Her logic and her sympathy are in excellent balance.
His logic and acceptance of the deformity was amazingly positive and mature for a 9-year-old.
Logic began to drift back into Dean's thought process.
That sounds like your kind of logic - always thinking of the other person first.
The world is happiest when this process is one of persuasion, goodwill, reason, logic, and negotiation.
He saw the logic, even though he didn't want to.
But the pupil soon found his teacher to be a charlatan, and taught himself, aided by commentaries, to master logic, geometry and astronomy.
Hegelianism attempts to squeeze all life into the categories of logic: Aristotelianism deals with "things in general" and ignores the radical distinction between nature and spirit.
His logic was sound, but there was still the situation with the chair.
The human emotions were crippling the cold logic that brought her to this point.
(2) In logic there is considerable divergence of opinion as to the best definition.
His Logic, Metaphysics, Physics, De Caelo, are treatises giving a synoptic view of Aristotelian doctrine.
Once before he had used that logic, and it had been a prelude to a fiasco.
Natasha and Pierre, left alone, also began to talk as only a husband and wife can talk, that is, with extraordinary clearness and rapidity, understanding and expressing each other's thoughts in ways contrary to all rules of logic, without premises, deductions, or conclusions, and in a quite peculiar way.
To attach a clear and definite meaning to the Cartesian doctrine of God, to show how much of it comes from the Christian theology and how much from the logic of idealism, how far the conception of a personal being as creator and preserver mingles with the pantheistic conception of an infinite and perfect something which is all in all, would be to go beyond Descartes and to ask for a solution of difficulties of which he was 1 Ouvres, vi.
It was scrambling her logic and had completely decimated her self-control where he was concerned.
Like Alex, he saw the logic in surrogacy, as did Bill.
The Port Royalists, Pierre Nicole (1625-1695) and Antoine Arnauld (1612-1694), had applied it to grammar and logic; Jean Domat or Daumat (1625-1696) and Henri Francois Daugesseau (1668-1751) to jurisprudence; Fontenelle, Charles Perrault (1628-1703) and Jean Terrasson (1670-1750) to literary criticism, and a worthier estimate of modern literature.
In logic Antisthenes was troubled by the problem of the One and the Many.
All she had to do was find a way to prevent them from crippling her logic for now.
By what logic would anyone assume it will not go to zero?
"The earth," he adds elsewhere, "especially if fresh, has a certain magnetism in it, by which it attracts the salt, power, or virtue (call it either) which gives it life, and is the logic of all the labor and stir we keep about it, to sustain us; all dungings and other sordid temperings being but the vicars succedaneous to this improvement."
You won't escape!--from that moment this conversation began, contrary to all the laws of logic and contrary to them because quite different subjects were talked about at one and the same time.
She'd seen him take out a hospital administrator with pure logic to get his way to run a procedure on her.
At the age of sixty, having become widely known by his writings on philosophy, he was called to the chair of logic and metaphysics in the university of Naples, which he held till his death in November 1846.
These crude ideas of Cromwell's character were extinguished by Macaulay's irresistible logic, by the publication of Cromwell's letters by Carlyle in 1845, which showed Cromwell clearly to be "not a man of falsehoods, but a man of truth"; and by Gardiner, whom, however, it is somewhat difficult to follow when he represents Cromwell as "a typical Englishman."
vehement recoil from Kant's deification of formal logic with its principle of " analytic " tautology.
Some of his shorter essays on medicine, logic, &c., take a poetical form (the poem on logic was published by Schmoelders in 1836).
With the systematic study of the Latin, and to a slight extent also of the Greek classics, he conjoined that of logic in the prolix system of Crousaz; and he further invigorated his reasoning powers, as well as enlarged his knowledge of metaphysics and jurisprudence, by the perusal of Locke, Grotius and Montesquieu.
Maimonides also wrote an Arabic commentary on the Mishnah, soon afterwards translated into Hebrew, commentaries on parts of the Talmud (now lost), and a treatise on Logic. His breadth of view anti- and his Aristotelianism were a stumbling-block to the orthodox, and subsequent teachers may be mostly classified as Maimonists or anti-Maimonists.
The Russian military historians in so far as they submit to claims of logic must admit that conclusion, and in spite of their lyrical rhapsodies about valor, devotion, and so forth, must reluctantly admit that the French retreat from Moscow was a series of victories for Napoleon and defeats for Kutuzov.
inductive proof requiring, according to Mill's Logic, the " Method of Difference."
These, with an account of Aristotle's Logic appended to Lord Kames's Sketches of the History of Man (1774), conclude the list of works published in Reid's lifetime.
Finally, at Jorjan, near the Caspian, he met with a friend, who bought near his own house a dwelling in which Avicenna lectured on logic and astronomy.
The Logic, an eminently practical work, written from the point of view of Locke, is in five parts, dealing with (1) the nature of the human mind, its faculties and operations; (2) ideas and their kinds; (3) the true and the false, and the various degrees of knowledge; (4) reasoning and argumentation; (5) method and the ordering of our thoughts.
MacTaggart (Studies in Hegelian Dialectic) contends that direct contradiction is confined to the elementary portions of Hegel's Logic: but he does not deny its existence there, though his interpretation, could one accept it, softens the paradox.
With all its defective psychology, its barren logic, its immature technique, it emphasized two great and necessary truths, firstly, the absolute responsibility of the individual as the moral unit, and, secondly, the autocracy of the will.
His English works are an Inquiry into Speculative and Experimental Science (London, 1856); Introduction to Speculative Logic and Philosophy (St Louis, 1875), and a translation of Bretschneider's History of Religion and of the Christian Church.
Bradley's Logic: " If " or " As often as you have the cause working unimpeded, you get the effect."
To these lists should be added a paper on the mathematical basis of logic, published in the Mechanic's Magazine for 1848.
Their crude productions, for the most part, were conspicuous rather for insolence and abusiveness than for logic or learning.
Amongst his published works are Knowledge and Reality (q85); Logic, or the Morphology of Knowledge (1888); Essentials of Logic (1895); Psychology of.
He treated the question at issue as one of pure logic, and disliking the Reformers, the right of private judgment which Protestants claimed, and the somewhat prosaic uniformity of the English Church, he flung himself into a general campaign against Protestantism in general and the Anglican form of it in particular.
He always tried to govern his thinking by logic.
It wasn't the money he objected to so much as the irrational logic.
In quantitative judgments we may think x = y, or, as Boolero oses x = v ° p p y = - ° y, or, as Jevons proposes, x = xy, or, as Venn proposes, x which is not y=o; and equational symbolic logic is useful whenever we think in this quantitative way.
Her heart said no, but then there was logic.
While I remained eager to discuss the conversation, I couldn't disagree with Howie's logic.
She didn't expect it; she expected him to lie rather than point out the flaws in her desperate logic.
I wasn't thinking at my highest level of logic.
It was an illogical thought, but her mind was beyond logic.
Only the tiniest shred of doubt remained in her mind, and that was probably born of wishful thinking, not logic.
Mill's Logic, and with fuller sympathy in W.
Reason is called common sense to distinguish it from ratiocination with uses logic and rational reasoning.
' As a logic fencer, or parliamentary Hercules, one would be inclined to back him at first sight against all the extant world.
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.
But he was no merely destructive critic. He was determined to find a solid foundation for both morality and law, and to raise upon it an edifice, no stone of which should be laid except in accordance with the deductions of the severest logic. This foundation is "the greatest happiness of the greatest number," a formula adopted from Priestly or perhaps first from Beccaria.
His father's History of India was published in 1818; immediately thereafter, about the age of twelve, John began a thorough study of the scholastic logic, at the same time reading Aristotle's logical treatises in the original.
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).
He had been bred by his father in a great veneration for the syllogistic logic as an antidote against confused thinking.
Be this as it may, enthusiastic as he was for a new logic that might give certainty to moral and social conclusions, Mill was no less resolute that the new logic should stand in no antagonism to the old.
In his Westminster review of Whately's Logic in 1828 (invaluable to all students of the genesis of Mill's logic) he appears, curiously enough, as an ardent and brilliant champion of the syllogistic logic against highfliers such as the Scottish philosophers who talk of "superseding" it by "a supposed system of inductive logic."
His inductive logic must "supplement and not supersede."
It was in 1837, on reading Whewell's Inductive Sciences and re-reading Herschel, that Mill at last saw his way clear both to formulating the methods of scientific investigation and joining on the new logic as a supplement to the old.
