Logic Sentence Examples

logic
  • Her logic and her sympathy are in excellent balance.

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

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

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

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

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

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  • He always tried to govern his thinking by logic.

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

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

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

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

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

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

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

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  • His inductive logic must "supplement and not supersede."

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

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

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

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

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  • We have seen, for example, that he was led to investigate the subject of logic because he found in attempting to advance his humanitarian schemes in politics an absence of that fundamental agreement which he recognized as the basis of scientific advance.

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

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  • 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.

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

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

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  • 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.

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  • 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.

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  • 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.

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  • 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.

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  • 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.

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  • 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.

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  • 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.

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  • 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.

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  • 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).

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  • 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.

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  • 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.

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  • 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.

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  • 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.

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

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  • 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.

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

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  • 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.

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  • 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.

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  • 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.

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  • 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.

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  • 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.

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  • 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.

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

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  • 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.

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  • 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.

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  • 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.

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

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  • 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.

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  • 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.

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  • 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.

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  • 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.

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  • 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.

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

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  • 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.

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  • 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.

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  • 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.

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  • 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.

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

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  • 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."

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  • 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.

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  • 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.

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  • 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).

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

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  • 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.

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  • See the modern logic textbooks.

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  • 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.

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  • 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.

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  • 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.

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  • 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."

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  • 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.

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

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  • 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).

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  • 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.

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  • 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.

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

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

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

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

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

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  • 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.

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  • 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.

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  • 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.

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  • 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.

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  • 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 ?

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  • 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.

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  • 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.

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  • 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.

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  • 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.

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  • 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.

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  • 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.

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  • 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.

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  • 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.

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

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

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  • 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.

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  • 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.

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  • 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.

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  • 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.

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

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

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

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

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  • 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.

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  • 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.

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  • 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.

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  • 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.

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

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  • 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.

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  • 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.

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  • 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.

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  • 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.

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  • 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.

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  • 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.

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  • 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.

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

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  • 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.

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

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

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  • 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.

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

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  • Ethics had been based upon logic and metaphysics.

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  • 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.

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

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

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

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  • 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."

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

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  • 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.

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  • 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.

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  • 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).

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

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  • 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.

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  • 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.

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

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

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  • 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.

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  • 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.

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

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  • 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.

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

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  • 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.

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  • 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.

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

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  • 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.

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

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  • 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.

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  • 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.

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  • 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.

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

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

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  • 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.

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  • The beginning of the logic is an illustration of this.

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  • 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.

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

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  • 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.

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

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

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  • 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.

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  • 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.

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  • 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.

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  • 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.

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  • 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."

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

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  • This science of inference in general is logic.

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

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  • 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.

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  • He was therefore the founder of the science of logic.

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

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  • 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.

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

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  • 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.

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  • 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.

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  • Aristotle thus was the founder of logic as a science.

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  • 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.

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  • 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.

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

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  • 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.

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  • 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."

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

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  • 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.

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

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  • 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.

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

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  • 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.

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

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

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  • 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.

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  • 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.

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

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  • 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.

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

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  • 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.

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  • 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.

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  • 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.

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  • 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.

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

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

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  • 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.

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

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

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  • 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.

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  • 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.

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  • 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.

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  • 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.

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  • 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.

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  • 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.

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

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  • Logic is the science of the processes of inference.

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  • 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.

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  • 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.

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  • 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.

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  • 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.

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

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  • 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.

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  • 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.

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

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  • 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.

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  • 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."

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  • 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.

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  • 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.

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  • 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.

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  • 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.

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

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  • 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."

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  • 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).

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  • 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.

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  • 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.

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  • 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.

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  • 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.

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  • 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.

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  • Recent logic does scant justice to scientific analysis.

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

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  • 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.

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  • 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.

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  • 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.

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

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  • 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.

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

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

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  • 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.

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  • Green, Lectures on Logic, in Works, vol.

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  • 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.

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

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

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

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  • 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.

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  • 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.

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

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  • 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.'

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  • 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.

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

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  • 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.

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  • 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.

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  • 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.

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

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

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  • 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.

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

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

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

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  • 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.

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  • To return to logic proper.

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  • 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.

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

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

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  • In Epicureanism logic is still less in honour.

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  • 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.

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  • 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.

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

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  • 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.

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

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  • 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.

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  • 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.

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  • 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.

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

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

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  • 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.

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

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  • 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.

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

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  • He calls for a logic of discovery.

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  • 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.

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  • 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.

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

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

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  • 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.

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  • 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.

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

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  • 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.

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

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  • 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.

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  • 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.

