Logic Sentence Examples

Her logic and her sympathy are in excellent balance.

His logic and acceptance of the deformity was amazingly positive and mature for a 9-year-old.

Logic began to drift back into Dean's thought process.

That sounds like your kind of logic - always thinking of the other person first.

He saw the logic, even though he didn't want to.

I wasn't thinking at my highest level of logic.

He always tried to govern his thinking by logic.

It wasn't the money he objected to so much as the irrational logic.

It was an illogical thought, but her mind was beyond logic.

Mathematical Logic as based on the Theory of Types,"Amer.

She didn't expect it; she expected him to lie rather than point out the flaws in her desperate logic.

It was scrambling her logic and had completely decimated her self-control where he was concerned.

Only the tiniest shred of doubt remained in her mind, and that was probably born of wishful thinking, not logic.

But the pupil soon found his teacher to be a charlatan, and taught himself, aided by commentaries, to master logic, geometry andastronomy.

His inductive logic must "supplement and not supersede."

The Koran, sacred and secular law, logic, poetry, arithmetic, with some medicine and geography, are the chief subjects of study.

The world is happiest when this process is one of persuasion, goodwill, reason, logic, and negotiation.

His logic was sound, but there was still the situation with the chair.

His Logic, Metaphysics, Physics, De Caelo, are treatises giving a synoptic view of Aristotelian doctrine.

This suggestion has some interest, but is of no great value, either in logic or in the theory of knowledge.

Charles, however, has given good grounds for supposing that it is merely a preface, and that the work went on to discuss grammar, logic (which Bacon thought of little service, as reasoning was innate), mathematics, general physics, metaphysics and moral philosophy.

After that, apparently, logic was to be treated; then, possibly, mathematics and physics; then speculative alchemy and experimental science.

Sigwart, in the preface to the first edition of his Logic, makes "special mention" of the assistance he obtained from this book.

Appointed superintendent of the cathedral school of his native city, he taught with such success as to attract pupils from all parts of France, and powerfully contributed to diffuse an interest in the study of logic and metaphysics, and to introduce that dialectic development of theology which is designated the scholastic. The earliest of his writings of which we have any record is an Exhortatory Discourse to the hermits of his district, written at their own request and for their spiritual edification.

They were followed by treatises of a different character, clearer in matter, more systematic in arrangement, and reflecting the methods of the scholastic logic; these are farther from the Greek tradition, for although they contain sufficient traces of their ultimate Greek ancestry, their authors do not know the Greeks as masters and cite no Greek names.

Bartole, the official biographer of Ignatius, says that he would not permit any innovation in the studies; and that, were he to live five hundred years, he would always repeat "no novelties" in theology, in philosophy or in logic - not even in grammar.

Besides being a contributor to the magazines and encyclopedias on educational and philosophical subjects, he wrote An Introduction to the Study of Philosophy (1889); The Spiritual Sense of Dante's Divina Commedia (1889); Hegel's Logic (1890); and Psychologic Foundations of Education (1898); and edited Appleton's International Education Series and 'Webster's International Dictionary.

Haydn uses a true Straussian discord in The Seasons, in order to imitate the chirping of a cricket; but the harshest realism in Gatterdammerung (the discord produced by the horns of Hagen and his churls in the mustering-scene in the second act) has a harmonic logic which would have convinced Corelli.

Justinian himself, with the aid of Leontius of Byzantium (c. 4 8 5-543), a monk with a decided turn for Aristotelian logic and metaphysics, had tried to reconcile the Cyrillian and Chalcedonian positions, but he inclined more and'more towards the monophysite view, and even went so far as to condemn by edict three teachers (Theodore of Mopsuestia, Theodoret, the opponent of Cyril, and Ibas of Edessa) who were offensive to the monophysites.

Whatever be the historical worth of this story, it may safely be said that it cannot be disproved by deductive reasoning from the premisses of abstract logic. The most we can do is to assert that a universe in which such things are liable to happen on a large scale is unfitted for the practical application of the theory of cardinal numbers.

The eighth now extant is really an incomplete treatise on logic. Some critics have rejected this book as spurious, since its matter is so different from that of the rest.

He was professor of moral philosophy at Bourges (1845-1848) and Strassburg (1848-- 1857), and of logic at the lycee Louis-le-Grand, Paris (1857-1864).

Believers in law have put their trust in authority or logic; while believers in disposition chiefly look to our instinctive faculties - conscience, common-sense or sentiment.

But common-sense and conscience are quite as definite guides as logic or authority; and there seems no good reason for refusing to give the name of casuistry to their operations.

These logic must seize upon and develop as far as they will go; for the breach of some trifling consequence of a rule might mean the loss of the deity's favour.

In the preface to the first edition, Sigwart explains that he makes no attempt to appreciate the logical theories of his predecessors; his intention was to construct a theory of logic, complete in itself.

In formal logic the drawing of inferences is frequently called ratiocination.

The name doctor scholasticus was applied originally to any teacher in such an ecclesiastical gymnasium, but gradually the study of dialectic or logic overshadowed the more elementary disciplines, and the general acceptation of " doctor " came to be one who occupied himself with the teaching of logic. The philosophy of the later Scholastics is more extended in its scope; but to the end of the medieval period philosophy centres in the discussion of the same logical problems which began to agitate the teachers of the 9th and 1 oth centuries.

Prantl says that there is no such thing as philosophy in the middle ages; there are only logic and theology.

But the saying draws attention to the two great influences which shaped medieval thought - the tradition of ancient logic and the system of Christian theology.

Scholasticism opens with a discussion of certain points in the Aristotelian logic; it speedily begins to apply its logical distinctions to the doctrines of the church; and when it attains its full stature in St Thomas it has, with the exception of certain mysteries, rationalized or Aristotelianized the whole churchly system.

As aids to the study of logic, the doctors of this period, beside the commentaries and treatises of Boetius (q.v.), possessed two tracts attributed to St Augustine, the first of which, Principia dialecticae, is probably his, but is mainly grammatical in its import.

The next centuries show that peculiar combination of logic and theology which is the mark of Scholasticism, especially in the period before the r3th century.

