Whereas all other sciences needed long periods of time to acquire the definite, systematic form they now possess, nay, in many cases, to find their right path, logic has hit at once its legitimate procedure, and has been able to reach without delay its complete development. If it has not advanced a single step since Aristotle's time, if our modern university text-books do not give us any more nor less than the doctrine of the Stagirite, it is because logic had become in his hands a complete system, had grasped and accomplished its purpose. The reason of this advantage is obvious. Unlike all other sciences, logic has to deal with the form, not with the content, of thought. It does not examine the immediate assumptions from which we start; it is not concerned with the conclusions we derive from them; it deals only with the manner in which they are derived. It is merely the art or the science of reasoning.
Now, all men are endowed with similar faculties and reason in a similar way. The causes of the divergences of speculative conclusions, of the incompatibility of contradictory systems, are not to be found in the methods according to which these systems are built, but in the fundamental principles which lie at their basis.
In modern times, however, the Aristotelian logic has been criticized. Eminent authors have condemned its course of action, declaring its direction unnatural, its methods barren. It has been contended that upon the ruins of the effete Mediaeval dialectic a new science of logic had to be built. Induction has been produced and acclaimed as the sovereign guide of human speculation, while deductive methods have been regarded as useless and relegated to the background.
This view, due in great part to the progress of Physical science, has found an able representative and defender in John Stuart Mill. The great significance of his System of Logic lies in the endeavor to reverse the process which considered the syllogistic logic as fundamental, and to subordinate the syllogism to the induction. This superiority assigned to the induction is a natural consequence of the nominalistic principles. If we start from the assumption that the individual is the only reality, and that the universal is a mere meaningless name, the syllogism loses its force and becomes a mere tautology.
The syllogism, in its most perfect form, starts from a universal, subsumes a particular under that universal, and reaches the conclusion that the attribute which belongs to the universal belongs to the particular also. Now, as the universal does not possess any validity for the nominalists, they must regard the major premise as containing the conclusion not only formally, but materially, and hence the syllogism as devoid of all logical value.
In the example: Man is mortal, Socrates is a man, therefore, Socrates is mortal, the major premise: Man is Mortal, is not, from a nominalistic point of view, a universal proposition. The term man is only a shorthand register of individual cases. It means John, Peter, Thomas, etc., and the proposition: Man is mortal, may be resolved into particular propositions, and formulated as: John, Peter, Thomas, etc., are mortal.
Now, the subject Socrates of our conclusion either is or is not contained in the universal term man. If it is, then our reasoning is tautological, is even guilty of the fallacy called petitio principii, inasmuch as it implicitly assumes the conclusion it pretends to prove. If, on the other hand, the term Socrates is not contained in the term man, it is by a process of induction that we extend the meaning of the term man, which included John, Peter and Thomas, to Socrates; and the induction becomes the foundation of all truthful investigation, the basal stone of the syllogism itself.
That this depreciation of all syllogistic argumentation is openly professed by Mill, is well known to all who have read his System of Logic:
"It must be granted," says he, "that in every syllogism, considered as an argument to prove the conclusion, there is a petitio principii. When we say,
All men are mortal Socrates is a man therefore Socrates is mortal;
it is unanswerably urged by the adversaries of the syllogistic theory, that the proposition, Socrates is mortal, is presupposed in the more general assumption, All men are mortal: that we cannot be assured of the mortality of all men, unless we were previously certain of the mortality of every individual man; that if it be still doubtful whether Socrates, or any other individual you choose to name, be mortal or not, the same degree of uncertainty must hang over the assertion, All men are mortal: that the general principle, instead of being given as evidence of the particular case, cannot itself be taken for true without exception, until every shadow of doubt which could affect any case comprised with it, is dispelled by evidence aliunde; and then what remains for the syllogism to prove? that, in short, no reasoning from generals to particulars can, as such, prove anything; since from a general principle you cannot infer any particulars, but those which the principle itself assumes as foreknown.
This view, perfectly conclusive for the adherents of nominalism, loses its value if, with the great Scholastic masters, we admit the validity of the universal; if we regard the word man as meaning, not simply John, Peter and Thomas, but a universal essence common to all possible men. The error of the nominalists lies in the confusing the denotation of a term with its conotation; and, if Mill tries to clear himself from such an accusation, it is on account of an inconsistency which runs through the whole of his System of Logic, and appears as a continual puzzle to the uninitiated reader.
The conclusion of a syllogism is contained formally in the major premise, but not materially. As the universal term man denotes the essence common to all human beings, it also denotes the essence of the individual Socrates; and, if mortality is one of the characteristics of the human essence, it will undoubtedly be a characteristic of Socrates. The conclusion, Socrates is mortal, is, however, contained in the major premise implicitly only. We may be convinced of the truth of the assertion: Man is mortal, because we know that human nature as such involves the element of mortality (the human body being an organism, and all organic beings being subject to growth, decay, and dissolution); and not have realized that the individual Socrates is mortal also. The logical value of the syllogistic reasoning consists then in making explicitly known what was known implicitly in enlarging indefinitely the field of our a priori knowledge. Under its dominion lie all a priori sciences, pure mathematics as well as philosophy.
The inductive process was not unknown to the Mediaeval philosophers. Without mentioning Roger Bacon, who not only insists sisted upon the use of observation and experience, but condemned all deductive reasoning, we find well conducted examples of induction in Thomas Aquinas, Duns Scotus and Albert the Great. A remarkable passage of the work De motibus animalium, in which Albert the Great maintains the thesis that the origin of all motions of animals is on the back of the head, might have been written after Mill's System of Logic without any essential change.
These examples of induction in the modern sense were, however exceptional. Their authors themselves considered them as of little importance: "The science of nature, said Albert the Great, must not simply gather facts, it must look for the causes of the natural phenomena."
This undervaluation of inductive reasoning was due to the fact that the particular sciences had not yet acquired a field of their own, and were regarded as forming part of philosophy. Positive sciences, concerned with facts and laws, were as yet unknown.
The case being very different nowadays, neo-Scholastic logic is not satisfied with a repetition of the logical doctrines of the Middle Ages. In harmony with Leo XIII's formula: Vetera novis augere, it makes a thorough study of the inductive process.
Deductive reasoning, however, does not thereby disappear. It possesses a field of its own, in which induction has nothing to do. Enjoying an undisputed sovereignty in the science of nature, induction is absolutely powerless in the field of the a priori sciences, such as mathematics; in the field of all those which our mind in a certain sense creates.
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