The Logic was published in 1843.
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.
Reference to the articles on Logic, Metaphysics, &c., will show that subsequent criticism, however much it has owed by way of stimulus to Mill's strenuous rationalism, has been able to point to much that is inconsistent, inadequate and even superficial in his writings.
- Works: System of Logic (2 vols., 1843; 9th ed., 1875; "People's" ed., 1884); Essays on some Unsettled Questions of Political Economy (1844, ed.
See further LOGIC (Historical Sketch); PSYCHOLOGY; ASSOCIATION OF IDEAS.
This suggestion has some interest, but is of no great value, either in logic or in the theory of knowledge.
Charles, however, has given good grounds for supposing that it is merely a preface, and that the work went on to discuss grammar, logic (which Bacon thought of little service, as reasoning was innate), mathematics, general physics, metaphysics and moral philosophy.
After that, apparently, logic was to be treated; then, possibly, mathematics and physics; then speculative alchemy and experimental science.
Sigwart, in the preface to the first edition of his Logic, makes "special mention" of the assistance he obtained from this book.
From the age of sixteen to nearly twenty his health was so unsatisfactory that he attended neither school nor college, bilt worked at Chaldee and Syriac, began to read Arabic, and mastered 'S Gravesande's Natural Philosophy, together with various textbooks of logic and metaphysics.
Appointed superintendent of the cathedral school of his native city, he taught with such success as to attract pupils from all parts of France, and powerfully contributed to diffuse an interest in the study of logic and metaphysics, and to introduce that dialectic development of theology which is designated the scholastic. The earliest of his writings of which we have any record is an Exhortatory Discourse to the hermits of his district, written at their own request and for their spiritual edification.
They were followed by treatises of a different character, clearer in matter, more systematic in arrangement, and reflecting the methods of the scholastic logic; these are farther from the Greek tradition, for although they contain sufficient traces of their ultimate Greek ancestry, their authors do not know the Greeks as masters and cite no Greek names.
The favourite subjects of his lectures were logic and dogmatic theology.
Bartole, the official biographer of Ignatius, says that he would not permit any innovation in the studies; and that, were he to live five hundred years, he would always repeat "no novelties" in theology, in philosophy or in logic - not even in grammar.
Besides being a contributor to the magazines and encyclopedias on educational and philosophical subjects, he wrote An Introduction to the Study of Philosophy (1889); The Spiritual Sense of Dante's Divina Commedia (1889); Hegel's Logic (1890); and Psychologic Foundations of Education (1898); and edited Appleton's International Education Series and 'Webster's International Dictionary.
The Koran, sacred and secular law, logic, poetry, arithmetic, with some medicine and geography, are the chief subjects of study.
Haydn uses a true Straussian discord in The Seasons, in order to imitate the chirping of a cricket; but the harshest realism in Gatterdammerung (the discord produced by the horns of Hagen and his churls in the mustering-scene in the second act) has a harmonic logic which would have convinced Corelli.
Justinian himself, with the aid of Leontius of Byzantium (c. 4 8 5-543), a monk with a decided turn for Aristotelian logic and metaphysics, had tried to reconcile the Cyrillian and Chalcedonian positions, but he inclined more and'more towards the monophysite view, and even went so far as to condemn by edict three teachers (Theodore of Mopsuestia, Theodoret, the opponent of Cyril, and Ibas of Edessa) who were offensive to the monophysites.
Mathematical Logic as based on the Theory of Types,"Amer.
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.
Bertrand Russell, The Principles of Mathematics (Cambridge, 1903), and his article on "Mathematical Logic" in Amer.
The eighth now extant is really an incomplete treatise on logic. Some critics have rejected this book as spurious, since its matter is so different from that of the rest.
He was professor of moral philosophy at Bourges (1845-1848) and Strassburg (1848-- 1857), and of logic at the lycee Louis-le-Grand, Paris (1857-1864).
Believers in law have put their trust in authority or logic; while believers in disposition chiefly look to our instinctive faculties - conscience, common-sense or sentiment.
But common-sense and conscience are quite as definite guides as logic or authority; and there seems no good reason for refusing to give the name of casuistry to their operations.
These logic must seize upon and develop as far as they will go; for the breach of some trifling consequence of a rule might mean the loss of the deity's favour.
In the preface to the first edition, Sigwart explains that he makes no attempt to appreciate the logical theories of his predecessors; his intention was to construct a theory of logic, complete in itself.
In formal logic the drawing of inferences is frequently called ratiocination.
ratiocinari, to use the reasoning faculty) is classified from Aristotle downwards as deductive (from generals to particulars) and inductive (from particulars to generals); see Logic, Induction, Syllogism.
The name doctor scholasticus was applied originally to any teacher in such an ecclesiastical gymnasium, but gradually the study of dialectic or logic overshadowed the more elementary disciplines, and the general acceptation of " doctor " came to be one who occupied himself with the teaching of logic. The philosophy of the later Scholastics is more extended in its scope; but to the end of the medieval period philosophy centres in the discussion of the same logical problems which began to agitate the teachers of the 9th and 1 oth centuries.
Prantl says that there is no such thing as philosophy in the middle ages; there are only logic and theology.
The remark overlooks two facts - firstly that the main objects of theology and philosophy are identical, though the td°f ogyod method of treatment is different, and secondly that logical discussion commonly leads up to metaphysical problems, and that this was pre-eminently the case with the logic of the Schoolmen.
But the saying draws attention to the two great influences which shaped medieval thought - the tradition of ancient logic and the system of Christian theology.
Scholasticism opens with a discussion of certain points in the Aristotelian logic; it speedily begins to apply its logical distinctions to the doctrines of the church; and when it attains its full stature in St Thomas it has, with the exception of certain mysteries, rationalized or Aristotelianized the whole churchly system.
As aids to the study of logic, the doctors of this period, beside the commentaries and treatises of Boetius (q.v.), possessed two tracts attributed to St Augustine, the first of which, Principia dialecticae, is probably his, but is mainly grammatical in its import.
To this list must be added: (I) the Satyricon of Martianus Capella, the greater part of which is a treatise on the seven liberal arts, the fourth book dealing with logic; (2) the De artibus ac disciplinis liberalium literarum of Cassiodorus; (3) the Origines of Isidore of Seville (ob.
2 Hitherto, if dialectical studies had been sometimes viewed askance by the stricter churchmen, it was not because logic had dared to stretch forth its hands towards the ark of God, but simply on the ground of the old opposi tion between the church and the world.
The next centuries show that peculiar combination of logic and theology which is the mark of Scholasticism, especially in the period before the r3th century.
the end of the 11th and the first half of the 12th century logic - a period more original and more interesting in many ways than the great age of Scholasticism in the 13th century.
The earlier doctors who avail themselves of Aristotle's works, while bowing to his authority implicitly in matters of logic, are generally found defending a Christianized Platonism against the doctrine of the Metaphysics.
So also is Petrus Hispanus (Pope John XXI.), who is chiefly important, however, as the author of the much-used manual Summulae logicales, in which the logic of the schools was expanded by the incorporation of fresh matter of a semi-grammatical character.
Even in 1847 astronomy, physics, logic and other subjects of the kind had to be taught in several of the lyceums through the medium of Latin.
Although originally suggested by formal logic, it is most simply interpreted as an algebra of regions in space.
In logic, ignorance is that state of mind which for want of evidence is equally unable to affirm or deny one thing or another.
Among the works which he translated into Syriac and of which his versions survive are treatises of Aristotle, Porphyry and Galen, 3 the Ars grammatica of Dionysius Thrax, the works of Dionysius the Areopagite, and possibly two or three treatises of Plutarch.4 His own original works are less important, but include a " treatise on logic, addressed to Theodore (of Merv), which is unfortunately imperfect, a tract on negation and affirmation; a treatise, likewise addressed to Theodore, On the Causes of the Universe, according to the Views of Aristotle, showing how it is a Circle; a tract On Genus, Species and Individuality; and a third tract addressed to Theodore, On the Action and Influence of the Moon, explanatory and illustrative of Galen's IIEpi rcptaiµwv r t µepwv, bk.
Paul the Persian, a courtier of Khosrau Anosharwan, dedicated to the king a treatise on logic which has been published from a London MS. by Land in the 4th volume of his Anecdota.
to science, in which Lutheranism is expounded "nervose, solide, et copiose," in fact with a fulness of learning, a force of logic and .a minuteness of detail that had never before been approached.
