Logic

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Logic is thescience 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 ourideas and other mental images, consistency in our judgments, and validity in our processes of inference.

The name

The Greek wordlogos, meaning "reason", is the origin of the termlogic--logike (techen, pragmateia, orepisteme, understood), as the name of ascience or art, first occurs in the writings of theStoics.Aristotle, the founder of thescience, designates it as "analytic", and theEpicureans use the termcanonic. From the time of Cicero, however, the wordlogic is used almost without exception to designate thisscience. The namesdialectic andanalytic are also used.

The definition

It is a curious fact that, although logic is thescience 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.

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 theknowledge 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 ascience, and because, by the use of the termreasoning, they restrict the scope of logic to one class ofmental processes.

Hegel

Hegel (seeHEGELIANISM) goes to the other extreme when he defines logic as "thescience of the pureidea." Byidea he understands all reality, so that for him logic includes thescience of subjective reality (logic ofmental concepts) and thescience of objective reality (logic of being,metaphysics). In like manner the definitions which fail to distinguish between logic andpsychology, defining logic as "the science of mental processes", or "thescience of the operations of themind", 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.

St. Thomas Aquinas

In his commentary onAristotle's logical treatises (" In Post. Anal.", lect. i, Leonine ed., I, 138), he says: "Ars quædam 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 renderSt. Thomas's definition as follows: "Logic is thescience and art which directs the act of the reason, by which a man in the exercise of his reason is enabled to proceed withouterror, confusion, or unnecessary difficulty." Takingreason in its broadest sense, so as to include all the operations of the mind which are strictly cognitive, namely, the formation ofmental images, judgment, and ratiocination, we may expand St. Thomas' definition and define logic as "thescience 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 frompsychology, which is essentially speculative or theoretical, and which concerns itself only in an Incidental and secondary manner with the direction ofmental processes. Logic deals with processes of the mind. Therein it differs frommetaphysics, which has for its field of inquiry and speculation the wholeuniverse of being (seeMETAPHYSICS). Logic deals withmental processes in relation totruth or, more particularly, in relation to the attainment and exposition oftruth 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 andevil areethical 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 thescience 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 ascience or an art is now generally decided by asserting that it is both. It is ascience, 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 oftruth. It is an art, in so far as it is directly and immediately related to performance, namely, to the acts of the mind. As thefine arts direct thepainter or thesculptor in the actions by which he aims at producing a beautiful picture or a beautifulstatue, so logic directs the thinker in the actions by which he aims at attainingtruth, or expoundingtruth which he has attained.

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 thetruth of the content ofmental 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 aretrue orfalse. Material logic was styled by the old writers "major logic", "critical logic", or simply" criticism". In recent times the wordepistemology (science ofknowledge), meaning an inquiry into the value ofknowledge, has come into general use, and designates that portion ofphilosophy which inquires into the objective value of our concepts, the import and value of judgments and reasoning, the criteria oftruth, the nature of evidence, certitude, etc. Whenever this new term is adopted there is a tendency to restrict the termlogic to mean merely formal logic. Formal logic studies concepts, and othermental 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 andinductive, so as to direct the mind to use these processes validly. Finally, it studies sophisms (or fallacies) and method for the purpose of showing whaterrors are to be avoided, and what arrangement is to be followed in a complex series of reasoning processes. But, while it istrue 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 withinductive 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 termepistemology for that portion ofphilosophy which, while inquiring into the value ofhumanknowledge in general, covers the ground which was the domain of material logic.

There remain certain kinds of logic which are not included under the headsformal andmaterial. Transcendental logic (Kant) is the inquiry intohumanknowledge 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 thelaws 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 naturalsciences, Iogic applied toeducation, logic applied to the study of law, etc. Natural logic is that native power of the mind by which mostpersons 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 ascience and cultivated art.

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 thepsychologist 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 thephilosopher. Notwithstanding these tendencies towards variation, thescience of logic has undergone very few radical changes from the beginning of its history.

The Nyaya

A system ofphilosophy which was studied inIndia in the fifth century B.C., though it is perhaps, of much older date, takes its name from the wordnyaya, meaning logical argument, or syllogism. This philosophy, like all the Indian systems, busied itself with the Problem of the deliverance of thesoul from bondage, and its solution was that thesoul 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. Thenyaya, 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, thereason 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-cutAristotelean 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 hardlynecessary to say that there is no historical evidence thatAristotle was in any way influenced in his logic by Gotama, the reputed author of the nyaya.