The earlier doctors who avail themselves of Aristotle's works, while bowing to his authority implicitly in matters of logic, are generally found defending a Christianized Platonism against the doctrine of the Metaphysics.

So also is Petrus Hispanus (Pope John XXI.), who is chiefly important, however, as the author of the much-used manual Summulae logicales, in which the logic of the schools was expanded by the incorporation of fresh matter of a semi-grammatical character.

In logic, ignorance is that state of mind which for want of evidence is equally unable to affirm or deny one thing or another.

Among the works which he translated into Syriac and of which his versions survive are treatises of Aristotle, Porphyry and Galen, 3 the Ars grammatica of Dionysius Thrax, the works of Dionysius the Areopagite, and possibly two or three treatises of Plutarch.4 His own original works are less important, but include a " treatise on logic, addressed to Theodore (of Merv), which is unfortunately imperfect, a tract on negation and affirmation; a treatise, likewise addressed to Theodore, On the Causes of the Universe, according to the Views of Aristotle, showing how it is a Circle; a tract On Genus, Species and Individuality; and a third tract addressed to Theodore, On the Action and Influence of the Moon, explanatory and illustrative of Galen's IIEpi rcptaiµwv r t µepwv, bk.

Paul the Persian, a courtier of Khosrau Anosharwan, dedicated to the king a treatise on logic which has been published from a London MS. by Land in the 4th volume of his Anecdota.

He wrote Breviuscula Introductio ad Logicam, a treatise on logic and the psychology of the intellectual powers; Synopsis Theologiae Naturalis; and an edition of Pufendorf, De Officio Hominis et Civis, with notes and supplements of high value.

The term in Aristotelian logic is opposed to dialectic, as scientific proof to probable reasoning.

We feel its presence in his earliest notable work, The Rationale of Religious Enquiry, 1836; and may there see the rigour with which it applied audacious logic to narrow premisses, the tenacity with which it clung to a limited literal supernaturalism which it had no philosophy to justify, and so could not believe without historical and verbal authority.

In its speculative parts the book is quite equal to those that had gone before, but in its literary and historical parts there are indications of a mind in which a longpractised logic had become a rooted habit.

This tour de force was followed up by the publication in 1543 of Aristotelicae Animadversiones and Dialecticae Partitiones, the former a criticism on the old logic and the latter a new textbook of the science.

The logic of Ramus enjoyed a great celebrity for a time, and there existed a school of Ramists boasting numerous adherents in France, Germany and Holland.

It cannot be said, however, that Ramus's innovations mark any epoch in the history of logic. His rhetorical leaning is seen in the definition of logic as the "ars disserendi"; he maintains that the rules of logic may be better learned from observation of the way in which Cicero persuaded his hearers than from a study of the Organon.

Logic falls, according to Ramus, into two parts - invention (treating of the notion and definition) and judgment (comprising the judgment proper, syllogism and method).

Logic he probably despised as merely an instrument of pedants - a judgment for which, in his day, and especially at the universities, there was only too much ground.

In 1893 he went to Aberdeen, and finally in 1895 to the chair of logic at Glasgow, which he held till his death on the 5th of February 1902.

In 1842 he took a "double-first" and was elected fellow of B alliol, and lecturer in mathematics and logic. Four years later he took orders, and with the aim of helping forward the education of the very poor, he accepted the headship of Kneller Hall, a college which the government formed for the training of masters of workhouse and penal schools.

With the exception of a satiric comedy, Il Candelajo, all the works of this period are devoted to this logic - De Umbris Idearum, Ars Memoriae, De cornpendiosa architecture et complemento artis Lullii, and Cantus Circaeus.

It provided also a substitute for either the Aristotelian or the Ramist logic, which was an additional element in its favour.

Indeed, there still existed on the statute a provision that "Masters and Bachelors who did not follow Aristotle faithfully were liable to a fine of five shillings for every point of divergence, and for every fault committed against the logic of the Organon."

The Stoics divided XoytK17 (logic) into rhetoric and dialectic, and from their time till the end of the middle ages dialectic was either synonymous with, or a part of, logic.

This post he occupied for three successive sessions, during which he continued writing for the Westminster, and also in 1842 helped Mill with the revision of the MS. of his System of Logic. In 1843 he contributed the first review of the book to the London and Westminster.

In 1860 he was appointed by the crown to the new chair of logic and English in the university of Aberdeen (created on the amalgamation of the two colleges, King's and Marischal, by the Scottish Universities Commission of 1858).

Up to this date neither logic nor English had received adequate attention in Aberdeen, and Bain devoted himself to supplying these deficiencies.

But he also took a keen interest and frequently an active part in the political and social movements of the day; and so highly did the students of Aberdeen rate his practical ability, that, after his retirement from the chair of logic, they twice in succession elected him lord rector of the university, each term of office extending over three years.

See the modern logic textbooks.

As we advance from the logic to the metaphysics and from that to his ontology, it becomes clear that the concepts are only " categories " or predicates of a reality lying outside of them, and there is an ultimate division between the world as the object or matter of thought and the thinking or moving principle which gives its life.

The " Logic " of Hegel is merely the continuation of Kant's " Deduction " of the categories and ideas of the reason which has generally been recognized as the soberest of attempts to set forth the presuppositions which underlie all experience.

Similarly from the side of logic. It is not the teaching of idealism alone but of the facts which logical analysis has brought home to us that all difference in the last resort finds its ground in the quality or content of the things differentiated, and that this difference of content shows in turn a double strand, the strand of sameness and the strand of otherness - that in which and that by which they differ from one another.

If in a well-known passage (Logic § 212) he seems to countenance the Spinoxistic view he immediately corrects it by assigning an " actualizing force " to this illusion and making it a " necessary dynamic element of truth."

Perceiving the difficulty of the Socratic dictum he endeavoured to give to the word "knowledge" a definite content by divorcing it absolutely from the sphere of sense and experience, and confining it to a sort of transcendental dialectic or logic. The Eleatic unity is Goodness, and is beyond the sphere of sensible apprehension.

Logic he regarded as a practical art, and his Esercizioni logici has the further title, Art of deriving benefit from ill-constructed books.

