Chapter 6

Authorities.â€”J. Bergmann,Reine Logik(Berlin, 1879);Die Grundprobleme der Logik(2nd ed., Berlin, 1895); B. Bosanquet,Logic(Oxford, 1888);The Essentials of Logic(London, 1895); F. H. Bradley,The Principles of Logic(London, 1883); F. Brentano,Psychologie vom empirischen Standpunkte(Vienna, 1874); R. F. Clarke,Logic(London, 1889); W. L. Davidson,The Logic of Definition(London, 1885); E. DÃ¼hring,Logik und Wissenschaftstheorie(Leipzig, 1878); B. Erdmann,Logik(Halle, 1892); T. Fowler,Baconâ€™s Novum Organum, edited, with introduction, notes, &c. (2nd ed., Oxford, 1889); T. H. Green,Lectures on Logic, inWorks, vol. iii. (London, 1886); J. G. Hibben,Inductive Logic(Edinburgh and London, 1896); F. Hillebrand,Die neuen Theorien der kategorischen SchlÃ¼sse(Vienna, 1891); L. T. Hobhouse,The Theory of Knowledge(London, 1896); H. Hughes,The Theory of Inference(London, 1894); E. Husserl,Logische Untersuchungen(Halle, 1891, 1901); W. Jerusalem,Die Urtheilsfunction(Vienna and Leipzig, 1895); W. Stanley Jevons,The Principles of Science(3rd ed., London, 1879);Studies in Deductive Logic(London, 1880); H. W. B. Joseph,Introduction to Logic(1906); E. E. Constance Jones,Elements of Logic(Edinburgh, 1890); G. H. Joyce,Principles of Logic(1908); J. N. Keynes,Studies and Exercises in Formal Logic(2nd ed., London, 1887); F. A. Lange,Logische Studien(2nd ed., Leipzig, 1894); T. Lipps,GrundzÃ¼ge der Logik(Hamburg and Leipzig, 1893); R. H. Lotze,Logik(2nd ed., Leipzig, 1881, English translation edited by B. Bosanquet, Oxford, 1884);GrundzÃ¼ge der Logik (Diktate)(3rd ed., Leipzig, 1891, English translation by G. T. Ladd, Boston, 1887); Werner Luthe,BeitrÃ¤ge zur Logik(Berlin, 1872, 1877); Members of Johns Hopkins University,Studies in Logic(edited by C. S. Peirce, Boston, 1883); J. B. Meyer,Ueberwegâ€™s System der Logik, fÃ¼nfte vermehrte Auflage (Bonn, 1882); Max MÃ¼ller,Science of Thought(London, 1887); Carveth Read,On the Theory of Logic(London, 1878);Logic, Deductive and Inductive(2nd ed., London, 1901); E. SchrÃ¶der,Vorlesungen Ã¼ber die Algebra der Logik(Leipzig, 1890, 1891, 1895); W. Schuppe,Erkenntnistheoretische Logik(Bonn, 1878);Grundriss der Erkenntnistheorie und Logik(Berlin, 1894); R. Shute,A Discourse on Truth(London, 1877); Alfred Sidgwick,Fallacies(London, 1883);The Use of Words in Reasoning(London, 1901); C. Sigwart,Logik(2nd ed., Freiburg-i.-Br. and Leipzig, 1889-1893, English translation by Helen Dendy, London, 1895); K. Uphues,Grundlehren der Logik(Breslau, 1883); J. 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. Volkelt,Erfahren und Denken(Hamburg and Leipzig, 1886); T. Welton,A Manual of Logic(London, 1891, 1896); W. Windelband,PrÃ¤ludien(Freiburg-i.-Br., 1884); W. Wundt,Logik(2nd ed., Stuttgart, 1893-1895). Text-books are not comprised in this list.

(T. Ca.)

II. 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. A critical review of some of the chief types of logical theory, with a view to determine development, needs no further justification.

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. In any case no influence upon Greek thought can be shown. The movement which ends in the logic of Aristotle is demonstrably self-contained. When we have shaken ourselves free of the prejudice that all stars are first seen in the East, Oriental attempts at analysis of the structure of thought may be treated as negligible.

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 Platoâ€™s logic, is not unnaturally regarded as merely preliminary and subsidiary to it. What follows is inevitably, whether directly or indirectly, by sympathy or by antagonism, affected by the Aristotelian tradition.

A. 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 ofThe physical philosophers.thought should be recognized as the one way of solution. Thought is somewhat late in coming to self-consciousness. Implied in every contrast of principle and fact, of rule and application, involved as we see after the event, most decisively when we react correctly upon a world incorrectly perceived, thought is yet not reflected on in the common experience. 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.1The direction of their inquiry is persistently outward. They hope to explain the opposed appearance and reality wholly within the world of things, and irrespective of the thought that thinks things. Their universal is still a material one. The level of thought on which they move is still clearly pre-logical. It is an advance on this when Heraclitus2opposes to the eyes and ears which are bad witnesses â€œfor such as understand not their languageâ€ a common something which we would do well to follow; or again when in the incommensurability of the diagonal and side of a square the Pythagoreans stumbled upon what was clearly neither thing nor image of sense, but yet was endowed with meaning, and henceforth were increasingly at home with symbol and formula. So far, however, it might well be that thought, contradistinguished from sense with its illusions, was itself infallible. A further step, then, was necessary, and it was taken at any rate by the Eleatics, when they opposed their thought to the thought of others, as the way of truth in contrast to the way of opinion. If Eleatic thought stands over against Pythagorean thought as what is valid or grounded against what is ungrounded or invalid, we are embarked upon dialectic, or the debate in which thought is countered by thought. Claims to a favourable verdict must now be substantiated in this field and in this field alone. It was Zeno, the controversialist of the Eleatic school, who was regarded in after times as the â€œdiscovererâ€ of dialectic.3