Pre-Aristotelean logic in Greece

The firstphilosophers of Greece devoted attention exclusively to the problem of the origin of theuniverse (seeIONIAN SCHOOL OF PHILOSOPHY). The Eleatics, especiallyZeno of Elea, theSophists, and theMegarians 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, formulatedlaws or rules of reasoning. The same istrue ofSocrates andPlato, although the former laid great stress on definition and induction, and the latter exalted dialectic, or discussion, into an important instrument ofphilosophicalknowledge.

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 thelaws of thought. These treatises are

The first four treatises contain, with occasional excursions into the domain of grammar andmetaphysics, thescience 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 ofknowledge, namely, that all ourknowledge comes from experience,Aristotle recognizes the importance ofinductive 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 theSchoolmen andAristotle with the advocacy of an exclusivelydeductive logic.

Post-Aristotelean logicians among the Greeks

Among the immediate disciples ofAristotle, 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 theStoics. The latter, to whom, probably, we owe the name logic, recognized thisscience as one of the constitutive parts ofphilosophy. They included in it dialectic and rhetoric, or thescience of argumentation and thescience of persuasion. They busied themselves also with the question of the criterion oftruth, which is still an important problem in major logic, or, as it is now called,epistemology. Undoubtedly, they improved onAristotle'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 voluminousStoic treatises on logic. Their rivals, theEpicureans (seeEPICUREANISM) professed a contempt for logic — or "canonic", as they styled it. They maintained that it is an adjunct of physics, and that aknowledge of physical phenomena acquired through the senses is the onlyknowledge that is of value in the pursuit ofhappiness. After theStoics and theEpicureans came the commentators. These may, for convenience, be divided into the Greeks and the Latins. The Greeks from Alexander of Aphrodisias, in the second, toSt. John of Damascus in the eighth century of our era, flourished atAthens, at Alexandria, and inAsia 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 ofAristotle. In this work the author, by his explicit enumeration of the five predicables and his comment thereon, flung a challenge to themedieval logicians, which they took up in the famous controversy concerninguniversals (seeUNIVERSALS). 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 theAristotelean 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".

Latin commentators

Among the Latin commentators onAristotle we find almost in every case more originality and more inclination to add to thescience of logic than we do in the case of the Greeks. After the taking ofAthens by Sulla (84 B.C.) the works ofAristotle were carried toRome, where they were arranged and edited by Andronicus of Rhodes (seeARISTOTLE). 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 ofSt. Augustine belong the treatises "Categoriae Decem" and "Principia Dialectica". Both were attributed toSt. Augustine, though the first is certainly spurious, and the second ofdoubtful authenticity. They were very often transcribed in the earlyMiddle 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 (seeTHE SEVEN LIBERAL ARTS), and that portion of the work was the text in all the earlymedievalschools of logic. Another writer on logic who exerted a widespread influence during the first period ofScholasticism wasBoethius (470 524), who wrote two commentaries on the "Isagoge" of Porphyry, two onAristotle'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 ofAristotle's logical works. In fact, it was principally through his translations that the earlyScholastic writers, who as a rule, were entirelyignorant of Greek, had access toAristotle's writings.Cassiodorus a contemporary ofBoethius, wrote a treatise, "On the Seven Liberal Arts", in which, in the portion devoted to dialectic, he gave a summary and analysis of theAristotelean and Porphyrian writings on logic.Isidore of Seville (died 636),Venerable Bede (673-735) andAlcuin (736-804), the forerunners of theScholastics, were content with abridging in their logical works the writings ofBoethius andCassiodorus.