At the same time, it delights the pure theorist by the simplicity of the logic with which the fundamental theorems may be established, and by the elegance of its mathematical operations, insomuch that hydrostatics may be considered as the Euclidean pure geometry of mechanical science.
He wrote Breviuscula Introductio ad Logicam, a treatise on logic and the psychology of the intellectual powers; Synopsis Theologiae Naturalis; and an edition of Pufendorf, De Officio Hominis et Civis, with notes and supplements of high value.
The term in Aristotelian logic is opposed to dialectic, as scientific proof to probable reasoning.
Mill, who had been greatly impressed by Comte's philosophic ideas; Mill admits that his own System of Logic owes many valuable J.
thoughts to Comte, and that, in the portion of that work which treats of the logic of the moral sciences, a radical.
In 1866 the chair of the philosophy of mind and logic in University College, London, fell vacant, and Martineau became a candidate.
We feel its presence in his earliest notable work, The Rationale of Religious Enquiry, 1836; and may there see the rigour with which it applied audacious logic to narrow premisses, the tenacity with which it clung to a limited literal supernaturalism which it had no philosophy to justify, and so could not believe without historical and verbal authority.
In its speculative parts the book is quite equal to those that had gone before, but in its literary and historical parts there are indications of a mind in which a longpractised logic had become a rooted habit.
This tour de force was followed up by the publication in 1543 of Aristotelicae Animadversiones and Dialecticae Partitiones, the former a criticism on the old logic and the latter a new textbook of the science.
The logic of Ramus enjoyed a great celebrity for a time, and there existed a school of Ramists boasting numerous adherents in France, Germany and Holland.
It cannot be said, however, that Ramus's innovations mark any epoch in the history of logic. His rhetorical leaning is seen in the definition of logic as the "ars disserendi"; he maintains that the rules of logic may be better learned from observation of the way in which Cicero persuaded his hearers than from a study of the Organon.
The distinction between natural and artificial logic, i.e.
between the implicit logic of daily speech and the same logic made explicit in a system, passed over into the logical handbooks.
Logic falls, according to Ramus, into two parts - invention (treating of the notion and definition) and judgment (comprising the judgment proper, syllogism and method).
Again, the relation between logic in its widest sense and the theory of knowledge is extremely close.
to formal logic. An attempt has been made by some philosophers to substitute "Gnosiology" (Gr.
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.
ep. 199), held for a time the mathematical chair at Padua, and was successively professor of logic and of law at Basel, where he died on the 29th of November 1759.
Jevons in the chair of logic and philosophy, at Owens College, Manchester.
In 1893 he went to Aberdeen, and finally in 1895 to the chair of logic at Glasgow, which he held till his death on the 5th of February 1902.
In 1842 he took a "double-first" and was elected fellow of B alliol, and lecturer in mathematics and logic. Four years later he took orders, and with the aim of helping forward the education of the very poor, he accepted the headship of Kneller Hall, a college which the government formed for the training of masters of workhouse and penal schools.
With the exception of a satiric comedy, Il Candelajo, all the works of this period are devoted to this logic - De Umbris Idearum, Ars Memoriae, De cornpendiosa architecture et complemento artis Lullii, and Cantus Circaeus.
It provided also a substitute for either the Aristotelian or the Ramist logic, which was an additional element in its favour.
Indeed, there still existed on the statute a provision that "Masters and Bachelors who did not follow Aristotle faithfully were liable to a fine of five shillings for every point of divergence, and for every fault committed against the logic of the Organon."
Perhaps the most interesting are the lectures of 1812 on Transcendental Logic (Nach.
"Dialectic" in this sense is the equivalent of "logic."
The Stoics divided XoytK17 (logic) into rhetoric and dialectic, and from their time till the end of the middle ages dialectic was either synonymous with, or a part of, logic.
This post he occupied for three successive sessions, during which he continued writing for the Westminster, and also in 1842 helped Mill with the revision of the MS. of his System of Logic. In 1843 he contributed the first review of the book to the London and Westminster.
In 1860 he was appointed by the crown to the new chair of logic and English in the university of Aberdeen (created on the amalgamation of the two colleges, King's and Marischal, by the Scottish Universities Commission of 1858).
Up to this date neither logic nor English had received adequate attention in Aberdeen, and Bain devoted himself to supplying these deficiencies.
The year 1870 saw the publication of the Logic. This, too, was a work designed for the use of students; it was based on J.
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.
praedicabilis, that which may be stated or affirmed), in scholastic logic, a term applied to a classification of the possible relations in which a predicate may stand to its subject.
See the modern logic textbooks.
As we advance from the logic to the metaphysics and from that to his ontology, it becomes clear that the concepts are only " categories " or predicates of a reality lying outside of them, and there is an ultimate division between the world as the object or matter of thought and the thinking or moving principle which gives its life.
The " Logic " of Hegel is merely the continuation of Kant's " Deduction " of the categories and ideas of the reason which has generally been recognized as the soberest of attempts to set forth the presuppositions which underlie all experience.
Harris; 4 (b) of confident application to the central problems of logic, ethics and politics, fine art and religion, and as a principle of constructive criticism and interpretation chiefly in T.
7 Knowledge and Reality (1885); Logic (1888).
3 The issue between the two theories under this head may here be left with the remark that it is a curious comment on the logic of dualism that setting out to vindicate the reality of an objective standard of truth it should end in the most subjective of all the way a thing appears to the individual.
Similarly from the side of logic. It is not the teaching of idealism alone but of the facts which logical analysis has brought home to us that all difference in the last resort finds its ground in the quality or content of the things differentiated, and that this difference of content shows in turn a double strand, the strand of sameness and the strand of otherness - that in which and that by which they differ from one another.
If in a well-known passage (Logic § 212) he seems to countenance the Spinoxistic view he immediately corrects it by assigning an " actualizing force " to this illusion and making it a " necessary dynamic element of truth."
(B) Works on particular branches of philosophy: (a) Logic F.
Bradley, Principles of Logic (1883); B.
Bosanquet, Logic (1888) and Essentials of Logic (1895).
Perceiving the difficulty of the Socratic dictum he endeavoured to give to the word "knowledge" a definite content by divorcing it absolutely from the sphere of sense and experience, and confining it to a sort of transcendental dialectic or logic. The Eleatic unity is Goodness, and is beyond the sphere of sensible apprehension.
Logic he regarded as a practical art, and his Esercizioni logici has the further title, Art of deriving benefit from ill-constructed books.
in 1878 he was instructor in English literature and logic for four years at the university of California.
The most important of his numerous works are the Wissenschaftslehre, oder Versuch einer neuen Darstellung der Logik, advocating a scientific method in the study of logic (4 vols., Sulzbach, 1837); the Lehrbuch der Religionswissenschaft (4 vols., Sulzbach, 1834), a philosophic representation of all the dogmas of Roman Catholic theology; and Athanasia, oder Gri nde fiir die Unsterblichkeit der Seele (2nd ed., Mainz, 1838).
His religious unorthodoxy was condoned because he never scoffed; his political heresies, after their first effect was over, seemed harmless from the very want of logic and practical spirit in them, while part at least of his literary secret was the common property of almost every one who attempted literature.
(I) In formal logic it is applied to those terms which denote qualities, attributes, circumstances, as opposed to concrete terms, the names of things; thus "friend" is concrete, "friendship" abstract.
But some, especially those on Celestial Dynamics and Organic Motion, are admirable examples of what really valuable work may be effected by a man of high intellectual powers, in spite of imperfect information and defective logic.
The captious logic of the Megarian school was indeed in some cases closely related to sceptical results.
Logic and physical science they held to be useless, for all knowledge is immediate sensation (see Protagoras).
John of Salisbury attended Abelard's lectures in 1136, and, after spending two years in the study of logic in Paris, passed three more in the scholarly study of Latin literature at Chartres, where a sound and healthy tradition, originally due to Bernard of Chartres (fl.
Though he did not altogether neglect logic and physics, he maintained that virtue is the only real aim of men.
He excelled in logic, the theory of knowledge, ethics and physics.
Five years later he became professor ordinarius of logic and metaphysics; in 1759 he exchanged this for a professorship of rhetoric and poetry.
