Logic

Logic is the science and art which so directs the mind in the process of reasoning and subsidiary processes as to enable it to attain clearness, consistency, and validity in those processes. The aim of logic is to secure clearness in the definition and arrangement of our ideas and other mental images, consistency in our judgments, and validity in our processes of inference.

I. THE NAME

The Greek word logos, meaning "reason", is the origin of the term logic—logike (techen, pragmateia, or episteme, understood), as the name of a science or art, first occurs in the writings of the Stoics. Aristotle, the founder of the science, designates it as "analytic", and the Epicureans use the term canonic. From the time of Cicero, however, the word logic is used almost without exception to designate this science. The names dialectic and analytic are also used.

II. THE DEFINITION

It is a curious fact that, although logic is the science which treats of definition, logicians are not agreed as to how logic itself should be defined. There are, in all, about two hundred different definitions of logic. It would, of course, be impossible to enumerate even the principal definitions here. It will be sufficient to mention and discuss a few typical ones.

A. Port Royal logic

The Port Royal logic ("L'Art de penser", published 1662) defines logic as "the art of using reason well in the acquisition of the knowledge of things, both for one's own instruction and that of others." More briefly "Logic is the art of reasoning." The latter is Arnauld's definition. Definitions of this type are considered too narrow, both because they define logic in terms of art, not leaving room for its claim to be considered a science, and because, by the use of the term reasoning, they restrict the scope of logic to one class of mental processes.

Hegel

Hegel (see HEGELIANISM) goes to the other extreme when he defines logic as "the science of the pure idea." By idea he understands all reality, so that for him logic includes the science of subjective reality (logic of mental concepts) and the science of objective reality (logic of being, metaphysics). In like manner the definitions which fail to distinguish between logic and psychology, defining logic as "the science of mental processes", or "the science of the operations of the mind", are too wide. Definitions which characterize logic as "the science of sciences", "the art of arts", are also too wide: they set up too large a claim for logic.

C. St. Thomas Aquinas

In his commentary on Aristotle's logical treatises (" In Post. Anal.", lect. i, Leonine ed., I, 138), he says: "Ars qutedam necessaria est, quae sit directiva ipsius actus rationis, per quam scilicet homo in ipso actu rationis ordinate faciliter et sine errore procedat. Et haec ars est logica, id est rationalis scientia." Combining those two sentences, we may render St. Thomas's definition as follows: "Logic is the science and art which directs the act of the reason, by which a man in the exercise of his reason is enabled to proceed without error, confusion, or unnecessary difficulty." Taking reason in its broadest sense, so as to include all the operations of the mind which are strictly cognitive, namely, the formation of mental images, judgment, and ratiocination, we may expand St. Thomas' definition and define logic as "the science and art which so directs the mind in the process of reasoning and subsidiary processes as to enable it to attain clearness (or order), consistency, and validity in those processes". Logic is essentially directive. Therein it differs from psychology, which is essentially speculative or theoretical, and which concerns itself only in an Incidental and secondary manner with the direction of mental processes. Logic deals with processes of the mind. Therein it differs from metaphysics, which has for its field of inquiry and speculation the whole universe of being (see METAPHYSICS). Logic deals with mental processes in relation to truth or, more particularly, in relation to the attainment and exposition of truth by processes which aim at being valid, clear, orderly, and consistent. Therein it differs from ethics, which treats of human actions, external deeds as well as thoughts, in relation to man's final destiny. Validity, clearness, consistency, and order are logical qualities of thought, goodness and evil are ethical qualities. Finally, logic is not to be confounded with rhetoric. Rhetoric, in the old meaning of the word, was the art of persuasion; it used all the devices, such as emotional appeal, verbal arrangement, etc., in order to bring about a state of mind which had reference to action primarily, and to conviction only in a secondary sense. Logic is the science and art of conviction it uses only arguments, discarding emotional appeal and employing merely words as the symbols of thoughts.

The question whether logic is a science or an art is now generally decided by asserting that it is both. It is a science, in so far as it not merely formulates rules for right thinking, but deduces those rules from general principles which are based on the nature of mind and of truth. It is an art, in so far as it is directly and immediately related to performance, namely, to the acts of the mind. As the fine arts direct the painter or the sculptor in the actions by which he aims at producing a beautiful picture or a beautiful statue, so logic directs the thinker in the actions by which he aims at attaining truth, or expounding truth which he has attained.