The Scholastics

The first masters of theschools in the age ofCharlemagne and the century immediately following were not acquainted at first hand withAristotle's works. They used the works and translations ofBoethius, the pseudo-Augustinian treatises mentioned above, and the work by Marcianus Capella. Little by little their interest became centred on the metaphysical andpsychological problems suggested in those treatises especially on the problem ofuniversals and the conflict between Realism andNominalism. 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 inSwitzerland 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 ofNominalism concentrated the attention of his contemporaries and immediate successors on the problem ofuniversals. In the discussion of that problem the art ofdialectical disputation was developed, and a taste for argumentation was fostered, but none of the dialecticians of the twelfth century, with the exception ofAbelard, contributed to the advancement of thescience of logic. ThisAbelard 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 ascience. Not only is it thescience of disputation, but also thescience 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 religioustruth. HereAbelard, citing the authority ofSt. Augustine, contends that the methods of dialectic are applicable to the discussion of alltruth, revealed as well as rational; they are applicable even to the mysteries offaith. In principle he was right, although in practice he went further than the example ofSt. Augustine would warrant him in going. His subsequent condemnation had for its ground, not the use of dialectic intheology, but the excessive use of dialectic to the point ofrationalism.Abelard, it should be noted, was acquainted only with those treatises ofAristotle which had been translated byBoethius, and which constituted thelogica vetus. His contemporary, Gilbert de la Porrée, added to the old logic a work entitled "Liber Sex Principiorum", a treatise on the last six of theAristotelean Categories. Towards the middle of the twelfth century the remainder of theAristotelean "Organon" became known, so that the logic of theschools, thenceforth known aslogica nova, now contained:

This was the text in theschools whenSt. Thomas began to teach, and it continued to be used until superseded by thelogica moderna, which embodied the contributions of Petrus Hispanus. The first writer of importance who reveals an acquaintance with theAristotelean "Organon" in its entirety isJohn of Salisbury (died 1182), a disciple ofAbelard, who explains and defends the legitimate use of dialectic in his work "Metalogicus".

The definite triumph ofAristotelean logic in theschools of the thirteenth century was influenced by the introduction intoChristianEurope of the complete works ofAristotle in Greek. The occasion of this was the taking of Constantinople by thecrusaders in 1204. TheCrusades had also the effect of bringingChristianEurope into closer contact with the Arabian scholars who, ever since the ninth century, had cultivatedAristotelean logic as well as theneo-Platonic interpretation ofAristotle'smetaphysics. It was the Arabians who distinguishedlogica docens andlogica utens. The former is logic as a theoreticalscience; 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 ofScholastic logic; they contributed to that development only in an external manner, by helping to makeAristotelean literature accessible toChristian thinkers.St. Thomas Aquinas and his teacher, BlessedAlbertus Magnus (Albert the Great) did signal service toScholastic logic, not so much by adding to its technical rules as by defining its scope and determining the limits of its legitimate applications totheology. They both composed commentaries onAristotle'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" ofSt. 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 onAristotle'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 firstmedieval work to cover the whole ground ofAristotelean logic in an original way. All its predecessors were merely summaries or abridgments ofAristotle'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-centurymanuscript mentioned above being verses to aid the memory, without the use of arbitrary signs, such as the designation of types of propositions 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 themanuscripts, which shows that the Greek verses are of later date than those in the "Summulae". In fact, it was the Byzantine writer who copied theParisian 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 thedoctrine of supposition of terms. He did not, however, agree withSt. Thomas andSt. 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 ofdialectical methods broughtScholastic logic into disrepute. One of the most original of all theScholastic logicians wasRaymond Lully (1234-1315). In his "Dialectica" he expounds clearly and concisely the logic ofAristotle, together with the additions made to thatscience by Petrus Hispanus. In his "Ars Magna", however, he discards all the rules and prescriptions of the formalscience, and undertakes by means of his "logical machine" to demonstrate in a perfectly mechanical way alltruth,supernatural as well as natural.

Scholastic logic, as may be seen from this sketch, did not modify the logic ofAristotle in any essential manner. Nevertheless, the logic of the Schools is an improvement onAristotelean logic. TheSchoolmen made clear many points which were obscure inAristotle's works: for example, they determined more accurately than he did the nature of logic and its place in the plan ofsciences. This was brought about naturally by the exigencies oftheological controversy. Moreover, theSchoolmen 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 theScholastic logicians, its own work was very much facilitated by the efforts of theScholastics to distinguish the significations of words, and trace the relationship of language to thought. Finally, to theSchoolmen logic owes the various memory-aiding contrivances by the aid of which the task of teaching or learning the technicalities of thescience is greatly facilitated.