Zenoâ€™s amazing skill in argumentation and his paradoxical conclusions, particular and general, inaugurate a new era. â€œThe philosophical mind,â€ says waiter Pater,4â€œwill perhaps never be quite in health, quite sane or natural again.â€ The give and take of thought had by a swift transformation of values come by something more than its own. Zenoâ€™s paradoxes, notably, for example, the puzzle of Achilles and the Tortoise, are still capable of amusing the modern world. In his own age they found him imitators. And there follows the sophistic movement.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 anythingThe Sophists.can be debated and not yet aware of the sense in which all things cannot be so. It is the age of discussion used as a universal solvent, before it has been brought to book by a deliberate unfolding of the principles of the structure of thought determining and limiting the movement of thought itself. The sophists furthered the transition from dialectic to logic in two ways. In the first place they made it possible. Incessant questioning leads to answers. Hair-splitting, even when mischievous in intent, leads to distinctions of value. Paradoxical insistence on the accidents of speech-forms and thought-forms leads in the end to perception of the essentials. Secondly they made it necessary. The spirit of debate run riot evokes a counter-spirit to order and control it. The result is a self-limiting 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 nihilism5issues which are as much logical and epistemological as ontological. The meaning of the copula and the relation of thoughts to the objects of which they are the thoughts are as much involved as the nature of being. It is equally no accident that the name of Protagoras is to be connected, in Platoâ€™s view at least, with the rival school of Heracliteans. The problems raised by the relativism of Protagoras are no less fundamentally problems of the nature of knowledge and of the structure of thought. TheTheaetetusindeed, in which Plato essays to deal with them, is in the broad sense of the word logical, the first distinctively logical treatise that has come down to us. Other sophists, of course, with more practical interests, or of humbler attainments, were content to move on a lower plane of philosophical speculation. As presented to us, for example, in Platoâ€™s surely not altogether hostile caricature in theEuthydemus, they mark the intellectual preparation for, and the moral need for, the advance of the next generation.Among the pioneers of the sophistic age Socrates stands apart. He has no other instrument than the dialectic of his compeers, and he is as far off as the rest from a criticism of the instrument, but he uses it differently and with a difference of aim.Socrates.He construes the give and take of the debate-game with extreme rigour. The rhetorical element must be exorcised. The set harangue of teacher to pupil, in which steps in argument are slurred and the semblance of co-inquiry is rendered nugatory, must be eliminated. The interlocutors must in truth render an account under the stimulus of organized heckling from their equals or superiors in debating ability. And the aim is heuristic, though often enough the search ends in no overt positive conclusion. Something can be found and something is found. Common names are fitted for use by the would-be users being first delivered from abortive conceptions, and thereupon enabled to bring to the birth living and organic notions.Aristotle would assign to Socrates the elaboration of two logical functions:â€”general definition and inductive method.6Rightly, if we add that he gives no theory of either, and that his practical use of the latter depends for its value on selection.7It is rather in virtue of his general faith in the possibility of construction, which he still does not undertake, and because of his consequent insistence on the elucidation of general concepts, which in common with some of his contemporaries, he may have thought of as endued with a certain objectivity, that he induces the controversies of what are called the Socratic schools as to the nature of predication. These result in the formulation of a new dialectic or logic by Plato. Manifestly Socratesâ€™ use of certain forms of argumentation, like their abuse by the sophists, tended to evoke their logical analysis. The use and abuse, confronted one with the other, could not but evoke it.The one in the many, the formula which lies at the base of the possibility of predication, is involved in the Socratic doctrine of general concepts or ideas. The nihilism of Gorgias from the Eleatic point of view of bare identity, and the speechlessness of Cratylus from the Heraclitean ground of absolute difference, are alike disowned. But the one in the many, the identity in difference, is so far only postulated, not established. When the personality of Socrates is removed, the difficulty as to the nature of the Socratic universal, developed in the medium of the individual processes of individual minds, carries disciples of diverse general sympathies, united only through the practical inspiration of the masterâ€™s life, towards the identity-formula or the difference-formula of other teachers. The paradox of predication, that it seems to deny identity, or to deny difference, becomes apons asinorum. Knowledge involves synthesis or nexus. Yet from the points of view alike of an absolute pluralism, of a flux, and of a formula of bare identityâ€”anda fortioriwith any blending of these principles sufficiently within the bounds of plausibility to find an exponentâ€”all knowledge, because all predication of unity, in difference, must be held to be impossible. Platoâ€™s problem was to find a way of escape from this impasse, and among his Socratic contemporaries he seems to have singled out Antisthenes8as most in need of refutation. Antisthenes, starting with the doctrine ofAntisthenes.identity without difference, recognizes as the only expression proper to anything its own peculiar sign, its name. This extreme of nominalism for which predication is impossible is, however, compromised by two concessions. A thing can be described as like something else. And a compound can have aÎ»ÏŒÎ³Î¿Ï‚or account given of it by the (literally) adequate enumeration of the names of its simple elements orÏ€Ïá¿¶Ï„Î±.9This analyticalÎ»ÏŒÎ³Î¿Ï‚he offers as his substitute for knowledge.10The simple elements still remain, sensed and named but not known. The expressions of them are simply the speech-signs for them. The account of the compound simply sets itself taken piecemeal as equivalent to itself taken as aggregate. The subject-predicate relation fails really to arise. Euclides11found no difficulty in fixing Antisthenesâ€™ mode of illustrating his simple elements by comparison, and therewith perhaps the â€œinductionâ€ of Socrates, with the dilemma; so far as the example is dissimilar, the comparison is invalid; so far as it is similar, it is useless. It is better to say what the thing is. 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. The syllable or combination is, he shows, not known by resolution of it into letters or elements themselves not known. An aggregate analysed into its mechanical parts is as much and as little known as they. A whole which is more than its parts is from Antisthenesâ€™ point of view inconceivable. Propositions analytical of a combination in the sense alleged do not give knowledge. Yet knowledge is possible. The development of a positive theory of predication has become quite crucial.

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 anythingThe Sophists.can be debated and not yet aware of the sense in which all things cannot be so. It is the age of discussion used as a universal solvent, before it has been brought to book by a deliberate unfolding of the principles of the structure of thought determining and limiting the movement of thought itself. The sophists furthered the transition from dialectic to logic in two ways. In the first place they made it possible. Incessant questioning leads to answers. Hair-splitting, even when mischievous in intent, leads to distinctions of value. Paradoxical insistence on the accidents of speech-forms and thought-forms leads in the end to perception of the essentials. Secondly they made it necessary. The spirit of debate run riot evokes a counter-spirit to order and control it. The result is a self-limiting 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 nihilism5issues which are as much logical and epistemological as ontological. The meaning of the copula and the relation of thoughts to the objects of which they are the thoughts are as much involved as the nature of being. It is equally no accident that the name of Protagoras is to be connected, in Platoâ€™s view at least, with the rival school of Heracliteans. The problems raised by the relativism of Protagoras are no less fundamentally problems of the nature of knowledge and of the structure of thought. TheTheaetetusindeed, in which Plato essays to deal with them, is in the broad sense of the word logical, the first distinctively logical treatise that has come down to us. Other sophists, of course, with more practical interests, or of humbler attainments, were content to move on a lower plane of philosophical speculation. As presented to us, for example, in Platoâ€™s surely not altogether hostile caricature in theEuthydemus, they mark the intellectual preparation for, and the moral need for, the advance of the next generation.

Among the pioneers of the sophistic age Socrates stands apart. He has no other instrument than the dialectic of his compeers, and he is as far off as the rest from a criticism of the instrument, but he uses it differently and with a difference of aim.Socrates.He construes the give and take of the debate-game with extreme rigour. The rhetorical element must be exorcised. The set harangue of teacher to pupil, in which steps in argument are slurred and the semblance of co-inquiry is rendered nugatory, must be eliminated. The interlocutors must in truth render an account under the stimulus of organized heckling from their equals or superiors in debating ability. And the aim is heuristic, though often enough the search ends in no overt positive conclusion. Something can be found and something is found. Common names are fitted for use by the would-be users being first delivered from abortive conceptions, and thereupon enabled to bring to the birth living and organic notions.