About this time began his acquaintance with David Hume, which afterwards ripened into friendship. In 1751 he was elected professor of logic at Glasgow, and in 1752 was transferred to the chair of moral philosophy, which had become vacant by the death of Thomas Craigie, the successor of Hutcheson.
The cities thus privileged, however, though receiving complete Roman citizenship, were not, as the logic of public law might seem to demand, incorporated in Rome, but continued to exist as independent urban units; and this anomaly survived in the municipal system which was developed, on the basis of these grants of citizenship, after the Social War.
See also Denotation; and any text-books on elementary logic, e.g.
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.
But as yet he had given no sign of system, and-what is surprisingno trace of logic. Aristotle was primarily a metaphysician against Plato; a metaphysician before he was a logician; a metaphysician who made what he called primary philosophy pd.Yrri 4aXocr00La) the starting-point of his philosophical development, and ultimately of his philosophical system.
from 335-334 to 322; and from the references of one work to another Zeller has further suggested a chronological order of composition during this period of twelve years, beginning with the treatises on Logic and Physics, and ending with that on Metaphysics.
So also he might add the appendix to the Sophistical Elenchi, long after he had written that book, and perhaps, to judge from its being a general claim to have discovered the syllogism, when the founder of logic had more or less realized that he had written a number of connected treatises on reasoning.
How otherwise, we wonder, could one man writing alone and with so few predecessors compose the first systematic treatises on the psychology of the mental powers and on the logic of reasoning, the first natural history of animals, and the first civil history of one hundred and fifty-eight constitutions, in addition to authoritative treatises on metaphysics, biology, ethics, politics, rhetoric and poetry; in all penetrating to the very essence of the subject, and, what is most wonderful, describing more facts than any other man has ever done on so many subjects ?
On the other hand, in the case of logic, it is certain that he did not combine his works on the subject into one whole, but that the Peripatetics afterwards put them together as organic, and made them the parts of logic as an organon, as they are treated by Andronicus.
Again, according to both works, an individual substance is a subject, a universal its predicate; and they have in common the Aristotelian metaphysics, which differs greatly from the modern logic of subject and predicate.
In other words, to him subject meant real as well as nominal subject, and predicate meant real as well as nominal predicate; whereas modern logic has gradually reduced both to the nominal terms of a proposition.
- Another example of Aristotle's gradual desertion of Plato is exhibited by the De Interpretatione as compared with the Prior Analytics, and it shows another gradual history in Aristotle's philosophy, namely, the development of subject, predicate and copula, in his logic.
Here Aristotle, starting from the previous grammar of sentences in general, proceeded, for the first time in philosophical literature, to disengage the logic of the proposition, or that sentence which can alone be true or false, whereby it alone enters into reasoning.
The point of Aristotle was to draw a line between rational and other evidences, to insist on the former, and in fact to found a logic of rhetoric. But if in the Rhetoric to Alexander, not he, but Anaximenes, had already performed this great achievement, Aristotle would have been the meanest of mankind; for the logic of rhetoric would have been really the work of Anaximenes the sophist, but falsely claimed by Aristotle the philosopher.
As we cannot without a tittle of evidence accept such a consequence, we conclude that Aristotle formulated the distinction between argumentative and adventitious, artificial and inartificial evidences, both in the Rhetoric to Alexander and in the Rhetoric; and that the former as well as the latter is a genuine work of Aristotle, the founder of the logic of rhetoric.
In fact, this interesting treatise contains a rudimentary treatment of rational evidences in rhetoric and is therefore earlier than the Rhetoric, which exhibits a developed analysis of these rational evidences as special logical forms. Together, the earlier and the later Rhetoric show us the logic of rhetoric in the making, going on about 34 0, the last date of the Rhetoric to Alexander, and more developed in or after 336 B.C., the last date of the Rhetoric. Nor is this all: the earlier Rhetoric to Alexander and the later Rhetoric show us logic itself in the making.
He gradually became a logician out of his previous studies: out of metaphysics, for with him being is always the basis of thinking, and common principles, such as that of contradiction, are axioms of things before axioms of thought, while categories are primarily things signified by names; out of the mathematics of the Pythagoreans and the Platonists, which taught him the nature of demonstration; out of the physics, of which he imbibed the first draughts from his father, which taught him induction from sense and the modification of strict demonstration to suit facts; out of the dialectic between man and man which provided him with beautiful examples of inference in the Socratic dialogues of Xenophon and Plato; out of the rhetoric addressed to large audiences, which with dialectic called his attention to probable inferences; out of the grammar taught with rhetoric and poetics which led him to the logic of the proposition.
We cannot write a history of the varied origin of logic, beyond putting the rudimentary logic of the proposition in the De Interpretatione before the less rudimentary theory of categories as significant names capable of becoming predicates in the Categories, and before the maturer analysis of the syllogism in the Analytics.
But at any rate the process was gradual; and Aristotle was advanced in metaphysics, mathematics, physics, dialectics, rhetoric and poetics, before he became the founder of logic.
the Categories earlier than some parts of the Metaphysics, because under the influence of Platonic forms it talks of inherent attributes, and allows secondary substances which are universal; the De Interpretatione earlier than the Analytics, because in it the Platonic analysis of the sentence into noun and verb is retained for the proposition; the Eudemian Ethics and the Magna Moralia earlier than the Nicomachean Ethics, because they are rudimentary sketches of it, and the one written rather in the theological spirit, the other rather in the dialectical style, of Plato; and the Rhetoric to Alexander earlier than the Rhetoric, because it contains a rudimentary theory of the rational evidences afterwards developed into a logic of rhetoric in the Rhetoric and Analytics.
It gives too much weight to Aristotle's logic, and too little to his metaphysics, on account of two prejudices of the commentators which led them to place both logic and physics before metaphysics.
With some more show of authority it puts Logic before Metaphysics.
Acting on this hint, not Aristotle but the Peripatetics inferred that all logic is an instrument (6pyavov) of all sciences; and by the time of Andronicus, who was one of them and sometimes called " the eleventh from Aristotle," the order, LogicPhysics-Metaphysics, had become established pretty much as we have it now.
It is, however, not the real order for studying the philosophy of Aristotle, because there is more Metaphysics in his Physics than Physics in his Metaphysics, and more Metaphysics in his Logic than Logic in his Metaphysics.
The commentators themselves were doubtful about the order: Boethus proposed to begin with Physics, and some of the Platonists with Ethics or Mathematics; while Andronicus preferred to put Logic first as Organon (Scholia, 25 b 34 seq.).
Hence the Posterior Analytics, which is Aristotle's authoritative logic of science, is of peculiar interest because, after beginning by defining science as investigating necessary objects from necessary principles (i.
But what has become of Logic, with which the traditional order of Andronicus begins Aristotle's works (1-148 b 8)?
So far from coming first, Logic comes nowhere in his classification of science.
Aristotle was the founder of Logic; because, though others, and especially Plato, had made occasional remarks about reason (X yos), Aristotle was the first to conceive it as a definite subject of investigation.
He got so far as gradually to write short discourses and long treatises, which we, not he, now arrange in the order of the Categories or names; the De Interpretatione on propositions; the Analytics, Prior on syllogism, Posterior on scientific syllogism; the Topics on dialectical syllogism; the Sophistici Elenchi on eristical or sophistical syllogism; and, except that he had hardly a logic of induction, he covered the ground.
Secondly, he made no division of logic. In the Categories he distinguished names and propositions for the sake of the classification of names; in the De Interpretatione he distinguished nouns and verbs from sentences with a view to the enunciative sentence: in the Analytics he analysed the syllogism into premisses and premisses into terms and copula, for the purpose of syllogism.
But he never called any of these a division of all logic. Thirdly, he had no one name for logic. In the Posterior Analytics (i.
It is a commentator's blunder to suppose that the founder of logic elaborated it into a system, and then applied it to the sciences.
He really left the Peripatetics to combine his scattered discourses and treatises into a system, to call it logic, and logic Organon, and to put it first as the instrument of sciences; and it was the Stoics who first called logic a science, and assigned it the first place in their triple classification of science into logic, physics, ethics.
Is logic, then, according to him, not science but dialectic ?
The Analytics, the most important part, so far from being dialectic or logic in that narrow sense, is called by him not logic but analytic science (avaXvro taTiipn, Rhet.
then Aristotle himself regarded rhetoric as partly science and partly dialectic, perhaps he would have said that his works on reasoning are some science and others not, and that, while the investigation of syllogism with a view to scientific syllogism in the Analytics is analytic science, the investigation of dialectical syllogism, in the Topics, with its abuse, eristical syllogism, in the Sophistici Elenchi, is dialectic. At any rate, these miscellaneous works on reasoning have no right to stand first in Aristotle's writings under any one name, logic or Organon.