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  • 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.

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

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  • 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.

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

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

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

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  • 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.

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

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

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  • 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.

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  • 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.

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  • 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.

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  • 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.

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  • 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.

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  • 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."

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

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  • 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.

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  • 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.

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

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

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  • 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.

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  • The unit for logic is the concept taken for granted.

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  • The function of logic is to exhibit its formal implications and repulsions.

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  • As the living organism includes something of mechanism - the skeleton, for example - so an organic logic doubtless includes determinations of formal consistency.

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  • What was true in formal logic tended to be absorbed in the correlationist theories.

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  • His general theory of knowledge deriving from Kant and Reid, and including among other things a contaminatio of their theories of perception, 3 in no way sustains or mitigates his narrow view of logic. He makes no effective use of his general formula that to think is to condition.

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  • Hamilton's significance for the history of logic lies in the stimulus that he gave to the development of symbolic logic in England by his new analytic based upon his discovery or adoption of the principle of the quantification of the predicate.

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  • Formal logic of the extremest rigour is nowhere to be found more adequately expressed in all its strength, and it must be added in all its weakness, than in the writings of Mansel.

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  • The brief logic of Herbart 4 is altogether formal too.

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  • The first task of logic is to distinguish and group such concepts according to their marks, and from their classification there naturally follows their connexion in judgment.

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  • It is in the logic of judgment that Herbart inaugurates a new era.

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  • That is a thought which lies very near the surface for formal logic. He had been preceded too by Maimon in the attempt at a reduction of the traditional types of judgment.

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  • That it was the formal character of Herbart's logic which was ultimately fatal to its acceptance outside the school as an independent discipline is not to be doubted.

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  • It stands, however, on a different footing from that of the formal logic hitherto discussed, and is not to be condemned upon quite the same grounds.

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  • In the second, there is no claim that thought at one and the same time imposes form on " the given " and is susceptible of treatment in isolation by logic. With Herbart the forms of common experience, and indeed all that we can regard as his categories, are products of the psychological mechanism and destitute of logical import.

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  • It is for this reason that it finally lacks real affinity to the " pure logic " of Fries.

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  • It was in the pressing to its extreme consequences of the conception of uncompromising identity which is to be found in Leibnitz, that the contradictions took their rise which Herbart aimed at solving, by the method of relations and his doctrine of the ultimate plurality of " reals," The logic of relations between conceptual units, themselves unaltered by the relation, seems a kind of reflection of his metaphysical method.

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  • To those, of course, for whom the only real identity is identity in difference, while identity without difference, like difference without identity, is simply a limit or a vanishing point, Herbart's logic and metaphysic will alike lack plausibility.

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  • The setting of Herbart's logic in his thought as a whole might of itself perhaps justify separate treatment.

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  • His far-reaching influence in the development of later logic must certainly do so.

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  • In less direct relation stands Lotze, who, although under other influences he developed a different view even in logic, certainly let no point in the doctrine of his great predecessor at Gottingen escape him.

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  • Nor did he affect the logic of his successors through his logic alone.

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  • Reference has been made above to the effect upon the rise of the later psychological logic produced by Herbart's psychology of apperception, when disengaged from the background of his metaphysic taken in conjunction with his treatment in his practical philosophy of the judgment of value or what he calls the aesthetic judgment.

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  • Moreover, few of the writers who, whatsoever it was that they baptized with the name of logic, were at least earnestly engaged in an endeavour to solve the problem of knowledge within a circle of ideas which was on the whole Kantian, were under the dominance of a single inspiration.

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  • Accordingly, though he regards logic as formal, its forms come into relation to objectivity in some sort even within the logical field itself, while when taken in the setting of his system as a whole, its formal character is not of a kind that ultimately excludes psychological and metaphysical reference, at least speculatively.

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  • In Lotze's pure logic it is the Herbartian element that tends to be disconcerting.

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  • Logic is formal.

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  • The concept is accounted for in Kantian terms. There is no discontinuity between the pre-logical or sub-logical ' See Ueberweg, System of Logic and History of Logical Doctrines, § 34.

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  • The Book on Pure Logic follows in essentials the line of thought of an earlier work (3843).

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  • It is evident that thought, even as dealt with in pure logic, has an objectifying function.

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  • The formal conception of pure logic, then, is modified by Lotze in such a way as not only to be compatible with a view of the structural and functional adequacy of thought to that which at every point at which we take thinking is still distinguishable from thought, but even inevitably to suggest it.

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  • That the unit for logic is the concept and not the judgment has proved a stumblingblock to those of Lotze's critics who are accustomed to think in terms of the act of thought as unit.

