversion, repetition, and consequent confusion. Innumerable examples of those defects have been instanced from the order followed in Euclid's elements of geometry.2 The importance of explicitly examining and test ing every step of our progress cannot be exaggerated. In no other way can thoroughly scientific knowledge be either secured or retained in the mind : whereas, on the other hand, a clearly perceived, logical, organic connexion between truth and truth is necessarily a powerful aid to memory.
1 WELTON, op. cit., p. 216. " ibid., p. 225.
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Moreover, it is by careful separation of a problem or subject into its various parts and details that we are enabled to distin guish betweeen the accidental and the essential, and to avoid being misled by superficial resemblances and seeming connexions. Habit, association, familiarity, are apt to lead us astray. We very easily mistake invariable sequence for causality, and ap parent reasons for real ones.1 The principal sources and classes of such mistakes will be enumerated in the sections on Fallacies.
III. While, on the one hand, we must never accept anything as true which we do not clearly know to be so, on the other hand, we must not expect the same degree of certitude, or the same cogency of evidence, in all the sciences. Disregard of the second portion of this rule has led many, especially in modern times, into scepticism, i.e. doubt about the capacity of the human mind to attain to certitude about anything. Taking too narrow a view of " science," they expect cogent evidence in the concrete subject-matter of the human sciences — social, economic, and ethical — evidence which, of their very nature, these sciences cannot be expected to yield.- And when it is not forthcoming they drift into scepticism. One would imagine that St. Thomas Aquinas was writing for the twentieth century, rather than the thirteenth, when he penned these sentences : " There are some who will not receive anything that is told them unless it is mathematically proved. This is usual with those who have had a mathematical training, because custom is second nature. But it may be also due to the possession of a strong imagination, combined with an undeveloped judicial faculty. Others there are who will not receive anything unless there is put before them some illustration of it that can strike their senses. This, too, results either from habit, or from the predominance of the influence exerted over them by their senses, or from want of intellectual discrimination. . . . Others, however, there are who
1 " An Englishman resident in some city in South America sees united in the inhabitants a profession of the Catholic religion, a great laxity of morals, and an absence of all energy, fortitude or perseverance. Neglecting our rule, he comes to the conclusion that there is a necessary connexion between Catholicism and the vices around him. . . . Or, again, we may have observed in the newspapers that a larger number of persons lose their lives by drowning on a Sunday than on any other day. On this fact the Scotch Presbyterian makes the remark that it can only be explained by the anger of God with all who take their pleasure on His Holy day : quite overlooking the circumstance that it is on Sunday that a great number ot excursionists of the middle and lower classes, who are unskilled in the use of boats and can rarely swim, take their pleasure on the water."— CLARKE, Logic, pp. 469, 470.
2 Cf. JOSEPH, Logic, p. 489.
GENERAL OUTLINE OF METHOD 13
wish that everything offered them should be based on certitude, that is, as the fruit of diligent rational inquiry. This is the atti tude of a sound understanding in judging, and of sound reason in investigating : provided always that [such certitude] be not sought in matters where it cannot possibly be found" *
IV. We must keep before us, as dearly as we can, the end to be attained in our inquiry or argument, and suit our method to the attainment of this end. Of course, when the end in view is the discovery of new knowledge, as distinct from the communication of knowledge already possessed, to others, we cannot have a clear or definite conception of what we are looking for : if we had, our inquiry would be superfluous. Still, we must have some general suspicion of it : otherwise we should not think of looking for it at all. Discoveries are, no doubt, sometimes made haphazard, by groping in the dark ; but this is the exception. As a rule, our progress in knowledge is guided by hypotheses, based on analogies with what we already know.
Besides those general canons of method, special rules are sometimes formulated for the synthetic method, and special rules for the analytic. In the chapters dealing with Induction we shall examine the latter method at some length, and we shall there see that although the process by which we rise from the perception of concrete, individual facts of sense, to the apprehension of general truths, is one of very great importance, yet it is scarcely possible to formulate any mechanical set of guiding rules for it.
It is the synthetic method that systematizes the truths discovered by analysis, and explains concrete reality by applying to the latter analytically dis covered laws. The rules laid down by some logicians for its employment are almost too obvious to need special statement. For instance, we are reminded that we must start either from axioms that are indisputably self-evident, or from general truths already proved. The usual error here is by defect, by taking for granted what is neither sufficiently simple to be self-evident, nor has been clearly proved — the fallacy known as Undue Assumption of Axioms. But philosophers, nowadays, not unfrequently err by excess, by demanding proof for what is so clearly self-evident as to be indemonstrable. They call into question the claim of any principles, however self-evident, to our uncon ditional intellectual assent. They doubt or deny that such abstract, self-evid ent axioms give us any insight into the real nature of things, confining the validity of such axioms to the sphere of subjective mental appearances, and according them at most a merely provisional acceptance as " assumptions " or " postulates " which may perhaps be some day verified as objectively valid, or may perhaps be destined to remain as mere " directive " or " regulative " principles of our thought-processes. It is, of course, a grave mistake thus to confound self-evident truths about the data of our ex perience with those mere " working hypotheses " and " methodological
1 Lect. V. in Metaph. 2.
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assumptions " l which all investigators have sometimes to make, and which are perfectly legitimate in their proper sphere ; but an inquiry into the grounds of this erroneous tendency in modern philosophy would not be opportune here.
Aristotle and the Scholastics examined in minute detail the requirements of the synthetic processes through which we advance by demonstrative rea soning from simple, self-evident first principles to more complex scientific conclusions. Their teaching will be outlined in the chapter on Demonstration.
The remainder of the present chapter will be devoted to the application of analysis and synthesis to the teaching or exposition, as distinct from the discovery and proof, of truth.
204. DIDACTICS: ANALYSIS AND SYNTHESIS IN TEACHING.— When our object is not to discover truth as yet unknown to us, but to communicate what we know already to others, our method will be no longer constructive or inventive, but instructive or educative ; instructive if it aims merely at the communication of knowledge to the intellect ; educative if it aims at the formation of right mental habits and character as well. The latter is the scope of the art of Pedagogics ; the former alone, that of Didactics. This latter, therefore, is the sole concern of the logician.
What, then, is the proper method of teaching or exposition ? Broadly- speaking, it is laid down that while the analytic method is the great method of discovery the synthetic method is the great method of instruction. And in general terms this is correct. But the statement needs to be carefully limited and qualified.
The analytic method is not exclusively the method of discovery ; as witness the many discoveries of pure and applied mathematics. Nor, similarly, is the synthetic method always the best method of exposition. It is, of course, obviously the best in teaching the pure deductive sciences ; for in these the abstract principles, being simpler than their complex applications and conclusions, are more easily grasped by the beginner. But even here we need initial observation of concrete facts or instances as an aid to the abstrac tion of the simple notions, and to the intuition of the principles from which these sciences start. This initial stage is analytic in its character. The teacher familiarizes his pupils with concrete instances, facts, models, embodying the abstract principles he wishes them to grasp. In dealing with children especially, it is necessary to dwell at length on concrete things : these are more familiar : and the child's power of grasping even the simplest abstract principles, and reasoning from them, is comparatively undeveloped. The aim, at this early stage, will rather be to awaken the child's powers of obser vation and intuition, to arouse its curiosity and stimulate its interest by pre senting to it simple but attractive facts, combined with judicious interrogations and suggestions, calculated to draw out the pupil's powers of observation, comparison, and inference.2
1 Cf. JOSEPH, op. cit., p. 523. Cf. infra, 237.
2 Professor Willmann, in Germany, has published, under the title of Didaktik als Bildungslehre, a work of the highest merit on intellectual training. Habrich, a pupil of Willmann's, has supplied the teachers of intermediate education in Germany with a useful treatise on psychology, " Paedagogische Psychologic" in harmony with the principles of scholastic teaching. From another standpoint, cf. Herbert Spencer's works on Education.
GENERAL OUTLINE OF METHOD 15
Moreover, the pupil should be trained, as far as possible, to discover, himself, the reasons and causes of the things observed by him. This involves the use of the analytic method, and develops the spirit of analysis in the learner. Such initiation into the method of independent personal investigation constitutes the immense difference there is between intellectual education proper and mere instruction.
This method of teaching by suggestion, of drawing out the learner's powers by judicious questioning, is called the Socratic method, after the Grecian sage who made such a fruitful use of it. He, himself, appropriately called it the /iaievruoj Tt^vij, the art of intellectual obstetrics or mental mid wifery '.*
This stage of analysis and observation is a necessary step towards ab straction of ideas and intuition of first principles. These notions and principles become in turn the explanatory reasons of the facts in which they are realized. The learner will next be taught, by an application of the synthetic method, to make use of those principles and laws for the under standing and explanation of concrete phenomena.
Thus he will be taught to make use both of observation and of abstraction, both of analysis and of synthesis. The former without the latter would lead to narrowness of view, to the shortsighted philosophy of Positivism ; the latter without the former, to barren, empty speculations, and to the substitution of mere verbal explanation for real science. The sciences of observation develop the spirit of specialized research ; the mathematical and metaphysical sciences, the deductive, speculative turn of mind.
It will be seen, therefore, that as a rule the method employed in exposition is the same as that employed in discovery ; that the art of teaching must follow nature ; that the mind of the learner must follow substantially the same path, whether he discover truth on his own account or be guided into the knowledge of it by one who is already in possession of it.
Of course, when the exposition " is intended for well-prepared adults — as when one writes a text-book, the most appropriate method is, generally speaking, that of synthesis, as by that method the necessary relations of the parts of the subject to each other are most clearly shown." 2 But even here it is well to remember that the abstract, universal principle or law is not always the easiest to grasp at the starting-point. In an example from chemistry, given by Father Clarke in his Logic? we are told that "in each of these opposite processes [analysis and synthesis], the rule ... of commencing with what is more familiar, and thence proceeding to what is more remote and
] Socrates used to seek from others the knowledge they imagined they possessed, and which he himself pretended not to possess. His arguments took the form of dialogues, each in two parts. In the first, his " irony " confounded his interlocutor and convinced the latter of the weaknesses and drawbacks of his position. In the second, Socrates gradually drew from him a new and truer definition, a better under standing, of the matter in dispute. After silencing his opponent in the first or de structive stage of his discourse, he would begin by another series of questions to construct a new solution- of the problem — to substitute for the exploded error, or "spurious offspring," the " veritable fruit " of a " new-born " truth. The conclu sion of the dialogue thus became the " fruit of their personal reflection," the " child of their thought ".— C. PIAT, Socrate, pp. 106-109, Paris, Alcan, 1900.
8 WELTON, Logic, ii., p. 214. app. 471-74.
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unfamiliar, is observed by the chemist. In his investigation he commences with that which is most familiar to ordinary mortals (nobis notiora), the water of the spring where thousands have drunk or bathed, and thence proceeds to the various chemical agents it contains which are to us a mystery, though in themselves they may be so simple as to admit of no further analysis. In im parting to others the results of his experiments he begins from what is simpler in itself and therefore more familiar to nature (naturae notiora), and thence proceeds to the complex results with which ordinary men are familiar, however complex they may in themselves be." But, if the audience is composed of " ordinary mortals " to whom the elements — however much simpler and more knowable they may be in themselves — are so many " mysteries," would not the lecturer be better advised to commence his exposition with the more familiar water, and to lead his audience along substantially the same path as he himself had followed in the first instance ?
It seems rather a mistake, therefore, to apply the synthetic method exclusively, to the exposition of the subject-matter of those sciences in which analysis has been the main instrument of discovery. It is rightly used in the teaching of the pure deductive sciences such as mathematics ; but the exposition— at least the early stages of the exposition — of those sciences in which analysis, observation, and experiment have played a conspicuous part, should be rather analytic than synthetic. For example, the method followed by Maher and Mercier in their well-known treatises on psychology — the analytic or empirical phase leading up to the synthetic or rational one — is very much superior to the exclusively synthetic method adopted by many Scholastic writers in their Latin treatises on the subject. In accordance with the Scholastic axiom, Operari sequitur Esse, we ought to commence by examining and analysing the data on which our scientific knowledge of man is based, -viz, his activities, to arrive next at a knowledge of his faculties, and ultimately of his nature, origin, and destiny.
We are only following nature in adopting such a course of analytico- synthetic exposition. The manner of using analysis in teaching will, however, be slightly different from the manner of using it in discovery.1 In the process of discovery, our analysis is necessarily slow, tedious, tentative, guided merely by analogy and hypothesis, often erratic owing to our being misled by false analogies and wrong hypotheses ; our experiments are necessarily multi plied and often practically blind, though seldom quite aimless. But in the process of exposition it is manifest that, having traversed the way before, and being now in possession of the scientific knowledge which was our goal, our didactic analysis may be much more direct and definite. We may exclude all the gropings and deviations that occurred in the first search after the truth, the misleading analogies and wrong hypotheses ; we may carefully select the most appropriate instances and experiments for disclosing the law in question to our pupils, and thus shorten the road for them : but we shall be travelling substantially the same road and employing the same method as previously.
205. SCHOLASTIC METHODS OF EXPOSITION AND DEBATE. The mediaeval Schoolmen followed the advice of the founder of the Lyceum : " Before you try to solve any problem," wrote Aristotle, " set forth clearly the reasons or difficulties that militate against the solution you are about to propose. In that
1 Cf. WELTON, ii., p. 220.
GENERAL OUTLINE OF METHOD 17
way you will see better where is the heart or kernel of the question, the exact point in dispute ; you will fix your attention on it, and you will retain a firmer conviction of what you have seen to stand successfully the shock of the de bate." l
Open the Summa Theologica of St. Thomas, that monumental synthesis of mediaeval wisdom " ad eruditionem incipientium" ." At the beginning of each Question (Quaestio) or Sub-question (Articulus] will be found a resume" of all the arguments, from reason and authority, that can be brought against the intended solution. They are introduced by the familiar " Videtur quod non . . . >}. Next comes the doctrinal affirmation of the thesis or solution, introduced by the words " Sed contra . . .," and usually illustrated rather than proved by some quotation from Scripture or from the Fathers. Then comes the body of the article (Corpus Articuli), introduced by the phrase " Respondeo dicendum quod . . ., " and containing the principle on which the solution is based, together with its main proofs in the usual syllogistic form. Finally, we have the further application of this same principle to the solution of each of the various difficulties proposed against the thesis at the commence ment : " Ad primum dicendum quod . . . " " Ad secundum . . . ," etc.
At the public debates that were held in the mediaeval universities at certain fixed intervals during the year, usually before Christmas and Easter ("Zto- putationes Quodlibetales" as they were called), the procedure was slightly different. Any auditor might raise a question and indicate in a general way the arguments in favour of the solution that had his preference. The " re- spondens" i.e. the candidate for degrees, or his master, formulated their view, and based it on some fundamental argument. This position was at once attacked by the objector, and so the debate was opened. On the morrow, or one of the following days, the master repeated, arranged, and " determined," or settled definitively, the various questions discussed. These " Determina- tiones " have come down to us in the copious volumes of mediaeval philosophy and theology known as " Quodlibeta ".:i
The method of carrying on academic debates in Scholastic philosophy and theology, still in use in schools, colleges, and universities, where these subjects are taught, is the same in principle as the above, if somewhat different in de tail. The exercise is strictly syllogistic, and it undoubtedly gives the student
1 Metaphysics iii., i ; Nicomachaean Ethics, vii., i. Here is the comment of St. Thomas : " Postis his quae videntur probabilia circa praedicta, prius inducamus dubitationes, et sic ostendemus omnia quae sunt maxime probabilia circa praedicta . . . quia si in materia aliqua dissolvantur difficultates et relinquuntur ut vera ilia quae sunt probabilia, sufficienter est determinatum." — loc. cit., lect. i.
2 " Quia catholicae veritatis doctor non solum provectos debet instruere, sed ad eum pertinet etiam incipientes erudire, propositum nostrae intentionis in hoc opere est ea quae ad Christianam religionem pertinent, eo modo tradere, secundum quod congruit ad eruditionem incipientium." A few brief sentences next tell us why he undertook the work : to rid theology of many useless questions, and to give an orderly exposition of it for the benefit ol learners; and in what spirit: "cum confidentia divini auxilii." Those few simple sentences form the whole preface or prologue to one of the greatest works that human genius has ever produced.
3 Cf. DE WULF, History of Medieval Philosophy, p. 258, note from Mandonnet's Siger de Brabant, etc.
VOL. II. 2
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an invaluable training in exact reasoning. The following outline may be found helpful to academic disputants.
The professor fixes upon a thesis, appoints a pupil to " defend " it, and one or more others to " object " to it. At the appointed time the defender (" defendens" " respondens ") enters the pulpit or bema, announces the thesis, adding, if desirable, a very brief exposition and proof. The objector (" ob- jiciens ") then asserts the contradictory of the thesis, proving his assertion by a syllogism. The defender resumes with the introductory phrase, " Sic argu- mentaris, Domine " (" This is your argument, Sir "), repeats the syllogism slowly and clearly, deliberating on the way in which he ought to deal with each premiss, the consequence, and the conclusion. Having repeated the syllogism, and also the introductory phrase, he again takes up and repeats once more the major, and now passes judgment on it : "I grant the major " (" Concedo majorem "), if he considers it true ; " I distinguish the major " (" Distinguo majorem "), if he sees in it a true sense and a false sense, which two he will separate by the addition of some well-chosen technical phrase to show the true sense and the false one, qualifying the false by " I deny " ("Nego"), and the true by "I grant" (" Concedo ") ; "Please prove the major " (" Faveas probare majorem "), if he considers the major entirely false ; " Let the major pass " (" Transeat major "), if he considers it irrelevant, or does not wish to pass definite judgment on it. In general, the objector should so construct his syllogisms that the major will not admit of total denial. Should the defender thus request his adversary to prove the major, the former need not proceed to the minor of the original syllogism, but listen to and deal with the proof brought forward for the major. If the defender has granted, or " distinguished " the major, he proceeds to repeat the minor, and either " denies " or " centra-distinguishes " it (" Nego minorem " or " Contra-dis- tinguo minorem "). It is only when he " denies " either premiss, or " distin guishes " .one and " contra-distinguishes " the other, that he has a right to " deny " the " consequence " or probative force (consequentia\ and therefore also the conclusion (consequens), of the syllogism ("Nego consequens et consequentiam "). To " centra-distinguish " the minor is to introduce the same distinction into it as into the major, granting the member correspond ing to that denied, and denying the member corresponding to that admitted, in the case of the major. It may sometimes be necessary to introduce a further distinction into either or both members of a distinction in order to sift fully the true from the false : this process is called " subdistinguishing " (" Subdistinguo ").
