56Plato, Sophistes, pp. 261-262. φάσιν καὶ ἀπόφασιν. — ib. p. 263 E. In the so-called Platonic ‘Definitions,’ we read ἐν καταφάσει καὶ ἀποφάσει (p. 413 C); but these are probably after Aristotle’s time. In another of these Definitions (413 D.) we read ἀπόφασις, where the word ought to be ἀπόφανσις.
56Plato, Sophistes, pp. 261-262. φάσιν καὶ ἀπόφασιν. — ib. p. 263 E. In the so-called Platonic ‘Definitions,’ we read ἐν καταφάσει καὶ ἀποφάσει (p. 413 C); but these are probably after Aristotle’s time. In another of these Definitions (413 D.) we read ἀπόφασις, where the word ought to be ἀπόφανσις.
57Plato, Sophist. p. 263 A-C.
57Plato, Sophist. p. 263 A-C.
58Ibid. p. 257, B: Οὐκ ἀρ’, ἐναντίον ὅταν ἀπόφασις λέγηται σημαίνειν, συγχωρησόμεθα, τοσοῦτον δὲ μόνον, ὅτιτῶν ἄλλων τι μηνύει τὸ μὴ καὶ τὸ οὔπροτιθέμενα τῶν ἐπιόντων ὀνομάτων, μᾶλλον δὲ τῶν πραγμάτων, περὶ ἅττ’ ἂν κέηται τὰ ἐπιφθεγγόμενα ὕστερον τῆς ἀποφάσεως ὀνόματα.The term ἀντίφασις, and its derivative ἀντιφατικῶς, are not recognized in the Platonic Lexicon. Compare the same dialogue, Sophistes, p. 263; also Euthydêmus, p. 298, A. Plato does not seem to take account of negative propositions as such. See ‘Plato and the Other Companions of Sokrates,’ vol. II. ch. xxvii. pp.446-455.
58Ibid. p. 257, B: Οὐκ ἀρ’, ἐναντίον ὅταν ἀπόφασις λέγηται σημαίνειν, συγχωρησόμεθα, τοσοῦτον δὲ μόνον, ὅτιτῶν ἄλλων τι μηνύει τὸ μὴ καὶ τὸ οὔπροτιθέμενα τῶν ἐπιόντων ὀνομάτων, μᾶλλον δὲ τῶν πραγμάτων, περὶ ἅττ’ ἂν κέηται τὰ ἐπιφθεγγόμενα ὕστερον τῆς ἀποφάσεως ὀνόματα.
The term ἀντίφασις, and its derivative ἀντιφατικῶς, are not recognized in the Platonic Lexicon. Compare the same dialogue, Sophistes, p. 263; also Euthydêmus, p. 298, A. Plato does not seem to take account of negative propositions as such. See ‘Plato and the Other Companions of Sokrates,’ vol. II. ch. xxvii. pp.446-455.
59Aristot. Topica, I. xi. p. 104, b. 20; Metaphys.Δ.p. 1024, b. 32; Analytic. Poster. I. xxv. p. 86, b. 34.
59Aristot. Topica, I. xi. p. 104, b. 20; Metaphys.Δ.p. 1024, b. 32; Analytic. Poster. I. xxv. p. 86, b. 34.
60Diogon. Laert. ii. 134-135. See the long discussion in the Platonic Theætêtus (pp. 187-196), in which Sokrates in vain endeavours to produce some theory whereby ψευδὴς δόξα may be rendered possible. Hobbes, also, in his Computation or Logic (De Corp. c. iii. § 6), followed by Destutt Tracy, disallows the negative propositionper se, and treats it as a clumsy disguise of the affirmative ἐκ μεταθέσεως, to use the phrase of Theophrastus. Mr. John Stuart Mill has justly criticized this part of Hobbes’s theory (System of Logic, Book I. ch. iv. § 2).
60Diogon. Laert. ii. 134-135. See the long discussion in the Platonic Theætêtus (pp. 187-196), in which Sokrates in vain endeavours to produce some theory whereby ψευδὴς δόξα may be rendered possible. Hobbes, also, in his Computation or Logic (De Corp. c. iii. § 6), followed by Destutt Tracy, disallows the negative propositionper se, and treats it as a clumsy disguise of the affirmative ἐκ μεταθέσεως, to use the phrase of Theophrastus. Mr. John Stuart Mill has justly criticized this part of Hobbes’s theory (System of Logic, Book I. ch. iv. § 2).
Such being the conditions under which philosophers debated in the age of Aristotle, we can appreciate the full value of a positive theory of propositions such as that which we read in his treatise De Interpretatione. It is, so far as we know, the first positive theory thereof that was ever set out; the first attempt to classify propositions in such a manner that a legitimateAntiphasiscould be assigned to each; the first declaration that to each affirmative proposition there belonged one appropriate negative, and to each negative proposition one appropriate counter-affirmative, and one only; the earliest effort to construct a theory for this purpose, such as to hold ground against all the puzzling questions of acute disputants.61The clear determination of theAntiphasisin each case — the distinction of Contradictory antithesis from Contrary antithesis between propositions — this was an important logical doctrine never advanced before Aristotle; and the importance of it becomes manifest when we read the arguments of Plato and Antisthenes, the former overleaping and ignoring the contradictory opposition, the latter maintaining that it was a process theoretically indefensible. But in order that these two modes of antithesis should be clearly contrasted, each with its proper characteristic, it was requisite that the distinction of quantity between different propositions should also be brought to view, and considered in conjunction with the distinction of quality. Until this was done, the Maximof Contradiction, denied by some, could not be shown in its true force or with its proper limits. Now, we find it done,62for the first time, in the treatise before us. Here the Contradictory antithesis (opposition both in quantity and quality) in which one proposition must be true and the other false, is contrasted with the Contrary (propositions opposite in quality, but both of them universal). Aristotle’s terminology is not in all respects fully developed; in regard, especially, to the quantity of propositions it is less advanced than in his own later treatises; but from the theory of the De Interpretatione all the distinctions current among later logicians, take their rise.