Aristotle would assign to Socrates the elaboration of two logical functions:â€”general definition and inductive method.6Rightly, if we add that he gives no theory of either, and that his practical use of the latter depends for its value on selection.7It is rather in virtue of his general faith in the possibility of construction, which he still does not undertake, and because of his consequent insistence on the elucidation of general concepts, which in common with some of his contemporaries, he may have thought of as endued with a certain objectivity, that he induces the controversies of what are called the Socratic schools as to the nature of predication. These result in the formulation of a new dialectic or logic by Plato. Manifestly Socratesâ€™ use of certain forms of argumentation, like their abuse by the sophists, tended to evoke their logical analysis. The use and abuse, confronted one with the other, could not but evoke it.

The one in the many, the formula which lies at the base of the possibility of predication, is involved in the Socratic doctrine of general concepts or ideas. The nihilism of Gorgias from the Eleatic point of view of bare identity, and the speechlessness of Cratylus from the Heraclitean ground of absolute difference, are alike disowned. But the one in the many, the identity in difference, is so far only postulated, not established. When the personality of Socrates is removed, the difficulty as to the nature of the Socratic universal, developed in the medium of the individual processes of individual minds, carries disciples of diverse general sympathies, united only through the practical inspiration of the masterâ€™s life, towards the identity-formula or the difference-formula of other teachers. The paradox of predication, that it seems to deny identity, or to deny difference, becomes apons asinorum. Knowledge involves synthesis or nexus. Yet from the points of view alike of an absolute pluralism, of a flux, and of a formula of bare identityâ€”anda fortioriwith any blending of these principles sufficiently within the bounds of plausibility to find an exponentâ€”all knowledge, because all predication of unity, in difference, must be held to be impossible. Platoâ€™s problem was to find a way of escape from this impasse, and among his Socratic contemporaries he seems to have singled out Antisthenes8as most in need of refutation. Antisthenes, starting with the doctrine ofAntisthenes.identity without difference, recognizes as the only expression proper to anything its own peculiar sign, its name. This extreme of nominalism for which predication is impossible is, however, compromised by two concessions. A thing can be described as like something else. And a compound can have aÎ»ÏŒÎ³Î¿Ï‚or account given of it by the (literally) adequate enumeration of the names of its simple elements orÏ€Ïá¿¶Ï„Î±.9This analyticalÎ»ÏŒÎ³Î¿Ï‚he offers as his substitute for knowledge.10The simple elements still remain, sensed and named but not known. The expressions of them are simply the speech-signs for them. The account of the compound simply sets itself taken piecemeal as equivalent to itself taken as aggregate. The subject-predicate relation fails really to arise. Euclides11found no difficulty in fixing Antisthenesâ€™ mode of illustrating his simple elements by comparison, and therewith perhaps the â€œinductionâ€ of Socrates, with the dilemma; so far as the example is dissimilar, the comparison is invalid; so far as it is similar, it is useless. It is better to say what the thing is. 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. The syllable or combination is, he shows, not known by resolution of it into letters or elements themselves not known. An aggregate analysed into its mechanical parts is as much and as little known as they. A whole which is more than its parts is from Antisthenesâ€™ point of view inconceivable. Propositions analytical of a combination in the sense alleged do not give knowledge. Yet knowledge is possible. The development of a positive theory of predication has become quite crucial.

Platoâ€™s logic supplies a theory of universals in the doctrine of ideas. Upon this it bases a theory of predication, which, however, is compatible with more than one reading of the metaphysical import of the ideas. And it setsPlato.forth a dialectic with a twofold movement, towards differentiation and integration severally, which amounts to a formulation of inference. The more fully analysed movement, that which proceeds downward from less determinate to more determinate universals, is named Division. Its associations, accordingly, are to the modern ear almost inevitably those of a doctrine of classification only. Aristotle, however, treats it as a dialectical rival to syllogism, and it influenced Galilei and Bacon in their views of inference after the Renaissance. If we add to this logic of â€œidea,â€ judgment and inference, a doctrine of categories in the modern sense of the word which makes theTheaetetus, in which it first occurs, a forerunner of Kantâ€™sCritique of Pure Reason, we have clearly a very significant contribution to logic even in technical regard. Its general philosophical setting may be said to enhance its value even as logic.

(a) Of the idea we may say that whatever else it is, and apart from all puzzles as to ideas of relations such as smallness, of negative qualities such as injustice, or of human inventions such as beds, it is opposed to that of whichThe â€œIdea.â€it is the idea as its intelligible formula or law, the truth or validityâ€”Herbartâ€™s wordâ€”of the phenomenon from the point of view of nexus or system. The thing of sense in its relative isolation is unstable. It is and is not. What gives stability is the insensible principle or principles which it holds, as it were, in solution. These are the ideas, and their mode of being is naturally quite other than that of the sensible phenomena which they order. The formula for an indefinite number of particular things in particular places at particular times, and all of them presentable in sensuous imagery of a given time and place, is not itself presentable in sensuous imagery side by side with the individual members of the group it orders. The law,e.g., of the equality of the radii of a circle cannot be exhibited to sense, even if equal radii may be so exhibited. It is the wealth of illustration with which Plato expresses his meaning, and the range of application which he gives the ideaâ€”to the class-conceptsof natural groups objectively regarded, to categories, to aesthetic and ethical ideals, to the concrete aims of the craftsman as well as to scientific lawsâ€”that have obscured his doctrine, viz. that wherever there is law, there is an idea.

(b) The paradox of the one in the many is none, if the idea may be regarded as supplying a principle of nexus or organization to an indefinite multiplicity of particulars. But if Antisthenes is to be answered, a further step must beThe one in the many.taken. The principle of difference must be carried into the field of the ideas. Not only sense is a principle of difference. The ideas are many. The multiplicity in unity must be established within thought itself. Otherwise the objection stands: man is man and good is good, but to say that man is good is clearly to say the thing that is not. Plato replies with the doctrine of the interpenetration of ideas, obviously not of all with all, but of some with some, the formula of identity in difference within thought itself. Nor can the opponent fairly refuse to admit it, if he affirms the participation of the identical with being, and denies the participation of difference with being, or affirms it with not-being. TheSophistesshows among other things that an identity-philosophy breaks down into a dualism of thought and expression, when it applies the predicate of unity to the real, just as the absolute pluralism on the other hand collapses into unity if it affirms or admits any form of relation whatsoever. Identity and difference are all-pervasive categories, and the speech-form and the corresponding thought-form involve both. For proposition and judgment involve subject and predicate and exhibit what a modern writer calls â€œidentity of reference with diversity of characterization.â€ Plato proceeds to explain by his principle of difference both privative and negative predicates, and also the possibility of false predication. It is obvious that without the principle of difference error is inexplicable. Even Plato, however, perhaps scarcely shows that with it, and nothing else but it, error is explained.