The objector then continues the debate by proceeding to prove syllogis- tically the proposition denied by the defender, in the sense in which it was denied, commencing by the words, " I prove the major (or minor) denied " [" Probo majorem (or minorem} negatam "] ; and the defender proceeds to deal with the new syllogism as before.
The objector may, at any stage, request or allow the defender to explain the precise force of the distinctions he has made in an answer : which the defender does as briefly and clearly as possible, introducing his explanation by the words, " I explain the distinction (distinctions) introduced " [" Et explico distinctionem datam (distinctiones datas) "]. Various courses may here present themselves to the objector.
GENERAL OUTLINE OF METHOD 19
He may, notwithstanding the explanations offered, urge some proposition in the sense in which it has been denied. " But . . . Therefore the difficulty remains ". " Atqui . . . Ergo stat difficultas "). To which the defender replies, " I deny what you subsume " [" Nego subsumtum "]. The objector must then proceed to prove the proposition in the sense in which it has been denied. [" Probo subsumptum"~\
Or, again, the objector may urge the difficulty in a modified way, owing to some concessions made by the defender in his explanation ; which he does by commencing, " But I insist . . .," or, " But I urge the difficulty from your own admissions " (" Atqui insto . . .," or, " Atqui ex concessis urgeo difficultatem ". )
The real point of the difficulty ought to be kept in the minors as far as possible : the distinctions made ought to be real, not merely verbal, i.e. ex pressive of the same syllogism in different terms : quibbling and sophisms ought to be rigorously excluded : the questions selected ought to be the more serious ones, and the difficulties likewise : if the objector really feels the difficulty he is putting, so much the better ; waste of time, vain display of acuteness in making distinctions, or syllogisms more subtle than solid, should not be tolerated : the number of syllogistic steps leading up to the full solution of any difficulty will, of course, depend on the nature of the latter, but need not usually exceed four or five, unless, indeed, a modified phase of the difficulty, or a practically new difficulty, arises in the course of its solu tion : exactness, lucidity, brevity in the formation of syllogisms and distinctions, ought to be insisted on : and therefore, also, the necessary means to this end, viz. familiarity with the technical tertninology of the philosophical problems under discussion, and of philosophical terminology in general.
Such are the principal canons laid down for observance in those exercises.1 There is no reason why they should not be conducted in the vernacular if necessary, rather than in Latin. The method is not wedded to any language ; and philosophical thinking would be much less erratic and illogical than it is at the present day if such disciplines formed an essential part of philosophical training.
The Scholastic system of philosophy is identified with constructive and didactic methods which are nowadays eliciting a more accurate and sympa thetic appreciation from scholars, after a long period of prejudice and mis understanding. It took shape in the early mediaeval schools of Europe under the combined influence of St. Augustine, Plato, and a few of the logical writings of Aristotle. But the introduction of the latter's works into the Western schools towards the close of the twelfth century gave Scholasticism its predominantly Aristotelean character in the thirteenth.2 To its preponder ating use of synthesis as a constructive method we have already referred (201). Its elaborate system of teaching, too, has had a profound influence on the development of learning during many centuries. While recognizing its limitations, we are bound in the interests of historical truth to give it credit for many excellences. In general, we may say that the Scholastic method,
1 C/. ZIGLIARA, Logica, (46), De methodo disputandi.
2C/. DE WULF, History of Medieval Philosophy, pp. 101-48; Scholasticism Old and New, pp. 19-88, 168-82.
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whether constructive or didactic, trains the mind to careful reflection and develops the critical faculty.
In the first place, it certainly gives one the habit of disentangling and clearing up his ideas, of arranging them in order, of introducing rigorous logical sequence among them.
Then, secondly, it teaches us to distinguish certainty from probability, truth from appearances, science from plausible theorizing, and established conclusions from unverified hypotheses.
Thirdly, it inculcates a spirit of disinterested inquiry after the truth. In Scholastic philosophy truth is regarded in its native, unadorned beauty, so to speak ; it is sought for its own sake, and with a dispassionate calm : to the Scholastic, rhetoric makes no appeal : mere rhetoric excites the imagination and emotions, disturbs the balance of judgment, begets confusion of ideas, and hasty, ill-considered views. An inflammatory discourse that will arouse an untrained audience to the highest pitch of passion or enthusiasm may not be able to stand the test of a cold analysis, or the logic of the syllogism. The language of Scholasticism is the very antithesis of rhetorical. It " simply and solely expresses the intellectual concept, abstracting from all its relations to the other faculties of the soul, and from the reactions it may call forth in them. All possible obstacles between the mind and the objective truth are pitilessly set aside. Its style, stripped of all ornament, free from all feeling and senti ment and all the artifices of rhetoric, and hence so often accused of crudeness and barbarism, has all the exactness and precision of a mathematical formula or proposition ; it is pre-eminently truthful and clear. It was methodically and most successfully shaped into the aptest possible instrument for the systematization of thought : the instrument that was to build up the great Summae, whose materials lay scattered for generations through a whole world of literature. Reduced to the simple form and proportions of proposi tion and syllogism, those truths could be logically moulded into an organic whole in which each part received a prominence due to its relative import ance." 1 We are often nowadays reminded of what Plato said : We ought to tend to the truth with our whole soul — avv 6X17 rfj faxd • • • «»f TO Sv <at TOV ovros ro (fravoTorov . . . TOUTO 8' (ival (fraptv TayaBov.* The Schol astics receive those words with respect, but .also with caution. When the truth is known, yes, by all means, let us love it, embrace it with all the ardour of our souls, act up to it, work for it, suffer for it if needs be, and if duty demands the sacrifice. But in searching for the truth our chance of finding it will be in proportion to the degree in which our intellect succeeds in laying aside all considerations foreign to the truth itself. At bottom, the truth is always good, always truly useful, therefore ; of that there can be no doubt. But this or that doctrine, which is subjectively judged to be useful, may not be so in reality ; and some other, judged to be dangerous, may be the only one truly useful in the long run, because it happens to be the one that is really true.
Fourthly and finally, the Scholastic method counteracts the narrowing influence exerted on the mind by a constant and exclusive contact with the
1 P. RICHARD, Etude critique sur le but et la nature de la scolastique (Revue Thomiste, May and November, 1904).
2 PLATO, Republic, vii.
GENERAL OUTLINE OF METHOD 21
concrete, positive facts of sense ; it nourishes in the soul what we may call the craving for the universal, the desire to grasp the idea in the fact, the abiding law in the contingent phenomenon.
In a word : clearness, precision, severe logic, method ; a sense or percep tion of the true ; love of the truth simply for its own sake ; elevation of thought and a fresh and speculative turn of mind : such are the qualities developed by the Scholastic method in those who are formed upon it. Many great philo sophers have placed on record authoritative eulogiums of the syllogism.1 Such a writer as Huxley, who is certainly free from the suspicion of partiality in this matter, pays a willing tribute of admiration to " Scholastic philosophy, that marvellous monument of patience and genius, constructed by the human mind to give a logically unified answer to the problems raised by the spectacle of the universe ".a
But the Scholastic method is not without its limitations. A method, being a means to an end, becomes useless, or even injurious, when wrongly employed. The Scholastic method exercises mainly the speculative reason : it is primarily explicative, synthetic. It accustoms one to understand how a conclusion is connected with certain premisses, how conclusions follow from principles ; but it develops very little, if at all, the habit of observation ; it gives little or no stimulus to personal initiative in the discovery of new truth. A training in the positive sciences is, therefore, the necessary complement of a " Scholastic " formation or discipline of the mind. To round off and perfect this latter training, nothing is more efficacious than contact with facts ; since the intellect must derive all its ideas from external or internal sense experience, no mere verbal descriptions of phenomena can equal the direct and immediate perception of these latter. By his example and by his works, Aristotle is no less the master of scientists than of philosophers. Not only Roger Bacon, but Albert the Great, St. Thomas, Duns Scotus, were faithful to his method. Pope Leo XIII. has recommended us expressly, in his encyclical Aeterni Patris, to "receive with a willing and grateful mind every word of wisdom, every useful thing by whomsoever it may have been discovered or planned ". It must also be of very great utility to supplement a training in the Scholastic method by reviewing the history of scientific progress, so as to realize what provisional hypotheses and theories, what guesses and approximations, what deviations and errors even, the human mind has had to pass through in its journey towards the discovery of every new truth.
Again, the importance attached by Scholasticism to certain science in clines its disciple to depreciate the value of the merely probable and provi sional. To the " Scholastic " mind, the slowness of experimental work is irksome : it easily becomes impatient of the problematic character of most historical, sociological, political, and economic inductions, and of the many reserves with which the materials of the special sciences must be employed.3 But, while it is very right and proper to seek for certitude, and very praise worthy to look for demonstrative reasons, it is wrong to expect the impossible ; where certitude cannot be had it is unreasonable to demand it.4
1 Cf. Leibniz, Nouv. Ess., iv., 17, § 4. — apud WELTON, op. cit., i., p. 411.
2 HUXLEY, Animal Automatism and Other Essays, p. 41.
3 Cf. MERCIER, Origines de la psychologic contemporaine, pp. 450 sqq.
•» Sunt aliqui qui omnia volunt sibi dici per ccrtitudinem. . . . Et hoc contingit
22 THE SCIENCE OF LOGIC
Furthermore, exclusive preoccupation with the true, exclusive attention to the relation of things to the intellect alone, may disturb the harmony that ought to regulate the development of our faculties. The Scholastic method in terprets reality by referring the latter to intellect alone. Avowedly, and on principle, the standpoint of its research is above and beyond the domain of emotion and will ; it brings into action the intellect alone. Now, no one may, with impunity, submit himself exclusively to any such purely intellectual regime.1 It perfects and develops one side only of our being, the side that is fundamental and essential, no doubt, but which, nevertheless, is not the whole man. The mind that is excessively given to such a discipline develops an unduly abstract and speculative turn, and loses very largely all just ap preciation of the great complexity of concrete, actual things.2 All exclusive preoccupation with a special order of truths entails, of necessity, the incon venience just referred to. All specialists are prone to contract a peculiar sort of " mentality " that tends to make them narrow, and suspicious of truths out side their own chosen circle.
Finally, there is hardly any need to point out that the excessive use — that is, the abuse — of the Scholastic method, may make one insensible to form, to elegance of expression. A literary culture alone will counterbalance this danger of an exclusively abstract, logical, and " intellectualist " mental dis cipline.
MERCIER, Logique, pp. 271, 294-96, 371-84. WELTON, Logic, vol. ii., bk. vi. MELLONE, Introd. Text-Book of Logic, pp. 291, 383 sqq. DE WULF, History of Medieval Philosophy, pp. 137, 254 sqq.; Scholasticism Old and New, pp. 19-31. ZIGLIARA, Logica, (44), (45), (46).
propter bonitatem intellectus judicantis, et rationis inquirentis ; dummodo non qua- ratur certitude in his, in quibus certitude esse non potest. — ST. THOMAS, In II. Metaph., Lect. 5. Cf. supra, 203.
1 Cf. RICHARD, Revue Thomiste, Nov.-Dec., p. 564.
a Compare what Newman says in his Grammar of Assent about Inference, and about what he calls the Illative Sense; also Pascal's striking passage (Pensees, section i, p. 318. Brunsch. edit.) on the esprit geometrique and the esprit de finesse : " The reason why certain practically shrewd people (csprits fins) are not great geo metricians is because they are utterly unable to give their minds to the principles of geometry. But the reason why geometricians are not shrewd (fins) is because they do not see what is under their eyes ; accustomed to the clear truths of geometry, and to reasoning from well-grasped, tangible principles, they get lost in small things (chases de finesse) where the principles are not at all tangible. Here the principles are hardly seen at all, but rather felt ; they can only with the greatest difficulty be impressed on those who do not happen to feel them themselves ; and things of this sort are so delicate and so numerous that it requires an exceedingly keen and delicate faculty to feel them, and to judge them rightly according to this feeling, when, as happens oftenest, we cannot demonstrate them in geometrical order, seeing that we have not their principles in that way, and that it would be undertaking infinite labour to try to get at them so. We must, as it were, see the thing at a glance rather than by progressive reasoning, at least in a certain measure. And hence it is rarely we find shrewd geometricians . . . because they wish to treat complex things (chases fins) geometrically, and make themselves ridiculous by commencing with definitions and principles : which is not the way in that sort of reasoning. It is not that the mind does not reason ; it does, but tacitly, naturally, without art, in a way which none may mechanically express, and with which few indeed are adequately endowed."
CHAPTER II.
INDUCTION IN ITS VARIOUS SENSES. INTRODUCTORY AND HISTORICAL NOTIONS.
206. THE PROBLEM OF INDUCTION: ASCENT FROM THE PARTICULAR TO THE UNIVERSAL.— In the foregoing chapter we have gleaned some general notions about method, and about the processes of analysis and synthesis involved in method. We now purpose to deal with the analytic method and the doctrine of Induction. To the main problem of induction we have referred already (194, 198). How do we, from particular facts of sense experience, attain to a knowledge of necessary, universal truths? Such universal judgments we have seen to be essential not only to all deductive, but to all mediate, reasoning whatsoever (193, 195). We have called them abstract, general, universal, generic judg ments (92). They are likewise called logical and scientific prin ciples, axioms, laws of thought, laws of physical nature, etc. We have expressed them both categorically : " M as such is P " ; " All Ms are P" ; "Whatever is M is P" etc. — and hypotheti- cally : " If anything is M it is P" ; " If 5 is M it is P" etc. And now we have to analyse the conscious processes by which, from the apprehension of particular facts, instances, cases (con taining S, M, P, etc.), we reach a certain knowledge of such general truths or laws. Since, moreover, the essential merit and excellence of "scientific" knowledge lies in the fact that it is a knowledge of the universal truth, principle, law, etc. — and, through this, of the particular phenomena or instances under it, — the importance of clearly understanding the process by which, and the rational grounds on which, we give our assent to the universal truth, will be at once apparent.
We have distinguished three kinds of universal truths (195). There are, firstly, those absolutely necessary, self-evident axioms such as the laws of thought, metaphysical principles such as the principle of causality " Whatever happens has a
24 THE SCIENCE OF LOGIC
cause" ethical principles like " Virtue is praiseworthy" geo metrical and mathematical axioms such as " Two and two are four" ; and the whole vast body of truths that can be derived from such principles by pure demonstration. These truths are all in materia necessaria ; they have to do with abstract essences, or objects of thought considered in a possible state, apart from the changing conditions of actual existence in time and space.
The process by which we come into possession of truths of this class presents no logical difficulty. It is simply a process of forming abstract and universal concepts ; of analysing and comparing these with one another ; of thus seeing intellectually self-evident, necessary relations between them ; of generalizing these relations and formulating them in necessary or analytic propositions. The process embraces conception and judgment, but does not involve logical inference or reasoning proper. It is from sense observation of a few instances that we form the concepts : we need such observations in order to get, for example, the notions of "whole," and "part," and "greater". But having once abstracted these intellectual notions from sense experience, and compared them with one another, we have an immediate intellectual intuition of the necessary truth that " the whole is greater than its part " : and this truth we see to apply to every whole, actual arid possible, known and unknown : we assent to it not because we have examined all the instances — for we have not — but because we perceive the relation to be universal because it is necessary.^
Now, this simple process of abstraction, intuition, and general ization, by which we attain to a knowledge of self-evident, necessary principles, through the notions which we abstract from sense experience, is sometimes called Induction. But this is using the word in such a wide sense as to make it embrace every mental process by which we ascend from or through the particular to the universal. Aristotle used the equivalent Greek term in this wide sense : ' ETraywyrj rj cnro rwv icad' eKacrrov eVt ra tca66\ov
e(f>o8o<?.2
1 Cf. JOSEPH, Logic, pp. 356, 363 (2), 508 sqq,
*Top. i. 12. Truths oi the- class with which we are dealing are described in Scholastic philosophy as per se notae (86), i.e. knowable in themselves, by a full analysis of tlie notions involved in them. In some of these truths the notions are so simple as to be within the reach of all who are endowed with ordinary intelli gence. These are said to be per se notae quoad omnes. In other cases, however, the notions may be so complex — as, for instance, in the remoter mathematical con clusions — that although the truths embodying them are knowable in themselves
INDUCTION IN ITS VARIOUS SENSES 25
The processes we have just described as abstraction, intuition^ and generalization, of simple, self-evident, necessary axioms, are usually described by modern logicians as "geometrical" or " mathe matical" induction}" And the reason assigned for the superior cogency of the evidence and certitude we have in regard to these truths, as compared with those we reach by "physical" induc tion, is stated to be this : that in the former the objects compared, being abstract, have their essential qualities fixed for certain by ourselves, in the definitions we impose upon them ; while in the latter the essential qualities of the objects — which are now con crete things and agencies existing and acting in physical nature — are not fixed by definitions which we impose on them, but "have to be discovered and proved ". Thus Dr. Mellone writes : 2
"The universality of the result [that "the angles at the base of an isosceles triangle are equal "] depends upon our being absolutely certain of what are the essentials of the kind of triangle in question ; and we can be certain of these because in geometry definitions have not to be discovered. The geome trician can frame his own definitions, and change them, if necessary . . . the mathematician makes his own definitions of what is essential and argues from them. But in Nature the essential conditions have to be discovered and proved. This is the great difference between mathematical and physical in duction, and all the difficulties of physical induction result from it."