III. DIVISION OF LOGIC

The traditional mode of dividing logic, into "formal" and "material", is maintained in many modern treatises on the subject. In formal logic the processes of thought are studied independently of, or without consideration of, their content. In material logic the chief question is the truth of the content of mental processes. An example from arithmetic will serve to illustrate the function of formal logic. When we add two and two, and pronounce the result to be four, we are dealing with a process of addition in its formal aspect, without paying attention to the content. The process is valid whatever the content may be, whether the "two and two "refer to books, horses, trees, or circles. This is precisely how we study judgments and arguments in logic. From the judgment "All A is B" we infer "Therefore some B is A"; and the process is valid whether the original proposition be "All circles are round" or "All lions are carnivorous ". In material logic, on the contrary, we inquire into the content of the judgments or premises and endeavour to determine whether they are true or false. Material logic was styled by the old writers "major logic", "critical logic", or simply" criticism". In recent times the word epistemology (science of knowledge), meaning an inquiry into the value of knowledge, has come into general use, and designates that portion of philosophy which inquires into the objective value of our concepts, the import and value of judgments and reasoning, the criteria of truth, the nature of evidence, certitude, etc. Whenever this new term is adopted there is a tendency to restrict the term logic to mean merely formal logic. Formal logic studies concepts,and other mental images, for the purpose of securing clearness and order among those contents of the mind. It studies judgments for the purpose of showing when and how they are consistent or inconsistent, that is, when one may be inferred from another (conversion), and when they are opposed (opposition) . It studies the two kinds of reasoning, deductive and inductive, so as to direct the mind to use these processes validly. Finally, it studies sophisms (or fallacies) and method for the purpose of showing what errors are to be avoided, and what arrangement is to be followed in a complex series of reasoning processes. But, while it is true in general that in all these tasks formal logic preserves its purely formal character, and does not inquire into the content of thought, nevertheless, in dealing with inductive reasoning and in laying down the rules for definition and division, formal logic does take account of the matter of thought. For this reason, it seems desirable to abandon the old distinction between formal and material, to designate as logic what was formerly called formal logic, and to reserve the term epistemology for that portion of philosophy which, while inquiring into the value of human knowledge in general, covers the ground which was the domain of material logic.

There remain certain kinds of logic which are not included under the heads formal and material. Transcendental logic (Kant) is the inquiry into human knowledge for the purpose of determining what elements or factors in human thought are a priori, that is, independent of experience. Symbolic logic (Lambert, Boole) is an application of mathematical methods to the processes of thought. It uses certain conventional symbols to represent terms, propositions, and the relations among them, and then, without any further reference to the laws of thought, applies the rules and methods of the mathematical calculus (Venn, "Symbolic Logic", London, 1881). Applied logic, in the narrower sense, is synonymous with material logic in the wider sense, it means logic applied to the study of the natural sciences, Iogic applied to education, logic applied to the study of law, etc. Natural logic is that native power of the mind by which most persons are competent to judge correctly and reason validly about the affairs and interests of everyday life; it is contrasted with scientific logic, which is logic as a science and cultivated art.

IV. HISTORY OF LOGIC

The history of logic possesses a more than ordinary interest, because, on the one hand, every change in the point of view of the metaphysician and the psychologist tended to produce a corresponding change in logical theory and practice, while, on the other hand, changes in logical method and procedure tended to affect the conclusions as well as the method of the philosopher. Notwithstanding these tendencies towards variation, the science of logic has undergone very few radical changes from the beginning of its history.