The most important of his numerous works are the Wissenschaftslehre, oder Versuch einer neuen Darstellung der Logik, advocating a scientific method in the study of logic (4 vols., Sulzbach, 1837); the Lehrbuch der Religionswissenschaft (4 vols., Sulzbach, 1834), a philosophic representation of all the dogmas of Roman Catholic theology; and Athanasia, oder Gri nde fiir die Unsterblichkeit der Seele (2nd ed., Mainz, 1838).

His religious unorthodoxy was condoned because he never scoffed; his political heresies, after their first effect was over, seemed harmless from the very want of logic and practical spirit in them, while part at least of his literary secret was the common property of almost every one who attempted literature.

But some, especially those on Celestial Dynamics and Organic Motion, are admirable examples of what really valuable work may be effected by a man of high intellectual powers, in spite of imperfect information and defective logic.

The captious logic of the Megarian school was indeed in some cases closely related to sceptical results.

Logic and physical science they held to be useless, for all knowledge is immediate sensation (see Protagoras).

Though he did not altogether neglect logic and physics, he maintained that virtue is the only real aim of men.

He excelled in logic, the theory of knowledge, ethics and physics.

Five years later he became professor ordinarius of logic and metaphysics; in 1759 he exchanged this for a professorship of rhetoric and poetry.

About this time began his acquaintance with David Hume, which afterwards ripened into friendship. In 1751 he was elected professor of logic at Glasgow, and in 1752 was transferred to the chair of moral philosophy, which had become vacant by the death of Thomas Craigie, the successor of Hutcheson.

The cities thus privileged, however, though receiving complete Roman citizenship, were not, as the logic of public law might seem to demand, incorporated in Rome, but continued to exist as independent urban units; and this anomaly survived in the municipal system which was developed, on the basis of these grants of citizenship, after the Social War.

He had a distinguished university career at Edinburgh, and Balliol College, Oxford, and after being fellow of Jesus and tutor of Balliol was elected professor of logic and metaphysics at St Andrews.

So also he might add the appendix to the Sophistical Elenchi, long after he had written that book, and perhaps, to judge from its being a general claim to have discovered the syllogism, when the founder of logic had more or less realized that he had written a number of connected treatises on reasoning.

How otherwise, we wonder, could one man writing alone and with so few predecessors compose the first systematic treatises on the psychology of the mental powers and on the logic of reasoning, the first natural history of animals, and the first civil history of one hundred and fifty-eight constitutions, in addition to authoritative treatises on metaphysics, biology, ethics, politics, rhetoric and poetry; in all penetrating to the very essence of the subject, and, what is most wonderful, describing more facts than any other man has ever done on so many subjects ?

On the other hand, in the case of logic, it is certain that he did not combine his works on the subject into one whole, but that the Peripatetics afterwards put them together as organic, and made them the parts of logic as an organon, as they are treated by Andronicus.

Again, according to both works, an individual substance is a subject, a universal its predicate; and they have in common the Aristotelian metaphysics, which differs greatly from the modern logic of subject and predicate.

In other words, to him subject meant real as well as nominal subject, and predicate meant real as well as nominal predicate; whereas modern logic has gradually reduced both to the nominal terms of a proposition.

Here Aristotle, starting from the previous grammar of sentences in general, proceeded, for the first time in philosophical literature, to disengage the logic of the proposition, or that sentence which can alone be true or false, whereby it alone enters into reasoning.

The point of Aristotle was to draw a line between rational and other evidences, to insist on the former, and in fact to found a logic of rhetoric. But if in the Rhetoric to Alexander, not he, but Anaximenes, had already performed this great achievement, Aristotle would have been the meanest of mankind; for the logic of rhetoric would have been really the work of Anaximenes the sophist, but falsely claimed by Aristotle the philosopher.

As we cannot without a tittle of evidence accept such a consequence, we conclude that Aristotle formulated the distinction between argumentative and adventitious, artificial and inartificial evidences, both in the Rhetoric to Alexander and in the Rhetoric; and that the former as well as the latter is a genuine work of Aristotle, the founder of the logic of rhetoric.

Acting on this hint, not Aristotle but the Peripatetics inferred that all logic is an instrument (6pyavov) of all sciences; and by the time of Andronicus, who was one of them and sometimes called " the eleventh from Aristotle," the order, LogicPhysics-Metaphysics, had become established pretty much as we have it now.

It is, however, not the real order for studying the philosophy of Aristotle, because there is more Metaphysics in his Physics than Physics in his Metaphysics, and more Metaphysics in his Logic than Logic in his Metaphysics.

But what has become of Logic, with which the traditional order of Andronicus begins Aristotle's works (1-148 b 8)?

So far from coming first, Logic comes nowhere in his classification of science.

Aristotle was the founder of Logic; because, though others, and especially Plato, had made occasional remarks about reason (X yos), Aristotle was the first to conceive it as a definite subject of investigation.

He got so far as gradually to write short discourses and long treatises, which we, not he, now arrange in the order of the Categories or names; the De Interpretatione on propositions; the Analytics, Prior on syllogism, Posterior on scientific syllogism; the Topics on dialectical syllogism; the Sophistici Elenchi on eristical or sophistical syllogism; and, except that he had hardly a logic of induction, he covered the ground.

It is a commentator's blunder to suppose that the founder of logic elaborated it into a system, and then applied it to the sciences.

He really left the Peripatetics to combine his scattered discourses and treatises into a system, to call it logic, and logic Organon, and to put it first as the instrument of sciences; and it was the Stoics who first called logic a science, and assigned it the first place in their triple classification of science into logic, physics, ethics.

Is logic, then, according to him, not science but dialectic ?

The list of Wundt's works is long and comprehensive, including physiology, psychology, logic and ethics.

Hsiian Tsang informs us that Dinnaga, the celebrated Buddhist philosopher and controversialist, author of well-known books on logic, resided there.

He was educated at the university of Glasgow, where he graduated first in classics, logic and philosophy.

They saw also the logic of Kant's deduction, that all we can know from such mental data and mental categories must also be mental.

Schelling himself, as soon as he saw his own formulae exposed in the logic or rather dialectic of his disciple, began to reconsider his philosophy of identity, and brought some powerful objections against both the conclusions and the method of Hegel.