This explanation of the difference between metaphysically or absolutely necessary and universal truths on the one hand, and physically or contingently necessary and universal truths on the other, differs from the scholastic account of them only in one par ticular, but one which is all-important. Our definitions of the abstract objects of thought with which the mathematical sciences
(quoad se), yet we may not have grasped the intension of the notions sufficiently to see the necessity of the connexion between them : they may not be clear to us (quoad nos) (C/.MAHER, Psychology, p. 289, n. 33 ; JOYCE, Logic, p. 239). The truth of these we learn by Demonstration, i.e. by gradually tracing their rational, logical connexion with the former ones.
The demonstration of a remote geometrical conclusion is simply the process of showing how and why it is true, by revealing the rational connexions it has with simpler antecedent truths, and ultimately with first principles (195). This process is essentially deductive : a diagram may be necessary in order to help the imagina tion, and to serve as a concrete illustration or instance : but it is not from the diagram, from the instance, but, through it, from wider and simpler necessary prin ciples that the conclusion is derived. It is only by an improper use of language that this process can be described as "Geometrical Induction". Cf. Palaestra Logica, pp. 103-104.
1 It is in the mathematical sciences we find the simplest and most obvious examples of such axioms. Cf. MELLONE, op. cit., pp. 265-70. On the nature of mathematical reasoning, cf. JOSEPH, op. cit., chap. xxv. ; infra, 258.
2 ibid. pp. 267, 269.
26 THE SCIENCE OF LOGIC
are concerned are just as really and truly discovered by us in Nature, i.e. in the world revealed to our senses, as our " physical" definitions, our concepts of the nature and activities of physical agencies, are. They represent reality just as surely as the latter do. The " abstract objects " which they define are really em bodied in the world that is revealed to our senses, i.e. in the physical universe. These objects and these definitions are not arbitrary creations of our minds, fictions which we may modify at will. If they were so, the pure deductive sciences would give us no knowledge about reality, no real knowledge : they would be a mere dream about the unreal.
Besides the analytic, absolutely necessary, and universal judgments we have just examined, there are, secondly, those that we have called physically necessary and universal, and thirdly, those that we have described as morally necessary and uni versal. The judgments of these two latter classes are syn thetic ; and it is the process by which we reach these — more especially the physical truths or laws (201) — that most properly deserves the name of " induction " or " physical induction ". The discovery and proof of such laws is the aim of all the physical, natural, or positive sciences ; for in these laws lies the explanation of the facts and phenomena of those vast domains of sense experience. To determine the laws according to which those phenomena happen ; to get at the nature of the things of experience ; to understand phenomena by the laws that govern them, and individual things by the natures which abide and act in them : such is the ambition of the physical scientist. He sets out from the observation of complex, varying phenomena, to extract from them their common principles and abiding laws : his work is mainly a work of decomposing, dividing, analysing : his method is called analytic ; and his whole process of ascent from particular facts to general laws is called " scientific" or "physical" Induction.
The doctrine of induction has been developed from, and largely based upon, the remarkable growth of knowledge which the last few centuries have witnessed in the physical sciences. In these sciences, especially, it finds its application. From them, therefore, it naturally draws its aptest illustrations, and we need not be surprised to find treatises on inductive logic often read like pages from a handbook on some natural science (201). Nevertheless, it is important to remember that induction is equally applicable to the data of the social, anthropological, and philosophical sciences, as well as to physics : and, moreover, it is only in so far as it is thus universally applicable that it falls strictly within the scope of logic.
INDUCTION IN ITS VARIOUS SENSES 27
207. THE SO-CALLED " INDUCTIVE SYLLOGISM," OR " INDUC TION BY SIMPLE ENUMERATION OF INSTANCES"—" COMPLETE" AND " INCOMPLETE." — Since induction is an ascent from par ticular instances to general truths, from " some " to "all," it has been rightly described as a process of generalization. But we have already repeatedly distinguished between the mere concrete, collective, enumerative universal, and the really scientific universal which is an abstract judgment, embodying some more or less necessary principle or law (92, 195). It is this latter that scien tific induction proper aims at establishing. Before dealing with this, however, it will be convenient to examine the process by which the collective judgment is reached. This process, too, has been called " induction " : " induction by complete enumeration" " formal," " perfect " : to distinguish it from the other or " scien tific " induction, which has sometimes been described as " incom plete," " material," " imperfect ". The induction of the collective judgment from a complete enumeration of its constituent instances is " formal " and " perfect " merely by reason of the absolute cer titude which we necessarily possess about the sum-total when we have examined all the instances. But to call scientific induc tion, which attains to the general law by an analysis of some instances, " incomplete " and " imperfect," is singularly unfor tunate and misleading ; for it insinuates that this is a partial appli cation of the former process, that it, too, attains to the universal by enumeration, and that its result is " imperfect " or uncertain, inasmuch as the enumeration is " incomplete ". As a matter of fact, it does not reach the universal by enumeration at all. This we shall see later on.1 Let us here examine the process by which the collective judgment is reached : the so-called " inductive syllo gism ". " Induction by complete enumeration " may be defined as the process by which we predicate about a whole class or collection of things what we have already predicated of each thing separately.'''
1 C/. JOSEPH, Logic, pp. 467-68; infra, 209, 211.
2 Father Joyce (Principles of Logic, p. 228) confines this " inductive syllogism " to the " logical parts" (species} of a " logical whole" (genus). It applies equally well to the " individuals " of a " lowest class," when these are limited in number and can be exhaustively enumerated. Its principle, " Whatever can be predicated of each of the parts successively can be similarly predicated of the whole," is not to be re garded as the reciprocal of the Aristotelean Dictum de omni et nullo : for this latter must be interpreted to refer to an abstract, not to a concrete, universal : and, in pass ing from the abstract " M as such'1 to the " All M's" of the Dictum, we postu late the principle to be discussed below (223-25) called the Uniformity of Nature,
cf. 253-54-
28 THE SCIENCE OF LOGIC
It is described by Aristotle in his Prior Analytics}* It is the simple summing up of separate instances into an actual collec tion. He speaks of it as in a certain sense the opposite of the syllogism ; Kal rpoirov riva avri.K€i,rat r) eTraywyrj rat (rv\\o<yiarfi(a) inductio quodammodo opponitur syllogismo. The syllogism essen tially implies a comparison of two extreme terms (S, P} with a third middle term (M}. Enumerative induction has no middle term different from the minor extreme? The middle term (M] in the syllogism must be, at least once, strictly universal : the cor responding term, which stands as minor extreme in enumerative induction, is not a strict universal — applicable equally to an in definite number of realizations — but an actually complete collec tion, a collective, actual whole ; and the so-called minor extreme (S), which stands as middle term in enumerative induction, is a consecutive enumeration of the individual instances, equal in point of actual extension to the middle term. An example or two will make this clear : — S is P |l Saul, David, Solomon were men of remarkable
achievements ; S is M Saul, David, Solomon were all kings of the whole of
Palestine ; . : M is P I . '. All the kings of the whole of Palestine were men of
remarkable achievements.
Or, again, to take Aristotle's own example : 3
5 is P S is M . : M is P
Man, horse, mule, etc., are long-lived. Man, horse, mule, etc., are bile-less.* .•. All bile-less animals are long-lived.
From these examples we can understand Aristotle's definition of the "inductive syllogism " as " proving the major term of the middle by means of the minor," i.e. proving the universal, which stands as major of the deductive reasoning, " M is P" — proving that P can be predicated of the whole collection (AT) — by predicat ing P of each member individually (5). The class or collection is
1 Anal. Prior, ii., 23 (25). *ibid.
3 Aristotle's " individuals are not particular individual things, but species, which he combines under a genus. . . . He regarded an exhaustive summation of the species which compose a genus as quite feasible." — WELTON, Logic, vol. ii., p. 33. Cf. JOYCE, Logic, p. 228.
4 By bile-less animals Aristotle meant all those species of quadrupeds that have no excess of choleric humours — a list which he considered it quite possible to com plete. Cf. JOSEPH, Logic, p. 351 n.
INDUCTION IN ITS VARIOUS SENSES 29
symbolized by M as being greater in point of possible extension than the individuals enumerated (S\ though actually equal to them, and naturally less than the genus characterized by the attribute P.
What is to be said about the value of this process ?
Firstly, it will not be valid unless the enumeration is com plete. The enumeration must be Bia Trdvrwv, as Aristotle expresses it ; else the argument will be fallacious : there will be an illicit process of the subject of the conclusion. St. Thomas likewise insists that as long as we base our conclusion on enumera tion the latter must be complete.1 So long then as we concentrate our attention on the mere enumeration of instances, and disregard their nature, we can never be certain of our conclusion until we are certain that our enumeration is actually complete : " opportet sup- ponere quod accepta sint omnia ". Now we can practically never be certain, in regard to the occurrence of natural phenomena, that our enumeration of instances is complete : and this is the first obvious limitation of the process as a means of reaching certain knowledge. Mere " enumerative " induction, then, has only a pro visional value. It enables us to say that so far as our actual knowledge goes, such or such an enumeration may be regarded as complete ; that it is complete we usually have no warrant to affirm categorically. There are, of course, cases in which an incomplete enumeration of instances may yield a very high degree of proba bility for a universal conclusion, viz. when we are dealing with phenomena such that if an instance contrary to those examined existed we should in all probability have encountered it. The truth of such a generalization cannot reasonably be doubted so long as no negative instance turns up.2
Secondly, even where the enumeration of instances is complete, the process does not lead to scientific knowledge, i.e. the knowledge of a strictly universal conclusion embodying what can be called a law. And the reason is manifest. The conclusion expresses a simple addition of instances, and is, therefore, simply a collective proposition whose subject is an actual whole ; whereas the strict
1 " Opportet supponere quod accepta sint omnia quae continentur sub aliquo communi ; alioquin inducens non poterit ex singularibus acceptis concludere uni- versale. . . . Patet quod inducens facta inductione quod Socrates currat et Plato et Cicero, non potest ex necessitate concludere, quod omnis homo currit, nisi detur sibi a respondente, quod nihil aliud contineatur sub homine, quam ista quae inducta sunt " (In II. Anal. Post., lect. 4).
2 Cf. JOSEPH, Logic, p. 491 ; MELLONE, op. cit., p. 251, referring to Aristotle, Top., viii., 8.
3o THE SCIENCE OF LOGIC
universal proposition, the abstract universal, can be reached only by generalization of the abstract judgment which establishes some sort of necessary connexion of attributes between subject and predi cate. Adding parts to parts, to form a natural whole, gives us a collective idea. Considering an object in the abstract, apart from its individualizing characteristics, putting it into relation with its concrete realizations, actual or possible, indefinite in number, seeing that it is predicable of all, is to universalize and to make scientific progress. For " all science is of the universal and necessary";1 i.e. it is expressive of necessary, and therefore uni versal, relations between the objects of our thought. The strict universal is no mere actual collection ; it is applicable to an indefinite number of instances. Therefore, this kind of induction does not put us in possession of scientific or necessary truth.
It assumes, as we have seen, the external form of a syllogism in the> third figure, but it is no more a true syllogistic process than is the apparent syllogism whose premisses contain no true universal, but only collective propositions. In fact it is just the reverse of the process which John Stuart Mill erroneously put forward as the true type of syllogistic reasoning (195).
To observe successively that each of the planets describes an elliptical orbit around the sun, and then to say that all the planets describe such an ellipse, is simply to group together isolated observations in a formula to aid the memory, but this is not ascending from the particular to the universal. Similarly, to conclude that, because the senses a, b, c, d, e, are each an occasion of error, therefore all the senses are an occasion of error, is certainly not to go through a scientific reasoning process : but rather through an arithmetical process which simply tells us that five times one are five.
Examples might be multiplied indefinitely. They all point to the same conclusion : that observation pure and simple puts us in possession of par ticular facts, and that the grouping together of those facts in a collective notion may help the memory and abbreviate the expression of thought, but will not lead to scientific knowledge of any necessary truth or law.
Aristotle distinguished clearly between the formation of an actual whole from its parts and the elaboration of a universal notion ; " Even if we succeeded in showing separately," he writes,2 "whether by the same or by separate proofs, that equilateral, isosceles, and scalene triangles have each their in terior angles equal to two right angles, we should not yet have any right to assert the universal proposition ; ' The triangle, as such, has its interior angles equal to two right angles'." The separate proofs would not neces sarily have given us a universal knowledge ((cafldAov) of the triangle as such. Hence, we should not yet know whether the attribute, " having their interior
1 'H \t.\v bnarriW «ta0<$A.ov /coi 5i' ivayicalw.— ARISTOTLE, Post. Anal., i., 33. * Post. Anal., i.t 5(5-7).
INDUCTION IN ITS VARIOUS SENSES 31
angles equal to two right angles" belonged to the triangle as such, and, therefore, to all possible triangles.
Nor, even when we see that the three species, equilateral, isosceles, and scalene, are exhaustive of the genus triangle, can we be said to know scien tifically that the latter as such has the sum of its interior angles equal to two right angles : unless we have proved this attribute to belong to each of the three species, not on different grounds peculiar to each case, but on some common ground inherent in their common nature as triangles : " f i ravrov rfv rptywi/o) tlvcu. KOI IcroirXtvptf rj e»cdcm» rj iracriv — si eadem sit row esse ratio tn- angulo et aequilatero, aut cuique trianguli speciei aut omnibus."1 In order that such a conclusion be anything more than an enumerative judgment " it would be necessary to show that the reason for the inherence of P is the same in regard to all the parts of J/".2
But mere enumeration of the individuals of species (or of the species of a genus) cannot of itself reveal to us anything in their common nature to serve as a sufficient and necessary ground for predicating any attributes found in all the examined individuals (or species), about the species (or genus) as such.
That Aristotle was acquainted with the true method of arriv ing at such a scientific or necessary knowledge of the nature of things we shall presently show (208). That he realized the in ability of an incomplete enumeration as such to prove a really general principle, is manifest from what he says of the so-called " inductive syllogism " described above. When he speaks of it as a way of "proving the major term of the middle by means of the minor"3 i.e. of proving the universal principle " M is P" 11 If anything is M it is P" which stands as major in the demon strative syllogism in the first figure, he does not mean "proving" in the strict sense of demonstration (aVoSet^t?), for strict demon stration is always by syllogisms in the first figure. He only means that the inductive syllogism is a way of illustrating, making clearer by instances or examples (BrjXouv ; TriOavvTepov, <ra<f>eaT€-
1 ibid., (6).
2 JOYCE, Logic, p. 229. The author observes that Euclid is usually able to do this in cases where he proves successively that something is true of each of all the possible instances of a logical whole. Cf. JOSEPH (op. cit., p. 503) : " The peculiar nature of our subject-matter [here] enables us to see that no other alternatives are possible within the genus than those which we have considered ; and therefore we can be sure that our induction is ' perfect '. The nature of our subject-matter further assures us that it can be by no accident that every species of the genus exhibits the same property ; and therefore our conclusion is a genuinely universal judgment about the genus, and not a mere enumerative judgment about its species. We are sure that a general ground exists, although we have not found a proof by it." No doubt, if we are assured that the species exhibit the same property, "by no accident," our conclusion is universal ; but, even then, we only know that it is so, not why it is so : until we can " show that the reason for the " property " is the same in regard to all " triangles.
" Anal. Prior, ii., 23, (25).
32 THE SCIENCE OF LOGIC
pov, TToieiv},1 the general principle. " It is a mode of arranging a deductive argument so as to enable us to realize psychologically, the truth of the general principle (apx^i) which is the real major premise — a mode of illustrating the principle by bringing forward instances. Of course we cannot get ' all ' the instances, except where the number is limited ; but this fact does not vitiate an illustrative ' induction ' such as Aristotle had in view (cf. Anal, Post,!., 4, 73<*33)-"2
If, therefore, Aristotle regarded the conclusion of any enumer- ative induction as a strict, generic universal, he regarded the knowledge of this as reached not by enumeration, but by analysis.3
As long as we have any doubt about the completeness of our enumeration — which is nearly always, — and still rely on it alone for our conclusion, we can only have provisional and probable, not absolute and certain, knowledge, of the truth of the latter as a really general proposition. But both the process and the conclusion have in such cases this amount of utility, that they suggest to us, more or less forcibly, the existence of some natural law, i.e. some necessary natural connexion between the attribute predicated and the class of things in question. When we find that a, b, c, d, e, are P ; and know already that a, b, c, d, e, are 6" (whether all S or only some S, does not matter much), the surmise inevitably suggests itself that there may be something (say M~) in the nature of S (and therefore in all S's, whether examined or not) which is the natural ground for P. In other words, the conclusion ''Every S may, in virtue of the M that is in it, be P" suggests it self as an hypothesis worthy of investigation. Thus, our attention is drawn away from the number of S's ; and the tendency asserts itself not to aim at completing the enumeration — which is usually impossible, — but to examine the nature of the phenomena in ques tion, (the S's], and to seek in them for some natural attribute or pro perty (M} that will be the ground or reason for our predicating P of them. This marks the passage to scientific induction, whereby we are able, without a complete enumeration of instances, to rise from particular facts to the conception and discovery of some universal natural law.