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  • He starts, that is in logic, with conceptual units apparently self-contained and admitting of nothing but external relation, but proceeds to justify the intrinsic relation between the matter of his units by an appeal to the fact of the coherence of all contents of thought.

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  • Lotze's logic then, is formal in a sense in which a logic which does not find the conception of synthetic truth embarrassing is not so.

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  • Our task is not to realise correspondence with something other than thought, Logic, Eng.

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  • Logic as post-Kantian period by antagonism to the speculative movement which culminated in the dialectic of Hegel.

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  • Fichte cannot be said to have developed a logic, but this rhythm of thesis, antithesis and synthesis, foreshadowed in part for Fichte in Spinoza's formula, " omnis determinatio est negatio," and significantly in Kant's triadic grouping of his categories, gave a cue to the thought of Hegel.

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  • Schelling, too, called for a single principle and claimed to have found it in his Absolute, " the night " said Hegel, "in which all cows are black," but his historical influence lay, as we have seen, in the direction of a parallelism within the unity, and he also developed no logic. It is altogether otherwise with Hegel.

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  • Hegel's logic, 3 though it involves inquiries which custom regards as metaphysical, is not to be characterized as a meta.

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  • It is logic or a rationale of thought by thought, with a full development among other matters of all that the most separatist of logicians regards as thought forms. It offers a solution of what has throughout appeared as the logical problem.

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  • Erdmann, is at least a logic. Thought in its progressive unfolding, of which the history of philosophy taken in its broad outline offers a pageant, necessarily cannot find anything external to or alien from itself, though that there is something external for it is another matter.

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  • Bare or indeterminate being, for instance, the first of the determinations of Hegel's logic, as the being of that which is not anything determinate, of Kant's thing-in-itself, for example, positively understood, implicated at once the notion of not-being, which negates it, and is one with it, yet with a difference, so that we have the transition to determinate being, the transition being baptized as becoming.

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  • In truth the Hegelian logic suffers from the fact that the good to be reached is presupposed in the beginning.

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  • At Westminster school he obtained a reputation for Greek and Latin verse writing; and he was only thirteen when he was matriculated at Queen's College, Oxford, where his most important acquisition seems to have been a thorough acquaintance with Sanderson's logic. He became a B.A.

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  • How little this criticism was justified may be seen from the fact that Mill's inductive logic was the direct result of his aspirations after political stability as determined by the dominion of the wisest (Examiner letters).

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  • The Logic was published in 1843.

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  • See further LOGIC (Historical Sketch); PSYCHOLOGY; ASSOCIATION OF IDEAS.

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  • In 1866 the chair of the philosophy of mind and logic in University College, London, fell vacant, and Martineau became a candidate.

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  • It is a " theosophical logic."

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  • Lotze's logic then represents the statical aspect of the function of thought in knowledge, while, so far as we go in knowledge thought is always engaged in the unification of a manifold, which remains contradistinguished from it, though not, of course, completely alien to and unadapted to it.

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  • The further step to the determination of the ground of harmony is not to be taken in logic, where limits are present and untranscended.

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  • The position of the search for truth, for which knowledge is a growing organism in which thought needs, so to speak, to feed on something other than itself, is conditioned in the view of logic wholly metaphysical.

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  • Hegel's logic as a whole, however, stands and falls not with his thoughts on syllogism, but with the claim made for the dialectical method that it exhibits logic in its integral unity with metaphysic, the thought-process as the self-revelation of the Idea.

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  • In the Hegelian school in the narrower sense the logic of the master receives some exegesis and defence upon single points of doctrine rather than as a whole.

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  • Its effect upon logic is rather to be seen in the rethinking of the traditional body of logical doctrine in the light of an absolute presupposed as ideal, with the postulate that a regulative ideal must ultimately exhibit itself as constitutive, the justification of the postulate being held to lie in the coherence and all-inclusiveness of the result.

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  • In such a logic, if and so far as coherence should be attained, would be found something akin to the spirit of what Hegel achieves, though doubtless alien to the letter of what it is his pretension to have achieved.

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  • There is perhaps no serious misrepresentation involved in regarding a key-thought of this type, though not necessarily expressed in those verbal forms, as pervading such logic of the present as coheres with a philosophy of the absolute conceived from a point of view that is intellectualist throughout.

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  • Logic from1880-1910Logic in the present exhibits, though in characteristically modified shapes, all the main types that have been found in its past history.

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  • There is an intellectualist logic coalescent with an absolutist metaphysic as aforesaid.