Modern logic

The fifteenth century witnessed the first serious attempts to revolt against theAristotelean logic of the Schools. Humanists like Ludovicus Vico and Laurentius Valla made the methods of theScholastic logicians the object of their merciless attack onmedievalism. 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 inIreland by George Downame (or Downham),Bishop ofDerry, in the seventeenth century, and in the same century he had a most distinguished follower inEngland in theperson 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 amongProtestants.Melanchthon's "Erotemata Dialectica", which was substantiallyAristotelean, was extensively used in theProtestantschools, 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 theAristotelean method, contending that it was utterly barren of results inscience, 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, aninductive logic, to take the place of thedeductive logic ofAristotle and theSchoolmen. It is now recognized even by the partisans ofBacon that heerred in two respects. Heerred in describingAristotle's logic as exclusivelydeductive, and heerred in claiming for theinductive method the ability to direct the mind in scientific discovery and practical invention.Bacon did not succeed in overthrowing the authority ofAristotle. Neither didDescartes (1596-1649), who was as desirous to make logic serve the purposes of the mathematician asBacon was to make it serve the cause of scientific discovery. The Port Royal Logic ("L'Art de penser" 1662), written byDescartes's disciples, is essentiallyAristotelean. So, though in a less degree are the logical treatises of Hobbes (1588-1679) andGassendi (1592-1655), both of whom underwent the influence ofBacon'sideas. In the seventeenth and eighteenth centuries,Father Buffier, Le Clerc (Clericus), Wolff, and Lambert strove to modify theAristotelean 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 ofAristotle's services to thescience 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 asBacon andDescartes did in another. By withdrawing from the domain of logic what is empirical, and confining thescience 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 empiricalscience. Most of the recentGerman literature on logic is characterized by the amount of attention which it pays either to historical inquiries, or to inquiries into the value ofknowledge, or to investigation of thephilosophical foundations of thelaws of logic. It has added very little to the technical portion of thescience. InEngland, 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 byBacon, 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 thehumanmind, he rejected allnecessarytruth, 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 givinginductive 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: theidea had been put forward in the seventeenth century by theCatholicphilosopherCaramuel (1606-82). Recent logical literature in English has striven above all things to attain clearness, intelligibility, and practical utility in its exposition of thelaws of thought. Whenever it indulges in speculation as to the nature ofmental processes, it is, of course, coloured by the variousphilosophies of the time.

Indeed, the history of logic is interesting and profitable chiefly because it shows how thephilosophical theories influence the method and thedoctrine of the logician. The empiricism and sensism of the Englishschool, 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 allnecessarytruth. On the other hand,Descartes's exaltation of deduction and Leibniz's adoption of the mathematical method have their origin in thatdoctrine of innatism which is the opposite of empiricism. Again, the domination of industrialism, and the insistence for recognition on the part of the socialeconomist, 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 whichmysticism 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", whilerationalism on the other side set no bounds to the use of logic, going so far as to place it on a plane with Divinefaith. Out of this conflict issued theScholasticism 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 ofrationalism within the limits oforthodoxy and of reason.St. Thomas and his contemporaries looked upon logic as an instrument for the discovery and exposition of naturaltruth. They considered, moreover, that it is the instrument by which thetheologian is enabled to expound, systematize, and defendrevealedtruth. This view of thetheological use of logic is the basis for the charge of intellectualism whichModernistphilosophers imbued withKantism have made against theScholastics.Modernism asserts that the logical nexus is "the weakest link" between the mind and spiritualtruth. So that the contest waged in the twelfth century is renewed in slightly different terms in our own day, the application of logic totheology being now, as then, the principal point in dispute.

In every system of logic there is an underlyingphilosophical theory, though this is not always formulated in explicit terms. It is impossible to explain and demonstrate thelaws of thought without falling back on some theory of the nature of mind. For this reasonCatholicphilosophers and educators, as well as those who by their position in theChurch are responsible for the purity ofdoctrine inCatholic institutions, have recognized that there is in logic theCatholic 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 otherphilosophicaldoctrine, which underlies the logical theories of the author. Works on logic written byCatholics generally adhere very closely to the traditionalAristotelean logic of theschools. Yet that is not the reason why they are approved. They are approved because they are free fromfalsephilosophical assumptions. In many non-Catholic works on logic the underlying philosophy is not onlyerroneous, but subversive of the whole body of natural spiritualtruth which theCatholicChurch guards as carefully as she does the deposit offaith.

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