Hegel, he said, had only supplied the logic of negative philosophy; and it must be confessed that the most which could be extracted from the Hegelian dialectic would be some connexion of thoughts without proving any existence of corresponding things.

Sigwart in his Logic has also opposed the parallelistic view itself; and James has criticized it from the point of view that the soul selects out of the possibilities of the brain means to its own ends.

In his logic, and especially in his epistemology, Wundt appears as a mediator between Hume and Kant, but with more leaning to the latter.

On this false abstraction Sigwart has made an excellent criticism in an appendix at the end of his Logic, where he remarks that we cannot isolate events from the substances of which they are attributes.

The conclusion that reason in transcending experience can show no more than the necessity of " ideals " is the only conclusion which could follow from Wundt's phenomenalism in psychology, logic, and epistemology.

He forgets apparently that faith is a belief in things beyond ideas and ideals, which is impossible in his psychology of judgment and logic of inference.

It was counteracted to some extent by the study at the universities of the deductive logic of Aristotle and the inductive logic of Bacon, by parts of Mill's own logic, and by the natural realism of Reid, Stewart, and Hamilton, which met Hume's scepticism by asserting a direct perception of the external world.

At the same time, while the independence of metaphysics leads us to metaphysical realism, this is not to deny the value of psychology, still less of logic. Besides the duty of determining what we know, there is the duty of determining how we know it.

Philo tells us expressly that they rejected logic as unnecessary to the acquisition of virtue, and speculation on nature as too lofty for the human intellect.

It is important as an addition to the logic of the subject rather than on account of any practical advantages which it affords for purposes of calculation.

Mill held with his System of Logic to Hartley and James Mill.

In the logic of Mill, e.g., we find much of a special character that has no counterpart in Hume, much that is introduced ab extra, from general considerations of scientific procedure, but, so far as the groundwork is concerned, the System of Logic is a mere reproduction of Hume's doctrine of knowledge.

In logic it came to be used as the translation of the Gr.

Apart from this, Hobbes owed little to his university training, which was based on the scholastic logic then prevalent.

In the course of the next seven years in Derbyshire and abroad, Hobbes took his pupil over rhetoric, 2 logic, astronomy, and the principles of law, with other subjects.

The Epicurean philosophy is traditionally divided into the three branches of logic, physics and ethics.

Ethics had been based upon logic and metaphysics.

Logic must go, but so also must the state, as a specially-privileged and eternal order of things, as anything more than a contrivance serving certain purposes of general utility.

To the Epicureans the elaborate logic of the Stoics was a superfluity.

In place of logic we find canonic, the theory of the three tests of truth and reality.

The Epicurean canon is a rejection of logic; it sticks fast to the one point that " sensation is sensation, ?

Like Hamilton, Mansel maintained the purely formal character of logic, the duality of consciousness as testifying to both self and the external world, and the limitation of knowledge to the finite and "conditioned."

He despised logic, and rejected the philosophy of nature as beyond the powers of man.

A judgment which is not prompted by motives and inspired by interest, which has not for its aim the satisfaction of a cognitive purpose, is psychologically impossible, and it is, therefore, mistaken to construct a logic which abstracts from all these facts.

The "psychologicm" thus introduced into logic amounts to a systematic protest against the notion of a dehumanized thought and the study of logic in abstraction from actual psychic process.

Besides the three main disciplines the student takes up according to his tastes other subjects, such as rhetoric (ma`ani wabayan), logic (mantiq), prosody (`arud), and the doctrine of the correct pronunciation of the Koran (gira'a watajwid).

He was educated at Glasgow and Edinburgh, where, from 1846 to 1856, he was professor of Logic at New College.

He edited the North British Review from 1850 to 1857, and in 1856, having previously been a Free Church minister, he succeeded Sir William Hamilton as professor of Logic and Metaphysics at Edinburgh University.

After a childhood spent in an austerity which stigmatized as unholy even the novels of Sir Walter Scott, he began his college career at the age of fourteen at a time when Christopher North and Dr Ritchie were lecturing on Moral Philosophy and Logic. His first philosophical advance was stimulated by Thomas Brown's Cause and Effect, which introduced him to the problems which were to occupy his thought.

In 1836 Sir William Hamilton was appointed to the chair of Logic and Metaphysics, and Fraser became his pupil.

If the five ascetics to whom the words were addressed once admitted this implication, logic would drive them also to admit all that followed.

He published a work on logic (Vernunftlehre als Anweisung zum richtigen Gebrauche der Vernunft, 1756, 5th ed., 1790), and two popular books on the religious questions of the day.

For admission to the baccalaureate a preliminary test or " Responsions " was first required, at which the candidate had to dispute in grammar or logic with a master.

The nature of axiomatic certainty is part of the fundamental problem of logic and metaphysics.

In a MS. of 102 quarto sheets, of which the first three and the seventh are wanting, there is preserved the original sketch of the Hegelian system, so far as the logic and metaphysics and part of the philosophy of nature are concerned.

Hegel's lectures, in the winter of 1801-1802, on logic and metaphysics were attended by about eleven students.

Those on Aesthetics, on the Philosophy of Religion, on the Philosophy of History and on the History of Philosophy, have been published by his editors, mainly from the notes of his students, under their separate heads; while those on logic, psychology and the philosophy of nature are appended in the form of illustrative and explanatory notes to the sections of his Encykloptidie.

Hegel and his family retired for the summer to the suburbs, and there he finished the revision of the first part of his Science of Logic. On the beginning of the winter session, however, he returned to his house in the Kupfergraben.

The Phenomenology is neither mere psychology, nor logic, nor moral philosophy, nor history, but is all of these and a great deal more.

Reason abandons her efforts to mould the world, and is content to let the aims of individuals work out their results independently, only stepping in to lay down precepts for the cases where individual actions conflict, and to test these precepts by the rules of formal logic.

Accordingly the history of philosophy is the presupposition of logic, or the three branches of philosophy form a circle.

The exposition or constitution of the " idea " is the work of the Logic. As the total system falls into three parts, so every part of the system follows the triadic law.

They rejected as an illegitimate interpolation the eternal subject of development, and, instead of one continuing God as the subject of all the predicates by which in the logic the absolute is defined, assumed only a series of ideas, products of philosophic activity.