208. SCIENTIFIC INDUCTION AS TREATED BY ARISTOTLE AND THE MEDIAEVAL SCHOLASTICS. — We have seen that the general conclusion, when derived from an incomplete enumeration
1 Cf. Anal. Prior, ii., 23 ; Top., i., 12 ; Anal. Post, i., 31.
3 MELLONE, op. cit., p. 247. 3 Cf. JOSEPH, Logic, pp. 356-57.
INDUCTION IN ITS VARIOUS SENSES 33
of instances, is never certain, and that such induction is called "imperfect". We find it sometimes stated by modern logicians that the only way of ascending from the particular to the general, explicitly treated by Aristotle, and the only way known to the mediaeval Scholastic logicians, was that of enumerative induction, "complete " and " incomplete " ; that we find in these authors no trace of the method of modern scientific induction, the method of attaining to the universal by analysing a limited number of in stances and seeking therein a connexion of content, of attributes, a causal connexion, in the nature of the phenomena considered. Thus, Professor Welton writes : * " The scholastic logicians . . . made the essence of induction to consist in enumeration " ; and Dr. Mellone : 2 " With the mediaeval logicians induction became simply a process of counting particular things ". And these authors merely give expression to a traditional misconception, the origin and growth of which are clearly and succinctly accounted for by Father Joyce, in his Logic (p. 233):
" The error seems to have arisen from the fact that the most famous of the Scholastics (St. Thomas, Albert the Great, Scotus) do not employ the term induction as the distinctive name of the inference by which we establish uni versal laws of nature. Following the terminology of Aristotle . . . they called it proof from experience (e'^Treip/o, experimentum, experientia). The signi ficance of the term induction was somewhat vague. It covered all argument from the particular to the general \cf. 206]. Hence (as e.g. in Scotus, Anal. Prior., ii., q. 8) it might include this meaning among others. But it was more usually employed to denote the formal process of perfect induction [207] arranged as an inductive syllogism. Moreover, it was sometimes pointed out, that our argument might be thrown into the form of an inductive syllogism : for, though the enumeration was incomplete, yet in these few instances we have equivalently seen all \cf. infra, 209]. It was by a later generation that the term induction was restricted to its present signification. Incautious readers, finding in certain passages the inductive syllogism described as the formula of inductive argument, jumped too hastily to the conclusion that the mediaeval philosophers rested their knowledge of the laws of nature on no basis but enumeration."
Now, from the very fact that Aristotle and the Scholastics considered it possible to reach a truth about "#//," actual and possible, known and unknown, by an acquaintance with "some," they must have recognized a method of ascent to the " all" other than enumeration. And so they did : viz. the method nowadays known as Physical or Scientific Induction.
When, therefore, we hear it stated that Scientific Induction is
1 op. dt., p. 33. ao/>. dt., p. 247.
VOL. II. 3
34 THE SCIENCE OF LOGIC
an achievement of the modern mind, we must not infer that it was entirely unknown to the ancients. That to modern thought the honour was reserved of seizing upon the full significance of the method, and of applying it with such marked success, even the most ardent defenders of Aristotle and the Scholastics need not deny.1 But that the principle of this method was known to the latter, their works give unmistakable evidence. And, firstly, let us turn to Aristotle himself: —
"Repeated sensations," he writes, "leave impressions in the memory, and these engender experience (tpnfipia) ; experience suggests abstraction, which separates from the particular instances the one in relation with the many (TO iv napa ra TroXXa), that is to say, the universal. But the abstract put in relation with an indefinite number of individuals, is a principle of science and of art".2
Turning, now, to St. Thomas's full and lucid commentary 3 on the passage just quoted, it would be difficult to find a plainer illustration of the modern inductive Method of Agreement : A physician has learned by repeated experiences that a certain herb has cured several patients of fever. From these experiences he ascends to the apprehension of the universal principle that " this kind of herb cures patients afflicted with this kind of fever". St. Thomas does not explicitly state the principle, or examine the process by which the ascent is made ; obviously, however, it is not made by enumeration of instances, complete or incomplete.
1 Ueberweg rightly remarks that " The recognition of the full significance of the inductive method in the sciences was reserved for modern times " (System der Logik, § 127).
3 Post. Anal., ii., 19, (5).
3 " Ex memoria multoties facta circa eamdem rem in diversis tamen singulari- bus, fit experimentum : quia experimentum [^uirtipfa] nihil aliud videtur, quam accipere aliquid ex multis in memoria retentis. Sed, tamen, experimentum indiget aliqua ratiocinatione circa particularia, per quam confertur unum ad aliud, quod est pro- prium rationis. Puta, cum talis recordatur quod talis herba multoties sanavit multos a febre, dicitur esse experimentum quod talis herba sit sanativa febris. Ratio autem non sistit in experimento particularium ; sed ex multis particularibus in quibus expertus sit, accipit unum commune quod firmatur in anima, et considerat illud absque consideratione alicujus singularium, et hoc accipit ut principium artis et scientiae. Puta, diu medicusconsideravit hanc herbam sanasse Socratem febrien- tem, et Platonem, et multos alios singulares homines ; cum autem sua consideratio ad hoc ascendit quod talis species herbae sanat febrientem simpliciter, hoc accipitur ut quaedam regula artis medicinae " (St. Thomas, in loc. cit.). It will be observed that there is no mention here of " Inductio " but only of " Experimentum ". It is significant, too, that these passages from Aristotle and St. Thomas are from the Posterior Analytics, i.e. from that part of the Organon which treats of Certain Science, while the passages quoted above in reference to enumerative induction — complete and incomplete — are taken from the Prior Analytics and the Topics, i.e. the parts that refer, the one to the formal side of reasoning, the other to probable arguments.
INDUCTION IN ITS VARIOUS SENSES 35
But another leading Scholastic, Duns Scotus, has analysed with a good deal of precision the procedure by which the general ization is effected. When a phenomenon occurs repeatedly under the influence of a cause that is not free, we must conclude, he teaches, that the effect in question has a " natural " connexion with the cause. . . . For it is impossible that a necessary cause produce the same effect regularly, unless it is determined by its natural tendency — its directive principle or form, as he calls it — to produce this effect. The effect must spring from the nature of that cause and not from any accidental, concomitant agencies ; for accidental agencies do not produce regular effects. And that any such regular series of effects is due to the nature of a certain cause, we know from experience : because we have seen this cause followed by these effects, when acting now in one set of conditions, again in a different set, and altogether in many varieties of cir cumstances,1 Thus, Scotus points out as the rational, self- evident basis of induction, the judgment that what REGULARLY results front the action of NON-FREE causes cannot be the result of mere CHANCE, but must have a necessary connexion with the NATURE of those causes ; and he furthermore points to the neces sity of varying our experiences, in order to separate, from the changing and accidental circumstances that accompany the ap pearance of the phenomenon in question, the one agency or group of agencies on which it is really dependent, which forms its real cause : a plain application of the modern Method of Agreement.
Why, then, it may be asked, did the Scholastics of the Middle Ages, if they knew the theory of scientific induction, and the principle underlying it, not proceed to apply the method, and so anticipate by centuries the wonderful
1 " De cognitis per experientam dico, quod licet experientia non habeatur de om nibus singularibus, sed de pluribus, nee quod semper, sed quod pluries ; tamen expertus infallibiliter novit, quod ita est, et quod semper et in omnibus ; et hoc per istam propositionem quiescentem in anima : QUIDQUID EVENIT UT IN PLURIBUS AB
ALIQUA CAUSA NON LIBERA, EST EFFECTUS NATURALIS ILLIUS CAUSAE. Quae pro-
positio nota est intellectui, licet accepisset terminos ejus a sensu errante, quia causa non libera non potest producere ut in pluribus effectum, ad cujus oppositum ordinatur, vel ad quern ex forma sua non ordinatur . . . sed causa casualis ordinatur adprodu- cendum oppositum effectus naturalis, vel non ad istum producendum, ergo nihil est causa casualis respectu effectus frequenter producti ab eo, et ita si non est libera, est naturalis. . . . Quod autem iste effectus evenit a tali causa producente ut in pluribus, hoc acceptum est per experientiam ; quia inveniendo nunc talem naturam cum tali accidenie. nunc cum tali, inventum est, quod, quantumcumque esset diversitas acci- dentium talium, semper istam naturam sequebatur talis effectus. Ergo non per aliquod accidens, per accidens illius naturae, sed per naturam ipsam in se conse- quitur tallis effectus" (In. /. Sent. dist. iii., Q. iv, 9).
3*
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strides which physical science has made since the Renaissance ? Many good reasons may be assigned.
One is that in those ages philosophers were more preoccupied with the philosophy of mind than with that of external nature, with the application of reason to principles accepted on authority, with the explanation of revealed religion and the unfolding of the contents of the Divine deposit of Revelation by means of philosophical principles and methods (203). And, as the full mean ing and proper understanding of those great truths and principles are arrived at by the application of the deductive or synthetic method, the attention of those philosophers was not arrested ^y the possibilities of knowledge that might have been opened up through a more careful analysis of the complex phenomena of external nature.1
But another, and more important, consideration is that they had not the means of prosecuting such an analysis. They knew the method theoretically, but this knowledge in itself was of little use. When there is question of estab lishing a law of Physical Nature — such as the laws of the planetary motions, or of the refraction of light — it is not enough to know that " a non-free cause cannot regularly produce an effect that is opposed to its natural tendency, an effect it is not determined by its nature to produce," — " causa non libera non potest producere ut in pluribus effectum, ad cujus oppositum ordinatur, vel ad quern ex forma sua non ordinatur ". This abstract, hypothetical principle merely asserts that if " necessary " or " non-free " causes exist, causes predis posed by an internal tendency ("forma ") to produce definite effects, the latter will occur with the regularity of a " law " ; but it does not of itself authorize us to assert categorically that there are such internal tendencies or principles of finality in nature, that there are causes predisposed to manifest such fixed, unchanging activities (cf. 223) ; and still less to affirm with certainty that this or that oft-observed combination of particular phenomena is the expression of some one of those causal tendencies existing in nature.
Such a categorical conclusion as the latter can be justified only by a dili gent observation of the natural phenomena to which it refers. And nature is infinitely complex : so that the establishment of a certain conclusion that this series of phenomena reveals this universal physical law, necessarily presup poses a detailed and accurate weighing, reasoning, analysing, and comparing of all the elements that enter into the phenomena in question. The phe nomena of physical nature exist in space and time : accurate quantitative measurement is, therefore, at the basis of all experimental research : and hence, the discovery of instruments for delicate measurement was an indispensable condition for the progress of the physical sciences. But Aristotle and the mediaeval Scholastics had neither the clock for the accurate measurement of time, nor the balance for the exact estimation of weight, nor the thermometer for measuring temperature, nor the barometer for measuring atmospheric pressure, nor the telescope to observe the heavens, nor the microscope to reveal the mysteries of the minute structure and composition of organic tissues. It is true, indeed, that the sagacity of great genius, the patience of long reflection, and disinterested zeal in the pursuit of truth, can contribute much, even with the aid of mere ordinary observation, to the development of scientific speculation : witness the wonderful perfection of the Ptolemaic
1 Cf. CLARKE, Logic, p. 480.
INDUCTION IN ITS VARIOUS SENSES 37
astronomy. Indeed the superior powers of Aristotle, and of his mediaeval Christian commentators, in the domain of ordinary, unaided observation, are undisputed at the present day. But it would be wrong to arrogate to them an honour they would be themselves the first to disclaim,— the honour of creat ing sciences which could not possibly have arisen without the invention of the special instruments of observation and measurement just referred to.
Accurate experimentation was impossible in the Middle Ages, in the absence of those delicate means of weighing and measuring that are the inven tion of a more modern era. The thirteenth century, however, — the golden age of Scholasticism — produced at least one exceptional and extraordinary man, whose name cannot be passed over in connexion with the rise of scientific in duction. Roger Bacon, a Franciscan monk, who lived through the greater part of that century, dying at Oxford in 1 294, rose far above the commonplaces of his time in his advocacy of the experimental method. His life was one im passioned and even fanatical plea for the positive sciences. Nor did he con tent himself with pleading : he set an example by devoting his great genius to conducting scientific experiments and inventing instruments for that purpose.
He distinguished four possible ways of gaining a knowledge of nature : authority, (a priori) reasoning, observation, and experiment. And he tells us that of these four the first ranks lowest in worth : " auctoritas debilior est ratione " ; the second, dialectic reasoning, does not satisfy the mind : " non certificat " ; nor the third, which is ordinary, superficial observation. The fourth alone — " internal " or " intrinsic " experience — is convincing, and that owing to the aid it receives from mathematics and geometry. He anticipated more renowned and more modern philosophers in an attempt to establish one general science that would submit to mathematical principles all the varied interactions of the bodies that make up the physical universe.1
209. LORD BACON'S " NOVUM ORGANON": THE Two IDEALS OF GENERALIZATION. — The English monk of the thir teenth century understood the nature and method of experimental science as well as, if not better than, his namesake of the six teenth. Francis Bacon, Lord Verulam (1561-1626), is commonly regarded as the " founder of the inductive method ". Wrongly, however ; because, in the first place, his method of " interpreting nature " has never been adopted : " The value of this method," writes Jevons,2 " may be estimated historically by the fact that it has not been followed by any of the great masters of science."
Bacon blamed his predecessors, the " deductive " philosophers, for "anticipating" nature instead of " interpreting " it. After enumerating four great sources of such fallacious " anticipations " — the " Idola " or Phantoms : (a) of the Tribe (common to all men), (fr) of the Cave (due to personal idiosyncrasies), (c] of the Market-
1 Op. maj., p. iv., dist. i., c. iii., dist. ii.-iv. ; Opus tertium, c. 29-37, etc. ; cf. DELORME, Dictionnaire de theologie catholique, s.v. Bacon,
2 Principles of Science, p. 507.
38 THE SCIENCE OF LOGIC
Place (due to public catch-cries, shibboleths, etc.), (</) of the Theatre (due to fashion) — he goes on to expound his own " method ". He appears to have regarded all physical phenomena as collections and combinations of sensible properties of matter, each of the latter being a simple thing, a " simple nature," and each due to some "form," i.e. to some essential constitutive principle1 of the material agencies in which such sensible pro perties are revealed. This is merely a statement of the scholastic principle that the properties of an agent reveal its specific nature or " formal cause ". But Bacon conceived it to be the duty of the scientist to draw up a complete catalogue of all the sensible properties exhibited throughout all nature, and of all the "forms" to which these could be due : an utterly impracticable under taking. Next, in order to facilitate the process of tracing each property to its " form," or cause, tables or catalogues were to be drawn up, exhibiting the relations of conjunction or concomitance, separation, and variation, between the forms and the properties : a still more arduous and unpromising task. Bacon never at tempted to carry out these schemes himself. The first grave defect of his " method " is, therefore, its inutility.
Next, assuming the possibility of compiling such data, he pointed out that the cause, or " form," of a given sensible property could be best detected by a process that would suc cessively eliminate all the other rival " forms," and thus bring to light the proper one. Every "form*' which is present when the property in question is absent, or absent when the latter is present, or which does not increase and decrease concomitantly with the latter, is to be rejected as not being the "form " causally connected with the latter. Such is the principle on which the method pro ceeds, the principle of elimination, or exclusion of the non-causal or casual concomitants of a phenomenon. It is theoretically sound: "where you cannot (as in mathematics) see that a pro position must universally be true, but have to rely for the proof of it on the facts of your experience, there is no other way of establishing it than by showing that facts disprove its rivals".2
1 The tendency of the science of Bacon's time to substitute for the qualitative conceptions of the Scholastics, quantitative, picturable, measurable conceptions, is revealed in his changing and uncertain ways of conceiving " form ". He appears to have finally fixed upon the notion of something measurable in terms of " spatial and temporal relations of bodies " (WELTON, op. cit., ii., p. 36), something which has been described in present-day scientific language as a " principle of corpuscular structure" (JOSEPH, Logic, p. 364).
a JOSEPH, op. cit., p. 366.
INDUCTION IN ITS VARIOUS SENSES 39
We shall see this principle applied later on by J. S. Mill, and uni versally adopted. But, for its safe application we do not need, as Bacon. taught, to have antecedently elaborated a completely exhaustive catalogue of all the " forms " and " sense-qualities " in the universe. It will suffice to eliminate all the possible pertinent alternatives, suggested by a careful analysis of the matter under investigation.
But, owing to the enumerative character of the process as conceived by Bacon, and to the practical impossibility of a com plete enumeration of the alternative factors involved, the process, so applied, could never reach a necessary and universal law : for (to use Bacon's own words) when " the axiom being established is more extensive and broader " than " those particulars out of which it is extracted " (Novum Organon, i., 105, 106) — and this is what happens as long as his impossible "catalogues" are not complete and absolutely reliable — he fails to indicate any prin ciple (other than enumeration) which might justify him in drawing a universal conclusion from such a defective enumeration of alter natives. This, then, is a second serious defect of the " method ".
Next, it must be pointed out that although he says " In duction which proceeds by simple enumeration is a puerile thing and concludes uncertainly" (i., 105), and that "the syllogism is not applied at all to the principles of science" (i. , 13), yet, as a matter of fact, his whole process is a simple application of the categorical syllogism in the second figure, combined with the modus tollendo ponens of the mixed disjunctive syllogism ; in which latter, moreover, the disjunctive major is assumed to be complete, even though his catalogues of forms and qualities remained incom plete throughout. Bacon's own example will illustrate this.
Let / be the " form " of heat (the " form " we are en deavouring to detect or select from among all the known "forms"). Let h represent the sensible quality of heat. Let A, B, . . . Y, Z, represent the whole collection of " forms " or " natures " in the universe. Then :
/is either A or B or C or . . . X or Y or Z ;
(1) But A is not present with h, And / is present with h, Therefore /"is not A ;
(2) And B is present in the absence of h, While /is not present in the absence of ht Therefore /is not B ;
40 THE SCIENCE OF LOGIC
(3) And C does not vary concomitantly with h, While /"does vary concomitantly with ht Therefore/ is not C ;
and so on, until all the "forms" except one, say Z, are thus eliminated by syllogisms in Cesare or Camestres. Then we have, finally, this mixed disjunctive argument in the modus tollendo ponens, verifying the form of heat as Z : —
/"is either A or B or C or . . . X or Y or Z ; But/is neither A nor B nor ... X nor Y ; Therefore /"is Z.