A. The Nyaya

A system of philosophy which was studied in India in the fifth century B.C., though it is perhaps, of much older date, takes its name from the word nyaya, meaning logical argument, or syllogism. This philosophy, like all the Indian systems, busied itself with the Problem of the deliverance of the soul from bondage, and its solution was that the soul is to be freed from the trammels of matter by means of systematic reasoning. This view of the question led naturally to an analysis of the methods of thinking, and to the construction of a type of reasoning which bears a remote resemblance to the syllogism. The nyaya, or Indian syllogism, as it is sometimes called, consists of five propositions. If, for instance, one wishes to prove that the hill is on fire, one begins with the assertion: "The hill is on fire." Next, the reason is given: "For it smokes." Then comes an instance, "Like the kitchen fire"; which is followed by the application, "So also the hill smokes." Finally comes the conclusion, "Therefore it is on fire." Between this and the clear-cut Aristotelean syllogism, with its major and minor premises and conclusion, there is all the difference that exists between the Oriental and the Greek mode of thinking. It is hardly necessary to say that there is no historical evidence that Aristotle was in any way influenced in his logic by Gotama, the reputed author of the nyaya.

B. Pre-Aristotelean Logic in Greece

The first philosophers of Greece devoted attention exclusively to the problem of the origin of the universe (see IONIAN SCHOOL OF PHILOSOPHY). The Eleatics, especially Zeno of Elea, the Sophists, and the Megarians developed the art of argumentation to a high degree of perfection. Zeno was especially remarkable in this respect, and is sometimes styled the Founder of Dialectic. None of these, however, formulated laws or rules of reasoning. The same is true of Socrates and Plato, although the former laid great stress on definition and induction, and the latter exalted dialectic, or discussion, into an important instrument of philosophical knowledge.

C. Aristotle, the Founder of Logic

In the six treatises which he devoted to the subject, Aristotle examined and analysed the thinking processes for the purpose of formulating the laws of thought. These treatises are

• "The Categories",

• "Interpretation",

• "Prior Analytics",

• "Posterior Analytics",

• "Topics", and

• "Sophisms". These were afterwards given the title of "Organon", or "Instrument of Knowledge"; this designation, however, did not come into common use until the fifteenth century.

The first four treatises contain, with occasional excursions into the domain of grammar and metaphysics, the science of formal logic essentially the same as it is taught at the present day. The "Topics" and the "Sophisms" contain the applications of logic to argumentation and the refutation of fallacies. In conformity with the fundamental principle of his theory of knowledge, namely, that all our knowledge comes from experience, Aristotle recognizes the importance of inductive reasoning, that is to say, reasoning from particular instances to general principles. If he and his followers did not develop more fully this portion of logic, it was not because they did not recognize its importance in principle. His claim to the title of Founder of Logic has never been seriously disputed the most that his opponents in the modern era could do was to set up rival systems in which induction was to supplant syllogistic reasoning. One of the devices of the opponents of scholasticism is to identify the Schoolmen and Aristotle with the advocacy of an exclusively deductive logic.

D. Post-Aristotelean Logicians Among the Greeks

Among the immediate disciples of Aristotle, Theophrastus and Eudemus devoted special attention to logic. To the former is sometimes attributed the invention of the hypothetical syllogism, although the same claim is sometimes made for the Stoics. The latter, to whom, probably, we owe the name logic, recognized this science as one of the constitutive parts of philosophy. They included in it dialectic and rhetoric, or the science of argumentation and the science of persuasion. They busied themselves also with the question of the criterion of truth, which is still an important problem in major logic, or, as it is now called, epistemology. Undoubtedly, they improved on Aristotle's logic in many points of detail; but to what extent, and in what respect, is a matter of conjecture, owing to the loss of the voluminous Stoic treatises on logic. Their rivals, the Epicureans (see EPICUREANISM) professed a contempt for logic-or "canonic", as they styled it. They maintained that it is an adjunct of physics, and that a knowledge of physical phenomena acquired through the senses is the only knowledge that is of value in the pursuit of happiness. After the Stoics and the Epicureans came the commentators. These may, for convenience, be divided into the Greeks and the Latins. The Greeks from Alexander of Aphrodisias, in the second, to St. John of Damascus in the eighth century of our era, flourished at Athens, at Alexandria, and in Asia Minor. With Photius, in the ninth century, the scene is shifted to Constantinople. To the first period belong Alexander of Aphrodisias, known as "the Commentator" Themistius, David the Armenian, Philoponus, Simplicius and Porphyry, author of the Isagoge (Eisagoge), or "Introduction" to the logic of Aristotle. In this work the author, by his explicit enumeration of the five predicables and his comment thereon, flung a challenge to the medieval logicians, which they took up in the famous controversy concerning universals (see UNIVERSALS). To the second period belong Photius, Michael Psellus the younger (eleventh century), Nicephorus Blemmydes, George Pachymeres, and Leo Magentinus (thirteenth century). All these did little more than abridge, explain, and defend the text of the Aristotelean works on logic. An exception should, perhaps, be made in favour of the physician Galen (second century), who is said to have introduced the fourth syllogistic figure, and who wrote a special work, "On Fallacies of Diction".