Thought became only the result of organic conditions - subjective and human; and the system of Hegel was no longer an idealization of religion, but a naturalistic theory with a prominent and peculiar logic.

The logic of Hegel is the only rival to the logic of Aristotle.

His logic is an enumeration of the forms or categories by which our experience exists.

The fact which ordinary thought ignores, and of which ordinary logic therefore provides no account, is the presence of gradation and continuity in the world.

The beginning of the logic is an illustration of this.

The third part of logic evidently is what contains the topics usually treated in logic-books, though even here the province of logic in the ordinary sense is exceeded.

The first two divisions - the " objective logic " - are what is usually called metaphysics.

The merit of Hegel is to have indicated and to a large extent displayed the filiation and mutual limitation of our forms of thought; to have arranged them in the order of their comparative capacity to give a satisfactory expression to truth in the totality of its relations; and to have broken down the partition which in Kant separated the formal logic from the transcendental analytic, as well as the general disruption between logic and metaphysic. It must at the same time be admitted that much of the work of weaving the terms of thought, the categories, into a system has a hypothetical and tentative character, and that Hegel has rather pointed out the path which logic must follow, viz.

In trying to subject history to the order of logic they sometimes misconceive the filiation of ideas.

Complete or perfect knowledge is confined to the domain of pure thought, to logic and mathematics.

From 1801 to 1804 he was professor of philosophy at Frankfort-on-the-Oder, after which he succeeded Kant in the chair of logic and metaphysics at the university of Konigsberg.

When the Bourbons were restored, his hatred against Napoleon led him to become a Legitimist - a conclusion which says more for the simplicity of his character than for the strength or logic of his political creed.

Now skill in disputation is plainly a valuable accomplishment; and, as the Aristotelian logic grew out of the regulated discussions of the eristics and their pupils, the disputant sophistry of the 4th century deserves more attention and.

He is an earnest, sometimes stern and sometimes pathetic, preacher of righteousness, who despises the mere graces of style and the subtleties of an abstruse logic. He has no patience with mere antiquarian study of the Stoical writers.

He took a keen interest in all the work of the college, presented to it the Marmor Homericum, and finally bequeathed the reversion of £6000 for the endowment of a chair of philosophy of mind and logic. The emoluments of this sum were, however, to be held over and added to the principal if at any time the holder of the chair should be "a minister of the Church of England or of any other religious persuasion."

The present article is divided into The Problems of Logic, History.

This science of inference in general is logic.

Logic, however, did not begin as a science of all inference.

In this way the Presocratics and Sophists, and still more Socrates and Plato, threw out hints on sense and reason, on inferential processes and scientific methods which may be called anticipations of logic. But Aristotle was the first to conceive of reasoning itself as a definite subject of a special science, which he called analytics or analytic science, specially designed to analyse syllogism and especially demonstrative syllogism, or science, and to be in fact a science of sciences.

He was therefore the founder of the science of logic.

Hence, without his saying it in so many words, Aristotle's logic perforce became a logic of deductive reasoning, or syllogism.

As it happened this deductive tendency helped the development of logic. The obscurer premises of analogy and induction, together with the paucity of experience and the backward state of physical science in Aristotle's time would have baffled even his analytical genius.

As then the reasoning of the syllogism was the main problem of Aristotle's logic, what was his analysis of it?

The explanation is that outer speech is more obvious than inner thought, and that grammar and poetic criticism, rhetoric and dialectic preceded logic, and that out of those arts of language arose the science of reasoning.

All these points about speech, eloquence and argument between man and man were absorbed into Aristotle's theory of reasoning, and in particular the grammar of the sentence consisting of noun and verb caused the logic of the proposition consisting of subject and predicate.

Aristotle thus was the founder of logic as a science.

But he laid too much stress on reasoning as syllogism or deduction, and on deductive science; and he laid too much stress on the linguistic analysis of rational discourse into proposition and terms. These two defects remain ingrained in technical logic to this day.

Some have devoted themselves to induction from sense and experience and widened logic till it has become a general science of inference and scientific method.

Others have devoted themselves to the mental analysis of reasoning, and have narrowed logic into a science of conception, judgment and reasoning.

The former belong to the school of empirical logic, the latter to the school of conceptual and formal logic. Both have started from points which Aristotle indicated without developing them.

This empirical groundwork of Aristotle's logic was accepted by the Epicureans, who enunciated most distinctly the fundamental doctrine that all sensations are true of their immediate objects, and falsity begins with subsequent opinions, or what the moderns call " interpretation."

It remained for Francis Bacon to develop these beginnings into a new logic of induction.

Bacon, like Aristotle, was anticipated in this or that point; but, as Aristotle was the first to construct a system of deduction in the syllogism and its three figures, so Bacon was the first to construct a system of induction in three ministrations, in which the requisites of induction, hitherto recognized only in sporadic hints, were combined for the first time in one logic of induction.

In short, the comprehensive genius of Bacon widened logic into a general science of inference.

Mill in his Logic pointed out this defect, and without departing from Baconian principles remedied it by quoting scientific examples, in which deduction, starting from inductive principles, applies more general to less general universals, e.g.

Mill's logic has the great merit of copiously exemplifying the principles of the variety of method according to subject-matter.

The founder of logic anticipated the latest logic of science, when he recognized, not only the deduction of mathematics, but also the experience of facts followed by deductive explanations of their causes in physics.

The deepest problem of logic is the relation of sense and inference.

But we must first consider the mental analysis of inference, and this brings us to conceptual and formal logic.

Aristotle's logic has often been called formal logic; it was really a technical logic of syllogism analysed into linguistic elements, and of science rested on an empirical basis.

The history of logic shows that the linguistic distinction between terms and propositions was the sole analysis of reasoning in the logical treatises of Aristotle; that the mental distinction between conceptions (g vvocac) and judgments (a uiwara in a wide sense) was imported into logic by the Stoics; and that this mental distinction became the logical analysis of reasoning under the authority of St Thomas Aquinas.

Hence arose conceptual logic; according to which conception is a simple apprehension of an idea without belief in being or not being, e.g.