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  • There is an epistemological logic with sometimes formalist, sometimes methodological leanings.

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  • There is a formal-symbolic logic engaged with the elaboration of a relational calculus.

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  • Finally, there is what may be termed psychological-voluntaryist logic. It is in the rapidity of development of logical investigations of the third and fourth types and the growing number of their exponents that the present shows most clearly the history of logic in the making.

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  • All these movements are logic of the present, and a very brief indication may be added of points of historical significance.

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  • His metaphysical method, however, is like Herbart's, not identifiable with his logic, and the latter has for its central characteristic its thorough restatement of the logical forms traditional in language and the text-books, in such a way as to harmonize with the doctrine of a reality whose organic unity is all-inclusive.

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  • The act of judgment " which refers an ideal content (recognized as such) to a reality beyond the act " is the unit for logic. Grammatical subject and predicate necessarily both fall under the rubric of the adjectival, that is, within the logical idea or ideal content asserted.

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  • Bosanquet had the advantage that his logic was a work of a slightly later date.

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  • It is to Lotze, however, that he owes most in the characteristic feature of his logic, viz., the systematic development of the types of judgment, and inference from less adequate to more adequate forms. His fundamental continuity with Bradley may be illustrated by his definition of inference.

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  • Of epistemological logic in one sense of the phrase Lotze is still to be regarded as a typical exponent.

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  • Sigwart's aim was " to reconstruct logic from the point of view of methodology."

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  • Of the formal-symbolic logic all that falls to be said here is, that from the point of view of logic as a whole, it is to be regarded as a legitimate praxis as long as it shows itself aware of the sense in which alone form is susceptible of abstraction, and is aware that in itself it offers no solution of the logical problem.

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  • The future of symbolic logic as coherent with the rest of logic, in the sense which the word has borne throughout its history seems to be bound up with the question of the nature of the analysis that lies behind the symbolism, and of the way in which this is justified in the setting of a doctrine of validity.

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  • The " theory of the object," itself, while affecting logic alike in the formal and in the psychological conception of it very deeply, does not claim to be regarded as logic or a logic, apart from a setting supplied from elsewhere.

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  • Finally we have a logic of a type fundamentally psychological, if it be not more properly characterized as a psychology which claims to cover the whole field of philosophy, including the logical field.

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  • Historically this doctrine was formulated as the declaration of independence of the insurgents in revolt against the pretensions of absolutist logic. It drew for support upon the psychological movement that begins with Fries and Herbart.

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  • It has been chiefly indebted to writers, who were not, or were not primarily, logicians, to Avenarius, for example, for the law of the economy of thought, to Wundt, whose system, and therewith his logic,' is a pendant to his psychology, for the volitional character of judgment, to Herbert Spencer and others.

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  • The movement has, however, scarcely developed its logic s except as polemic. What seems clear is that it cannot be the whole solution.

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  • Yet there are, of course, works devoted to the history of logic prcper.

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  • Of these Prantl's Geschichte der Logik im Abendlande (4 vols., 1855-1870), which traces the rise, development and fortunes of the Aristotelian logic to the close of the middle ages, is monumental.

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  • Blakey's Historical Sketch of Logic (1851), though, like all this writer's works, closing with a bibliography of some pretensions, is now negligible.

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  • Wallace's prolegomena and notes to his Logic of Hegel (1874, revised and augmented 1892-1894) are of use for the history and terminology, as well as the theory.

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  • Venn's Symbolic Logic (1881) gave a careful history and bibliography of that development.

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  • Not in proofs by formal logic but in the reality of consciousness was the certainty of God.

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  • Man's place is not even central, as he appears a temporary inhabitant of a minor planet in one of the lesser stellar systems. Every science is involved, and theology has come into conflict with metaphysics, logic, astronomy, physics, chemistry, geology, zoology, biology, history and even economics and medicine.

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  • Its early logic, ontology and cosmology, with many of its distinctive doctrines, are shown to be the natural offspring of the races and ages which gave them birth.

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  • No great institution lives or dies by logic. Christianity rests on great religious needs which it meets and gratifies, so that its life (like all other lives) is in unrationalized emotions.

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  • To them at best theology with its cosmology and its logic is only a shadow of shadows, for God reveals himself to the pure in heart, and it matters not what science may say of the material and fleeting world.

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  • In these pieces, as in almost every production of his, in lieu of melody Liszt offers fragments of melody - touching and beautiful, it may be, or passionate, or tinged with triviality; in lieu of a rational distribution of centres of harmony in accordance with some definite plan, he presents clever combinations of chords and ingenious modulations from point to point; in lieu of musical logic and consistency of design, he is content with rhapsodical improvisation.