E. Latin Commentators

Among the Latin commentators on Aristotle we find almost in every case more originality and more inclination to add to the science of logic than we do in the case of the Greeks. After the taking of Athens by Sulla (84 B.C.) the works of Aristotle were carried to Rome, where they were arranged and edited by Andronicus of Rhodes (see ARISTOTLE). The first logical treatise in Latin is Cicero's abridgment of the "Topics". Then came a long period of inactivity. About A.D.160, Apuleius wrote a short account of the "Interpretation". In the middle of the fourth century Marius Victorinus translated Porphyry's "Isagoge". To the time of St. Augustine belong the treatises "Categoriae Decem" and "Principia Dialectica". Both were attributed to St. Augustine, though the first is certainly spurious, and the second of doubtful authenticity. They were very often transcribed in the early Middle Ages, and the logical treatises of the ninth and tenth centuries make very free use of their contents. The most popular however, of all the Latin works on logic was the curious medley of prose and verse "De Nuptiis Mercurii et Philologiae" by Marcianus Capella (about A. D. 475). In it dialectic is treated as one of the seven liberal arts (see ARTS, THE SEVEN LIBERAL), and that portion of the work was the text in all the early medieval schools of logic. Another writer on logic who exerted a widespread influence during the first period of Scholasticism was Boethius (470 524), who wrote two commentaries on the "Isagoge" of Porphyry, two on Aristotle's "Interpretation", and one on the "Categories". Besides, he wrote the original treatises,"On Categorical Syllogisms", "On Division", and "On Topical Differences", and translated several portions of Aristotle's logical works. In fact, it was principally through his translations that the early Scholastic writers, who as a rule, were entirely ignorant of Greek, had access to Aristotle's writings. Cassiodorus a contemporary of Boethius, wrote a treatise, "On the Seven Liberal Arts", in which, in the portion devoted to dialectic, he gave a summary and analysis of the Aristotelean and Porphyrian writings on logic. Isidore of Seville (died 636), Venerable Bede (673-735) and Alcuin (736-804), the forerunners of the Scholastics, were content with abridging in their logical works the writings of Boethius and Cassiodorus.

F. The Scholastics

The first masters of the schools in the age of Charlemagne and the century immediately following were not acquainted at first hand with Aristotle's works. They used the works and translations of Boethius, the pseudo-Augustinian treatises mentioned above, and the work by Marcianus Capella. Little by little their interest became centred on the metaphysical and psychological problems suggested in those treatises especially on the problem of universals and the conflict between Realism and Nominalism. As a consequence of this shifting of the centre of interest, very little was done towards perfecting the technic of logic, and there is a very noticeable dearth of original work during the ninth and tenth centuries. John Scotus Eriugena, Eric and Remi of Auxerre, and the teachers at St. Gall in Switzerland confined their activity to glossing and commenting on the traditional texts, especially Pseudo-Augustine and Marcianus Capella. In the case of the St. Gall teachers we have however, by way of exception, a work on logic, which bears evident traces of the influence of Eriugena, and a collection of mnemonic verses containing the nineteen valid syllogisms.

Roscelin (about 1050-1100), by his outspoken profession of Nominalism concentrated the attention of his contemporaries and immediate successors on the problem of universals. In the discussion of that problem the art of dialectical disputation was developed, and a taste for argumentation was fostered, but none of the dialecticians of the twelfth century, with the exception of Abelard, contributed to the advancement of the science of logic. This Abelard did in several ways. In his work to which Cousin gave the title "Dialectica", and in his commentaries, he strove to widen the scope and enhance the utility of logic as a science. Not only is it the science of disputation, but also the science of discovery, by means of which the arguments supplied by a study of nature are examined. The principal application of logic, however, is in the discussion of religious truth. Here Abelard, citing the authority of St. Augustine, contends that the methods of dialectic are applicable to the discussion of all truth, revealed as well as rational; they are applicable even to the mysteries of faith. In principle he was right, although in practice he went further than the example of St. Augustine would warrant him in going. His subsequent condemnation had for its ground, not the use of dialectic in theology, but the excessive use of dialectic to the point of rationalism. Abelard, it should be noted, was acquainted only with those treatises of Aristotle which had been translated by Boethius, and which constituted the logica vetus. His contemporary, Gilbert de la Porree (q.v.), added to the old logic a work entitled "Liber Sex Principiorum", a treatise on the last six of the Aristotelean Categories. Towards the middle of the twelfth century the remainder of the Aristotelean "Organon" became known, so that the logic of the schools, thenceforth known as logica nova, now contained:

• Aristotle's "Categories" and "Interpretation" and Porphyry's "Isagoge" (contents of the logica vetus);

• Aristotle's "Analytics", "Topics", and "Sophisms";

• Gilbert's "Liber Sex Principiorum".

This was the text in the schools when St. Thomas began to teach, and it continued to be used until superseded by the logica moderna, which embodied the contributions of Petrus Hispanus. The first writer of importance who reveals an acquaintance with the Aristotelean "Organon" in its entirety is John of Salisbury (died 1182), a disciple of Abelard, who explains and defends the legitimate use of dialectic in his work "Metalogicus". The definite triumph of Aristotelean logic in the schools of the thirteenth century was influenced by the introduction into Christian Europe of the complete works of Aristotle in Greek. The occasion of this was the taking of Constantinople by the crusaders in 1204. The Crusades had also the effect of bringing Christian Europe into closer contact with the Arabian scholars who, ever since the ninth century, had cultivated Aristotelean logic as well as the neo-Platonic interpretation of Aristotle's metaphysics. It was the Arabians who distinguished logica docens and logica utens. The former is logic as a theoretical science; the latter is logic as an applied art, practical logic. To them also is attributed the distinction between first intentions and second intentions. The Arabians, however, did not exert a determining influence on the development of Scholastic logic; they contributed to that development only in an external manner, by helping to make Aristotelean literature accessible to Christian thinkers. St. Thomas Aquinas and his teacher, Blessed Albertus Magnus (Albert the Great) did signal service to Scholastic logic, not so much by adding to its technical rules as by defining its scope and determining the limits of its legitimate applications to theology. They both composed commentaries on Aristotle's logical works and, besides, wrote independent logical treatises. The work, however, which bears the name "Summa Totius Logicae", and is found among the "Opuscula" of St. Thomas, is now judged to be from the pen of a disciple of his, Herve of Nedellac (Hervaeus Natalis). John Duns Scotus was also a commentator on Aristotle's logic. His most important original treatises on logic are "De Universalibus", in which he goes over the ground covered by Porphyry in the "Isagoge", and "Grammatica Speculativa". The latter is an interesting contribution to critical logic.

The technic of logic received special attention from Petrus Hispanus (Pope John XXI, died 1277), author of the "Summulae Logicales". This is the first medieval work to cover the whole ground of Aristotelean logic in an original way. All its predecessors were merely summaries or abridgments of Aristotle's works. In it occur the mnemonic lines, "Barbara, Celarent", etc., and nearly all the devices of a similar kind which are now used in the study of logic. They are the first of the kind in the history of logic, the lines in the ninth-century manuscript mentioned above being verses to aid the memory, without the use of arbitrary signs, such as the designation of types of propositlons by means of vowels. And the credit of having introduced them is now almost unanimously given to Petrus himself. The theory that he borrowed them from a Greek work by Psellus (see above) is discredited by an examination of the manuscripts, which shows that the Greek verses are of later date than those in the "Summulae". In fact, it was the Byzantine writer who copied the Parisian teacher, and not, as Prantl contended, the Latin who borrowed from the Greek. William of Occam (1280-1349) improved on the arrangement and method of the "Summulae" in his "Summa Totius Logicae". He also made important contributions to the doctrine of supposition of terms. He did not, however, agree with St. Thomas and St. Albert the Great in their definition of the scope and application of logic. His own conception of the purpose of logic was sufficiently serious and dignified. It was his followers, the Occamists of the fourteenth and fifteenth centuries, who, by their abuse of dialectical methods brought Scholastic logic into disrepute. One of the most original of all the Scholastic logicians was Raymond Lully (1234-1315). In his "Dialectica" he expounds clearly and concisely the logic of Aristotle, together with the additions made to that science by Petrus Hispanus. In his "Ars Magna", however, he discards all the rules and prescriptions of the formal science, and undertakes by means of his "logical machine" to demonstrate in a perfectly mechanical way all truth, supernatural as well as natural.