This latter form of argument is regarded by many as the typically " inductive " inference.1 The various arguments, (i), (2), and (3), by which we apply various methods of elimination, sug gest that instances (of the circumstances accompanying heat) are no longer being merely enumerated, but that the nature of their connexion (with heat) is being sifted by experiment. This marks the transition from enumerative to scientific induction.
As was pointed out already, two possible tendencies may arise from an incomplete enumeration of instances. The first, with which many of the Scholastics, and Bacon himself, seem to have been preoccupied, is to realize, somehow or other, the ideal of a complete enumeration. To realize it actually is, for the most part, chimerical, and moreover, it does not lead us to the true universal. To realize it virtually, i.e. by falling back on some rational principle which might justify us in saying : " and so on of the unexamined instances " — " et sic de ceteris " — is to yield in reality to the second tendency, while under the traditional sway of the first : the second tendency being to abandon the mere enumeration of the instances, to concentrate attention on their material side, on the quality, the nature of the facts we are dealing with, and to ask ourselves : Is it not possible and per missible to rise to the conception and enunciation of a strictly universal physical law from an examination of some instances only ? It is possible to do so; and the difficulty of the process of physical induction, by which we accomplish this ascent, is not a difficulty of principle or method, but rather of application : it is a difficulty that belongs not to the logical, but to the practical, order.2
The ancient Greek philosophers, and the Scholastics of the Middle Ages, were quite as well aware as any modern exponent 1 Cf. 197 ; JOSEPH, op. cit., p. 405. 2 C/. JOYCE, op. cit., p. 217.
INDUCTION IN ITS VARIOUS SENSES 41
of the inductive method that (i) Explanation of the phenomena of physical nature consists in a thorough knowledge of their connexion with their respective causes ; (2) that physical causes act regularly, uniformly ; (3) that, therefore, if we could be sure of having discovered and fixed upon the natural cause of a given phenomenon, amid all its complex surroundings (by a process of abstraction], we could at once (by generalization] formulate the physical law that always and everywhere this cause will act in the same way and produce this same phenomenon. But the difficulties that beset the work of bringing to light with certitude the causal connexion — the work of observing, analysing, experimenting, etc. — were so great that neither the ancient nor the mediaeval nature-philosophers had the courage and perseverance to grapple with them. Hence, they made little or no serious effort to test the worth of the probable conclusions which they based upon an incom plete enumeration of superficially observed instances. The scientists of the seventeenth and eighteenth centuries, Galileo, Torricelli, Pascal, Descartes, Newton, etc., were making practical efforts in many directions to scrutinize and question physical nature more closely, long before logicians attempted to formulate and interpret the theory of these researches. Lord Bacon's attempt at the conscious formulation of a theory was a failure. Sir Isaac Newton (1642-1727) was conspicuously successful both in theory and in practice. Since the latter's day, many workers, both in the natural and in the mental sciences, have sought to formulate the Theory of inductive research. But those sciences are so progressive in their methods, and views so fundamentally divergent as to the nature of knowledge are propounded by philosophers, that there is still comparatively little uniformity of treatment in the domain of inductive logic.1
210. MODERN CONCEPTIONS OF INDUCTION: NEWTON, WHEWELL, J. S. MILL, JEVONS.— Newton taught that in the pursuit of knowledge we must start with an analysis of observed facts: that we must suppose and formulate some general law suggested by these facts : that we must, by synthetic or deductive reasoning, derive consequences from this law, thus to determine whether the law coincides with all observed facts or not.
Indeed, most writers on induction agree in recognizing certain well-defined steps or stages in our progress from particular facts
1 For varieties of treatment cf. VENN, Empirical Logic, pp. 353 sqq. ; WELTON, op, cit., ii., bk. v., chap. ii.
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to general laws : the formulation of an hypothesis suggested somehow or other by an initial observation of phenomena ; the moulding, remodelling, generalizing of this hypothesis, by suc cessive eliminations and exclusions — under the guidance of certain canons of more or less practical utility, commonly known (after J. S. Mill) as the "experimental methods" or "inductive methods"; the final "verification" or "establishment" of the hypothesis as a " law " ; the attempted " explanation " of this law by wider laws ; the commencement of the synthetic or deductive stage by the application of the established law to particular facts for the " explanation" of these latter.
Not all writers, however, attach the same importance to the various stages. Whewell,1 for instance, lays great stress on the invention of hypotheses, or, in his own language, the " colligation of facts by means of an exact and appropriate conception," 2 as the most important step in the discovery of scientific truths. To the subsequent process of generalizing the abstract hypothesis, of remoulding and remodelling and verifying it by the application of fixed canons, he devotes much less attention. Its verification or proof 'he holds to consist in deducing consequences from it, and ascertaining whether it thus foretells phenomena, at least those of the same kind as the phenomena for the explanation of which it was invented. Should an hypothesis, invented to explain " one class of facts," be also found " to explain another class of a different nature," it is more firmly established than by any other means : this Whewell calls Consilience of Inductions?
J. S. Mill, on the other hand, almost entirely ignored the theory of the initial step of conceiving an hypothesis. He ad dressed himself to the process of generalizing directly from particulars — a process quite impossible apart from the abstract conception of some guiding hypothesis, — and to the establishment of rules or canons for the correct carrying out of this process. No doubt, this latter stage lends itself to methodical treatment, while the former stage does not ; and Mill tried to justify his mode of treatment by the plea that as a logician he was con cerned only with the proof of general truths, not with their discovery. There does not seem to be much force in such a plea.
1 Flourished 1794-1866; among his writings are the History of the Inductive Sciences (3 vols., 1837; 2nd edit. 1847; 3rd, 1857) and a Philosophy of the Inductive Sciences (2 vols., 1840 ; 2nd edit. 1847 ; 3rd, in three vols., bearing separate titles, of which one was called Novum Organon Renovatum, 1858-60).
2 apud WBLTON, op. cit., ii., p. 50. » ibid., p. 51.
INDUCTION IN ITS VARIOUS SENSES 43
A truth cannot be said to be discovered in the full and complete sense of the word until it is thoroughly verified, or proved to be a truth. It may be formulated and held as true with more or less probability — as the result of an enumerative induction or of an analogical argument, as an hypothesis or as an "empirical general ization," — but it cannot be fairly said to be fully "discovered" until we have both " verified " it, or proved that it is true, and "explained" it, or shown why and wherefore it is true, by connecting it necessarily with already known and established truths. In any case, Mill de facto regarded his " inductive methods " as methods of discovery as well as of proof, and de scribed induction itself as " the operation of discovering and proving general propositions".1
Finally, we may mention Jevons,2 as an author who takes a thoroughly enumerative view of induction, making the whole process consist in a succes sive enumeration and determination of all the mathematically possible hypo theses that might account for a given result or phenomenon. Obviously, in this view certitude about our inductive conclusions is practically never attainable, for the ideal of a perfect enumeration of instances is beyond our reach.3 The method is open to the same objections as Bacon's method, which Jevons him self criticizes. In the " infinite ballot-box " of nature, the determination of the chances of an invariable sequence of any two " balls " is a problem in the mathematical theory of probability, the solution of which cannot of its nature give us certitude (267). Nor can the result of this " inverse problem " be made any more certain or definite by arbitrarily limiting the elements in the ante cedent to those contained in the consequent, nor, indeed, by arbitrarily limiting them in any way. " If, for instance, we ... say : Given that certain com binations of A, B, and C, are the existent ones, find a solution in terms of A, B, C, and nothing else, from which this result shall follow, no complaint can be made. The problem is a very limited one, but it may be useful. . . . But to make the same restriction when the problem is, Given that dew is copious on a cold, clear night, or given that a magnetic needle is deflected by an electric current, find a solution which shall introduce no fresh terms into the statement of the phenomena, would be a mere parody of physical investigation."4 In deed, the only way of reaching certitude is that precluded by Jevons's view of induction ; namely, by abandoning the enumerative ideal and addressing our selves to an analysis of the nature of the phenomena in question, on the rational assumption that constant coexistences or sequences of phenomena have their explanation in the existence of fixed natures, of stable tendencies and lines of action, in the phenomena themselves, and with the conviction that these fixed
1 Logic, iii., I., § 2.
2 Flourished 1835-1882 ; Logical writings : Principles of Science (2 \ols. 1874; 2nd edit, i vol. 1877) ; Elementary Lessons in Logic (1870) ; Primer of Logic (1876) Studies in Deductive Logic (1880).
*Cf. JOSEPH, Logic, p. 487. <VENN, Empirical Logic, pp. 360, 361.
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natures, these stable tendencies, have their ultimate explanation in the omni potent will of an all-wise ruler of the universe (224).
The views of an individual author on these latter ultimate presuppositions and foundations of induction are pretty sure to influence and colour his concep tion of the various steps in the mental process itself by which the mind moves inductively from particular to general, from fact to law. Some such views, propounded by recent writers, will be examined in due course.
211. ANALYSIS AND ILLUSTRATION OF THE PROCESS OF SCIENTIFIC INDUCTION. — From the preceding paragraphs of the present chapter we can gather what the main problem of induc tion is, and what its method of procedure ought to be. It seeks a scientific knowledge of the concrete, particular phenomena of our experience, i.e. a knowledge of them through their causes and laws, a knowledge, which, bringing to light their nature, their origin, the purpose of their existence or occurrence, will lay hold of what is universal, permanent, abiding, in them. Amid the changing and chaotic elements that make up our world of unanal- ysed and unexplored sense experience, induction will try to trace the permanent connexions of cause and effect, to eliminate the variable conditions and surroundings of each phenomenon, and to lay bare its connexion with its real ground or cause. Now, in order to do this, we must not merely observe with accuracy the phenomenon we wish to explain ; but next, and necessarily, we must suppose that amid all its immediate conditions and surround ings some element or elements constitute its determining cause, and yield the law of its occurrence ; and then we must proceed to test or verify our supposition by deducing consequences from the latter, and comparing our conclusions with actual facts, analysed by further observation and experiment. This process of testing we must prosecute until we reach a full conviction that the sup posed cause of the phenomenon is the necessitating and indispens able, and therefore the true or real, cause, of the facts examined. When we have thus established an isolated law, we may on the one hand endeavour to explain this law itself by seeking its connexions with other already known laws, and on the other hand apply the law itself to the explanation of all facts that come under it.
(i) Preliminary observation of facts; (2) supposition as to their cause ; (3) verification of our supposition ; (4) explanation, and (5) application, of the established law : such are the essential steps in the inductive discovery and proof of scientific truths. The deductive application of the general law to the facts is the
INDUCTION IN ITS VARIOUS SENSES 45
final step, by which we reach a scientific knowledge of those facts in the observation of which the whole process had its origin.1
The method here outlined is recognized by Mill :2 he calls it " deductive," admitting its application only to the more complex phenomena due to a combination of causes ; yet he is forced to allow that it is to this method " the human mind is indebted for its most conspicuous triumphs in the investigation of nature ". 3 The advocacy of this method by many of our more recent induc tive logicians, Bosanquet, Sigwart, Welton, Joseph, etc., is a wholesome reaction against the Empiricism of the school of Mill.
The various steps indicated above will form the subject-matter of subsequent chapters. The whole process, however, is based upon certain fundamental principles and postulates which call for explanation and justification at the outset (Chaps. III. and IV.). With an example 4 to illustrate the inductive process, and a com parison of the latter with deductive inference, we may conclude the present chapter.
" Let a chemist take some hydrogen, a gas without colour, taste, or smell ; which burns with an intensely hot bluish flame ; which is 14-4 times lighter than air, 23-326 litres weighing 2 grammes. Let him take another and very different sort of gas, chlorine ; of a yellowish colour and an unpleasant, suffocating smell ; density 2-44, weighing 35-5 times more than hydrogen, 22-326 litres weighing 71 grammes.
" Let the chemist mix those two gases in a glass vessel, and place it in the sunlight : a violent combination will suddenly take place, disengaging 22 thermal units or calories of heat ; after which the chemist finds in the vessel a new body, whose distinctive properties have acquired for it the name of hydro chloric acid. This new body will attack most of the metals and combine with them to form various salts ; it will combine with the aqueous vapour of the atmosphere to form a colourless, acid solution, etc.
" So far he has observed a fact [first step]. Next, how is it to be explained ? Why did it happen ? What is its cause ? He supposes that it is due to some law of nature [second step] ; he supposes the formation of hydrochloric acid to be due to some property inherent in those two gases, acting in certain con ditions, still to be determined. This suspicion of his is an hypothesis, which he must now proceed to verify.
" For this latter purpose [third step] he will multiply and vary his ex periments. For example, he will let the sunshine act on a mixture of chlorine and oxygen ; supposing a priori that they too will combine ; but he finds that they will not. It is not every two gases, therefore, that will combine under the action of the sunlight. But, perhaps, at least any quantities whatever of hydrogen and chlorine will combine ? A priori, again, the supposition is permissible ; but again it is negatived by the facts. For repeated experiments
1 C/. 252: Regressive Demonstration. 7 Logic, iii., xi. and xlv.
3 ibid, xi., § 3. 4 From Mercier's Logiqtie, pp. 300 iqq.
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establish that they will combine only in the proportion of I to 35-5 by weight, or— which is the same— of i to I by volume. When those proportions are brought together under the influence of sunlight— no matter how little or great the absolute quantities may be, milligrammes, centigrammes, decigrammes — the combination will take place. On the other hand, when those proportions are not maintained, the quantity of the one which is in excess of its due propor tion to the total quantity of the other, will remain over, unaffected by the combination.
" Here, then, are other facts in presence of which the observer finds him self : Two definite gases, mixed in definite proportions of i to i by volume or i to 35-5 by weight, combine under the action of sunlight— the absolute quantities of each being indifferent to the result and indefinitely variable. Neither of these gases, mixed with any other gases, combine with the latter in the same conditions and proportions ; if mixed with each other in any other proportions than those indicated, they will not combine completely, but will leave the surplus above the proportion unmolested. Further, the chemist remarks that, after the combination, one volume of hydrogen and one volume of chlorine, combining under definite conditions of temperature and pressure, yield two volumes of hydrochloric acid gas.
" Are all those facts — which recur repeatedly in similar circumstances — the result of mere chance coincidences of disconnected and indifferent causes ? They are not : they cannot be. Reason will not admit that any such complex, harmonious, stable series of facts could be due to chance. They must be the ex pression of a law ; they must find their sufficient reason in the nature of the combining bodies.
" The chemist finds this sufficient reason in what he calls the ' affinities ' of the reacting bodies ; the metaphysician, in 'properties inherent in the nature ' of those bodies, and indicative of the energies of those natures. The language is different, but at bottom the idea is the same : There are in the world such complex, harmonious, stable series of facts as cannot be due to chance activities, but must be the result and expression of natural laws ; and the formation of hydrochloric acid from hydrogen and chlorine is a mani festation of such a law.
" Thus it is that, from the total complex groups of circumstances in which he has witnessed the formation of hydrochloric acid, the chemist abstracts or gathers by induction the truth that hydrogen and chlorine have the property of combining in the proportions indicated, with a disengagement of 22 calories of heat for the formation of each molecule-gramme of hydrochloric acid. The combination being, moreover, found to be independent of the particular place and time, and of the absolute quantities of the bodies used, he can foretell with certainty that always and everywhere those gases will combine in those definite proportions to form the compound body, when submitted to the action of the sunlight under the same general conditions.
" In a word, the law of hydrogen and chlorine is to combine, always and everywhere, under the above-mentioned conditions. The chemist who has ob served all the facts and extracted that law from them has made an induction."
"Thus, the chemist has verified his hypothesis that the two gases, hydrogen and chlorine, have the natural property of combining in the definite
INDUCTION IN ITS VARIOUS SENSES 47
proportions of i to 35-5 by weight. They have an innate, inherent, intrinsic tendency to do so, in certain recognized conditions and under the influence of certain known natural agencies. Such is the law of their nature ; for, as St. Thomas profoundly remarks, the law of a being is the ' natural inclination which carries it towards the end it has to realize in the universe '.*
" Of course, the knowledge of that law does not exhaust all that is know- able about the nature of the bodies in question. By no means. It merely lifts a corner of the veil. The chemical property discovered simply shows us the natures of the bodies that possess it, under one of their aspects."
Writers on induction do not usually emphasize the next step, which is the deductive application of the verified law to facts. Yet, if we regard in duction as the total process by which we reach a scientific knowledge of the individual phenomena of nature, this deductive step is essential. The utility of our abstract knowledge of law will always lie in its applicability to concrete facts. " It is a natural property of hydrogen and chlorine to com bine in certain proportions under certain conditions to form hydrochloric acid ". Such is our abstract law. " Here are quantities of those gases in the due proportions ; therefore if submitted to the action of sunlight, they will form a certain quantity of hydrochloric acid with a disengagement of a certain quantity of heat." Such is our deductive application. It will be seen at once, therefore, how induction contributes to that " knowledge of things by their causes " which is the only knowledge dignified by Aristotle with the title of " scientific ". It will be easy, likewise, to see wherein lies the difference between the method of the rational or deductive sciences and that of the inductive sciences, and what is their point of contact (202). In the former, deduction is immediately possible after the conception of a few definitions or first principles, seen intuitively on a simple analysis and comparison of a few very simple concepts (206). In the latter, on the contrary, deduction from the general law cannot commence until the law •. has been established by a process that is often tedious and difficult.2
Hence, if we give the name of Induction to that whole method of pro cedure by which we establish the conclusions of the positive sciences, we must distinguish two phases in it (202) : one deductive, which gives us science, in the Aristotelean sense of the word, i.e. the explanation of observed facts by their causes ; the other, preliminary to this explanation, the stage in which the general law is reached, and which alone modern logicians call Induction, in the special and restricted meaning of this term.3
Whether this strictly inductive phase of the whole procedure — the side by which we ascend from concrete, particular facts to abstract, universal laws — involves any reasoning process which is not syllogistic or deductive (192), a comparison of induction with deduction will now enable us to determine.
