The successors of Aristotle added but little of permanent value to his great achievement. Enduring importance however attaches to a small treatise by the Neo-platonist Porphyry (233 — 304 AD) entitled the Isagogé or Introduction to the Categories of Aristotle.

In a certain sense the name of Boethius (B. Severinus Boethius 470 — 525 AD) constitutes a landmark in the history of Logic: for it was through the medium of his translation of the Organon, and his commentaries on the Categories and the Isagogé, that the works of Aristotle and Porphyry were available for educational purposes in Western Europe from the sixth to the thirteenth century.' Through this period some knowledge of Logic was widely possessed, as it was one of the seven liberal arts — Grammar, Dialectic i.e., Logic, Rhetoric, Geometry, Arithmetic, Astronomy, and Music — of which higher education was held to consist.

Two works attributed to St. Augustine were also recognized authorities at this period. St. Augustine's interest in the science was not shared by all the fathers, we are told of St. Ambrose, that he used to exclaim "A Logica Augustini, libera me Domine".

At the beginning of the thirteenth century the numerous other treatises of Aristotle, and the works of his Arabian commentators Avicenna (Ibn Sina 980 — 1037 AD) and Averroes (Ibn Roshd 1126 — 1189 AD) were translated into Latin, and gave an immense impetus to philosophic study. The mediaeval Scholastics availed themselves of these works, to build up a thoroughly systematic science of Logic.

It may perhaps be said that their main advance on Aristotle's treatment lay in the greater accuracy with which they discriminated the respective spheres of Logic and Metaphysics, and in their more precise arrangement of the various parts of Logic itself.

The 15th and 16th centuries witnessed the decadence of Scholasticism, and in 1620 an attack was made on the very foundations of the Aristotelian Logic by Francis Bacon in his Novum Organum.

Much of his criticism was unfounded, since he believed that the purpose of Logic was to provide men with a means towards making discoveries regarding the laws and phenomena of nature. Yet it was of service in calling fresh attention to the theory of Induction, a part of Logic to which too little attention had been given by the later Scholastics.

Since the time of Bacon the whole question of Induction has been very fully discussed by writers on Logic. The most eminent of these among English thinkers was John Stuart Mill (1806 — 1873), whose treatment of the subject long held rank as the classical work on Induction.

Many of the points, however, raised by these writers do not strictly speaking belong to the province of Logic. For, influenced by Bacon, they have dealt not merely with Induction as a process of thought, but also with a very different subject, namely the general theory of scientific investigation.

It was indeed natural that a keen interest should be felt in this question.

The rapid growth and multiplication of the physical sciences during the last three centuries could not but lead to the codification of their rules and to reflection on their methods — in other words to the formation of a philosophy of evidence.

Such a science was impossible in the middle ages, before the great era of physical investigation had dawned. At the present day the treatment of this subject forms a part of every work on Logic. By many writers it is termed Material or Inductive Logic, the traditional part of the science receiving by way of distinction the name of Formal or Deductive Logic.

These names are misleading. The traditional Logic was, as we have seen not purely formal. And though the treatment of Induction, properly so called by many of the medieval writers, was inadequate; yet they all regarded it as falling within their scope.

We have therefore preferred to designate the two portions of this series of lectures The Logic of Thought and Applied Logic or the Method of Science respectively.

Induction as a process of thought, finds its place in the first of these two divisions.

The difference of opinion as to the true scope of Logic is far wider than would appear from the triple division which is usually recognized in logical text-books: and special names are now employed by logicians to indicate the point of view from which the science is treated. Moreover the threefold division is, as we have noticed, open to the further objection that it compels us to group the Scholastic logicians either with the school of Mansel or with that of Mill, though they have little enough in common with either of these. It seems, therefore, desirable to enter somewhat more into detail on the subject.

It is therefore important to give a very brief explanation of the special designations referred to, viz.: Scholastic Logic, Formal Logic, Symbolic Logic, Inductive Logic, Transcendental Logic, Logic of the Pure Idea, Modern Logic.

As far as possible we have availed ourselves of citations from authors representative of the various views, in order to make clear the meaning of their different terms.

(I) Scholastic Logic. We have explained above that the Scholastic or Traditional Logic holds the subject-matter of the science to be the conceptual representation of the real order. This may be otherwise expressed by saying that it deals with things, not as they are in themselves, but as they are in thought. Cardinal Mercier says: "There are two sciences whose object is in the highest degree abstract, and hence universal in its applicability. These are Metaphysics and Logic. The object of Metaphysics is Being considered in abstraction from all individua1 determinations and material properties, in other words the Real as such. . . . Logic also has Being for its object.