(c) Platoâ€™s Division, or the articulation of a relatively indeterminate and generic concept into species and sub-species with resultant determinate judgments, presumes of course the doctrine of the interpenetration of ideas laid downDivision.in theSophistesas the basis of predication, but its use precedes the positive development of that formula, though not, save very vaguely, the exhibition of it, negatively, in the antinomies of the one and the many in theParmenides. It is its use, however, not the theory of it, that precedes. The latter is expounded in thePoliticus(260 sqq.) andPhilebus(16csqq.). The ideal is progressively to determine a universe of discourse till trueinfimae speciesare reached, when no further distinction in the determinate many is possible, though there is still the numerical difference of the indefinite plurality of particulars. The process is to take as far as possible the form of a continuous disjunction of contraries. We must bisect as far as may be, but the division is after all to be into limbs, not parts. The later examples of thePoliticusshow that the permission of three or more co-ordinate species is not nugatory, and that the precept of dichotomy is merely in order to secure as little of asaltusas possible; to avoide.g.the division of the animal world into men and brutes. It is the middle range of theÎ¼ÎÏƒÎ±ofPhilebus17athat appeals to Bacon, not only this but their mediating quality that appeals to Aristotle. Themedia axiomataof the one and themiddle termof the other lie in the phrase. Platoâ€™s division is nevertheless neither syllogism norexclusiva. It is not syllogism because it is based on the disjunctive, not on the hypothetical relation, and so extends horizontally where syllogism strikes vertically downward. Again it is not syllogism because it is necessarily and finally dialectical. It brings in the choice of an interlocutor at each stage, and so depends on a concession for what it should prove.12Nor is it Baconâ€™s method of exclusions, which escapes the imputation of being dialectical, if not that of being unduly cumbrous, in virtue of the cogency of the negative instance. The Platonic division was, however, offered as the scientific method of the school. A fragment of the comic poet Epicrates gives a picture of it at work.13And the movement of disjunction as truly has a place in the scientific specification of a concept in all its differences as the linking of lower to higher in syllogism. The two are complementary, and the reinstatement of the disjunctive judgment to the more honourable rÃ´le in inference has been made by so notable a modern logician as Lotze.

(d) The correlative process of Combination is less elaborately sketched, but in a luminous passage in thePoliticus(Â§ 278), in explaining by means of an example the nature and use of examples, Plato represents it as the bringingCombination.of one and the same element seen in diverse settings to conscious realization, with the result that it is viewed as a single truth of which the terms compared are now accepted as the differences. The learner is to be led forward to the unknown by being made to hark back to more familiar groupings of the alphabet of nature which he is coming to recognize with some certainty. To lead on,á¼Ï€Î¬Î³ÎµÎ¹Î½, is to refer back,á¼€Î½Î¬Î³ÎµÎ¹Î½,14to what has been correctly divined of the same elements in clearer cases. Introduction to unfamiliar collocations follows upon this, and, only so, is it possible finally to gather scattered examples into a conspectus as instances of one idea or law. This is not only of importance in the history of the terminology of logic, but supplies a philosophy of induction.

(e) Back of Platoâ€™s illustration and explanation of predication and dialectical inference there lies not only the question of their metaphysical grounding in the interconnexion of ideas, but that of their epistemological presuppositions.Mental synthesis.This is dealt with in the Theaetetus (184bsqq.). The manifold affections of sense are not simply aggregated in the individual, like the heroes in the Trojan horse. There must be convergence in a unitary principle, soul or consciousness, which is that which really functions in perception, the senses and their organs being merely its instruments. It is this unity of apperception which enables us to combine the data of more than one sense, to affirm reality, unreality, identity, difference, unity, plurality and so forth, as also the good, the beautiful and their contraries. Plato calls these pervasive factors in knowledgeÎºÎ¿Î¹Î½á½°, and describes them as developed by the soul in virtue of its own activity. They are objects of its reflection and made explicit in the few with pains and gradually.15That they are not, however, psychological or acquired categories, due to â€œthe workmanship of the mindâ€ as conceived by Locke, is obvious from their attribution to the structure of mind16and from their correlation with immanent principles of the objective order. Considered from the epistemological point of view, they are the implicit presuppositions of the construction orÏƒÏ…Î»Î»Î¿Î³Î¹ÏƒÎ¼ÏŒÏ‚17in which knowledge consists. But as ideas,18though of a type quite apart,19they have also a constitutive application to reality. Accordingly, of the selected â€œkindsâ€ by means of which the interpenetration of ideas is expounded in theSophistes, only motion and rest, the ultimate â€œkindsâ€ in the physical world, have no counterparts in the â€œcategoriesâ€ of theTheaetetus. In his doctrine as toá¼•Î½ Ï„á½¸ Ï€Î¿Î¹Î¿á¿¦Î½orÎºÏá¿–Î½Î¿Î½, as generally in that of the activity of theÎ½Î¿á¿¦Ï‚ á¼€Ï€Î±Î¸Î®Ï‚, Aristotle in thede Anima20is in the main but echoing the teaching of Plato.21

ii.Aristotle.

Platoâ€™s episodic use of logical distinctions22is frequent. His recourse to such logical analysis as would meet the requirements of the problem in hand23is not rare. In the â€œdialecticalâ€ dialogues the question of method and of the justification of its postulates attains at least a like prominence with the ostensible subject matter. There is even formal recognition of the fact that to advance in dialectic is a greater thing than to bring any special inquiry to a successful issue.24But to the end there is a lack of interest in, and therefore a relative immaturity of, technique as such. In the forcing atmosphere, however, of that age of controversy, seed such as that sown in the masterâ€™s treatment of the utteredÎ»ÏŒÎ³Î¿Ï‚25quickly germinated. Platoâ€™s successors in the Academy must have developed a system of grammatico-logical categories which Aristotle could make his own. Else much of his criticism of Platonic doctrine26does, indeed, miss fire. The gulf too, which thePhilebus27apparently left unbridged between the sensuous apprehension of particulars and the knowledge of universals of even minimum generality led with Speusippus to a formula of knowledge in perception (á¼Ï€Î¹ÏƒÏ„Î·Î¼Î¿Î½Î¹Îºá½´ Î±á¼´ÏƒÎ¸Î·ÏƒÎ¹Ï‚). These and like developments, which are to be divined from references in the Aristotelian writings, jejune, and, for the most part, of probable interpretation only, complete the material which Aristotle could utilize when he seceded from the Platonic school and embarked upon his own course of logical inquiry.