But at length many of them became formal logicians, who held that logic is the investigation of formal thinking, or consistent conception, judgment and reasoning; that it shows how we infer formal truths of consistency without material truth of signifying things; that, as the science of the form or process, it must entirely abstract from the matter, or objects, of thought; and that it does not tell us how we infer from experience.

Thus has logic drifted further and further from the real and empirical logic of Aristotle the founder and Bacon the reformer of the science.

The great merit of conceptual logic was the demand for a mental analysis of mental reasoning, and the direct analysis of reasoning into judgments which are the sole premises and conclusions of reasoning and of all mental inferences.

The Schoolmen, however, gradually came to realize that the result to their logic was to make it a sermocionalis scientia, and to their metaphysics the danger of nominalism.

St Thomas made a great advance by making logic throughout a rationalis scientia; and logicians are now agreed that reasoning consists of judgments, discourse of propositions.

This distinction is, moreover, vital to the whole logic of inference, because we always think all the judgments of which our inference consists, but seldom state all the propositions by which it is expressed.

The conceptual logic supposes that conception always precedes judgment; but the truth is that sensory judgment begins and inferential judgment ends by preceding conception.

The conceptual logic has made the mistake of making ideation a stage in thought prior to judgment.

It was natural enough that the originators of conceptual logic, seeing that judgments can be expressed by propositions, and conceptions by terms, should fall into the error of supposing that, as propositions consist of terms, so judgments consist of conceptions, and that there is a triple mental order - conception, judgment, reasoning - parallel to the triple linguistic order - term, proposition, discourse.

Empirical logic, the logic of Aristotle and Bacon, is on the right way.

Conceptual logic, on the other hand, is false from the start.

It is not the first business of logic to direct us how to form conceptions signified by terms, because sense is a prior cause of judgment and inference.

It is not the second business of logic to direct us how out of conceptions to form judgments signified by propositions, because the real causes of judgments are sense, memory, experience and inference.

It is, however, the main business of logic to direct us how out of judgments to form inferences signified by discourse; and this is the one point which conceptual logic has contributed to the science of inference.

Formal logic has arisen out of the narrowness of conceptual logic. The science of inference no doubt has to deal primarily with formal truth or the consistency of premises and conclusion.

The question of logic is how we infer in fact, as well as perfectly; and we cannot understand inference unless we consider inferences of probability of all kinds.

Lastly, the science of inference is not indeed the science of sensation, memory and experience, but at the same time it is the science of using those mental operations as data of inference; and, if logic does not show how analogical and inductive inferences directly, and deductive inferences indirectly, arise from experience, it becomes a science of mere thinking without knowledge.

Logic is related to all the sciences, because it considers the common inferences and varying methods used in investigating different subjects.

Logic is the science of the processes of inference.

The real point is their interdependence, which is so intimate that one sign of great philosophy is a consistent metaphysics, psychology and logic. If the world of things is known to be partly material and partly mental, then the mind must have powers of sense and inference enabling it to know these things, and there must be processes of inference carrying us from and beyond the sensible to the insensible world of matter and mind.

It is clear then that a man's metaphysics and psychology must colour his logic. It is accordingly necessary to the logician to know beforehand the general distinctions and principles of things in metaphysics, and the mental operations of sense, conception, memory and experience in psychology, so as to discover the processes of inference from experience about things in logic.

Hegel, having identified being with thought, merged metaphysics in logic. But he divided logic into objective and subjective, and thus practically confessed that there is one science of the objects and another of the pro cesses of thought.

Psychologists, seeing that inference is a mental operation, often extemporize a theory of inference to the neglect of logic. But we have a double consciousness of inference.

This elaborate consciousness of inferential process is the justification of logic as a distinct science, and is the first step in its method.

But it is not the whole method of logic, which also and rightly considers the mental process necessary to language, without substituting linguistic for mental distinctions.

Logic has to consider the things we know, the minds by which we know them from sense, memory and experience to inference, and the sciences which systematize and extend our knowledge of things; and having considered these facts, the logician must make such a science of inference as will explain the power and the poverty of human knowledge.

General Tendencies Of Modern Logic There are several grounds for hope in the logic of our day.

It does not, with the former, regard logic as purely formal in the sense of abstracting thought from being, nor does it follow the latter in amalgamating metaphysics with logic by identifying being with thought.

That is, logic is grounded by them, not upon an effete tradition but upon a new investigation of thought as it actually is in its psychological foundations, in its significance for knowledge, and its actual operation in scientific methods."

Wundt's comprehensive view that logic looks backwards to psychology and forward to epistemology was hundreds of years ago one of the many discoveries of Aristotle.

Sense is the evidence of inference; directly of analogical and inductive, directly or indirectly of deductive, inference; and therefore, if logic refuses to include sensory beliefs among judgments, it will omit the fundamental constituents of inference, inference will no longer consist of judgments but of sensory beliefs plus judgments, and the second part of logic, the logic of judgment, the purpose of which is to investigate the constituents of inference, will be like Hamlet without the prince of Denmark.

The sensory judgment then, which is nothing but a belief that at the moment of sense something sensible exists, is a proof that not all judgment requires conception, or synthesis or analysis of ideas, or decision about the content, or about the validity, of ideas, or reference of an ideal content to reality, as commonly, though variously, supposed in the logic of our day.

Starting, then, from this fundamental distinction between judgments of existence and judgments of non-existence, we may hope to steer our way between two extreme views which emanate from two important thinkers, each of whom has produced a flourishing school of psychological logic.

Here, as usual in logic, tradition is better than innovation.

Here Sir William Hamilton did a real service to logic in pointing out that " Logic postulates to be allowed to state explicitly in language all that is implicitly contained in the thought."

In ordinary life we may say, " All men are mortal," " All centaurs are figments," " All square circles are impossibilities," " All candidates arriving five minutes late are fined " (the last proposition being an example of the identification of categorical with hypothetical in Keynes's Formal Logic).

The symbolic logic, which confuses " is " with " is equal to," having introduced a particular kind of predicate into the copula, falls into the mistake of reducing all predication to the one category of the quantitative; whereas it is more often in the substantial, e.g.