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  • In details of execution and harmonic combinations they illustrate the precision, logic, lucidity and cheerful spirit of the national genius.

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  • This process, which forms the essence of the new method, may in its entirety, as a ministration to the reason, be called a logic; but it differs widely from the ordinary or school logic in end, method and form.

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  • Its aim is to acquire command over nature by knowledge, and to invent new arts, whereas the old logic strove only after dialectic victories and the 1 Thus the last step in the theoretical analysis gives the first means for the practical operation.

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  • Now the first step in accurate progress from sense to reason, or true philosophy, is to frame a bona notio or accurate conception of the thing; but the received logic never does this.

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  • This elimination of the non-essential, grounded on the fundamental propositions with regard to forms, is the most important of Bacon's contributions to the logic of induction, and that in which, as he repeatedly says, his method differs from all previous philosophies.

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  • It may be freely admitted that in the domain of logic there is nothing in the Organum that has not been more instructively analysed either by Aristotle himself or in modern works; at the same time, there is probably no work which is a better and more stimulating introduction to logical study.

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  • After five years he returned to Leiden, where he accepted the chair of logic and moral philosophy, and afterwards that of natural philosophy.

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  • His Logic was at one time widely used, and is still valuable.

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  • The students are instructed in Arabic and Persian literature, religion, interpretation of the Koran, Mussulman law, logic, rhetoric, philosophy and other subjects necessary for admittance to the clergy, for doctors of law, &c., while modern sciences are neglected.

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  • In 1866 he was elected professor of logic and mental and moral philosophy and Cobden professor of political economy in Owens college.

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  • It would be difficult to exaggerate the loss which logic and political economy sustained through the accident by which his life was prematurely cut short.

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  • Jevons arrived quite early in his career at the doctrines that constituted his most characteristic and original contributions to economics and logic. The theory of utility, which became the keynote of his general theory of political economy, was practically formulated in a letter written in 1860; and the germ of his logical principles of the substitution of similars may be found in the view which he propounded in another letter written in 1861, that "philosophy would be found to consist solely in pointing out the likeness of things."

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  • Jevons's work in logic went on par/ passe with his work in political economy.

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  • In 1864 he published a small volume, entitled Pure Logic; or, the Logic of Quality apart from Quantity, which was based on Boole's system of logic, but freed from what he considered the false mathematical dress of that system.

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  • In the following year appeared the Elementary Lessons on Logic, which soon became the most widely read elementary textbook on logic in the English language.

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  • In this work Jevons embodied the substance of his earlier works on pure logic and the substitution of similars; he also enunciated xv.

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  • His Studies in Deductive Logic, consisting mainly of exercises and problems for the use of students, was published in 1880.

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  • These articles and one other were republished after Jevons's death, together with his earlier logical treatises, in a volume, entitled Pure Logic, and other Minor Works.

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  • In logic he is reported to have agreed with Eusebius, Iamblichus and Porphyry in asserting the validity of the second and third figures of the syllogism.

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  • If the recognition of physics and logic as two studies coordinate with ethics is sufficient to differentiate the mature Zeno from the Cynic author of the Republic, no less than from his own heterodox disciple Aristo, the Cleanthes.

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  • So absolutely is the " rare and priceless wisdom " for which we strive identical with virtue itself that the three main divisions of philosophy current at the time and accepted by Zeno - logic, physics and ethics - are defined as the most generic or comprehensive virtues.

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  • Of the three divisions logic is the least important; ethics is the outcome of the whole, and historically the all-important vital element; but the foundations of the whole system are best discerned in the science of nature, which deals pre-eminently with the macrocosm and the microcosm, the universe and man, including natural theology and an anthropology or psychology, the latter forming the direct introduction to ethics.

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  • With this exposition we have already invaded the province of logic. To this the Stoics assigned a miscellany of studies - rhetoric, dialectic, including grammar, in addition to formal Logic. logic - to all of which their industry made contributions.

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  • But although in strict logic the feudal causes concerning them should have been judged by them alone, they could not maintain this right in the curia regis; the other persons sitting in it could also take part in judging causes which concerned the peers.

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  • The chair of Hebrew at the Carolinum was added in 1643, and in 1653 he was appointed professor ordinarius of logic, rhetoric and theology.

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  • Thus arose the foundations of the modern " germ theory of disease;" and, in the midst of the wildest conjectures and the worst of logic, a nucleus of facts was won, which has since grown, and is growing daily.

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  • He composed, it is said, nearly 500 treatises on various subjects, including logic, ethics and grammar.