This is embodied in the group of treatises later known as theOrganon28and culminates in the theory of syllogism and of demonstrative knowledge in theAnalytics. All else is finally subsidiary. In the well-known sentencesSyllogism.with which theOrganoncloses29Aristotle has been supposed to lay claim to the discovery of the principle of syllogism. He at least claims to have been the first to dissect the procedure of the debate-game, and the larger claim may be thought to follow. In the course of inquiry into the formal consequences from probable premises, the principle of mediation or linking was so laid bare that the advance to the analytic determination of the species and varieties of syllogism was natural. Once embarked upon such an analysis, where valid process from assured principles gave truth, Aristotle could find little difficulty in determining the formula of demonstrative knowledge or science. It must be grounded in principles of assured certainty and must demonstrate its conclusions with the use of such middle or linking terms only as it is possible to equate with the real ground or cause in the object of knowledge. Hence the account of axioms and of definitions, both of substances and of derivative attributes. Hence the importance of determining how first principles are established. It is, then, a fair working hypothesis as to the structure of theOrganonto place theTopics, which deal with dialectical reasoning, before theAnalytics.30Of the remaining treatises nothing of fundamental import depends on their order. One, however, theCategories, may be regarded with an ancient commentator,31as preliminary to the dialectical inquiry in theTopics. The other, on thought as expressed in language (Î ÎµÏá½¶ á¼ÏÎ¼Î·Î½ÎµÎ¯Î±Ï‚) is possibly spurious, though in any case a compilation of the Aristotelian school. If genuine, its naÃ¯ve theory that thought copies things and other features of its contents would tend to place it among the earliest works of the philosopher.

Production in the form of a series of relatively self-contained treatises accounts for the absence of a name and general definition of their common field of inquiry. A more important lack which results is that of any clear intimation asThe logical treatises.to the relation in which Aristotle supposed it to stand to other disciplines. In his definite classification of the sciences,32into First Philosophy, Mathematics and Physics, it has no place. 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. The speculative sciences, indeed, are classified according to their relation to form, pure, abstract or concrete,i.e.according to their objects. The logical inquiry seems to be conceived as dealing with the thought of which the objects are objects. It is to be regarded as a propaedeutic,33which, although it is in contact with reality in and through the metaphysical import of the axioms, or again in the fact that the categories, though primarily taken as forms of predication, must also be regarded as kinds of being, is not directly concerned with object-reality, but with the determination for the thinking subject of what constitutes the knowledge correlative to being. Logic, therefore, is not classed as one, still less as a branch of one, among the â€™ologies, ontology not excepted.

The way in which logical doctrine is developed in the Aristotelian treatises fits in with this view. Doubtless what we have is in the main a reflex of the heuristic character of Aristotleâ€™s own work as pioneer. But it at least satisfies the requirement that the inquiry shall carry the plain man along with it. Actual modes of expression are shown to embody distinctions which average intelligence can easily recognize and will readily acknowledge, though they may tend by progressive rectification fundamentally to modify the assumption natural to the level of thought from which he begins. Thus we start34from the point of view of a world of separate persons and things, in which thought mirrors these concrete realities, taken as ultimate subjects of predicates. It is a world of communication of thought, where persons as thinkers need to utter in language truths objectively valid for themundus communis. In these truths predicates are accepted or rejected by subjects, and therefore depend on the reflection of fact inÎ»ÏŒÎ³Î¿Î¹(propositions). These are combinatory of parts, attaching or detaching predicates, and so involvingsubject, predicate and copula.35At this stage we are as much concerned with speech-forms as the thought-forms of which they are conventional symbols, with Platoâ€™s analysis, for instance, into a noun and a verb, whose connotation of time is as yet a difficulty. The universal of this stage is the universal of fact, what is recognized as predicable of a plurality of subjects. The dialectical doctrine of judgment as the declaration of one member of a disjunction by contradiction, which is later so important, is struggling with one of its initial difficulties,36viz. the contingency of particular events future, the solution of which remains imperfect.37

The doctrine of theCategoriesis still on the same level of thought,38though its grammatico-logical analysis is the more advanced one which had probably been developed by the Academy before Aristotle came to think of hisThe Categories.friends there as â€œthemâ€ rather than â€œus.â€ It is what in one direction gave the now familiar classification of parts of speech, in the other that of thought-categories underlying them. If we abstract from any actual combination of subject and predicate and proceed to determine the types of predicate asserted in simple propositions of fact, we have on the one hand a subject which is never object, a â€œfirst substanceâ€ or concrete thing, of which may be predicated in the first place â€œsecond substanceâ€ expressing that it is a member of a concrete class, and in the second place quantity, quality, correlation, action and the like. The list follows the forms of the Greek language so closely that a category emerges appropriated to the use of the perfect tense of the middle voice to express the relation of the subject to a garb that it dons. In all this the individual is the sole self-subsistent reality. Truth and error are about the individual and attach or detach predicates correctly and incorrectly. There is no committal to the metaphysics in the light of which the logical inquiry is at last to find its complete justification. The point of view is to be modified profoundly by what followsâ€”by the doctrine of the class-concept behind the class, of the form or idea as the constitutive formula of a substance, or, again, by the requirement that an essential attribute must be grounded in the nature or essence of the substance of which it is predicated, and that such attributes alone are admissible predicates from the point of view of the strict ideal of science. But we are still on the ground of common opinion, and these doctrines are not yet laid down as fundamental to the development.

Dialectic then, though it may prove to be the ultimate method of establishing principles in philosophy,39starts from probable and conceded premises,40and deals with them only in the light of common principles such as may be reasonablyThe Topics.appealed to or easily established against challenge. To the expert, in any study which involves contingent matter,i.e.an irreducible element of indetermination,e.g.to the physician, there is a specific form of this, but the reflection that this is so is something of an afterthought. We start with what is prima facie given, to return upon it from the ground of principles clarified by the sifting process of dialectic41and certified byÎ½Î¿á¿¦Ï‚. TheTopicsdeal with dialectic and constitute an anatomy of argumentation, or, according to what seems to be Aristotleâ€™s own metaphor, a survey of the tactical vantage-points (Ï„ÏŒÏ€Î¿Î¹) for the conflict of wits in which the prize is primarily victory, though it is a barren victory unless it is also knowledge. It is in this treatise that what have been called â€œthe conceptual categoriesâ€42emerge, viz. thepredicables, or heads of predication as it is analysed in relation to the provisional theory of definition that dialectic allows and requires. A predicate either is expressive of the essence or part of the essence of the subject, viz. that original group of mutually underivable attributes of which the absence of any one destroys its right to the class-name, or it is not. Either it is convertible with the subject or it is not. Here then judgment, though still viewed as combinatory, has the types which belong to coherent systems of implication discriminated from those that predicate coincidence or accident,i.e.any happening not even derivatively essential from the point of view of the grouping in which the subject has found a place. In the theory of dialectic any predicate may be suggested for a subject, and if not affirmed of it, must be denied of it, if not denied must be affirmed. The development of a theory of the ground on which subjects claim their predicates and disown alien predicates could not be long postponed. In practical dialectic the unlimited possibility was reduced to manageable proportions in virtue of the groundwork of received opinion upon which the operation proceeded. It is in theTopics, further, that we clearly have a first treatment of syllogism as formal implication, with the suggestion that advance must be made to a view of its use for material implication from true and necessary principles. It is in theTopics,43again, that we have hints at the devices of an inductive process, which, as dialectical, throw the burden of producing contradictory instances upon the other party to the discussion. In virtue of the common-stock of opinion among the interlocutors and their potentially controlling audience, this process was more valuable than appears on the face of things. Obviously tentative, and with limits and ultimate interpretation to be determined elsewhere, it failed to bear fruit till the Renaissance, and then by the irony of fate to the discrediting of Aristotle. In any case, however, definition, syllogism, induction all invited further determination, especially if they were to take their place in a doctrine of truth or knowledge. The problem of analytic,i.e.of the resolution of the various forms of inference into their equivalents in that grouping of terms or premises which was most obviously cogent, was a legacy of theTopics. The debate-game had sought for diversion and found truth, and truth raised the logical problem on a different plane.