"It must not however be thought that Logic and Metaphysics consider Being from the same point of view. . . . The object Metaphysics is the thing considered as a real substance endowed with real attributes. The object of Logic is likewise the thing, but considered as an object of thought endowed with attributes of the conceptual order"

(2) Formal Logic. The characteristic of this school is to consider the mental processes in entire abstraction from the relation which the concept bears to the real order. Logic, says Dean Mansel, "accepts as valid, all such concepts, judgments and reasonings, as do not directly or indirectly imply contradictions: pronouncing them thus far to be legitimate as thoughts, that they do not in ultimate analysis destroy themselves"

(4) Inductive, Empirical, Material or Applied Logic is a science developed on the basis of the views set forth in Bacon's Novum Organum. Mill terms it "a general theory of the sufficiency of Evidence," and "a philosophy of Evidence and of the Investigation of Nature" (Exam. of Hamilton, p. 402). "Everyone", he says, "who has obtained any knowledge of the physical sciences from really scientific study, knows that the questions of evidence presented . . . are such as to tax the very highest capacities of the human intellect" (ibid.) and he severely calls to task those who hold "that the problem which Bacon set before himself, and led the way towards resolving, is an impossible one . . . that the study of Nature, the search for objective truth, does not admit of any rules." Granted that there be such a science it must belong, he urges, to Logic, "for if the consideration of it does not belong to Logic, to what science does it belong?" (ibid. p. 400). It is manifest that the science Mill here describes, differs essentially from Logic, as heretofore it had been understood. This philosophy of evidence deals, not with thought, but with things as they are in the real order; and its function is to prescribe the due methods of enquiry in each several science — not merely in the physical sciences as this passage might suggest. H. Spencer with more consistency than Mill refuses altogether the name of Logic to the traditional science of that name, and prefers to term it the Theory of Reasoning (Psychology, pt. vi., c. viii.).

(5) Transcendental Logic is the name given by Kant to the most fundamental portion of his Critical Philosophy. Kant started with the assumption that all our knowledge, whether sensitive or intellectual, is internal to the mind — that we have no immediate knowledge of the external world. He further assumed that the material of all our knowledge can be nought but successive pulses of sensation without unity of any kind. If these purely subjective feelings undergo such a transmutation within us as to present to our experience an orderly world of matter and motion, this must be in virtue of an a priori element — an internal mechanism providing certain 'forms' according to which we perceive, think and reason. In the Transcendental Aesthetic — the work in which he treats of sensible perception — he endeavours to show that space and time are the 'forms' of our sensitive faculty, while the pulses of sensation constitute its matter. In the Transcendental Logiche deals with the 'forms' of intellect (Transcendental Analytic), and of reasoning (Transcendental Dialectic). The intellectual forms will be noticed later. He gave them the name of Categories, a term employed in a very different sense by Aristotle and his followers. They are "the regular lines imposed by the intellect, on which sensations settle down with unities, orders, sequences, identities" (Wallace, Kant, p. 70). The problems raised in the Transcendental Dialectic fall outside the scope of these lectures.

(6) Logic of the Pure Idea. This is the name given by Hegel to his system. It will be sufficient for us to advert in the briefest manner to this philosophy, with which we are only concerned because of its bearing on Modern Logic. Its salient feature is the identification of Logic and Metaphysics. Hegel would not admit the existence of two orders — an order of thought and an order of reality. Thought, according to him, constitutes reality. Hence the science of the real — Metaphysics, is to be found in Logic — the science of thought: "Logic in our sense coincides with Metaphysics" (Wallace, Logic of Hegel, p. 38). The Universe has its origin in the inner necessity of the categories of thought. But thought in its fullest development — the thought of the Whole or the Absolute Idea passes over into reality. Thought becomes things, and realizes itself as the universe which we know.

Hegelianism is in fact a form of Pantheism. In it things are thoughts, and these thoughts are a Divine Mind evolving itself in the process of the Universe.

(7) Modern Logic. The treatment of logical problems known by this name owes its origin to the Hegelian Philosophy. It is plain that thinkers who deny the distinction between the order of things external to us, and the order of thought within, were bound to institute a new enquiry into the nature of those mental acts, which had hitherto been regarded as representative of the real order. The principal exponents of Modern Logic in England are Mr. Bradley and Mr. Bosanquet: Their work, however, is very largely based on that of the eminent German logicians Lotze and Sigwart. According to Mr. Bosanquet the only difference between Logic and Metaphysics lies in the aspect under which they view the same subject matter. "I make no doubt," he says, "that in content Logic is one with Metaphysics, and differs if at all simply in mode of treatment — in tracing the evolution of knowledge in the light of its value and import instead of attempting to summarise its value and import apart from the details of its evolution" (Logic, I. 248). The operations of the mind — judgment and reasoning — are according to this view regarded as vital functions, by which the totality we call "the real world" is intellectually constituted. The task of Logic is to analyse the process of constitution (ibid. p. 3).
 

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