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  • Galen, who in his youth was carefully trained in the Stoic philosophy, was an unusually prolific writer on logic. Of the numerous commentaries and original treatises, a catalogue of which is given in his work De propriis libris, one only has come down to us, the treatise on Fallacies in dictione (IIepi TWV KaTa T1jv M Gi' oocio-µarouv).

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  • His name is perhaps best known in the history of logic in connexion with the fourth syllogistic figure, the first distinct statement of which was ascribed to him by Averroes.

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  • Of this work, which contains no direct intimation of a fourth figure, and which in general exhibits an astonishing mixture of the Aristotelian and Stoic logic, Prantl speaks with the bitterest contempt.

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  • It is true that he is severe towards infidels; and his approval of the knight who, finding a Jew likely to get the better of a theological argument, resorted to the baculine variety of logic, does not meet the views of the 10th century.

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  • In 1832 he returned to Tubingen and became repetent in the university, lecturing on logic, history of philosophy, Plato, and history of ethics, with great success.

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  • His logic, while never obtruded, was rarely at fault; but lie loved the flash of the rapier, and was never happier than when he had to face down a mob and utterly foil it by sheer superiority in fencing.

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  • For an account of his logic, see Prantl, Geschichte der Logik (1855-1870); for his philosophy, see Stockl, Geschichte der Philosophie des Mittelalters (1864-1866), vol.

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  • The education which he received at Malmesbury included a smattering of logic and physics; but moral philosophy and history, especially the latter, were the subjects to which he devoted most attention.

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  • He was lecturer on logic in 1J401541.

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  • Major's voluminous writings may be grouped under (a) logic and philosophy, (b) Scripture commentary, and (c) history.

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  • Thus they amplified - the Aristotelian logic by the theory of the hypothetical and disjunctive syllogism, and added to the first figure of the categorical syllogism the five moods out of which the fourth figure was afterwards constructed.

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  • As a boy, he showed an extraordinary quickness of apprehension, and, choosing a learned life instead of the knightly career natural to a youth of his birth, early became an adept in the art of dialectic, under which name philosophy, meaning at that time chiefly the logic of Aristotle transmitted through Latin channels, was the great subject of liberal study in the episcopal schools.

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  • Of his immediate followers Joseph Bellamy is distinctly Edwardean in the keen logic and in the spirit of his True Religion Delineated, but he breaks with his master in his theory of general (not limited) atonement.

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  • Logic, ethics and physics, psychology, theory of knowledge and metaphysics are all fused together by Plato in a semi-religious synthesis.

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  • To this correspond the Platonic confusion of logic and ethics and the attempt to substitute a theory of concepts for a metaphysic of reality.

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  • He became the founder of logic, psychology, ethics and aesthetics as separate sciences; while he prefixed to all such (comparatively) special inquiries the investigation of the ultimate nature of existence as such, or of those first principles which are common to, and presupposed in, every narrower field of knowledge.

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  • Subsidiary to metaphysics, as the central inquiry, stand the sciences of logic and ethics, to which may be added aesthetics, constituting three normative sciences - sciences, that is, which do not, primarily, describe facts, but rather prescribe ends or set forth ideals.

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  • It is evident, however, that if logic deals with conceptions which may be considered constitutive of knowledge as such, and if ethics deals with the harmonious realization of human life, which is the highest known form of existence, both sciences must have a great deal of weight in the settling of the general question of metaphysics.

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  • This is not unnatural, seeing that it is only so far as they bear on the one central question of the nature of existence that philosophy spreads its mantle over psychology, logic or ethics.

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  • Similarly, logic, so far as it is an art of thought or a doctrine of fallacies, and ethics, so far as it is occupied with a natural history of impulses and moral sentiments, do neither of them belong, except by courtesy, to the philosophic province.

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  • With Hegel it passes into a completely articulated "logic," which apparently claims to be at the same time a metaphysic, or an ultimate expression of the nature of the real.

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  • If the theory of knowledge thus passes insensibly into metaphysics it becomes somewhat difficult to assign a distinct sphere to logic (q.v.).

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  • In this reference logic does not tell us how our intellections connect themselves as mental phenomena, but how we ought to connect our thoughts if they are to realize truth (either as consistency with what we thought before or as agreement with observed facts).

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  • But, if we desire to keep by older landmarks and maintain a distinction between the two disciplines, a ground for doing so may be found in the fact that all the main definitions of logic point to the investigation of the laws of thought in a subjective reference - with a view, that is, by an analysis of the operation, to ensure its more correct performance.