At first the problem of formal analysis only. We proceed with the talk of instances and concern ourselves first with relations of inclusion and exclusion. The question is as to membership of a class, and the dominant formulaClass concept.is thedictum de omni et nullo. Until the view of the individual units with which we are so far familiar has undergone radical revision, the primary inquiry must be into the forms of a class-calculus. Individuals fall into groups in virtue of the possession of certain predicates. Does one group include, or exclude, or intersect another with which it is compared? We are clearly in the field of the diagrams of the text-books, and much of the phraseology is based upon an original graphic representation in extension. The middle term, though conceived as an intermediary or linking term, gets its name as intermediate in a homogeneous scheme of quantity, where it cannot be of narrower extension than the subject nor wider than the predicate of the conclusion.44It is also, as Aristotle adds,45middle in position in the syllogism that concludes to a universal affirmative.45Again, so long as we keep to the syllogism as complete in itself and without reference to its place in the great structure of knowledge, the nerve of proof cannot be conceived in other than a formal manner. In analytic we work with an ethos different from that of dialectic. We presume truth and not probability or concession, but a true conclusion can follow from false premises, and it is only in the attempt to derive the premises in turn from their grounds that we unmask the deception. The passage to the conception of system is still required. ThePrior AnalyticsThe Prior Analytics.then are concerned with a formal logic to be knit into a system of knowledge of the real only in virtue of a formula which is at this stage still to seek. The forms of syllogism, however, are tracked successfully through their figures,i.e.through the positions of the middle term that Aristotle recognizes as of actual employment, and all their moods,i.e.all differences of affirmative and negative, universal and particular within the figures, the cogent or legitimate forms arealone left standing, and the formal doctrine of syllogism is complete. Syllogism already defined46becomes through exhibition in its valid forms clear in its principle. It is a speech-and-thought-form (Î»ÏŒÎ³Î¿Ï‚) in which certain matters being posited something other than the matters posited necessarily results because of them, and, though it still needs to receive a deeper meaning when presumed truth gives way to necessary truth of premises, the notion of the class to that of the class-concept, collective fact to universal law, its formal claim is manifest. â€œCertain matters being posited.â€ Subject and predicate not already seen to be conjoined must be severally known to be in relation with that which joins them, so that more than one direct conjunction must be given. â€œOf necessity.â€ If what are to be conjoined are severally in relation to a common third it does perforce relate or conjoin them. â€œSomething other.â€ The conjunction was by hypothesis not given, and is a new result by no means to be reached, apart from direct perception save by use of at least two given conjunctions. â€œBecause of them,â€ therefore. Yet so long as the class-view is prominent, there is a suggestion of a begging of the question. The class is either constituted by enumeration of its members, and, passing by the difficulty involved in the thought of â€œitsâ€ members, is an empirical universal of fact merely, or it is grounded in the class-concept. In the first case it is a formal scheme which helps knowledge and the theory of knowledge not at all. We need then to develop the alternative, and to pass from the external aspect of all-ness to the intrinsic ground of it in the universalÎºÎ±Î¸á¾½ Î±á½‘Ï„á½¸ ÎºÎ±á½¶ á¾— Î±á½Ï„ÏŒ, which, whatsoever the assistance it receives from induction in some sense of the word, in the course of its development for the individual mind, is secured against dependence on instances by the decisive fiat or guarantee ofÎ½Î¿á¿¦Ï‚, insight into the systematic nexus of things. The conception of linkage needs to be deepened by the realization of the middle term as the ground of nexus in a real order which is also rational.

Aristotleâ€™s solution of the paradox of inference, viz. of the fact that in one sense to go beyond what is in the premises is fallacy,Problem of inference.while in another sense not to go beyond them is futility, lies in his formula of implicit and explicit, potential and actual.47The real nexus underlying the thought-process is to be articulated in the light of the voucher by intelligence as to the truth of the principles of the various departments of knowledge which we call sciences, and at the ideal limit it is possible to transform syllogism into systematic presentation, so that, differently written down, it is definition. But for human thought sense, with its accidental setting in matter itself incognizableNous.is always with us. The activity ofÎ½Î¿á¿¦Ï‚is never so perfectly realized as to merge implication in intuition. Syllogism must indeed be objective,i.e.valid for any thinker, but it is also a process in the medium of individual thinking, whereby new truth is reached. A man may know that mules are sterile and that the beast before him is a mule, and yet believe her to be in foal â€œnot viewing the several truths in connexion.â€48The doctrine, then, that the universal premise contains the conclusion not otherwise than potentially is with Aristotle cardinal. The datum of sense is only retained through the universal.49It is possible to take a universal view with some at least of the particular instances left uninvestigated.50Recognition that the class-concept is applicable may be independent of knowledge of much that it involves. Knowledge of the implications of it does not depend on observation of all members of the class. Syllogism as formula for the exhibition of truth attained, and construction or what not as the instrumental process by which we reach the truth, have with writers since Hegel and Herbart tended to fall apart. Aristotleâ€™s view is other. Both are syllogisms, though in different points of view. For this reason, if for no other, the conception of movement from the potential possession of knowledge to its actualization remains indispensable. Whether this is explanation or description, a problem or its solution, is of course another matter.

In thePosterior Analyticsthe syllogism is brought into decisive connexion with the real by being set within a system in which its function is that of material implication from principles which are primary, immediate andPosterior Analytics.necessary truths. Hitherto the assumption of the probable as true rather than as what will be conceded in debate51has been the main distinction of the standpoint of analytic from that of dialectic. But the true is true only in reference to a coherent system in which it is an immediate ascertainment ofÎ½Î¿á¿¦Ï‚, or to be deduced from a ground which is such. The ideal of science or demonstrative knowledge is to exhibit as flowing from the definitions and postulates of a science, from its special principles, by the help only of axioms or principles common to all knowledge, and these not as premises but as guiding rules, all the properties of the subject-matter,i.e.all the predicates that belong to it in its own nature. In the case of any subject-kind, its definition and its existence being avouched byÎ½Î¿á¿¦Ï‚, â€œheavenly bodyâ€ for example, the problem is, given the fact of a non-self-subsistent characteristic of it, such as the eclipse of the said body, to find a ground, aÎ¼ÎÏƒÎ¿Î½which expressed theÎ±á¼´Ï„Î¹Î¿Î½, in virtue of which the adjectival concept can be exhibited as belonging to the subject-conceptÎºÎ±Î¸á¾½ Î±á½‘Ï„á½¸in the strictly adequate sense of the phrase in which it means alsoá¾– Î±á½‘Ï„á½¸.52We are under the necessity then of revising the point of view of the syllogism of all-ness. We discard the conception of the universal as a predicate applicable to a plurality, or even to all, of the members of a group. To know merelyÎºÎ±Ï„á½° Ï€Î±Î½Ï„á½¸Ï‚is not to know, save accidentally. The exhaustive judgment, if attainable, could not be known to be exhaustive. The universal is the ground of the empirical â€œallâ€ and not conversely. A formula such as the equality of the interior angles of a triangle to two right angles is only scientifically known when it is not of isosceles or scalene triangle that it is known, nor even of all the several types of triangle collectively, but as a predicate of triangle recognized as the widest class-concept of which it is true, the first stage in the progressive differentiation of figure at which it can be asserted.53

Three points obviously need development, the nature of definition, its connexion with the syllogism in which the middle term is cause or ground, and the way in which we have assurance of our principles.