1 Stimma Theologica, ia, iae, q. 93, a. 7 sqq. Cf. infra, 217.
2 "In the former [mathematical], generalization is unnoticed because it is all- pervading; for the relevant conditions are distinguished from the first. In the latter, generalization comes to an end and attracts attention as the result of a long effort ; for all our task is to distinguish the relevant from the irrelevant conditions." — JOSEPH, Logic, p. 509.
*C/. MELLONE, op. cit., 382-86.
48 THE SCIENCE OF LOGIC
212. SCIENTIFIC INDUCTION AND DEDUCTIVE INFERENCE. — We have already compared Induction with Deduction, under standing these terms as descriptive of Method (202 ; cf. 187). They are sometimes contrasted with each other as forms of logical inference. But, since induction is not a form of logical inference at all,1 such a comparison is misleading. The so- called " Induction by Complete Enumeration " we have shown to be as unworthy of the name of a reasoning process as is the so-called " syllogism " understood in the sense attached to this term by John Stuart Mill (207). Both processes deal with mere collective propositions, and are simply additions of actual parts to form an actual whole (" induction "), or redistribution of that whole into its parts (" syllogism "). The one process is the reverse of the other, but neither is a reasoning process : the one is summation of individuals into a group ; the other, distribution of the group into its members : neither reaches the abstract, universal judgment. Complete enumerative induction, therefore, cannot be compared with the genuine syllogism in any figure. Incomplete enumerative induction, however, in so far as it shows a connexion between two objects (M and P} to be possible, and suggests that the connexion may be necessary and universal, is naturally formulated, as we have seen, in the third figure of syllogism (172, 207) ; but it is, in a certain sense, the opposite of the scientific syllogism (in the first figure) : inasmuch, namely, as it seeks to establish a general principle from instances, while the latter applies an already established principle to instances.
Does scientific induction, however, admit of any comparison with deduction, or deductive inference, or the syllogism ? With deduction as a method, yes. If we take both as methods, and understand by induction the method whereby we ascend from the consideration of particular facts to the establishment of some general truth, in this meaning it is, of course, the reverse of the whole deductive method, by which — in the mathematical sciences, for example — we descend from the conception of some simple and general truth to the understanding of some less simple and less general one in the light of the former (202). The two processes move in opposite directions: they view things from opposite standpoints : they lead the mind along reality and into the understanding of it by presenting opposite aspects of it : in
1 Cf, supra, 197. JOYCE, Logic, p. 217.
INDUCTION IN ITS VARIOUS SENSES 49
the one case the concrete and particular aspect comes first, in the other the abstract and universal aspect.
In the positive sciences, or sciences of observation as they are called, the ascent to the general is difficult ; the descent to the explanation of familiar facts by applying the principle is comparatively easy ; in the abstract, rational sciences, the ascent from particular to general is easy, the descent from the general to its applications is difficult (202). Here, however, the contrast between induction and deduction ceases. As mental processes they are both essential to the attainment of science ; for this is the knowledge of fact by law, of effect by cause, of particular by general.
But, apparently owing to Aristotle's conception and treatment of enurnerative induction as a sort of syllogism without a middle term, and to the fact that induction aims at generalizing from particular experiences, some logicians have sought to represent induction as a special form of logical inference, distinct from, and in contrast with, those forms of inference which they conceive as deductive. Now, to represent induction as simply a form of inference is rather a misleading simplification of what is in reality a whole series or combination of processes, some of which " are not processes of reasoning- at all ".l Others of them, no doubt, are logical inferences ; but not of any new form, distinct from the various forms of mediate inference, categorical, hypothe tical and disjunctive, that were known and analysed in logic prior to the modern development of induction. These are the only forms of inference known to induction ; and a glance at the various steps in the inductive process (21 1) will show how far they enter into it. The preliminary observation of the facts to be investigated, and of all their surrounding circumstances, is, of course, not a logical inference of any sort, though it may indeed involve inferences, both immediate and mediate (238, 263). The conception of an hypothesis as to the general law connecting the facts with their causes, is not itself an inference either. But the verification of an hypothesis may be expressed in a series of inferences, each taking the form of a mixed hypothetical syllogism : " If this hypothesis is true, certain events ought to follow from a certain combination of agencies ; but (by observation or experi ment we proceed to find that) they do follow (or do not, as the
JOSEPH, op. cit., p. 482. VOL. II. 4
5o THE SCIENCE OF LOGIC
case may be) ; therefore the hypothesis is probably true (or cer tainly false, as the case may be)." From this we see that the modus tollens efficaciously disproves, and so eliminates, all hypotheses that are unable to account for the facts under investigation. No single application of the modus ponens, however, can verify the hypo thesis with certitude. Nor, indeed, strictly speaking, could any ac cumulation of them give us certitude about the antecedent, regarding the matter from the point of view of formal inference ; though often, as we shall see, hypotheses are sufficiently verified in this manner (230). We usually try to verify our hypothesis by showing not only that it will account for the facts, but that no other hypothesis will account for them. We may sometimes be able to do this by showing the facts to be such that they necessarily involve the cause supposed in our hypothesis : " If this hypothesis were not true, the facts could not be such and such ; but they are such and such ; therefore, the hypothesis is true." * It is rarely, however, we can directly show the facts to be such that of their nature they necessarily involve the supposed cause : for the most part we have to be content with showing that they must involve it for the reason that no other conceivable supposition can account for them. That is to say, we verify our hypothesis by eliminating all competing alternatives. Now, this process naturally assumes the form of a mixed disjunctive syl logism in the modus tollendo ponens : —
" The cause of x is either a or b or c or d . . . or z
JIn his admirably clear exposition of Newton's researches on gravitation, Mr. Joseph (Logic, pp. 477-82), illustrating the various stages of the inductive process, says that "the final argument, in which the agreement of the facts with the results of this hypothesis and of no other is shown to require the acceptance of this hypothesis, is inductive" (p. 482). The term "inductive " cannot here be used in a sense opposed to syllogistic, for the argument to which he applies it is a mixed hypothetical syllogism. It is as follows : " Assuming that the continual deflexion of the planets from a rectilinear path is due to an attractive form [force?], their actual motions, if my statement of the law of attraction is true, would be thus and thus ; if it is false, they would be otherwise : but they are thus and thus, and there fore my statement is true" (ibid.). It may be symbolized thus : " If A then C, and if not A then not C ; but C ; therefore A ". The standard syllogism, embodying the axiom applied in this reasoning, and analogous to the standard syllogisms applying the Dictum de omni, etc., in 192, might be expressed thus : " If a supposed cause accounts adequately for any real fact, and is the only cause which can account for it, then that supposed cause is real ; but (by analysis of the facts, through observa tion and experiment) we see that this supposed cause, and it alone, can adequately account tor this real fact ; therefore this supposed cause is real ". The author applies the term " inductive " to reasonings which are not explanatory, which merely convince us that a judgment must be true, without giving us any insight into the reason why it is true.
INDUCTION IN ITS VARIOUS SENSES 51
It is not b or c or d . . . or z .: It is*"1
— where a, b, c, . . . z are supposed alternative causes of the phenomenon x. This reasoning is, as Mr. Joseph observes,2 " in form very simple ; but the discovery of proper premisses is very hard ". How is the investigator to determine the extent of the major premiss, the field of pertinent alternative hypotheses? — since he cannot realize Bacon's ideal of cataloguing all the causes in the universe (209). Obviously, it is to be defined by prudence rather than by inference. Then he must verify the minor premiss " piecemeal by hypothetical arguments that rest upon one or other of the [usual] grounds of elimination ".3
Finally, when, having verified our hypothesis, we apply it to the explanation of facts, or when we explain itself by the appli cation to it of wider laws, our reasoning is obviously syllogistic and deductive.
Is any of the forms of inference outlined above, so characteristic of the inductive method as to merit the title of " inductive reasoning " ? It matters little whether we so describe any of them, provided we bear in mind that " Induction " is much more than any of them : that it involves many pro cesses other than mere inference. And, indeed, the same may be said of the title " Deduction " as applied to forms of inference rather than to method. We have already seen (192) that there is no uniformity of usage in the application of the titles " deductive " and " syllogistic " to forms of inference. A " de ductive " inference is perhaps most commonly understood to signify an infer ence in which it is sought to subordinate some special cases (or classes of cases) under some wider principle or law. This would be chiefly characteristic of syllogisms in the first figure, whether categorical or hypothetical. But then, syllogisms in the second or third figures would not be deductive in this sense ; for in them there is not usually any subordination of instances to a rule. Mathematical reasoning, too, proceeds in large part from known principles not to subordinate cases, but to other co-ordinate and coextensive principles : in these sciences the cognate truths are so related that very often either of a pair, a and b, can be used equally well to prove the other : the related truths are reciprocal ; and yet mathematical reasoning is universally regarded as deductive.4 Hence, the subordination or subsumption of a case under a rule is hardly a satisfactory criterion of " deductive " inference.
Mr. Joseph's treatment of the contrast between deduction and induction is instructive. " Inductive Logic," he rightly remarks, " has not really laid bare any new forms of reasoning ; we have already seen that Bacon's Induction is a disjunctive argument ... Or if anyone likes ... to call inference deductive when it proceeds from conditions to their consequences, and inductive when it proceeds from facts to the conditions that account for them, he will find
JOSEPH, op. cit,, p. 406. *ibid. sibid.
4 C/. JOSEPH, op. cit., p. 368, 369 n. 2 : also pp. 503 sqq.
4*
52 THE SCIENCE OF LOGIC
" a. that the two processes cannot be kept rigidly apart. Whoever infers from the facts of experience the conditions which- account for them must at the same time in thought deduce those facts from those conditions.
" b. that what has been called Deductive Logic, what Inductive Logic has been contrasted with, analyses forms of inference which, if the antithesis between Induction and Deduction be thus understood, must be called in ductive." 1
He himself regards the mixed disjunctive argument as a typically induc tive form of inference, owing to the use that is made of it in verifying an hypothesis by the exclusion or elimination of alternative hypotheses. But he suggests a deeper distinction between deductive and inductive inference : " The true antithesis is, as Aristotle saw, the antithesis between Dialectic and Demon stration ; or in more modern phrase, between Induction and Explanation ".2 Inductive inference, then, would be the inference which convinces us that a proposition is true (because certain facts are incompatible with any other alternative), without, however, explaining -why it is true, without demonstrating it ; while deductive inference would not only prove that a proposition is true, but would also explain or demonstrate it, or, in other words, show us why it is true. This is an intelligible and useful distinction ; but, obviously, it is based on the matter of our inferences : it cannot be regarded as a distinction between forms of inference, except in so far as some of the recognized forms of logical inference are found to be more naturally applicable to matter in which we can demonstrate our conclusions, and others to matter in which we can only set up our conclusions as de facto true, without seeing why they are so. Now, the disjunctive form of reasoning is, as we have seen, the form into which the inductive verification of an hypothesis naturally falls. And to verify an hypo thesis in this way is merely to show that it is true, without further explaining it or showing why it is true : " the essence of inductive reasoning lies in the use of ... facts to disprove erroneous theories of causal connexion. It is ... a process of elimination. The facts will never show directly that a is the cause of x ; you can only draw that conclusion, if you show that nothing else is." '
" You establish a particular hypothesis about the cause of a phenomenon, by showing that, consistently with the relation of cause and effect, the facts do not permit you to regard it as the effect of anything else (and mutatis mutandis if you are inquiring into the effect of anything). It is this which makes the reasoning merely inductive. If you could show in accordance with known or accepted scientific principles that the alleged cause was of a nature to produce the effect ascribed to it, your reasoning would be deductive ; . . . you would be applying them to produce a conclusion which you see to be involved in their truth ; and if we suppose the principles to be of such a nature that we can see they must be true, then the conclusion will appear necessary, and a thing that could not conceivably be otherwise." 4
1 C/. JOSEPH, op. cit., p. 369.
2 ibid., p. 369. " The two antitheses." he adds, " are not quite identical, because some dialectical arguments are not inductive, and explanation is not demonstrative unless the premisses from which it proceeds are known to be true. The reasoning from those premisses is however the same, whether the premisses are known or only believed to be true." — ibid. n. i.
3 ibid., p. 395. 4ibid., p. 399.
INDUCTION IN ITS VARIOUS SENSES 53
" There is an enormous number of general propositions, which we accept for no better reason than that the facts are inconsistent with our denying them, and not because in themselves they have anything which could have led us to suppose them true, antecedently to our experience. When it is said that we ought always to follow experience, it is meant that we ought not to trust our notions of what seems antecedently fit to be true, or mere guesses as to the connexions that subsist in nature, but accept only those connexions which our experience forces us to accept because it is inconsistent with any alternative. Such reasoning is called a posteriori, because it starts from the facts, which are conceived as logically dependent on, or posterior to, their principles, and thence infers the principles on which they are dependent. Conversely, deductive reasoning is often called a priori, because it starts from the principles or conditions, which are conceived as logically prior to the con sequences that follow from them l. . . . But it is an error to suppose that all general principles are arrived at a posteriori or by process of merely showing that facts are not consistent with any other. . . . Still it is true that in the inductive sciences the vast majority of our generalizations are reached either in this a posteriori manner, or by the help of deductions from other general izations so reached. And it may be well to show by one or two examples how generalizations that rest merely on induction present as it were a blank wall to our intelligence, as something at which we cannot help arriving, but which we can in no way see through or make intrinsically plausible." 2 The author goes on to cite examples " to illustrate . . . what Bacon would call the ' surd and positive ' character of conclusions resting only on induction ".3 One of these examples will be sufficient here : " Facts show that the excision of the thyroid gland dulls the intelligence : could any one see that this must be so ? Explanation may show that on a contribution which the gland, when properly functioning, makes to the circulating blood depends the health of the brain ; but that comes later than the discovery of the effects of excision ; and even so can we understand the connexion, which facts establish, between1 the state of the mind and the health of the brain ? " 4
These extracts will show a clear and intelligible distinction between two ideals of the knowledge we aim at by inference : the knowledge that ceitain things are so, and the further knowledge why they are so ; and, by way of consequence, between " inductive " forms of inference, which naturally sub serve the former ideal, and " deductive," " demonstrative," " explanatory " forms of inference, which subserve the latter ideal. Some of these points will receive further notice later, in the chapter on Explanation.
213. RELATION OF ANTECEDENT TO CONSEQUENT IN DE DUCTION AND INDUCTION : THE LATTER CONSIDERED AS AN " INVERSE PROCESS ". — We have seen that the logical inferences involved in the inductive process assume one or other of the forms commonly recognized in " formal " or " deductive " logic ; and that
1 " Or, in another sense, illustrated inmost mathematical reasoning, because the premisses, without being more general than the conclusion, or giving the cause why it is true, are not based upon an appeal to facts which might conceivably have been otherwise."
3 JOSEPH, op. cit.t pp. 400, 401. 3»6»<f., p. 402. *ibid., p. 401.
54 THE SCIENCE OF LOGIC
the whole ascent from particular to general cannot be intelligibly described as an " inductive syllogism," or as the opposite of the " deductive syllogism ". We may, however, regard both pro cesses in a light which will admit of their being compared and contrasted. The relation of premisses to conclusion in the syllogism is identical with the relation of antecedent to consequent in a hypothetical proposition (134, 148, 165); the premisses or antecedent being regarded as a "ground" or "reason" whose affirmation gives us a right to affirm the conclusion or consequent, though not as the sole, exclusive, only possible ground for affirming the latter. Hence, given the antecedent, we may infer the conse quent, though we cannot, conversely, affirm the antecedent if we are given the consequent (140). In other words, a given logical antecedent is regarded as necessitating some definite consequent, while this same logical consequent is not regarded as definitely necessitating that antecedent. Now, if we regard deduction as the passage of thought from logical antecedent to logical consequent (understanding these terms in the sense just indicated), deduction may be described as a direct or definite process, reaching a de finite result. And if we regard induction as the passage of thought from the real consequent or effect, regarded as logical consequent, to the real antecedent or cause, regarded as logical antecedent, induction will appear to be an inverse or indefinite process, reaching only indefinite results: since, for any given effect, considered as logical consequent, there may be a plurality of causes, considered as logical antecedents. This leads us to the consideration of induction as an " inverse problem," or " inverse process," in comparison with deduction regarded as a " direct problem," or " direct process ".
In what sense, then, may induction be fairly described as an " inverse process," the inverse of deduction? It has been some times so described by logicians. The term is borrowed from mathematics, and there it has a quite intelligible meaning. A direct process is one by which, given certain data and laws of inference, we arrive at a definite conclusion : the inverse process is that by which, given the conclusion, we try to get back to the data. While the former always gives a definite result, the latter may yield very indefinite ones. For example, given 4x4, what is the product? Answer (definitely): 16. Given the product 1 6, what number multiplied by itself yields this product ? Answer (indefinitely): plus 4, or minus 4. Or again, of what factors is
INDUCTION IN ITS VARIOUS SENSES 55
1 6 the product? Answer (indefinitely) : 2 x 8, or 4 x 4 (inverse processes).
Transferred to logic, this character of indefiniteness in the in verse process is further emphasized. Given the conclusion of a syllogism, find the premisses. An entirely indefinite problem, this, since any one out of an immense number of middle terms may con ceivably mediate the conclusion : and the inventio medii, the finding of a real or true, as opposed to an imaginary, middle term (167), like the invention and verification of an hypothesis, is amenable to no law or method. The specifying of a middle term would remove some of the indefiniteness, leaving only the possible moods of the syllogism to be determined ; the assigning of one whole premiss would leave the other premiss (definitely) to be deter mined.1 Something like this Professor Welton must have in mind * when he agrees, with Jevons, that " induction is ... an inverse process ; it is the finding major premisses when the conclusions are given ". But why major premisses ? The inductive problem seems rather that of finding the whole (proper and correct) antecedent (major and minor], given the consequent or conclusion. Given certain facts or effects, construct and verify an hypothesis as to their cause. And from what we have already said about the indefiniteness of the passage from a given effect or consequent to a definite cause or antecedent, as compared with the direct process of arguing from cause to effect, from antecedent to consequent, it will easily be understood why the former process has been de scribed as inverse, and the latter as direct. Yet, by describing induction as an inverse process, the impression may be conveyed that it reaches, de facto, only indefinite results. Such an impres sion would be erroneous ; for the aim of induction is precisely to eliminate this indefiniteness by proving some one of the conceiv able alternative antecedents to be the real antecedent : which it does, as we have seen, by the indirect method of disproving the other alternatives.