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  • According to the old phrase, logic is the art of correct thinking.

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  • Occupying a position, therefore, within the wider sphere of the general theory of knowledge, ordinary logic consists in an analysis of the nature of general statement, and of the conditions under which we pass validly from one general statement to another.

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  • More jurist than theologian, John defended the rights of the papacy with rigorous zeal and as rigorous logic. For the restoration of the papacy to its old independence, which had been so gravely compromised under his immediate predecessors, and for the execution of the vast enterprises which the papacy deemed useful for its prestige and for Christendom, considerable sums were required; and to raise the necessary money John burdened Christian Europe with new taxes and a complicated fiscal system, which was fraught with serious consequences.

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  • The secret of success, here as elsewhere, is the writer's marvellous imperturbability in paradox, his teeming imagination and his rigid logic. Grant his premises, and all the rest follows; his world may be turned topsy-turvy, but the relative situation of its contents is unchanged.

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  • In Lange's Logische Studien, which attempts a reconstruction of formal logic, the leading idea is that reasoning has validity in so far as it can be represented in terms of space.

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  • Of Xenocrates's logic we know only that with Plato he distinguished auro and rejecting the Aristotelian list of ten categories as a superfluity.

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  • His practice as a college lecturer in logic is better evidenced by these "cases" than by his Compendium of Logic, first published in 1618.

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  • Among the Franciscans themselves it has been the occasion of endless strife, and has been kept alive only by dint of successive reforms and fresh starts, each successful for a time, but doomed always, sooner or later, to yield to the inexorable logic of facts.

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  • The cause which Bunyan had defended with rude logic and rhetoric against Kiffin and Danvers has since been pleaded by Robert Hall with an ingenuity and eloquence such as no polemical writer has ever surpassed.

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  • The name of " abacus " is also given, in logic, to an instrument, often called the " logical machine," analogous to the mathematical abacus.

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  • His reputation soon widened, and in 1754 he became professor of logic, metaphysics and Greek in the university of Reggio, and in 1760 was translated to Modena, where he continued to teach with great assiduity and success, but devoted his whole leisure to natural science.

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  • It is known that while still at Woolsthorpe Sanderson's Logic had been read by him to such purpose that his tutor at Trinity College excused his attendance at a course of lectures on that subject.

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  • This teacher, as he tells us, "by the severity of his logic, the gravity and weight of his words, turned me by degrees, and not without resistance, from the beaten path of Condillac into the way which has since become so easy, but which was then painful and unfrequented, that of the Scottish philosophy."

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  • This is one among many flaws in the Hegelian dialectic, and it paralyzes the whole of the Logic. Secondly, the conditions of intelligence, which Cousin allows, necessarily exclude the possibility of knowledge of the absolute - they are held to be incompatible with its unity.

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  • Cousin made no reply to Hamilton's criticism beyond alleging that Hamilton's doctrine necessarily restricted human knowledge and certainty to psychology and logic, and destroyed metaphysics by introducing nescience and uncertainty into its highest sphere - theodicy.

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  • Every governor who followed him was forced by the logic of events and truth tacitly to acknowledge that right lay with the free-state party.

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  • Nevertheless he was driven by the logic of events to attack Normandy, for as long as his brother reigned there, and as long as many English barons retained great holdings on both sides of the Channel and were subjects of the duke as well as of the king, intrigues and plots never ceased.

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  • The logic of this plan was not applied to Ireland; there it was to be Ireland for the English for many a generation yet to come; and so Ireland remained Achilles heel, the vulnerable part of the United Kingdom.

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  • It is one of the inscrutable perplexities of human affairs, that in the logic of practical life, in order to reach conclusions that cover enough for truth, we are constantly driven to premises that cover too much, and that in order to secure their right weight to justice and reason good men are forced to fling the two-edged sword of passion into the same scale.

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  • In 1839 he produced a small work called First Notions of Logic, giving what he had found by experience to be much wanted by students commencing with [[Euclid]].

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  • The details of this dispute will be found in the original pamphlets, in the [[Athenaeum]] and in the appendix to De Morgan's Formal Logic. Suffice it to say that the independence of De Morgan's discovery was subsequently recognized by Hamilton.

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  • Late in 1847 De Morgan published his principal logical treatise, called Formal Logic, or the Calculus of Inference, Necessary and Probable.

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  • These papers taken together constitute a great treatise on logic, in which he substituted improved systems of notation, and developed a new logic of relations, and a new onymatic system of logical expression.