Scholastic logic, as may be seen from this sketch, did not modify the logic of Aristotle in any essential manner. Nevertheless, the logic of the Schools is an improvement on Aristotelean logic. The Schoolmen made clear many points which were obscure in Aristotle's works: for example, they determined more accurately than he did the nature of logic and its place in the plan of sciences. This was brought about naturally by the exigencies of theological controversy. Moreover, the Schoolmen did much to fix the technical meanings of terms in the modern languages, and, though the scientific spirit of the ages that followed spurned the methods of the Scholastic logicians, its own work was very much facilitated by the efforts of the Scholastics to distinguish the significations of words, and trace the relationship of language to thought. Finally, to the Schoolmen logic owes the various memory-aiding contrivances by the aid of which the task of teaching or learning the technicalities of the science is greatly facilitated.

G. Modern Logic

The fifteenth century witnessed the first serious attempts to revolt against the Aristotelean logic of the Schools. Humanists like Ludovicus Vico and Laurentius Valla made the methods of the Scholastic logicians the object of their merciless attack on medievalism. Of more importance in the history of logic is the attempt of Ramus (Pierre de La Ramee, 1515-72) to supplant the traditional logic by a new method which he expounded in his works "Aristotelicae Animadversiones" and "Scholae Dialecticae". Ramus was imitated in Ireland by George Downame (or Downham), Bishop of Derry, in the seventeenth century, and in the same century he had a most distinguished follower in England in the person of John Milton, who, in 1672, published "Artis Logicae Plenior Institutio ad Petri Rami Methodum Concinnata". Ramus's innovations, however, were far from receiving universal approval, even among Protestants. Melanchthon's "Erotemata Dialectica", which was substantially Aristotelean, was extensively used in the Protestant schools, and exerted a wider influence than Ramus's "Animadversiones". Francis Bacon (1561-1626) inaugurated a still more formidable onslaught. Profiting by the hints thrown out by his countryman and namesake, Roger Bacon (1214-1294), he attacked the Aristotelean method, contending that it was utterly barren of results in science, that it was, in fact, essentially unscientific, and needed not so much to be reformed as to be entirely supplanted by a new method. This he attempted to do in his "Novum Organum", which was to introduce a new logic, an inductive logic, to take the place of the deductive logic of Aristotle and the Schoolmen. It is now recognized even by the partisans of Bacon that he erred in two respects. He erred in describing Aristotle's logic as exclusively deductive, and he erred in claiming for the inductive method the ability to direct the mind in scientific discovery and practical invention. Bacon did not succeed in overthrowing the authority of Aristotle. Neither did Descartes (1596-1649), who was as desirous to make logic serve the purposes of the mathematician as Bacon was to make it serve the cause of scientific discovery. The Port Royal Logic ("L'Art de penser" 1662), written by Descartes's disciples, is essentially Aristotelean. So, though in a less degree are the logical treatises of Hobbes (1588-1679) and Gassendi (1592-1655), both of whom underwent the influence of Bacon's ideas. In the seventeenth and eighteenth centuries, Father Buffier, Le Clerc (Clericus), Wolff, and Lambert strove to modify the Aristotelean logic in the direction of empiricism, sensism, or Leibnizian innatism. In the treatises which they wrote on logic there is nothing that one might consider of primary importance.