We shall begin therefore with that primary philosophy which is the real basis of his philosophy, and proceed in the order of his classification of science to give his chief doctrines on: (1) Speculative philosophy, metaphysical and physical, including his psychology, and with it his logic.
The list of Wundt's works is long and comprehensive, including physiology, psychology, logic and ethics.
See Association Of Ideas; Metaphysics; Psychology; Logic;.
Hsiian Tsang informs us that Dinnaga, the celebrated Buddhist philosopher and controversialist, author of well-known books on logic, resided there.
He was educated at the university of Glasgow, where he graduated first in classics, logic and philosophy.
- THE Science Of Being Side by side with psychology, the science of mind, and with logic, the science of reasoning, metaphysics is tending gradually to reassert its ancient Aristotelian position as the science of being in general.
They saw also the logic of Kant's deduction, that all we can know from such mental data and mental categories must also be mental.
Schelling himself, as soon as he saw his own formulae exposed in the logic or rather dialectic of his disciple, began to reconsider his philosophy of identity, and brought some powerful objections against both the conclusions and the method of Hegel.
Hegel, he said, had only supplied the logic of negative philosophy; and it must be confessed that the most which could be extracted from the Hegelian dialectic would be some connexion of thoughts without proving any existence of corresponding things.
Sigwart in his Logic has also opposed the parallelistic view itself; and James has criticized it from the point of view that the soul selects out of the possibilities of the brain means to its own ends.
His psychology poisons his logic.
In his logic, and especially in his epistemology, Wundt appears as a mediator between Hume and Kant, but with more leaning to the latter.
On this false abstraction Sigwart has made an excellent criticism in an appendix at the end of his Logic, where he remarks that we cannot isolate events from the substances of which they are attributes.
The conclusion that reason in transcending experience can show no more than the necessity of " ideals " is the only conclusion which could follow from Wundt's phenomenalism in psychology, logic, and epistemology.
He forgets apparently that faith is a belief in things beyond ideas and ideals, which is impossible in his psychology of judgment and logic of inference.
It was counteracted to some extent by the study at the universities of the deductive logic of Aristotle and the inductive logic of Bacon, by parts of Mill's own logic, and by the natural realism of Reid, Stewart, and Hamilton, which met Hume's scepticism by asserting a direct perception of the external world.
1856; professor of logic and metaphysics at Edinburgh University from 1880) in his Scottish Philosophy (1885), and Hegelianism and Personality (1887).
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.
another body similar to my other lip. On this theory, then, founded on the conscious facts of double and single pressure in touch, and on the logic of inference, we have at once a reason for our knowledge of external bodies, and an explanation of the early appearance of that knowledge.
Philo tells us expressly that they rejected logic as unnecessary to the acquisition of virtue, and speculation on nature as too lofty for the human intellect.
It is important as an addition to the logic of the subject rather than on account of any practical advantages which it affords for purposes of calculation.
Mill held with his System of Logic to Hartley and James Mill.
In the logic of Mill, e.g., we find much of a special character that has no counterpart in Hume, much that is introduced ab extra, from general considerations of scientific procedure, but, so far as the groundwork is concerned, the System of Logic is a mere reproduction of Hume's doctrine of knowledge.
In logic it came to be used as the translation of the Gr.
Apart from this, Hobbes owed little to his university training, which was based on the scholastic logic then prevalent.
In the course of the next seven years in Derbyshire and abroad, Hobbes took his pupil over rhetoric, 2 logic, astronomy, and the principles of law, with other subjects.
The Epicurean philosophy is traditionally divided into the three branches of logic, physics and ethics.
Ethics had been based upon logic and metaphysics.
Logic must go, but so also must the state, as a specially-privileged and eternal order of things, as anything more than a contrivance serving certain purposes of general utility.
To the Epicureans the elaborate logic of the Stoics was a superfluity.
In place of logic we find canonic, the theory of the three tests of truth and reality.
The Epicurean canon is a rejection of logic; it sticks fast to the one point that " sensation is sensation, ?
Like Hamilton, Mansel maintained the purely formal character of logic, the duality of consciousness as testifying to both self and the external world, and the limitation of knowledge to the finite and "conditioned."
enlarged 1862), in which the limits of logic as the "science of formal thinking" are rigorously determined.
He despised logic, and rejected the philosophy of nature as beyond the powers of man.
A judgment which is not prompted by motives and inspired by interest, which has not for its aim the satisfaction of a cognitive purpose, is psychologically impossible, and it is, therefore, mistaken to construct a logic which abstracts from all these facts.
The "psychologicm" thus introduced into logic amounts to a systematic protest against the notion of a dehumanized thought and the study of logic in abstraction from actual psychic process.
The application to logic, therefore, was mainly made by his followers, John Dewey and his pupils, in the Chicago Decennial Publications and especially in their Studies in Logical Theory (1903), where, however, the term used is "instrumentalism," and by F.
Besides the three main disciplines the student takes up according to his tastes other subjects, such as rhetoric (ma`ani wabayan), logic (mantiq), prosody (`arud), and the doctrine of the correct pronunciation of the Koran (gira'a watajwid).
He was educated at Glasgow and Edinburgh, where, from 1846 to 1856, he was professor of Logic at New College.
He edited the North British Review from 1850 to 1857, and in 1856, having previously been a Free Church minister, he succeeded Sir William Hamilton as professor of Logic and Metaphysics at Edinburgh University.
After a childhood spent in an austerity which stigmatized as unholy even the novels of Sir Walter Scott, he began his college career at the age of fourteen at a time when Christopher North and Dr Ritchie were lecturing on Moral Philosophy and Logic. His first philosophical advance was stimulated by Thomas Brown's Cause and Effect, which introduced him to the problems which were to occupy his thought.
In 1836 Sir William Hamilton was appointed to the chair of Logic and Metaphysics, and Fraser became his pupil.
If the five ascetics to whom the words were addressed once admitted this implication, logic would drive them also to admit all that followed.
He published a work on logic (Vernunftlehre als Anweisung zum richtigen Gebrauche der Vernunft, 1756, 5th ed., 1790), and two popular books on the religious questions of the day.
For admission to the baccalaureate a preliminary test or " Responsions " was first required, at which the candidate had to dispute in grammar or logic with a master.
The nature of axiomatic certainty is part of the fundamental problem of logic and metaphysics.
In a MS. of 102 quarto sheets, of which the first three and the seventh are wanting, there is preserved the original sketch of the Hegelian system, so far as the logic and metaphysics and part of the philosophy of nature are concerned.
Hegel's lectures, in the winter of 1801-1802, on logic and metaphysics were attended by about eleven students.
Those on Aesthetics, on the Philosophy of Religion, on the Philosophy of History and on the History of Philosophy, have been published by his editors, mainly from the notes of his students, under their separate heads; while those on logic, psychology and the philosophy of nature are appended in the form of illustrative and explanatory notes to the sections of his Encykloptidie.
Hegel and his family retired for the summer to the suburbs, and there he finished the revision of the first part of his Science of Logic. On the beginning of the winter session, however, he returned to his house in the Kupfergraben.
The Phenomenology is neither mere psychology, nor logic, nor moral philosophy, nor history, but is all of these and a great deal more.
Reason abandons her efforts to mould the world, and is content to let the aims of individuals work out their results independently, only stepping in to lay down precepts for the cases where individual actions conflict, and to test these precepts by the rules of formal logic.
Accordingly the history of philosophy is the presupposition of logic, or the three branches of philosophy form a circle.
The exposition or constitution of the " idea " is the work of the Logic. As the total system falls into three parts, so every part of the system follows the triadic law.
They rejected as an illegitimate interpolation the eternal subject of development, and, instead of one continuing God as the subject of all the predicates by which in the logic the absolute is defined, assumed only a series of ideas, products of philosophic activity.
Thought became only the result of organic conditions - subjective and human; and the system of Hegel was no longer an idealization of religion, but a naturalistic theory with a prominent and peculiar logic.
The logic of Hegel is the only rival to the logic of Aristotle.
His logic is an enumeration of the forms or categories by which our experience exists.