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  • In 1860 De Morgan endeavoured to render their contents better known by publishing a [[Syllabus]] of a Proposed System of Logic, from which may be obtained a good idea of his symbolic system, but the more readable and interesting discussions contained in the memoirs are of necessity omitted.

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  • The article "Logic" in the English Cyclopaedia (1860) completes the list of his logical publications.

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  • Throughout his logical writings De Morgan was led by the idea that the followers of the two great branches of exact science, logic and mathematics, had made blunders, - the logicians in neglecting mathematics, and the mathematicians in neglecting logic. He endeavoured to reconcile them, and in the attempt showed how many errors an acute mathematician could detect in logical writings, and how large a field there was for discovery.

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  • The refusal of the council to accept the recommendation of the senate, that they should appoint an eminent Unitarian minister to the professorship of logic and mental philosophy, revived all De Morgan's sensitiveness on the subject of sectarian freedom; and, though his feelings were doubtless excessive, there is no doubt that gloom was thrown over his life, intensified in 1867 by the loss of his son George Campbell De Morgan, a young man of the highest scientific promise, whose name, as De Morgan expressly wished, will long be connected with the London Mathematical Society, of which he was one of the founders.

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  • Here, says Ritschl, the involuntary logic of predestinarianism speaks its last word.

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  • He denounced the trial by ordeal of fire and water, the belief in witchcraft, and the ascription of tempests to magic,maintained the Carolingian opposition to image-worship, but carried his logic farther and opposed the adoration of the saints.

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  • Determinism is not necessarily the logic of despair.

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  • Even philosophies such as logic and aesthetic would be necessary for such an investigation, if thought and artistic production are normal.

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  • In logic and metaphysics it investigates either the process of apprehension itself, or conceptions such as cause, substance, space, time, which the ordinary scientific consciousness never criticizes.

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  • Though Calvin built his theology on the foundations laid by earlier reformers, and especially by Luther and Bucer, his peculiar gifts of learning, of logic and of style made him pre-eminently the theologian of the new religion.

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  • He lectured on logic, deductive and inductive, systematic psychology and ethical theory.

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  • Nevertheless, he left an enduring mark upon Greek speculation, inasmuch as he not only recognized the need of a logic, and grappled, however unsuccessfully, with one of the most obvious of logical.

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  • Owing largely to the simplicity and symmetry of the syllogism it has been a commonplace of logic to make the syllogistic form the type of all thought.

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  • Discussions of the syllogism will be found in all textbooks on Logic, and the more elaborate syllogistic forms are discussed in the article Logic.

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  • Arabian philosophy, at the outset of its career in the 9th century, was able without difficulty to take possession of those resources for speculative thought which the Latins had barely achieved at the close of the 12th century by the slow process of rediscovering the Aristotelian logic from the commentaries and verses of Boetius.

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  • Up to the time when the religious zeal of the emperor Zeno put a stop to the Nestorian school at Edessa, this " Athens of Syria " was active in translating and popularizing the Aristotelian logic. Their banishment from Edessa in 489 drove the Nestorian scholars to Persia, where the Sassanid rulers gave them a welcome; and there they continued their labours on the Organon.

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  • A new seminary of logic and theology sprang up at Nisibis, not far from the old locality; and at Gandisapora (or Nishapur), in the east of Persia, there arose a medical school, whence Greek medicine, and in its company Greek science and philosophy, ere long spread over the lands of Iran.

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  • Their school at Resaina is known from the name of Sergius, one of the first of these translators, in the days of Justinian; and from their monasteries at Kinnesrin (Chalcis) issued numerous versions of the introductory treatises of the Aristotelian logic. To the Isagoge of Porphyry, the Categories and the Hernieneutica of Aristotle, the labours of these Syrian schoolmen were confined.

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  • In him too is found the union of Platonism and Aristotelianism expressed in Neo-Platonic terms. Towards the close of the 10th century the presentation of an entire scheme of knowledge, beginning with logic and mathematics, and ascending through the various departments of physical inquiry to the region of religious doctrine, was accomplished by a society which had its chief seat at Basra, the native town of al-Kindi.

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  • His paraphrases of Aristotle formed the basis on which Avicenna constructed his system, and his logical treatises produced a permanent effect on the logic of the Latin scholars.

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  • Still, the logic of Albertus Magnus and succeeding doctors was largely indebted to him for its formulae.

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  • In logic Avicenna starts from distinguishing between the isolated concept and the judgment or assertion; from which two primitive elements of knowledge there is artificially generated a complete and scientific knowledge by the two processes of definition and syllogism.

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  • But the chief interest for the history of logic belongs to his doctrine in so far as it bears upon the nature and function of abstract ideas.

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