Kant and the other German Transcendentalists of the nineteenth century took a more equitable view of Aristotle's services to the science of logic. As a rule, they recognized the value of what he had accomplished and, instead of trying to undo his work, they attempted to supplement it. It is a question, however, whether they did not do as much harm to logic in one way as Bacon and Descartes did in another. By withdrawing from the domain of logic what is empirical, and confining the science to an examination of "the necessary laws of thought", the Transcendentalists gave occasion to Mill and other Associationists to accuse logic of being unreal, and out of touch with the needs of an age which was, above all things, an age of empirical science. Most of the recent German literature on logic is characterized by the amount of attention which it pays either to historical inquiries, or to inquiries into the value of knowledge, or to investigation of the philosophical foundations of the laws of logic. It has added very little to the technical portion of the science. In England, the most important event in the history of logic in the nineteenth century was the publication, in 1843, of John Stuart Mill's "System of Logic". Mill renewed all the claims put forward by Bacon, and with some measure of success. At least, he brought about a change in the method of teaching logic at the great English seats of learning. Carrying Locke's empiricism to its ultimate conclusion, and adopting the association theory of the human mind, he rejected all necessary truth, discarded the syllogism as not only useless but fallacious, and maintained that all reasoning is from particulars to particulars. He did not make many converts to these views, but he succeeded in giving inductive logic a place in every textbook on logic published since his time. Not so successful was the attempt of Sir William Hamilton to establish a new logic (the "new analytic"), on the principle that the predicate as well as the subject of a proposition should be quantified. Nor, indeed, was he quite original in this: the idea had been put forward in the seventeenth century by the Catholic philosopher Caramuel (1606-82). Recent logical literature in English has striven above all things to attain clearness, intelligibility, and practical utility in its exposition of the laws of thought. Whenever it indulges in speculation as to the nature of mental processes, it is, of course, coloured by the various philosophies of the time.

Indeed, the history of logic is interesting and profitable chiefly because it shows how the philosophical theories influence the method and the doctrine of the logician. The empiricism and sensism of the English school, descending from Hobbes through Locke, Hume, and the Associationists, could lead in logic to no other conclusion than that to which it does lead in Mill's rejection of the syllogism and of all necessary truth. On the other hand, Descartes's exaltation of deduction and Leibniz's adoption of the mathematical method have their origin in that doctrine of innatism which is the opposite of empiricism. Again, the domination of industrialism, and the insistence for recognition on the part of the social economist, have had in our own day the effect of pushing logic more and more towards the position of a purveyor of rules for scientific discovery and practical invention. The materialism of the last half of the nineteenth century demanded that logic prove its utility in a practical way. Hence the prominence given to induction. But, of all the crises through which logic has passed, the most interesting is that which is known as the "Storm and Stress of Scholasticism", in which mysticism on the one side rejected dialectic as "the devil's art", and maintained that "God did not choose logic as a means of saving his people", while rationalism on the other side set no bounds to the use of logic, going so far as to place it on a plane with Divine faith. Out of this conflict issued the Scholasticism of the thirteenth century, which gave due credit to the mystic contention in so far as that contention was sound, and at the same time acknowledged freely the claims of rationalism within the limits of orthodoxy and of reason. St. Thomas and his contemporaries looked upon logic as an instrument for the discovery and exposition of natural truth. They considered, moreover, that it is the instrument by which the theologian is enabled to expound, systematize, and defend revealed truth. This view of the theological use of logic is the basis for the charge of intellectualism which Modernist philosophers imbued with Kantism have made against the Scholastics. Modernism asserts that the logical nexus is "the weakest link" between the mind and spiritual truth. So that the contest waged in the twelfth century is renewed in slightly different terms in our own day, the application of logic to theology being now, as then, the principal point in dispute.

In every system of logic there is an underlying philosophical theory, though this is not always formulated in explicit terms. It is impossible to explain and demonstrate the laws of thought without falling back on some theory of the nature of mind. For this reason Catholic philosophers and educators, as well as those who by their position in the Church are responsible for the purity of doctrine in Catholic institutions, have recognized that there is in logic the Catholic and the non-Catholic point of view. Our objection to a good deal of recent logical literature is not based on an unfavourable estimate of its scientific quality: what we object to is the sensism, subjectivism, agnosticism or other philosophical doctrine, which underlies the logical theories of the author. Works on logic written by Catholics generally adhere very closely to the traditional Aristotelean logic of the schools. Yet that is not the reason why they are approved. They are approved because they are free from false philosophical assumptions. In many non-Catholic works on logic the underlying philosophy is not only erroneous, but subversive of the whole body of natural spiritual truth which the Catholic Church guards as carefully as she does the deposit of faith.

WILLIAM TURNER