JOSEPH, Logic, chaps, xviii., xx., xxiii. MELLONE, op. cit., pp. 244 sgq., 265 sqq. JOYCE, Logic, chap. xiv. WELTON, op. cit., bk. v., chap. ii. VENN, Empirical Logic, chap. xiv. MILL, Logic III., ii., iii. MERCIER, Logique, pp. 298-307.
1 C/. VENN, Empirical Logic, pp. 359 sqq, a Logic, vol. ii., p. 59 (italics ours).
CHAPTER III.
PRESUPPOSITIONS OF INDUCTION : CONCEPTS OF « REASON " AND "CAUSE".
214. JUSTIFICATION OF CHAPTERS III. AND IV.— Since the days of Lord Bacon, many conflicting theories on the nature and grounds of induction have been advocated by logicians. Seeing that induction is the method by which we attain to a knowledge of uni versal truths about the nature and activities of the things of the visible universe, animate and inanimate, it is easy to understand the importance of the whole subject. Before, therefore, we proceed to analyse more closely the process of ascent from phenomena to their laws, we must examine the rational principles that underli- the process. Modern logicians have analysed these principles in great detail, thus importing into the logic of induction long disquisitions which would, perhaps, find a more appropriate place in psychology, criteriology, and cosmology.
No doubt, the logic of induction cannot be understood with out a statement of the principles which underlie the process. But a treatise on logic is hardly the proper place for their full ex position and vindication ; nor is it our intention to go into them here at any great length. We shall endeavour to confine our selves to a brief explanation of the rational foundations of the inductive process, i.e. the principles that justify us in rising from particular facts to the conception of a general law ; and to a brief criticism of some current views that seem more or less erroneous, regarding those principles. In doing this, however, we cannot avoid some reference to numerous notions which must be left for fuller treatment to more suitable branches of philosophy. What these notions are, will be at once suggested by any ordinary example of a natural phenomenon that calls for interpretation from us. Let us take an instance.1
This morning, for example, at half-past eight o'clock, the ash-
1 Adapted from Mercier's Logique, pp. 298 $qq. 56
CONCEPTS OF " REASON " AND « CA USE " 5 7
tree on the hill in front of my window was struck by lightning, its foliage withered and burned, and its trunk rent asunder. This individual event has happened once. With its own peculiar train of circumstances, it had never happened before and it will never happen again. But, at other times and places, other trees — and houses and people — have been similarly struck by lightning. We examine the effects produced by lightning in such cases. We try to find out under what conditions exactly they have been produced. How is it that the brilliant flash, which dazzles our eyes in the storm, is accompanied by such effects? If our search be successful, we shall learn the nature of the lightning, the law (that is, the how? the quomodo ?} of its action, and we shall then understand, " by their causes" the effects produced.
To understand things by a knowledge of their causes is the aim of all science. Now, even the most superficial observation of the phenomena of nature convinces us that their variability is bounded and ruled by a certain general sameness, or fixity, or uniformity. The things of nature differ, no doubt, in many ways from one another ; yet each of them belongs to a certain class, in virtue of some common attributes — else how or why would they have common class names ? Each belongs to some specific type, inorganic, vegetable, animal, human, whose fundamental uni formity, and relative fixity, are ever conspicuous throughout the incessant evolution and change of circumstance to which the transient individuals of the class are subject. And what is true of " things " is equally true of " events ".
It will be observed, from the expressions italicized in the foregoing paragraphs, that in the inductive process by which we rise from facts to laws we are seeking for reasons, or explana tions, for the how and the why of some phenomenon : we regard this latter as an effect, and look for its cause : we observe similarity amid variety : we study the conditions and circumstances in which the phenomenon takes place: we analyse the causes that lead up to it, and try to find out the nature of these causes and the law according to which they act. Obviously, therefore, our understanding of the inductive process will depend on our manner of conceiving cause, reason, law, uniformity, identity, etc. Hence, some explanation of the principles of " Sufficient Reason," and "Causality," and "Uniformity of Nature," and of their bearing on the inductive process, is evidently called for at the present stage. And first as to the Principle of Sufficient Reason.
58 THE SCIENCE OF LOGIC
215. "REALITY" AND THE "PRINCIPLE OF SUFFICIENT REASON V — Among the presuppositions of induction, many authors set down in the first place the Principle of Sufficient Reason : that " whatever is judged to be true must have a reason in our thought for being so judged ; and whatever is or happens in the real order must have a sufficient reason or cause for so being or happening ". As a matter of fact, this principle is a presupposition not of induction alone, but of all search whatever after truth. It simply postulates that reality is intelligible, and its explanation attainable — at least to some extent. Unless we assume that we can discover truth, it is idle to seek for truth. All actual search after truth presupposes that some truth can be found, and the gradual discovery of truth justifies the assumption. The postulate is, therefore, reasonable and necessary. But at the outset its meaning is essentially vague, and it is only by progress in the discovery of truth that we can gradually attach definite meanings to the terms "sufficient reason," "intelligible," "ex planation," etc.
The principle refers to two orders, the logical and the real. In the logical order, the order of thought, the premisses are the sufficient reason of the conclusion, the antecedent of the conse quent, until finally we come to some antecedent which, being self-evident, has the sufficient reason of its truth in itself; that is, in the reality which the judgment in question interprets by means of two concepts carrying in them the evident ground for the relation which the mind sets up between them. So, too, in the real order, in the order of things, everything that exists, every fact that happens, must have a sufficient reason, either beyond itself — in that its happening or inception is the effect of a cause distinct from it, — or in itself — in that it exists necessarily and of itself , and is itself the explanation of its own existence.
But the two orders — of thought and reality — are not mutually isolated and independent: the "objective evidence" which is the logical ground or reason of first principles, is simply REAL BEING put into relation with the MlND.2 " Objectum Intellects est Ens": "The object of Intellect is Reality". This maxim of scholastic philosophy is the assertion, against subjective
J C/. brochure entitled " The Inductive Sciences : An Inquiry into some of their Methods and Postulates" by the present writer (Dublin : Browne & Nolan Ltd., 1910), pp. 10 sqq.
3 i.e. ontological truth. C/. 248.
CONCEPTS OF « REASON " AND « CA USE " 59
phenomenism, of the power of the human mind to reach real, objective truth.
The Principle of Sufficient Reason is, therefore, not merely formal 'but raz/(i6). Not only can we not judge of a thing without a sufficient reason in the thing itself for that judgment ; but also, the thing itself, the reality itself, which is the object of our thought, cannot be what it is, and as it is, unless it have a sufficient reason in itself, or connected with itself, why it is, or why it is so and not otherwise.
But when we ask what shall we be obliged to regard as the ultimate "sufficient reason" or "explanation" of our experience as a whole, the answer will obviously depend upon the view which careful and prolonged re flection on that experience will lead us to form about the nature and meaning of all reality. And the conclusions we may reach on this fundamental question will, of course, determine our interpretation of the exact scope and significance of the principle under consideration. Two erroneous interpreta tions of the principle, based on erroneous views about the nature of reality, may be noticed here, in contrast with the scholastic interpretation which is based on the philosophy of theism.
One is variously known as Empiricism, Sensism, Positivism, Agnosti cism. It is a mistake in method, no less than an error in fact, to assume, even in regard to the inorganic universe, that no judgment about the latter can be accepted as true without the same sort of cogent evidence which compels in tellectual assent in the mathematical science of abstract mechanics ; that a fact is " intelligible " or " knowable " only in so far forth as it illustrates the laws of mechanical motion and inertia ; that the introduction of " purpose," " design," " intelligence," " final causes," as factors to help in explaining the processes of physical nature, is " unscientific " inasmuch as these factors cannot be " computed " in terms of the laws and principles of mechanics, and are, therefore, themselves not scientifically " intelligible ". Any such narrow ing of the concept of what is " knowable " or " intelligible " is entirely gratuitous and unwarranted. Yet the Positivist philosophy, which has been popular in modern scientific circles, insinuates this misleading interpretation of what is in itself a true and reasonable principle. For this philosophy would have us believe that what is beyond the range of sense experience is " un knowable " (Agnosticism) ; and that the phenomena of sense experience are " knowable " or " intelligible " only in so far as their uniform coexistences and sequences throughout space and time exemplify and constitute the " laws " of mechanics (Mechanical Atomism). Reality may surely be " knowable," even though not amenable to any such laws ; and there may be some reality within the reach of our intellect, even though it be beyond the reach of our senses.1 It was the misfortune of English philosophy, under the influence of such men as Hume and Mill, to sink into this Sensism. By declaring all reality to be, in ultimate analysis, a flow of sensations in the individual con sciousness, they really declared all " knowledge," all " rational explanation " of
1 Cf. JOSEPH, Logic, pp. 382 sqq.
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human experience, to be impossible. We shall see an illustration of this in their futile attempts to explain and justify men's belief in the Uniformity of Physical Causation. The Positivism which endeavours to interpret all human ex perience as a process ruled by mechanical necessity has for its obverse side Agnosticism— that is, a declaration of inability to assign any ultimate rational ground that will explain human experience as a whole. This, like all scepticism, is really an abandonment of the principle of sufficient reason ; for it says, in effect, " We believe certain things, but, ultimately, we do not and cannot know why we believe them ". The empiricist so interprets experience as to end in agnosticism about the suprasensible, and in inconsistency about what he calls the " scientific laws or generalizations " of sense phenomena. In his attempt to account for the reliability of those generalizations, their stability, their characteristic of necessity, he really explains this away, and leaves no rational ground for human certitude (cf. 219, 224).
Another extreme and erroneous interpretation of the principle of sufficient reason, another narrow view about the " intelligibility " of experience, and the possibility of " explaining " the latter, is that of Hegelian Idealism. This is the very antithesis to Empiticism. The latter fails to account for the " must" the element of necessity, which characterizes, in varying degrees, our judg ments about reality ; the former errs by attributing the same absolute intel lectual necessity to all our judgments about reality. In a word, it claims that the world as a whole is " intelligible " and capable of " rational explanation " only on the assumption that it is one vast self-contained and self-explain ing system of ideas, or thought-relations, which reveal themselves to in dividual minds as endowed with the same metaphysical necessity which characterizes our abstract judgments about the possible essences of things. This, too, is an assumption which unduly narrows the scope of " explanation " and the sphere of what is " knowable " or " intelligible ". If we reduce the reality of things, in this fashion, to a mental fabrication of thought-relations, if we make reality a ' theory? a mere mental ' constitution? a "determina tion " of things " by each other as constituents of one order, a determination which only exists for thought " ; if we say : " It is not that there is first the reality of things,1 and then a theory about it. The reality is a theory " ; 3 if, we contend that " mere feelings . . . except as related to each other through relation to thought, are not facts at all," 3 that it is only by thinking them we make them real and give them a nature : 4 are we not setting up a mental creation, a system of abstract thought-relations, in the place of reality, and ignoring the claims of that sense experience which certainly puts us into con tact with reality ?
This Idealistic Monism misinterprets reality. Nor is the postulate involved in it a necessary one : the postulate that all reality is one great mental or intellectual system, one great thought or idea, unfolding itself in individual minds according to necessary laws of logical thought ; for, surely, we can make
1 But surely there is some reality in the " things " themselves ? Surely reality does not lie exclusively in any " determination " of relations established by thought between those " things " ?
3 GREEN, Philosophical Works, vol. ii., p. 269; — apud WELTON, ii., p. 2.
3 ibid., pp. 385-86.
4C/. HERSCHEL, Nat. Phil., ioq\—apnd WELTON, ibid.
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progress in knowledge without the aid of such an assumption ; and, besides, there is at least this other alternative postulate — the postulate of Theism — that the sense world reveals itself to the human intellect not as the self-evolution, at once logical and real, of a Sole Being that is at once thought and reality, but, rather, as a distinct system, dependent no less on a Supreme Will for its actuality than on a Supreme Intelligence for its intelligibility.
This, then, is another possible alternative, and it is the true one : that the whole world of human experience (including the human mind itself) is the creation of a Supreme Free Will, governed by laws laid down by a Supreme Intelligence {Philosophy of Theism] ; and not the logically necessary unfold ing or evolution of one Sole Idea-Being (Idealistic Pantheism) ; or the ob verse and unknowable background of the transient panorama which con stitutes the individual man's sense consciousness (Empiricism, Agnosticism).
These are three alternative points of view — there are others also — from which individual writers on inductive logic may proceed to lay down principles for the guidance of the student in his search after truth, whether in science, in philosophy, or in theology. The differences between them are revealed in the respective ways in which writers of each of these schools treat of causality, hypothesis, and generalization (based on the law of Nature's Uniformity), as well as in the different ideals they set up regarding Scientific Explanation and Physical Certitude. In the chapters that follow, we shall, therefore, have oc. casion to recur repeatedly to the views we have just mentioned ; and the principle itself of sufficient reason will arise again explicitly, in connexion with the theory of Demonstration and Scientific Explanation.
2 1 6. THE PRINCIPLE OF CAUSALITY IN INDUCTION: ARIS TOTLE'S CLASSIFICATION OF CAUSES. — When applied to contin gent things, to the phenomena of nature around us, the principle of sufficient reason resolves itself into the Principle of Causality. This latter is an a priori, self-evident principle, like the former. Cause and effect being correlative, to say that " Every effect has a cause" is to state a truism. The principle is usually stated thus : " Whatever happens (occurs, takes place, begins to be) has a cause ". The axiom ' Ex nihilo nihil fit' is a negative statement of the same principle. And another statement of it, "Whatever is contingent (i.e. whatever does not contain in itself, in its own essence, the sufficient reason of its actual existence) has a cause," shows the connexion of the principle of causality with the principle of sufficient reason. Being that is necessary and self-existent has no cause. It is itself the reason of its own existence ; whereas all contingent being is caused. The principle of causality is evidently a necessary principle in regard to con tingent being, i.e. it is essentially involved in our very concept of contingent being. Nothing can happen without a cause: whatever happens has necessarily a cause, i.e. something which
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brings it about, which makes it happen, whether this cause be free (i.e. self-determining) or not, in its mode of action.
Now, induction being mainly concerned with the discovery of the causes which bring about the phenomena that constitute our experience, it is important to have a clear understanding in the first place about what scientists, logicians, and philosophers mean by a " cause ".
What we may call the common and traditional notion of " cause " is that of "anything which contributes in any positive way to the existence or happening of something else ". Aristotle distinguished between two intrinsic causes, the " formal " and the "material," which constituted that "something," and two other causes, the "efficient" and the "final," extrinsic to the "some thing," and in regard to which the latter is properly called an " effect ". The notions of " formal " and " final " causes are closely connected with the Aristotelean view of nature as re vealing Purpose and Design (217). We shall see that modern science and philosophy are not the better for discarding these notions.1 Inductive logicians confine their attention almost ex clusively to the study of efficient causality ; and of this many have perverted, or rather abandoned, the traditional notion.
The popular idea of " efficient cause " is that of an agent or agency — something which by means of perceptible action, motion, or change, produces some new state or condition of things. Thus understood, a cause is clearly distinguished from a condition ; the latter being anything which, though necessary for the happening of the effect, does not contribute positively thereto: windows, for instance, being the condition, not the cause, of the daylight in a room. Most logicians of induction, however, ignore this distinc tion 2 : the reason being that, so far as physical science is concerned, it is of no importance. Nor indeed is it, provided we assume that the duty of the physical scientist as such is merely to discover all the antecedents, positive and negative, of whatsoever sort, which are sufficient and indispenable for the happening of any given phenomenon, without troubling himself about the manner in which they contribute thereto.8 But not all are willing to set such limits to the scope of physical science ; though, of course,
1 Cf. VENN, Empirical Logic, pp. 47-62, as an example of the attitude of the empirical school of logicians towards them.
3 Cf. WELTON, op. cit.t ii., p. 19, where " cause " is defined as the " totality of con ditions " requisite to the happening of a phenomenon.
* Cf. JOYCB, Op. Cit., p. 221.
CONCEPTS OF " REASON " AND « CA USE " 63
philosophers of the positivist school claim that when physical science has discovered the invariable antecedents of a pheno menon nothing further remains for investigation. Moreover, the logician of induction should not confine his investigations to the data of the physical sciences alone ; he must investigate our thinking processes about all conceivable data. The distinction, therefore, between condition and cause, need not be altogether ignored.
We must next consider that the same thing or reality, the same phenomenon or agency, may evidently be the effect of cer tain efficient causes, and itself the efficient cause of other effects : looked at in one connexion, from one point of view, it is an effect ; in another connexion and from another point of view it is an efficient cause. Thus we see, in physical nature, innumerable series or chains of efficient causes, wherein each link has others depending on it while itself in turn depends on others : whether each follows the other in time or all exist simultaneously. Every event in nature is the result of a long series of causal antecedents stretching indefinitely backward and outward in time and space, or rather of the convergence and co-operation of many such series. It is precisely owing to this fact that inductive research for the " efficient causes " of the phenomena of nature constitutes such a difficult problem. When can we be said to have discovered in ductively the group of agencies which are to be regarded as the " total " efficient cause of any phenomenon ? What portion of all the converging series of influences are we supposed to bring to light explicitly, and to designate as the total efficient cause of an event ? How far backward and outward from the event, and how far forward and inward towards the event, are we to proceed in our analysis of its concomitant and antecedent circumstances ?