Definition is either of the subject-kind or of the property that is grounded in it. Of the self-subsistent definition isÎ¿á½ÏƒÎ¯Î±Ï‚ Ï„Î¹Ï‚ Î³Î½Ï‰ÏÎ¹ÏƒÎ¼ÏŒÏ‚54by exposition of genus and differentia.55It is indemonstrable. It presumes the reality of its subjectDefinition.in a postulate of existence. It belongs to the principles of demonstration.Summa generaand groups belowinfimae speciesare indefinable. The former are susceptible of elucidation by indication of what falls under them. The latter are only describable by their accidents. There can here be no true differentia. The artificiality of the limit to the articulation of species was one of the points to which the downfall of Aristotleâ€™s influence was largely due. Of a non-self-subsistent or attributive conception definition in its highest attainable form is a recasting of the syllogism, in which it was shown that the attribute was grounded in the substance or self-subsistent subject of which it is. Eclipse of the moon,e.g.is privation of light from the moon by the interposition of the earth between it and the sun. In the scientific syllogism the interposition of the earth is the middle term, the cause or â€œbecauseâ€ (Î´Î¹ÏŒÏ„Î¹), the residue of the definition is conclusion. The difference then is in verbal expression, way of putting, inflexion.56If we pluckthe fruit of the conclusion, severing its nexus with the stock from which it springs, we have an imperfect form of definition, while, if further we abandon all idea of making it adequate by exhibition of its ground, we have, with still the same form of words, a definition merely nominal or lexicographical. In the aporematic treatment of the relation of definition and syllogism identical as to one form and in one view, distinct as to another form and in another view, much of Aristotleâ€™s discussion consists.The middle term.The rest is a consideration of scientific inquiry as converging inÎ¼ÎÏƒÎ¿Ï… Î¶Î®Ï„Î·ÏƒÎ¹Ï‚, the investigation of the link or â€œbecauseâ€ as ground in the nature of things.Î¤á½¸ Î³á½°Ï Î±á¼´Ï„Î¹Î¿Î½ Ï„á½¸ Î¼ÎÏƒÎ¿Î½57real ground and thought link fall together. The advance from syllogism as formal implication is a notable one. It is not enough to have for middle term acausa cognoscendimerely. We must have acausa essendi. The planets are near, and we know it by their not twinkling,58but science must conceive their nearness as the cause of their not twinkling and make thepriusin the real order the middle term of its syllogism. In this irreversible catena proceeding from ground to consequent, we have left far behind such things as the formal parity of genus and differentia considered as falling under the same predicable,59and hence justified in part Porphyryâ€™s divergence from the scheme of predicables. We need devices, indeed, to determine priority or superior claim to be â€œbetter known absolutely or in the order of nature,â€ but on the whole the problem is fairly faced.60

Of science Aristotle takes for his examples sometimes celestial physics, more often geometry or arithmetic, sometimes a concrete science,e.g.botany.61In the field of pure form, free from the disconcerting surprises of sensible matter and so of absolute necessity, no difficulty arises as to the deducibility of the whole body of a science from its first principles. In the sphere of abstract form, mathematics, the like may be allowed, abstraction being treated as an elimination of matter from theÏƒÏÎ½Î¿Î»Î¿Î½by one act. When we take into account relative matter, however, and traces of a conception of abstraction as admitting of degree,62the question is not free from difficulty. In the sphere of the concrete sciences where law obtains onlyá½¡Ï‚ á¼Ï€á½¶ Ï„á½¸ Ï€Î¿Î»á½ºthis ideal of science can clearly find only a relative satisfaction with large reserves. In any case, however, the problem as to first principles remains fundamental.

