Page:EB1911 - Volume 16.djvu/903

PROBLEMS] by its subject and predicate are one and the same thing which cannot exist apart from itself. Thus by combined induction and identification we apprehend that one and one are the same as two, that there is no difference between a triangle and a three-sided rectilineal figure, that a whole must be greater than its part by being the whole, that inter-resisting bodies necessarily force one another apart, otherwise they would not be inter-resisting but occupy the same place at the same moment. Necessary principles, discovered by this process of induction and identification, become premises of deductive demonstration to conclusions which are not only necessary consequents on the premises, but also equally necessary in reality. Induction thus is the source of deduction, of its truth, of its probability, of its moral certainty; and induction, combined with identification, is the origin of the necessary principles of demonstration or deduction to necessary conclusions.

Analogical inference in its turn is as closely allied with induction. Like induction, it starts from a particular premise, containing one or more examples or instances; but, as it is easier to infer a particular than a universal conclusion, it supplies particular conclusions which in their turn become further particular premises of induction. Its second premise is indeed merely a particular apprehension that one particular is similar to another, whereas the second premise of induction is a universal apprehension that a whole number of particulars is similar to those from which the inference starts; but at bottom these two apprehensions of similarity are so alike as to suggest that the universal premise of induction has arisen as a generalized analogy. It seems likely that man has arrived at the apprehension of a whole individual, e.g. a whole animal including all its parts, and thence has inferred by analogy a whole number, or class, e.g. of animals including all individual animals; and accordingly that the particular analogy of one individual to another has given rise to the general analogy of every to each individual in a class, or whole number of individuals, contained in the second premise of induction. In this case, analogical inference has led to induction, as induction to deduction. Further, analogical inference from particular to particular suggests inductive-deductive inference from particular through universal to particular.

Newton, according to Dr Pemberton, thought in 1666 that the moon moves so like a falling body that it has a similar centripetal force to the earth, 20 years before he demonstrated this conclusion from the laws of motion in the Principia. In fact, analogical, inductive and deductive inferences, though different processes of combining premises to cause different conclusions, are so similar and related, so united in principle and interdependent, so consolidated into a system of inference, that they cannot be completely investigated apart, but together constitute a single subject of science. This science of inference in general is logic.

Logic, however, did not begin as a science of all inference. Rather it began as a science of reasoning ( ), of syllogism ( ), of deductive inference. Aristotle was its founder. He was anticipated of course by many generations of spontaneous thinking (logica naturalis). Many of the higher animals infer by analogy: otherwise we cannot explain their thinking. Man so infers at first: otherwise we cannot explain the actions of young children, who before they begin to speak give no evidence of universal thinking. It is likely that man began with particular inference and with particular language; and that, gradually generalizing thought and language, he learnt at last to think and say “all,” to infer universally, to induce and deduce, to reason, in short, and raise himself above other animals. In ancient times, and especially in Egypt, Babylon and Greece, he went on to develop reason into science or the systematic investigation of definite subjects, e.g. arithmetic of number, geometry of magnitude, astronomy of stars, politics of government, ethics of goods. In Greece he became more and more reflective and conscious of himself, of his body and soul, his manners and morals, his mental operations and especially his reason. One of the characteristics of Greek philosophers is their growing tendency, in investigating any subject, to turn round and ask themselves what should be the method of investigation. In this way the Presocratics and Sophists, and still more Socrates and Plato, threw out hints on sense and reason, on inferential processes and scientific methods which may be called anticipations of logic. But Aristotle was the first to conceive of reasoning itself as a definite subject of a special science, which he called analytics or analytic science, specially designed to analyse syllogism and especially demonstrative syllogism, or science, and to be in fact a science of sciences. He was therefore the founder of the science of logic.

Among the Aristotelian treatises we have the following, which together constitute this new science of reasoning:—

1. The Categories, or names signifying things which can become predicates;

2. The De Interpretatione, or the enumeration of conceptions and their combinations by (1) nouns and verbs (names), (2) enunciations (propositions);

3. The Prior Analytics, on syllogism;

4. The Posterior Analytics, on demonstrative syllogism, or science;

5. The Topics, on dialectical syllogism; or argument;

6. The Sophistical Elenchi, on sophistical or contentious syllogism, or sophistical fallacies.

So far as we know, Aristotle had no one name for all these investigations. “Analytics” is only applied to the Prior and Posterior Analytics, and “logical,” which he opposed to “analytical,” only suits the Topics and at most the Sophistical Elenchi; secondly, while he analyzed syllogism into premises, major and minor, and premises into terms, subject and predicate, he attempted no division of the whole science; thirdly, he attempted no order and arrangement of the treatises into a system of logic, but only of the Analytics, Topics and Sophistical Elenchi into a system of syllogisms. Nevertheless, when his followers had arranged the treatises into the Organon, as they called it to express that it is an instrument of science, then there gradually emerged a system of syllogistic logic, arranged in the triple division—terms, propositions and syllogisms—which has survived to this day as technical logic, and has been the foundation of all other logics, even of those which aim at its destruction.

The main problem which Aristotle set before him was the analysis of syllogism, which he defined as “reasoning in which certain things having been posited something different from them of necessity follows by their being those things” (Prior Analytics, i. 1). What then did he mean by reasoning, or rather by the Greek word  of which “reasoning” is an approximate rendering? It was meant (cf. Post. An. i. 10) to be both internal, in the soul ( ), and external, in language ( ): hence after Aristotle the Stoics distinguished  and . It meant, then, both reason and discourse of reason (cf. Shakespeare, Hamlet, i. 2). On its mental side, as reason it meant combination of thoughts. On its linguistic side, as discourse it was used for any combination of names to form a phrase, such as the definition “rational animal,” or a book, such as the Iliad. It had also the mathematical meaning of ratio; and in its use for definition it is sometimes transferred to essence as the object of definition, and has a mixed meaning, which may be expressed by “account.” In all its uses, however, the common meaning is combination. When Aristotle called syllogism , he meant that it is a combination of premises involving a conclusion of necessity. Moreover, he tended to confine the term  to syllogistic inference. Not that he omitted other inferences ( ). On the contrary, to him (cf. Prior Analytics, ii. 24) we owe the triple distinction into inference from particular to particular (, example, or what we call “analogy”), inference from particular to universal (, induction), and inference from universal to particular (, syllogism, or deduction). But he thought that inferences other than syllogism are imperfect; that analogical inference is rhetorical induction; and that induction, through the necessary preliminary of syllogism and the sole process of ascent from sense, memory and experience to the principles of science, is itself neither reasoning nor science. To be perfect he thought that all inference must be reduced to syllogism of the first figure, which he regarded as the specially scientific inference. Accordingly, the syllogism appeared to him to be the rational process ( ), and the demonstrative syllogism from inductively discovered principles to be science