Let us take, as an instance of natural causation, the formation of water from oxygen and hydrogen. If we draw through the process a line of demarcation (220) at the moment the water begins to appear, and regard the appearance of the latter as the effect to be explained, we shall evidently need to examine the antecedents down to this very line itself, lest any indispensable factor escape our notice. And in the backward direction, in enu merating remoter antecedents which were indispensable steps lead ing up to the final result, where are we to stop? Are we to in clude not only the necessary heat, but the source of the latter — the electric machine? and its maker? Are we to include not
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only the gases, but the vessels containing them ? and the agencies that produced them ? and those that brought them together in the proper proportions ? Evidently not. We must, clearly, draw the line limiting our backward search somewhere. And from the region between it and the line bordering on the effect we must set aside all the individual modes and circumstances which may indeed be essential for this individual instance of the effect, but which are indifferent and irrelevant so far as the production of this kind of effect is concerned : * for it is not with the individual effect, but with the kindvi effect, the production of water as such (i.e. with the abstract and universal], that science is concerned. We must, therefore, confine our attention to a limited group of ante cedents in close proximity to the effect, analyse this group, and set forth, as the " total proximate cause " of the phenomenon, only that collection of factors which we regard as the sufficient (or necessitating) and indispensable PROXIMATE factors in its production. Moreover, the scientist, in enumerating these, will omit, and usually does omit, such factors as are obviously necessary for the result : he assumes it to be universally understood that they are present. His concern rather is to detect some one factor (or collection and collocation of factors) which immediately precedes the effect, and which actually determines the effective co-operation of the existing forces in the production of this specific kind of effect.2 This factor he usually calls the " determining cause (or condition)" of the phenomenon. All the factors in this proximate collection — all the proximate factors sufficient and indispensable for the effect — constitute what the scientist regards as the "proximate (efficient) cause " of the phenomenon in question.
Although the principle of causality refers primarily to efficient causes, i.e. causes which, by means of action, of real change or motion, produce their effects ; and although modern writers on in duction have concentrated their attention almost exclusively on physical efficient causes — i.e. those which are, in themselves or their action, perceptible to the senses — as being the more capable of exact physical investigation, and even of mechanical measure ment : still, the scope of inductive logic must necessarily embrace the investigation of material, formal, and final causes, no less than of efficient causes.3 To know a thing scientifically, we must know
1 Cf. JOYCE, op. cit., p. 221. a Cf. JOSEPH, op. cit., p. 393.
3 On this point we may refer the reader to a suggestive article by W. J. ROBERTS in Mind (N.S., no. 32, October, 1909), connecting the theory of induction with Aristotle's doctrine on formal cause. — Cf. JOSEPH, Logic, p. 457.
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not merely its efficient cause or causes, but its inner nature, its formal and material causes. But its specific nature, or formal cause, is revealed by its sensible energies and properties : it is only by studying these — which are nearer and more familiar to us, whose knowledge comes through the senses — that we can know that which is more remote from us, though prior and simpler in itself, viz. the specific nature, the ground of the universal law. The principle underlying this progress of thought is expressed in the Scholastic aphorism : Operari sequitur esse, or, Qua/is est operatic ', talis est natura : As a thing is so it acts: Action is the index of essence. And a knowledge of the formal cause or specific nature of a thing helps to bring to light its purpose or function in the universe, i.e. its final cause, the reason why it exists and acts, the design it accomplishes in nature. Without a knowledge of the " why and wherefore " of a thing, our knowledge of it is incomplete.
When, for example, Pasteur's experiments demonstrated that fermentation is due to the action of a living microbe, or that every living cell has its origin from some other living Cell, he discovered in the microbe the efficient cause of fermentation, in the parent-cell the efficient cause of the younger cell.
Again, the chemical elements combine to form compounds in certain definite proportions by weight. The components, hydrogen and chlorine, enter into the formation of hydrochloric acid in the proportion of i part of hydrogen t° 35-5 parts of chlorine by weight. Those definite quantities are material causes of the various combinations into which these elements enter, for the material mass or quantity is independent of specific change, i.e. change of substance or substantial " form," and attaches to the material cause or prin ciple in corporeal substances and agents.
Again, the combination of hydrogen and chlorine to form hydrochloric acid is seen to depend on the chemical affinities of the two reacting bodies for each other. These affinities being themselves specific properties of the respective components, the formation of the acid is the result of the specific natures of these components. But the specific nature and the specific pro perties of a body depend on, and are determined by, its specific, essential or substantial "form": its " formal" cause. So that when we determine the law of a chemical combination, i.e. the fixed, uniform mode of action of the substances involved— elements or compounds, — we are bringing to light the formal causes, the specific constituent principles, the specific natures, of those substances.
Again, the peculiar affinities of the chemical elements determine the combinations which their respective natures incline them to realize. Hence, to detect the affinities of these elements, and to characterize the latter by those affinities, is to discover the innate tendencies which incline these elements to form certain combinations. In other words, it is to discover the internal purpose of the reacting bodies. The establishment of the laws of a chemical combination is, therefore, the discovery not merely of the formal, but VOL. II. 5
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also of the final causes, of such combination. That is to say, it shows the realization or formation of the compound as the internal reason why the bodies in question combine in that way ; it reveals the finis operis, the intrinsic aim of that activity which is the product and complement of their respective natures or formal causes.
In some cases, the final cause is even the primary object of inductive re search. This occurs very commonly in physiological investigations into the functions of living organs — as, for example, in the efforts of physiologists to discover the functions of the thyroid gland, or of the vermiform appendix.
217. "PURPOSE" OR "DESIGN" : " FINAL CAUSES" AND
"LAW" IN PHYSICAL NATURE. — It is intelligible that when inquiring into the causes and reasons of phenomena that may be due to human activity we should seek for their final causes, i.e. the motive, the design, the end in view in their production ; but the meaning of seeking for final causes in the natural agencies even of the inorganic world may not be at first apparent : for, how can an agent devoid of perception and appetite, nay, even of life, act "for an end"? Such agents cannot, of course, act "for an end " in the same way as men (" electivJ"\ who, by free will, elect or choose the ends for which they act ; or in the same way as animals (" apprehensive r"), which are conscious of the ends towards which their appetites move instinctively ; but the inani- . mate agencies of the physical universe can and do act, each "for an end," effectively or equivalently (" executive""\ i.e. in such a way as to make it clear that they are directed or oriented in their action by a ruling intelligence, and for a purpose. That this is so in fact, we are convinced by the manifest order, harmony, regularity of natural phenomena. We know by experience that the causes at work in the whole vast physical universe act each in its own fixed way, uniformly, regularly : whence we conclude that every such agency must have impressed on its very essence, on its inner constitution, by the Creator, a definite " bent " or " tendency " or " inclination " (" appetitus naturalis ") to act along certain definite lines, and so to discharge its appointed function in the universe. This inner principle of uniform action (which is its substantial or specific formal cause] we call the nature of the agent in question : and when it acts in the ordinary, normal way, we speak of its acting " according to its nature" or " according to the law of its nature ". By the nature of a cause or agent we therefore primarily mean the inner directive principle of its activity : its essence regarded as a source or principle of orderly, intelligible
CONCEPTS OF " REASON " AND « CA USE " 67
activity. * When we speak of Physical Nature, or the Order of Nature, or the Course of Nature, or External or Visible Nature, we use the term " Nature," in a collective sense, to signify the sum- total of all the created agencies that make up the visible (i.e. sensible, perceptible) material universe.
Hence, the extension of the concept of purpose from the do main of rational or human agents to the animal, vegetable, and inorganic kingdoms of nature, by Aristotelean and Scholastic philosophers, is no mere > verbal metaphor. There is a true and proper sense, as these philosophers contend, in which all created agencies act in fulfilment of purpose, in which "ALL agents act for an end " : " OMNE agens agit propter finem ".
The conviction is gradually forced in upon us by our experi ence of natural phenomena, that every agency in nature must have some fixed, intrinsic principle of activity, in virtue of which it acts uniformly, and concurs with other physical agencies, not capriciously or indifferently, but along certain prearranged and predetermined lines ; so that " exceptions " to this uniformity must be due in reality to the influence of some unknown natural causes, or, possibly, to the intervention of the First Cause. Here, at all events, is the great fact we gather from sense experience : that very complex combinations of numerous natural agents re peatedly concur to produce uniform series of effects. Of this great fact there can apparently be one, and only one, rational in terpretation : that which conceives the proximate causes of such uniform series of phenomena as endowed each with a fixed natural inclination or tendency to act steadily and consistently along de finite lines, as having each an internal law which dominates it, and in conformity with which it will act always and everywhere. This innate, stable tendency is what the mind grasps when it apprehends the law of the Uniformity of Nature. The great fact of experience revealed in the regular, constant, harmonious concurrence of numerous and varied forces and agencies to produce uniform series of results, finds its sufficient reason and explanation only in a
1 The Essence of a thing (" Essentia " or " Quidditas ") is that which makes the thing what it is (" id quo res est id quod est " : the answer to the question " Quid est ilia res'} "). The Nature (" Natura ") is the essence itself looked on as the directive principle of the thing's activities (the " principium operationis "). It was conceived by the Scholastics as the impression of a divine directive plan or design on the inner constitution of the created agency : "Stabilis inclinatio vel appetitus finis, rebus a Deo inditus" or again, " Ars quaedam Divina indita rebus, per quam ad fines pro- prios non solum ducuntur sed quodammodo vadunt." — St. Thomas, Q(^. DD. De Veritatc, Q. xxii, a. i.
5*
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fixed NATURAL INCLINATION or tendency of the agents which pro duce such results. The expression " natural inclination " embodies a fundamental doctrine of Aristotelean philosophy ; it implies that the agencies whose effects or manifestations we observe in the world around us are not, as the advocates of mechanical de terminism (215) would have them, mere efficient agents capable of producing any or every result indifferently, but that each of them is endowed with an internal tendency in virtue of which it manifests a manner of being and acting proper to itself; which manner is called a property of the substance, and reveals the specific nature of this latter.
This view of the universe, as the expression of a divine plan, — hence called ideological, — renders intelligible the use of a term that is constantly recurring in the logic of induction : the term Law (Lex). Law means primarily an order, mandate, precept, emanating from the will of a superior (the legislator), and imposed upon a community subject to him.1 The law, as abiding in their minds and hearts, by their knowledge of it and submission to it, secures a certain uniformity in their conduct: it becomes the immediate source and principle, in them, of a series of similar acts. Next, the term Law came to be applied to what was really its effect, to this uniform series of similar acts. It was then extended, in this latter sense, from the domain of human activity to the domain of physical, even inanimate, nature ; and here it is now used, as, for example, in all the " physical " and " natural " 2 sciences, to denote any uniform series of connected phenomena, whether the connected elements exist simultaneously (" coexist ences ") or successively (" sequences "). The general propositions or statements which formulate such connexions are commonly referred to as "laws of physical nature": e.g. "Water seeks its own level," " All bodies fall with the same acceleration in a vacuum," "At a given temperature the volume of a given quantity of gas varies inversely as the pressure it sustains," " Heat can produce mechanical work, and vice versa, in definite, measurable proportions," "The strength of an electric current varies directly as the electromotive force and inversely as the resistance," "Every living cell has its origin from some other living cell," "Fermentation is due to the action of microbes".
1 Cf. The Inductive Sciences, etc., pp. 70 sqq.
a These terms are commonly regarded as synonymous ; when they are distin guished, the former refers to the sciences of inorganic, inanimate nature, the latter to those of the living universe,
CONCEPTS OF "REASON" AND "CAUSE" 69
Most of these "laws" are merely formulae descriptive of con stant connexions which have been discovered to exist between phenomena, and of the conditions and circumstances in which such connexions are found to obtain. But those uniform happen ings must, after the analogy of the uniform conduct of a com munity subject to the law of a superior, be themselves due to fixed principles of action inherent in the constitution of the natural agencies which manifest those uniform activities. Now, if we bring to light the agencies which are operative — and co-operative — in producing those regular coexistences and sequences, the mode of action and interaction of the efficient causes that are at work, the inner constitution or nature of those agencies, i.e. their material and formal causes, and the scope or purpose of those activities, we can formulate explanatory or causal laws, i.e. laws which will not merely express the existence of uniformities, but which, furthermore, will give us an insight into the "how" and the "why" of such uniformities (222).
The Aristotelean conception and classification of causes, and the Scholastic view of physical nature as a " cosmos," revealing purpose, design, intelligence, and subject to " law " in the sense just explained, have been almost completely ignored by modern exponents of the logic of induction.1 Some of these latter have substituted a purely mechanical view of the universe, eliminating the notions of " design " and " efficiency " as superfluous, and retaining merely the notions of " invariable " or " necessary " " sequences " and " coexistences " of material phenomena, as the ultimate factors of a rational explanation of the universe. These writers have been induced by a rather superficial materialism to abandon, and even to ridicule, the r61e of final causes in philosophical research. Yielding too hastily to the natural craving for a simple solution of the problems raised by the universe, they have thought to satisfy themselves and others by proclaiming the sufficiency of physical efficient causality, i.e. of invariable connexions between masses of matter in motion, for the adequate explanation of all things. The attempt was necessarily futile, and is nowadays generally recognized as such. " The mechanical theory of the universe," writes Professor Welton,2 " is simple, but inadequate even in inorganic nature ; in organic nature it must be supplemented by the principle of development, and finally by the conception of rational purpose." To which we may add Mr. Joseph's testimony,3 that " to a physical theory of the world consciousness remains unaccountable ; such a theory therefore cannot be complete or final ".
We shall see later (219, 224) that the "necessity" of those "uniform con nexions " or " laws " can have no rational basis in the " mechanical " view of nature. Neither, however, does it receive a satisfactory explanation on the Hegelian, idealist view, that nature is merely a system of thought-relations ; and that its "necessities" are identical with the necessities of thought (215).
1 Cf. VENN, Empirical Logic, pp. 47-52.
8 Logic, ii., pp. 206, 210; cf. p. 30 (italics ours). sop. cit., p. 384.
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Writers who support this latter view bring out very clearly the shortcomings of Empiricism ; l but, though they rightly include the concept of " final cause " i.e. of purpose, design, in their philosophical explanation of natural phenomena, they still fail to recognize explicitly the " formal " and " material " causes, as distinct from the "efficient causes," of phenomena, and are thus led to identify the cause with the process, and this latter with the effect.
In most of the physical sciences we are mainly concerned with the dis covery and explanation of processes, changes, motions, activities, actions and interactions between material agencies : and our main concern here must be to find out what are the proximate agencies at work in a given process, to separate these from irrelevant and accidental surroundings, to detect the total (proximate) agens and the total (proximate) pattens in question, and to discover and understand the connexion of physical efficient causality between these.
But the discovery of a connexion of efficient causality, of action and interaction, between physical agents, is the discovery of active and passive powers or properties in these agents : and the discovery of such properties or powers leads to a knowledge of the intrinsic constitution, the nature, of these agents. As a thing acts, so it is : Qua/is operatic, talis natura. All the insight we have into the inner nature and constitution of things is got by inference from their observed activities : Operari sequitur esse. And our knowledge of the inner nature and constitution of a physical cause, of the manner and conditions of its activities, will help us to understand its raison d'etre, its function or role in the universe, the purpose it serves, the end it is designed to fulfil, the final cause of the processes in which it plays a part.
Thus we see that the search for any one class of cause is by no means incompatible with a search for the others. When one line of inquiry cannot be prosecuted, another may ; and each often helps the others.
2 1 8. CONTRAST BETWEEN TRADITIONAL AND EMPIRICAL CONCEPTIONS OF EFFICIENT CAUSALITY. — When the word "cause" is used without qualification "efficient cause" is meant. Used in this sense, the term " cause " has almost completely changed its traditional signification ; and with very confusing results. We must, therefore, note these changes of meaning carefully.
The traditional notion of efficient cause is that of " anything which positively contributes by way of action or change or motion to the production or happening or existence of anything else". Positive influence by way of action is what we mean by the "effici ency " of a cause. This traditional conception of efficiency, or efficient causality, we can find no reason or justification for abandon ing. We shall therefore retain it. Furthermore, we must dis tinguish between the individual, substantial cause or agent itself (" the agens" the " principium quod agit ") ; the power, faculty, force, potential energy, of that cause (the "principium quo agens agit"); and the action ("actio") by which it produces its effect.
1 Cf. Professor WELTON'S criticisms of Mill, op. cit., passim.
CONCEPTS OF " REASON " AND " CA USE ' ^ i
And, of efficient causes themselves, we may distinguish several kinds : the First or Uncreated Cause, and second or created causes ; the free cause — which has the power of choice to act or not to act, which can determine itself to act or not, which has "do minion " or control of its act, — and the non-free or necessary or " natural" cause, — which, when placed in a definite set of circum stances, does always act, because it must act, because it has no power or control over its own act, but is by its very nature so constituted (by the First Cause) that (unless the First Cause miraculously interferes) it will, by a necessity of its nature, always act in those circumstances.
Now, most modern writers on induction have come to use the terms cause, and efficient cause, in the sense of a non-free or necessary l cause. This in itself is not surprising, seeing that they have mainly, if not exclusively, in view the physical universe, inorganic and organic, exclusive of man ; and they may, perhaps, regard the adjective " physical," applied to " cause," as a suf ficient indication that they are dealing only with causes under stood to be connected "naturally" or "by a necessity of their nature " with their effects.2 With this usage, then, we will not quarrel, provided it be distinctly understood that there are, or may be, in existence, free causes. Where ambiguity would be likely to arise, we should use the adjectives " free " or " necessary ".
An unfortunate result, however, of identifying efficient causality with the uniform causality of necessary causes, calls for notice here. It is the confusion of two quite distinct principles, the "principle of causality " (216) and the "principle of the uni formity of nature" (223), under the common title of the "law of universal causation ".3 But it is one assertion that " The same causes, acting in similar circumstances, will always produce the same effect " ; it is another and quite a different assertion that " Whatever happens has a cause ". The former, which is known as the " principle of the uniformity of physical nature," is not universally true, of all causes : as we shall see later (223), it applies, strictly speaking