Finally, the great difficulty of the logic of judgment is to find the mental act behind the linguistic expression, to ascribe to it exactly what is thought, neither more nor less, and to apply the judgment thought to the logical proposition, without expecting to find it in ordinary propositions.

Beneath Hamilton's postulate there is a deeper principle of logic - _A rational being thinks only to the point, and speaks only to understand and be understood.

Quasi-syllogisms. - Besides reconstructions of the syllogistic fabric, we find in recent logic attempts to extend the figures of the syllogism beyond the syllogistic rules.

No distinction is more vital in the logic of inference in general and of scientific inference in particular; and yet none has been so little understood, because, though analysis is the more usual order of discovery, synthesis is that of instruction, and therefore, by becoming more familiar, tends to replace and obscure the previous analysis.

Recent logic does scant justice to scientific analysis.

Since Mill's time, however, the logic of induction tends to revert towards syllogisms more like that of Aristotle.

Nevertheless, simple as this account appears, it is opposed in every point to recent logic. In the first place, the point of Bradley's logic is that " similarity is not a principle which works.

The basis of Bradley's logic is the fallacious dialectic of Hegel's metaphysics, founded on the supposition that two things, which are different, but have something in common, are the same.

Hence also induction is a real process, because, when we know that this individual magnet attracts iron, we are very far from knowing that all alike do so similarly; and the question of inductive logic, how we get from some similars to all similars, remains, as before, a difficulty, but not to be solved by the fallacy that inference is identification.

Secondly, a subordinate point in Bradley's logic is that there are inferences which are not syllogisms; and this is true.

But it is often thought without being expressed, and to judge the syllogism by its mere explicit expression is to commit an ignoratio elenchi; for it has been known all along that we express less than we think, and the very purpose of syllogistic logic is to analyse the whole thought necessary to the conclusion.

Logic cannot, it is true, decide what these things are, nor what the senses know about them, without appealing to metaphysics and psychology.

Logic is the science of all inference, beginning from sense and ending in reason.

The logic of the last quarter of the 19th century may be said to be animated by a spirit of inquiry, marred by a love of paradox and a corresponding hatred of tradition.

Green, Lectures on Logic, in Works, vol.

History Logic cannot dispense with the light afforded by its history so long as counter-solutions of the same fundamental problems continue to hold the field.

Logic arose, at least for the Western world, in the golden age of Greek speculation which culminated in Plato and Aristotle.

There is an Indian logic, it is true, but its priority is more than disputable.

The movement which ends in the logic of Aristotle is demonstrably self-contained.

It is with Aristotle that the bookish tradition begins to dominate the evolution of logic. The technical perfection of the analysis which he offers is, granted the circle of presuppositions within which it works, so decisive, that what precedes, even Plato's logic, is not unnaturally regarded as merely preliminary and subsidiary to it.

Before Aristotle Logic needs as its presuppositions that thought should distinguish itself from things and from sense, that the problem of validity should be seen to be raised in the field of thought itself, and that analysis of the structure of physical thought should be recognized as the one way of solution.

Its so-called natural logic is only the potentiality of logic. The same thing is true of the first stage of Greek philosophy.

In seeking for a single material principle underlying the multiplicity of phenomena, the first nature-philosophers, Thales and the rest, did indeed raise the problem of the one and the many, the endeavour to answer which must at last lead to logic. But it is only from a point of view won by later speculation that it can be said that they sought to determine the predicates of the single subject-reality, or to establish the permanent subject of varied and varying predicates.'

The sophists have other claims to consideration than their service to the development of logic. In the history of the origins of logic the sophistic age is simply the age of the free play of thought in which men were aware that in a sense anything can be debated and not yet aware of the sense in which all things cannot be so.

The sophists furthered the transition from dialectic to logic in two ways.

The result is a selflimiting dialectic. This higher dialectic is a logic. It is no accident that the first of the philosophical sophists, Gorgias, on the one hand, is Eleatic in his affinities, and on the other raises in the characteristic formula of his intellectual nihilism' issues which are as much logical and epistemological as ontological.

Between Euclides and Antisthenes the Socratic induction and universal definition were alike discredited from the point of view of the Eleatic logic. It is with the other point of doctrine that Plato comes to grips, that which allows of a certainty or knowledge consisting in an analysis of a compound into simple elements themselves not known.

If we add to this logic of " idea," judgment and inference, a doctrine of categories in the modern sense of the word which makes the Theaetetus, in which it first occurs, a forerunner of Kant's Critique of Pure Reason, we have clearly a very significant contribution to logic even in technical regard.

This is not only of importance in the history of the terminology of logic, but supplies a philosophy of induction.

For Plato's logic this question only has interest on account of the introduction of an 'AptoToTO?

Its axioms, such as the law of contradiction, belong to first philosophy, but the doctrine as a whole falls neither under 'this head nor yet, though the thought has been entertained, under that of mathematics, since logic orders mathematical reasoning as well as all other.

Logic, therefore, is not classed as one, still less as a branch of one, among the 'ologies, ontology not excepted.

The Prior A T h e Analytics then are concerned with a formal logic to niytics.

What then is meant by principles when we ask in the closing chapter of his logic how they become known ?

Enough has been said to justify the great place assigned to Aristotle in the history of logic. Without pressing metaphysical formulae in logic proper, he analysed formal;implica tion, grounded implication as a mode of knowledge Summary.

To return to logic proper.

The Aristotelian theory of the universal of science as secure from dependence on its instances and the theory of linking in syllogism remain a heritage for all later logic, whether accepted in precisely Aristotle's formula or no.

Later Greek Logic. After Aristotle we have, as regards logic, what the verdict of after times has rightly characterized as an age of Epigoni.

Logic is their word, and consciousness, impression and other technical words come to us, at least as technical words, from Roman Stoicism.

In Epicureanism logic is still less in honour.

Yet, in falling back, with a difference, upon the atomism of Democritus, Epicurus had to face some questions of logic. In the inference from phenomena to further phenomena positive verification must be insisted on.

Some reading between the lines of Lucretius has led the " logic " of Epicurus to have an effect on the modern world, but scarcely because of its deserts.

Logic and theory of knowledge go together, and without living science, theory of knowledge loses touch with life, and logic becomes a perfunctory thing.