The fact which ordinary thought ignores, and of which ordinary logic therefore provides no account, is the presence of gradation and continuity in the world.
The beginning of the logic is an illustration of this.
The third part of logic evidently is what contains the topics usually treated in logic-books, though even here the province of logic in the ordinary sense is exceeded.
The first two divisions - the " objective logic " - are what is usually called metaphysics.
The merit of Hegel is to have indicated and to a large extent displayed the filiation and mutual limitation of our forms of thought; to have arranged them in the order of their comparative capacity to give a satisfactory expression to truth in the totality of its relations; and to have broken down the partition which in Kant separated the formal logic from the transcendental analytic, as well as the general disruption between logic and metaphysic. It must at the same time be admitted that much of the work of weaving the terms of thought, the categories, into a system has a hypothetical and tentative character, and that Hegel has rather pointed out the path which logic must follow, viz.
In trying to subject history to the order of logic they sometimes misconceive the filiation of ideas.
Hutcheson Stirling's Secret of Hegel (2 vols., London, 1865) contains a translation of the beginning of the Wissenschaft der Logik; the " Logic " from the Encyklopeidie has been translated, with Prolegomena, by W.
Harris, Hegel's Logic (1890); J.
Baillie, Origin and Significance of Hegel's Logic (1901), and Outline of the Idealistic Construction of Experience (1906); P. Barth, Die Geschichtsphilosophie Hegels (1890); J.
McTaggart, Commentary on Hegel's Logic (1910).
Complete or perfect knowledge is confined to the domain of pure thought, to logic and mathematics.
From 1801 to 1804 he was professor of philosophy at Frankfort-on-the-Oder, after which he succeeded Kant in the chair of logic and metaphysics at the university of Konigsberg.
When the Bourbons were restored, his hatred against Napoleon led him to become a Legitimist - a conclusion which says more for the simplicity of his character than for the strength or logic of his political creed.
Thus, though, in so far as he asserted his fundamental doctrine without doubt or qualification, he was a dogmatist, in all else he was a sceptic. Again, the Eleatic Parmenides, deriving from the theologian Xenophanes the distinction between E 71'caT77 /, 07 and (W a, conceived that, whilst the One exists and is the object of knowledge, the Multiplicity of things becomes and is the object of opinion; but, when his successor Zeno provided the system with a logic, the consistent application of that logic resolved the fundamental doctrine into the single proposition " One is One," or, more exactly, into the single identity " One One."
5, 6), show that, in defending these propositions, Gorgias availed himself of the arguments which Zeno had used to discredit the popular belief in the existence of the Many; in other words, that Gorgias turned the destructive logic of Zeno against the constructive ontology of Parmenides, thereby not only reducing Eleaticism to nothingness, but also, until such time as a better logic than that of Zeno should be provided, precluding all philosophical inquiry whatsoever.
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.
Pointing out that the sophists of that dialogue " profess Eis ap€riffs E7rt,u XELav 7rporpNiaL by means of dialogue," that ' they challenge the interlocutor inr w Xoyov," that " their examples are drawn from common objects and vulgar trades," that " they maintain positions that we know to have been held by Megarians and Cynics," he infers that " what we have here presented to us as ' sophistic ' is neither more nor less than a caricature of the Megarian logic "; and further, on the ground that " the whole conception of Socrates and his effect on his contemporaries, as all authorities combine to represent it, requires us to assume that his manner of discourse was quite novel, that no one before had systematically attempted to show men their ignorance of what they believed themselves to know," he is " disposed to think that the art of disputation which is ascribed to sophists in the Euthydemus and the Sophistes (and exhaustively analysed by Aristotle in the HEpi originated entirely with Socrates, and that he is altogether responsible for the form at least of this second species of sophistic."
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.
of England, or one of his sons, the heir to the Scottish throne, and by David's marriage with Margaret Logic. In 1363 he rose in rebellion, and after having made his submission was seized and imprisoned together with four of his sons, being only released a short time before David's death in February 1371.
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."
LOGIC (Xoyu, sc. r xvr i, the art of reasoning), the name given to one of the four main departments of philosophy, though its sphere is very variously delimited.
The present article is divided into The Problems of Logic, History.
The Problems of Logic. Introduction.
- Logic is the science of the processes of inference.
This science of inference in general is logic.
Logic, however, did not begin as a science of all inference.
In this way the Presocratics and Sophists, and still more Socrates and Plato, threw out hints on sense and reason, on inferential processes and scientific methods which may be called anticipations of logic. But Aristotle was the first to conceive of reasoning itself as a definite subject of a special science, which he called analytics or analytic science, specially designed to analyse syllogism and especially demonstrative syllogism, or science, and to be in fact a science of sciences.
He was therefore the founder of the science of logic.
Hence, without his saying it in so many words, Aristotle's logic perforce became a logic of deductive reasoning, or syllogism.
As it happened this deductive tendency helped the development of logic. The obscurer premises of analogy and induction, together with the paucity of experience and the backward state of physical science in Aristotle's time would have baffled even his analytical genius.
Nevertheless, the wider question remained for logic: what is the nature of all inference, and the special form of each of its three main processes?
As then the reasoning of the syllogism was the main problem of Aristotle's logic, what was his analysis of it?
The explanation is that outer speech is more obvious than inner thought, and that grammar and poetic criticism, rhetoric and dialectic preceded logic, and that out of those arts of language arose the science of reasoning.
All these points about speech, eloquence and argument between man and man were absorbed into Aristotle's theory of reasoning, and in particular the grammar of the sentence consisting of noun and verb caused the logic of the proposition consisting of subject and predicate.
Aristotle thus was the founder of logic as a science.
But he laid too much stress on reasoning as syllogism or deduction, and on deductive science; and he laid too much stress on the linguistic analysis of rational discourse into proposition and terms. These two defects remain ingrained in technical logic to this day.
Some have devoted themselves to induction from sense and experience and widened logic till it has become a general science of inference and scientific method.
Others have devoted themselves to the mental analysis of reasoning, and have narrowed logic into a science of conception, judgment and reasoning.
The former belong to the school of empirical logic, the latter to the school of conceptual and formal logic. Both have started from points which Aristotle indicated without developing them.
This empirical groundwork of Aristotle's logic was accepted by the Epicureans, who enunciated most distinctly the fundamental doctrine that all sensations are true of their immediate objects, and falsity begins with subsequent opinions, or what the moderns call " interpretation."
Beneath deductive logic, in the logic of Aristotle and the canonic of the Epicureans, there already lay the basis of empirical logic: sensory experience is the origin of all inference and science.
It remained for Francis Bacon to develop these beginnings into a new logic of induction.
Bacon, like Aristotle, was anticipated in this or that point; but, as Aristotle was the first to construct a system of deduction in the syllogism and its three figures, so Bacon was the first to construct a system of induction in three ministrations, in which the requisites of induction, hitherto recognized only in sporadic hints, were combined for the first time in one logic of induction.
In short, the comprehensive genius of Bacon widened logic into a general science of inference.
Mill in his Logic pointed out this defect, and without departing from Baconian principles remedied it by quoting scientific examples, in which deduction, starting from inductive principles, applies more general to less general universals, e.g.
Mill's logic has the great merit of copiously exemplifying the principles of the variety of method according to subject-matter.
The founder of logic anticipated the latest logic of science, when he recognized, not only the deduction of mathematics, but also the experience of facts followed by deductive explanations of their causes in physics.
The deepest problem of logic is the relation of sense and inference.
But we must first consider the mental analysis of inference, and this brings us to conceptual and formal logic.
Aristotle's logic has often been called formal logic; it was really a technical logic of syllogism analysed into linguistic elements, and of science rested on an empirical basis.
At the same time his psychology, though maintaining his empiricism, contained some seeds of conceptual logic, and indirectly of formal logic. Intellectual development, which according to the logic of the Analytics consists of sense, memory, experience, induction and intellect, according to the psychology of the De Anima consists of sense, imagination and intellect, and one division of intellect is into conception of the undivided and combination of conceptions as one (De An.
But the same passage relegates conceptions and their combinations to the De Anima, and confines the De Inter pretatione to names and propositions in conformity with the linguistic analysis which pervades the logical treatises of Aristotle, who neither brought his psychological distinction between conceptions and their combinations into his logic, nor advanced the combinations of conceptions as a definition of judgment (Kcp16cs), nor employed the mental distinction between conceptions and judgments as an analysis of inference, or reasoning, or syllogism: he was no conceptual logician.