If we reject the infinite regress and the circle in proof (circulus in probando) which resolves itself ultimately into proving A by B and B by A,63we are confronted by the need for principles of two kinds, those which condition all searchFormal and scientific principles.for truth, and those which are the peculiar or proper principles of special sciences, their â€œpositions,â€ viz. the definitions of their subjects and the postulates of the existence of these. All are indemonstrable and cannot be less sure than the body of doctrine that flows from them. They must indeed be recognized as true, primary, causative and the like. But64they are not congenitally present in the individual in a determinate shape. The doctrine of latency is mystical and savours of Platoâ€™s reminiscence (anamnesis). Yet they must have something to develop from, and thereupon Aristotle gives an account of a process in the psychological mechanism which he illustrates by comparative psychology, wherein aÎ»ÏŒÎ³Î¿Ï‚or meaning emerges,Induction and dialectic.a â€œfirstâ€ universal recognized by induction. YetÎ½Î¿á¿¦Ï‚, intelligence, is the principle of first principles. It is infallible, while, whatever the case with perception of the special sensibles,65the process which combines particulars is not. On the side of induction we find that experience is said to give the specific principles,66â€œthe phenomena being apprehended in sufficiency.â€ On the side of intuition, self-evidence of scientific principles is spoken of.67Yet dialectic is auxiliary and of methodological importance in their establishment.68Mutually limiting statements occur almost or quite side by side. We cannot take first principles â€œas the bare precipitate of a progressively refined analysisâ€69nor on the other as constitutive a priori forms. The solution seems to lie in the conception of a process that has a double aspect. On the one hand we have confrontation with fact, in which, in virtue of the rational principle which is the final cause of the phenomenal order, intelligence will find satisfaction. On the other we have a stage at which the rational but as yet not reasoned concepts developed in the medium of the psychological mechanism are subjected to processes of reflective comparison and analysis, and, with some modification, maintained against challenge, till at length the ultimate universals emerge, which rational insight can posit as certain, and the whole hierarchy of concepts from the â€œfirstâ€ universals toÏ„á½° á¼€Î¼ÎµÏá¿†are intuited in a coherent system. Aristotleâ€™s terminology is highly technical, but, as has often been observed, not therefore clear. Here two words at least are ambiguous, â€œprincipleâ€ and â€œinduction.â€ By the first he means any starting-point, â€œthat from which the matter in question is primarily to be known,â€70particular facts therefore, premises, and what not. What then is meant by principles when we ask in the closing chapter of his logic how they become known? The data of sense are clearly not the principles in question here. The premises of scientific syllogisms may equally be dismissed. Where they are not derivative they clearly are definitions or immediate transcripts from definitions. There remain, then, primary definitions and the postulates of their realization, and the axioms or common principles, â€œwhich he must needs have who is to reach any knowledge.â€71In the case of the former, special each to its own science, Aristotle may be thought to hold that they are the product of the psychological mechanism, but are ascertained only when they have faced the fire of a critical dialectic and have been accepted from the point of view of the integral rationality of the system of concepts. Axioms, on the other hand, in which the sciences interconnect72through the employment of them in a parity of relation, seem to be implicit indeed in the psychological mechanism, but to come to a kind of explicitness in the first reflective reaction upon it, and without reference to any particular content of it. They are not to be used as premises but as immanent laws of thought, save only when an inference from true or admitted premises and correct in form is challenged. The challenge must be countered in areductio ad impossibilein which the dilemma is put. Either this conclusion or the denial of rationality. Even these principles, however, may get a greater explicitness by dialectical treatment.73The relation, then, of the two orders of principle to the psychological mechanism is different. The kind of warrant that intelligence can give to specific principles falls short of infallibility. Celestial physics, with its pure forms and void of all matter save extension, is not such an exemplary science after all. Rationality is continuous throughout. AÎ»ÏŒÎ³Î¿Ï‚emerges with some beings in direct sequence upon the persistence of impressions.74Sense is of the â€œfirstâ€ universal, the form, though not of the ultimate universal. The rally from the rout in Aristotleâ€™s famous metaphor is of units that already belong together, that are of the same regiment or order. On the other hand, rationality has two stages. In the one it is relatively immersed in sense, in the other relatively free. The same break is to be found in the conception of the relation of receptive to active mind in the treatiseOf the Soul.75The one is impressed by things and receives their form without their matter. The other is free from impression. It thinks its system of concepts freely on the occasion of the affections of the receptivity. Aristotle is fond of declaring that knowledge is of the universal, while existence or reality is individual. It seems to follow that the cleavage between knowledge and realityis not bridged by the function ofÎ½Î¿á¿¦Ï‚in relation to â€œinduction.â€ What is known is not real, and what is real is not known. TheKnowledge and reality.nodus76has its cause in the double sense of the word â€œuniversalâ€ and a possible solution in the doctrine ofÎµá¼¶Î´Î¿Ï‚. The â€œformâ€ of a thing constitutes it what it is, and at the same time, therefore, is constitutive of the group to which it belongs. It has both individual and universal reference. The individual is known in theÎµá¼¶Î´Î¿Ï‚, which is also the first universal in which by analysis higher universals are discoverable. These are predicates of the object known, ways of knowing it, rather than the object itself. The suggested solution removes certain difficulties, but scarcely all. On seeing Callias my perception is of man, not Callias, or even man-Callias. The recognition of the individual is a matter of his accidents, to which even sex belongs, and the gap from lowest universal to individual may still be conceived as unbridged. It is in induction, which claims to start from particulars and end in universals,77that we must, if anywhere within the confines of logical inquiry, expect to find the required bridge. The Aristotelian conception of induction, however, is somewhat ambiguous. He had abandoned for the most partConclusions as to induction.the Platonic sense of the corresponding verb, viz. to lead forward to the as yet unknown, and his substitute is not quite clear. It is scarcely the military metaphor. The adducing of a witness for which he uses the verb78is not an idea that covers all the uses.79Perhaps confrontation with facts is the general meaning. But how does he conceive of its operation? There is in the first place the action of the psychological mechanism in the process from discriminative sense upwards wherein we realize â€œfirstâ€ universals.80This is clearly an unreflective, pre-logical process, not altogether lighted up by our retrojection upon it of our view of dialectical induction based thereon. The immanent rationality of this first form, in virtue of which at the stage when intelligence acts freely on the occasion of the datum supplied it recognizes continuity with its own self-conscious process, is what gives the dialectical type its meaning. Secondly we have this dialectical â€œinduction as to particulars by grouping of similarsâ€81whose liability to rebuttal by an exception has been already noted in connexion with the limits of dialectic. This is the incomplete induction by simple enumeration which has so often been laughed to scorn. It is a heuristic process liable to failure, and its application by a nation of talkers even to physics where non-expert opinion is worthless somewhat discredited it. Yet it was the fundamental form of induction as it was conceived throughout the scholastic period. Thirdly we have the limiting cases of this in the inductive syllogismÎ´Î¹á½° Ï€Î¬Î½Ï„Ï‰Î½,82a syllogism in the third figure concluding universally, and yet valid because the copula expresses equivalence, and in analogy83in which, it has been well said, instances are weighed and not counted. In the former it has been noted84that Aristotleâ€™s illustration does not combine particular facts into a lowest concept, but specific concepts into a generic concept, and85that in the construction of definite inductions the ruling thought with Aristotle is already, though vaguely, that of causal relation. It appears safer, notwithstanding, to take the less subtle interpretation86that dialectical induction struggling with instances is formally justified only at the limit, and that this, where we have exhausted and know that we have exhausted the cases, is in regard to individual subjects rarely and accidentally reached, so that we perforce illustrate rather from the definite class-concepts falling under a higher notion. After all, Aristotle must have had means by which he reached the conclusions that horses are long-lived and lack gall. It is only then in the rather mystical relation ofÎ½Î¿á¿¦Ï‚to the first type of induction as the process of the psychological mechanism that an indication of the direction in which the bridge from individual being to universal knowledge is to be found can be held to lie.

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 implication grounded implication as a mode of knowledgeSummary.in the rationality of the real, and developed a justificatory metaphysic. He laid down the programme which the after history of logic was to carry out. We have of course abandoned particular logical positions. This is especially to be noted in the theory of the proposition. The individualism with which he starts, howsoever afterwards mitigated by his doctrine ofÏ„á½¸ Ï„á½¶ á¼¦Î½ Îµá¼°Î½Î±Î¹orÎµá¼¶Î´Î¿Ï‚constituting the individual in a system of intelligible relations, confined him in an inadmissible way to the subject-attribute formula. He could not recognize such vocables as the impersonals for what they were, and had perforce to ignore the logical significance of purely reciprocal judgments, such as those of equality. There was necessarily a â€œsenseâ€ or direction in every proposition, with more than the purely psychological import that the advance was from the already mastered and familiar taken as relatively stable, to the new and strange. Many attributes, too, were predicable, even to the end, in an external and accidental way, not being derivable from the essence of the subject. The thought of contingency was too easily applied to these attributes, and an unsatisfactory treatment of modality followed. It is indeed the doctrine of the intractability of matter to form that lies at the base of the paradox as to the disparateness of knowledge and the real already noted. On the one hand Aristotle by his doctrine of matter admitted a surd into his system. On the other, he assigned toÎ½Î¿á¿¦Ï‚with its insight into rationality too high a function with regard to the concrete in which the surd was present, a power to certify the truth of scientific principles. The example of Aristotleâ€™s view of celestial physics as a science of pure forms exhibits both points. On the Copernican change the heavenly bodies were recognized as concrete and yet subject to calculable law. Intelligence had warranted false principles. The moral is that of the story of the heel of Achilles.

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