In the history of logic it is of importance because of its production of a whole series of commentators on the Aristotelian logic. Not only the Introduction of Porphyry, which had lasting effects on the Scholastic tradition, but the commentaries of Themistius, and Simplicius.

It was the acceptance of the Aristotelian logic by Neoplatonism that determined the Aristotelian complexion of the logic of the next age.

Neoplatonism had accepted the Aristotelian logic with its sharper definition than anything handed down from Plato, and, except the logic of the Sceptics, there was no longer any rival discipline of the like prestige.

The logic of the Stoics had been discredited by the sceptical onset, but in any case there was no organon of a fitness even comparable to Aristotle's for the task of drawing out the implications of dogmatic premises.

Aristotelian logic secured the imprimatur of the revived Platonism, and it was primarily because of this that it passed into the service of Christian theology.

Orthodoxy needed to counter heretical logic not with mysticism, itself the fruitful mother of heresies, but with argument.

There is no place for a reformed Aristotelian logic, though the genius of Zabarella was there to attempt it.

The transformation of logic lay with the man of science, hindered though he might be by the enthusiasm of some of the philosophers of nature.

Henceforth the Aristotelian logic, the genuine no less than the traditional, was to lie on the other side of the Copernican change.

The reformed Aristotelian logic of the first-named with its inductio demonstrativa, the mathematicophysical analysis followed by synthesis of the second, the exclusiva, or method of exclusions of the last, agree at least in this, that the method of science is one and indivisible, while containing both an inductive and a deductive moment.

Yet he offers an ambitious logic of science, and the case is typical.

He calls for a logic of discovery.

In his doctrine of forms, too, the " universals " of his logic, Bacon must at least be held to have been on a path which led forward and not back.

Bacon's Logic, then, like Galilei's, intended as a contribution to scientific method, a systematization of discovery by which, given the fact of knowledge, new items of knowledge may be acquired, failed to convince contemporaries and successors alike of its efficiency as an instrument.

The Logic of Empiricism The path followed by English thought was a different one.

With Hobbes logic is a calculus of marks and signs in the form of names.

Finally Mill took from him his definition of cause as sum of conditions,9 which played no small part in the applied logic of the 19th century.

Apart from the adoption by Hume of the association of ideas as the explanatory formula of the school - it had been allowed by Malebranche within the framework of his mysticism and employed by Berkeley in his theory of vision - there are few fresh notes struck in the logic of sensationalism.

What, however, Hume describes as " all the logic I think proper to employ in my reasoning," viz.

Stuart Mill's System of Logic marked a fresh stage in the history of empiricism, for the reason that it made the effort to hold an even balance between the two moments in the thought of the school.

In the field covered by scholastic logic Mill is frankly associationist.

In Mill's inductive logic, the nominalistic convention has, through his tendency to think in relatively watertight compartment,s, 2 faded somewhat into the background.

It is because of the failure of this endeavour to bring the technique of induction within the setting of his Humian psychology of belief that the separation of his contribution to the applied logic of science from his sensationism became necessary, as it happily 1 Mill, Examination of Sir William Hamilton's Philosophy, cap. 17.

It is deservedly, nevertheless, that Mill's applied logic has retained its pride of place amid what has been handed on, if in modified shape, by writers, e.g., Sigwart, and Professor Bosanquet, whose theory of knowledge is quite alien from his.

In the history of logic the latter thinker is of the more importance.

Grounds for a variety of developments are to be found in the imperfect harmonization of the rationalistic heritage from the Wolffian tradition which still dominates Kant's pure general logic with the manifest epistemological intention of his transcendental theory.

Kant's treatment of technical logic was wholly traditional, and in itself is almost negligible.

Logic was of necessity formal, dealing as it must with those rules without which no exercise of the understanding would be possible at all.

Applied logic is merely psychology, and not properly to be called logic at all.

Unless the doctrine of Kant's " transcendental logic " must be held to supply a point of view from which a logical development of quite another kind is inevitable, Kant's mantle, so far as logic is concerned, must be regarded as having fallen upon the formal logicians.

Such a logic, however, is a dialectic of illusion, perplexed by paralogisms and helpless in the face of antinomies.

The reserve, therefore, that it was abstraction and not a decomposing that was in question remained to the admirers of his logic quite nugatory.

They passed easily from the acceptance of a priori forms of thinking to that of forms of a priori thinking, and could plead the example of Kant's logic.

Kant's theory of knowledge, then, needed to be pressed to other consequences for logic which were more consonant with the spirit of the Critique.

The determination too of the sense in which Kant's theory of knowledge involves an unresolved antithesis is for the logical purpose necessary so far only as it throws light upon his logic and his influence upon logical developments.

Along this line of speculation we have a logic which claims that whatsoever is in one plane or at one stage in the development of thought a residuum that apparently defies analysis must at another stage and on a higher plane be shown so to be absorbed as to fall altogether within thought.

This is the view of Hegel upon which logic comes to coincide with the progressive self-unfolding of thought in that type of metaphysic which is known as absolute, i.e.

The exponent of logic as metaphysic, for whom the rational is the real is necessarily in revolt against all that is characteristically Kantian in the theory of knowledge, against the transcendental method itself and against the doctrine of limits which constitutes the nerve of " criticism."

Finally, to logic as metaphysic the polar antithesis is psychology as logic. The turn of this also was to come again.

If logic were treated as merely formal, the stress of the problem of knowledge fell upon the determination of the Log and processes of thepsychological mechanism.

If alleged Psycho- P g Logy.ic a priori constituents of knowledge - such rubrics as substance, property, relation - come to be explained psychologically, the formal logic that has perforce to ignore all that belongs to psychology is confined within too narrow a range to be able to maintain its place as an independent discipline, and tends to be merged in psychology.

It is of course a newer type of psychological logic that is in question, one that is aware of Kant's " answer to Hume."

Kant's influence, then, upon subsequent logic is least of all to be measured by his achievement in his professed contribution.

They are confined to the determination of what the truth of any matter of thought, taken for granted upon grounds psychological or other, which are extraneous to logic, includes or excludes.

The unit for logic is the concept taken for granted.