The history of logic shows that the linguistic distinction between terms and propositions was the sole analysis of reasoning in the logical treatises of Aristotle; that the mental distinction between conceptions (g vvocac) and judgments (a uiwara in a wide sense) was imported into logic by the Stoics; and that this mental distinction became the logical analysis of reasoning under the authority of St Thomas Aquinas.
Hence arose conceptual logic; according to which conception is a simple apprehension of an idea without belief in being or not being, e.g.
man is running or not running; and reasoning is a combination of judgments: conversely, there is a mental analysis of reasoning into judgments, and judgment into conceptions, beneath the linguistic analysis of rational discourse into propositions, and propositions into terms. Logic, according to this new school, which has by our time become an old school, has to co-ordinate these three operations, direct them, and, beginning with conceptions, combine conceptions into judgments, and judgments into inference, which thus becomes a complex combination of conceptions, or, in modern parlance, an extension of our ideas.
But at length many of them became formal logicians, who held that logic is the investigation of formal thinking, or consistent conception, judgment and reasoning; that it shows how we infer formal truths of consistency without material truth of signifying things; that, as the science of the form or process, it must entirely abstract from the matter, or objects, of thought; and that it does not tell us how we infer from experience.
Thus has logic drifted further and further from the real and empirical logic of Aristotle the founder and Bacon the reformer of the science.
The great merit of conceptual logic was the demand for a mental analysis of mental reasoning, and the direct analysis of reasoning into judgments which are the sole premises and conclusions of reasoning and of all mental inferences.
The Schoolmen, however, gradually came to realize that the result to their logic was to make it a sermocionalis scientia, and to their metaphysics the danger of nominalism.
St Thomas made a great advance by making logic throughout a rationalis scientia; and logicians are now agreed that reasoning consists of judgments, discourse of propositions.
This distinction is, moreover, vital to the whole logic of inference, because we always think all the judgments of which our inference consists, but seldom state all the propositions by which it is expressed.
The conceptual logic supposes that conception always precedes judgment; but the truth is that sensory judgment begins and inferential judgment ends by preceding conception.
The conceptual logic has made the mistake of making ideation a stage in thought prior to judgment.
It was natural enough that the originators of conceptual logic, seeing that judgments can be expressed by propositions, and conceptions by terms, should fall into the error of supposing that, as propositions consist of terms, so judgments consist of conceptions, and that there is a triple mental order - conception, judgment, reasoning - parallel to the triple linguistic order - term, proposition, discourse.
Empirical logic, the logic of Aristotle and Bacon, is on the right way.
Conceptual logic, on the other hand, is false from the start.
It is not the first business of logic to direct us how to form conceptions signified by terms, because sense is a prior cause of judgment and inference.
It is not the second business of logic to direct us how out of conceptions to form judgments signified by propositions, because the real causes of judgments are sense, memory, experience and inference.
It is, however, the main business of logic to direct us how out of judgments to form inferences signified by discourse; and this is the one point which conceptual logic has contributed to the science of inference.
Formal logic has arisen out of the narrowness of conceptual logic. The science of inference no doubt has to deal primarily with formal truth or the consistency of premises and conclusion.
The question of logic is how we infer in fact, as well as perfectly; and we cannot understand inference unless we consider inferences of probability of all kinds.
Lastly, the science of inference is not indeed the science of sensation, memory and experience, but at the same time it is the science of using those mental operations as data of inference; and, if logic does not show how analogical and inductive inferences directly, and deductive inferences indirectly, arise from experience, it becomes a science of mere thinking without knowledge.
Logic is related to all the sciences, because it considers the common inferences and varying methods used in investigating different subjects.
Logic is the science of the processes of inference.
The real point is their interdependence, which is so intimate that one sign of great philosophy is a consistent metaphysics, psychology and logic. If the world of things is known to be partly material and partly mental, then the mind must have powers of sense and inference enabling it to know these things, and there must be processes of inference carrying us from and beyond the sensible to the insensible world of matter and mind.
It is clear then that a man's metaphysics and psychology must colour his logic. It is accordingly necessary to the logician to know beforehand the general distinctions and principles of things in metaphysics, and the mental operations of sense, conception, memory and experience in psychology, so as to discover the processes of inference from experience about things in logic.
Hegel, having identified being with thought, merged metaphysics in logic. But he divided logic into objective and subjective, and thus practically confessed that there is one science of the objects and another of the pro cesses of thought.
Psychologists, seeing that inference is a mental operation, often extemporize a theory of inference to the neglect of logic. But we have a double consciousness of inference.
This elaborate consciousness of inferential process is the justification of logic as a distinct science, and is the first step in its method.
But it is not the whole method of logic, which also and rightly considers the mental process necessary to language, without substituting linguistic for mental distinctions.
Logic has to consider the things we know, the minds by which we know them from sense, memory and experience to inference, and the sciences which systematize and extend our knowledge of things; and having considered these facts, the logician must make such a science of inference as will explain the power and the poverty of human knowledge.
General Tendencies Of Modern Logic There are several grounds for hope in the logic of our day.
It does not, with the former, regard logic as purely formal in the sense of abstracting thought from being, nor does it follow the latter in amalgamating metaphysics with logic by identifying being with thought.
That is, logic is grounded by them, not upon an effete tradition but upon a new investigation of thought as it actually is in its psychological foundations, in its significance for knowledge, and its actual operation in scientific methods."
Aristotle's was a logic which steered, as Trendelenburg has shown, between Kantian formalism and Hegelian metaphysics; it was a logic which in the Analytics investigated the syllogism as a means to understanding knowledge and science: it was a logic which, starting from the psychological foundations of sense, memory and experience, built up the logical structure of induction and deduction on the profoundly Aristotelian principle that " there is no process from universals without induction, and none by induction without sense."
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.
- The emphasis now laid on judgment, the recovery from Hume's confusion of beliefs with ideas and the association of ideas, and the distinction of the mental act of judging from its verbal expression in a proposition, are all healthy signs in recent logic. The most fundamental question, before proceeding to the investigation of inference, is not what we say but what we think in making the judgments which, whether we express them in propositions or not, are both the premises and the conclusion of inference; and, as this question has been diligently studied of late, but has been variously answered, it will be well to give a list of the more important theories of judgment as follows: a.
Sense is the evidence of inference; directly of analogical and inductive, directly or indirectly of deductive, inference; and therefore, if logic refuses to include sensory beliefs among judgments, it will omit the fundamental constituents of inference, inference will no longer consist of judgments but of sensory beliefs plus judgments, and the second part of logic, the logic of judgment, the purpose of which is to investigate the constituents of inference, will be like Hamlet without the prince of Denmark.
The sensory judgment then, which is nothing but a belief that at the moment of sense something sensible exists, is a proof that not all judgment requires conception, or synthesis or analysis of ideas, or decision about the content, or about the validity, of ideas, or reference of an ideal content to reality, as commonly, though variously, supposed in the logic of our day.
Starting, then, from this fundamental distinction between judgments of existence and judgments of non-existence, we may hope to steer our way between two extreme views which emanate from two important thinkers, each of whom has produced a flourishing school of psychological logic.
Venn, in his Symbolic Logic, proposes the four forms, xy = o, xy = o, xy>o, xy> o (where y means " not-y "), but only as alternative to the ordinary forms. Bradley says that " ` S-P is real' attributes S-P, directly or indirectly, to the ultimate reality," and agrees with Brentano that " ` is ' never stands for anything but ` exists ' "; while Bosanquet, who follows Bradley, goes so far as to define a categorical judgment as " that which affirms the existence of its subject, or, in other words, asserts a fact."
Here, as usual in logic, tradition is better than innovation.
Nevertheless these obvious applications of Aristotelian traditions have been recently challenged, especially by Sigwart, who holds in his Logic (secs.
Here Sir William Hamilton did a real service to logic in pointing out that " Logic postulates to be allowed to state explicitly in language all that is implicitly contained in the thought."
In ordinary life we may say, " All men are mortal," " All centaurs are figments," " All square circles are impossibilities," " All candidates arriving five minutes late are fined " (the last proposition being an example of the identification of categorical with hypothetical in Keynes's Formal Logic).
The symbolic logic, which confuses " is " with " is equal to," having introduced a particular kind of predicate into the copula, falls into the mistake of reducing all predication to the one category of the quantitative; whereas it is more often in the substantial, e.g.
Finally, the great difficulty of the logic of judgment is to find the mental act behind the linguistic expression, to ascribe to it exactly what is thought, neither more nor less, and to apply the judgment thought to the logical proposition, without expecting to find it in ordinary propositions.
Beneath Hamilton's postulate there is a deeper principle of logic - _A rational being thinks only to the point, and speaks only to understand and be understood.
No logic can be sound which leads to the following analysis: If anything is a body it is extended.
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.
Wundt's Logic has the following forms: (I) 1st Fig.
No distinction is more vital in the logic of inference in general and of scientific inference in particular; and yet none has been so little understood, because, though analysis is the more usual order of discovery, synthesis is that of instruction, and therefore, by becoming more familiar, tends to replace and obscure the previous analysis.
Recent logic does scant justice to scientific analysis.
Since Mill's time, however, the logic of induction tends to revert towards syllogisms more like that of Aristotle.
The fact is that the uniformity of nature stands to induction as the axioms of syllogism do to syllogism; they are not premises, but conditions of inference, which ordinary men use spontaneously, as was pointed out in Physical Realism, and afterwards in Venn's Empirical Logic. The axiom of contradiction is not a major premise of a judgment: the dictum de omni et nullo is not a major premise of a syllogism: the principle of uniformity is not a major premise of an induction.
Nevertheless, simple as this account appears, it is opposed in every point to recent logic. In the first place, the point of Bradley's logic is that " similarity is not a principle which works.
The basis of Bradley's logic is the fallacious dialectic of Hegel's metaphysics, founded on the supposition that two things, which are different, but have something in common, are the same.
The consequence of this true metaphysics to logic is twofold: on the one hand, one singular or particular judgment, e.g.
Hence also induction is a real process, because, when we know that this individual magnet attracts iron, we are very far from knowing that all alike do so similarly; and the question of inductive logic, how we get from some similars to all similars, remains, as before, a difficulty, but not to be solved by the fallacy that inference is identification.
Secondly, a subordinate point in Bradley's logic is that there are inferences which are not syllogisms; and this is true.
But it is often thought without being expressed, and to judge the syllogism by its mere explicit expression is to commit an ignoratio elenchi; for it has been known all along that we express less than we think, and the very purpose of syllogistic logic is to analyse the whole thought necessary to the conclusion.
We may now then reassert two points about inference against Bradley's logic: the first, that it is a process from similar to similar, and not a process of identification, because two different things are not at all the same thing; the second, that it is the mental process from judgments to judgment rather than the linguistic process from propositions to proposition, because, besides the judgments expressed in propositions, it requires judgments which are not always expressed, and are sometimes even unconscious.
Logic cannot, it is true, decide what these things are, nor what the senses know about them, without appealing to metaphysics and psychology.
The aim of logic in general is to find the laws of all inference, which, so far as it obeys those laws, is always consistent, but is true or false according to its data as well as its consistency; and the aim of the special logic of knowledge is to find the laws of direct and indirect inferences from sense, because as sense produces sensory judgments which are always true of the sensible things actually perceived, inference from sense produces inferential judgments which, so far as they are consequent on sensory judgments, are always true of things similar to sensible things, by the very consistency of inference, or, as we say, by parity of reasoning.
We return then to the old view of Aristotle, that truth is believing in being; that sense is true of its immediate objects, and reasoning from sense true of its mediate objects; and that logic is the science of reasoning with a view to truth, or Logica est ars ratiocinandi, ut discernatur verum a (also.
Logic is the science of all inference, beginning from sense and ending in reason.
The logic of the last quarter of the 19th century may be said to be animated by a spirit of inquiry, marred by a love of paradox and a corresponding hatred of tradition.
If, and only if, the study of deductive logic begins with Aristotle, and the study of inductive logic with Aristotle and Bacon, it will be profitable to add the works of the following recent German and English authors: Authorities.
Bosanquet, Logic (Oxford, 1888); The Essentials of Logic (London, 1895) F.
Bradley, The Principles of Logic (London, 1883); F.
Clarke, Logic (London, 1889); W.
Davidson, The Logic of Definition (London, 1885); E.
Green, Lectures on Logic, in Works, vol.
Hibben, Inductive Logic (Edinburgh and London, 1896); F.
Stanley Jevons, The Principles of Science (3rd ed., London, 1879); Studies in Deductive Logic (London, 1880); H.
Joseph, Introduction to Logic (1906); E.
Constance Jones, Elements of Logic (Edinburgh, 1890); G.
Joyce, Principles of Logic (1908); J.
Keynes, Studies and Exercises in Formal Logic (2nd ed., London, 1887); F.
Ladd, Boston, 1887); Werner Luthe, Beitrage zur Logik (Berlin, 1872, 18 77); Members of Johns Hopkins University, Studies in Logic (edited by C. S.
Meyer, Ueberweg's System der Logik, fiinfte vermehrte Auflage (Bonn, 1882); Max Miller, Science of Thought (London, 1887); Carveth Read, On the Theory of Logic (London, 1878); Logic, Deductive and Inductive (2nd ed., London, 1901); E.
Veitch, Institutes of Logic (Edinburgh and London, 1885); J.
Venn, Symbolic Logic (2nd ed., London, 1894); The Principles of Empirical or Inductive Logic (London, 1889); J.
Welton, A Manual of Logic (London, 1891, 1896); W.
History Logic cannot dispense with the light afforded by its history so long as counter-solutions of the same fundamental problems continue to hold the field.
Logic arose, at least for the Western world, in the golden age of Greek speculation which culminated in Plato and Aristotle.
There is an Indian logic, it is true, but its priority is more than disputable.
The movement which ends in the logic of Aristotle is demonstrably self-contained.
It is with Aristotle that the bookish tradition begins to dominate the evolution of logic. The technical perfection of the analysis which he offers is, granted the circle of presuppositions within which it works, so decisive, that what precedes, even Plato's logic, is not unnaturally regarded as merely preliminary and subsidiary to it.
Greek Logic i.
Before Aristotle Logic needs as its presuppositions that thought should distinguish itself from things and from sense, that the problem of validity should be seen to be raised in the field of thought itself, and that analysis of the structure of physical thought should be recognized as the one way of solution.
Its so-called natural logic is only the potentiality of logic. The same thing is true of the first stage of Greek philosophy.
In seeking for a single material principle underlying the multiplicity of phenomena, the first nature-philosophers, Thales and the rest, did indeed raise the problem of the one and the many, the endeavour to answer which must at last lead to logic. But it is only from a point of view won by later speculation that it can be said that they sought to determine the predicates of the single subject-reality, or to establish the permanent subject of varied and varying predicates.'
Heidel, " The Logic of the Pre-Socratic Philosophy," in Dewey's Studies in Logical Theory (Chicago, 1903).
The sophists have other claims to consideration than their service to the development of logic. In the history of the origins of logic the sophistic age is simply the age of the free play of thought in which men were aware that in a sense anything can be debated and not yet aware of the sense in which all things cannot be so.
The sophists furthered the transition from dialectic to logic in two ways.
The result is a selflimiting dialectic. This higher dialectic is a logic. It is no accident that the first of the philosophical sophists, Gorgias, on the one hand, is Eleatic in his affinities, and on the other raises in the characteristic formula of his intellectual nihilism' issues which are as much logical and epistemological as ontological.
These result in the formulation of a new dialectic or logic by Plato.
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.
Plato's logic supplies a theory of universals in the doctrine of ideas.
If we add to this logic of " idea," judgment and inference, a doctrine of categories in the modern sense of the word which makes the Theaetetus, in which it first occurs, a forerunner of Kant's Critique of Pure Reason, we have clearly a very significant contribution to logic even in technical regard.
This is not only of importance in the history of the terminology of logic, but supplies a philosophy of induction.
1 ° For Plato's Logic, the controversies as to the genuineness of the dialogues may be treated summarily.
For Plato's logic this question only has interest on account of the introduction of an 'AptoToTO?
Its axioms, such as the law of contradiction, belong to first philosophy, but the doctrine as a whole falls neither under 'this head nor yet, though the thought has been entertained, under that of mathematics, since logic orders mathematical reasoning as well as all other.
Logic, therefore, is not classed as one, still less as a branch of one, among the 'ologies, ontology not excepted.
The Prior A T h e Analytics then are concerned with a formal logic to niytics.
What then is meant by principles when we ask in the closing chapter of his logic how they become known ?