61Aristot. De Interpr. p. 17, a. 36: πρὸς τὰς σοφιστικὰς ἐνοχλήσεις.
61Aristot. De Interpr. p. 17, a. 36: πρὸς τὰς σοφιστικὰς ἐνοχλήσεις.
62We see, from the argument in the Metaphysica of Aristotle, that there were persons in his day who denied or refused to admit the Maxim of Contradiction; and who held that contradictory propositions might both be true or both false (Aristot. Metaph.Γ.p. 1006, a. 1; p. 1009, a. 24). He employs several pages in confuting them.See the Antinomies in the Platonic Parmenides (pp. 154-155), some of which destroy or set aside the Maxim of Contradiction (‘Plato and the Other Companions of Sokrates,’ vol. II. ch. xxv.p. 306).
62We see, from the argument in the Metaphysica of Aristotle, that there were persons in his day who denied or refused to admit the Maxim of Contradiction; and who held that contradictory propositions might both be true or both false (Aristot. Metaph.Γ.p. 1006, a. 1; p. 1009, a. 24). He employs several pages in confuting them.
See the Antinomies in the Platonic Parmenides (pp. 154-155), some of which destroy or set aside the Maxim of Contradiction (‘Plato and the Other Companions of Sokrates,’ vol. II. ch. xxv.p. 306).
The distinction of Contradictory and Contrary is fundamental in ratiocinative Logic, and lies at the bottom of the syllogistic theory as delivered in the Analytica Priora. The precision with which Aristotle designates the Universal proposition with its exact contradictory antithesis, is remarkable in his day. Some, however, of his observations respecting the place and functions of the negative particle (οὐ), must be understood with reference to the variable order of words in a Greek or Latin sentence; for instance, the distinction betweenKallias non est justusandKallias est non justusdoes not suggest itself to one speaking English or French.63Moreover, the Aristotelian theory of theProposition is encumbered with various unnecessary subtleties; and the introduction of the Modals (though they belong, in my opinion, legitimately to a complete logical theory) renders the doctrine so intricate and complicated, that a judicious teacher will prefer, in explaining the subject, to leave them for second or ulterior study, when the simpler relations between categorical propositions have been made evident and familiar. The force of this remark will be felt more when we go through the Analytica Priora. The two principal relations to be considered in the theory of Propositions — Opposition and Equipollence — would have come out far more clearly in the treatise De Interpretatione, if the discussion of the Modals had been reserved for a separate chapter.
63The diagram or parallelogram of logical antithesis, which is said to have begun with Apuleius, and to have been transmitted through Boethius and the Schoolmen to modern times (Ueberweg, System der Logik, sect. 72, p. 174) is as follows:—A. Omnis homo est justus.---E. Nullus homo est justus.✕I. Aliquis homo est justus.---O. Aliquis homo non est justus.But the parallelogram set out by Aristotle in the treatise De Interpretatione, or at least in the Analytica Priora, is different, and intended for a different purpose. He puts it thus:—1. Omnis homo est justus… … … …2. Non omnis homo est justus.4. Non omnis homo est non justus… … … …3. Omnis homo est non justus.Here Proposition (1) is an affirmative, of which (2) is the direct and appropriate negative: also Proposition (3) is an affirmative (Aristotle so considers it), of which (4) is the direct and appropriate negative. The great aim of Aristotle is to mark out clearly what is the appropriate negative or Ἀπόφασις to each Κατάφασις (μία ἀπόφασις μιᾶς καταφάσεως, p. 17, b. 38), making up together the pair which he calls Ἀντίφασις, standing in Contradictory Opposition; and to distinguish this appropriate negative from another proposition which comprises the particle of negation, but which is really a new affirmative.The true negatives ofhomo est justus — Omnis homo est justusare,Homo non est justus — Non omnis homo est justus. If you say,Homo est non justus — Omnis homo est non justus, these are not negative propositions, but new affirmatives (ἐκ μεταθέσεως in the language of Theophrastus).
63The diagram or parallelogram of logical antithesis, which is said to have begun with Apuleius, and to have been transmitted through Boethius and the Schoolmen to modern times (Ueberweg, System der Logik, sect. 72, p. 174) is as follows:—
A. Omnis homo est justus.---E. Nullus homo est justus.✕I. Aliquis homo est justus.---O. Aliquis homo non est justus.
A. Omnis homo est justus.---E. Nullus homo est justus.✕I. Aliquis homo est justus.---O. Aliquis homo non est justus.
But the parallelogram set out by Aristotle in the treatise De Interpretatione, or at least in the Analytica Priora, is different, and intended for a different purpose. He puts it thus:—
1. Omnis homo est justus… … … …2. Non omnis homo est justus.4. Non omnis homo est non justus… … … …3. Omnis homo est non justus.
1. Omnis homo est justus… … … …2. Non omnis homo est justus.4. Non omnis homo est non justus… … … …3. Omnis homo est non justus.
Here Proposition (1) is an affirmative, of which (2) is the direct and appropriate negative: also Proposition (3) is an affirmative (Aristotle so considers it), of which (4) is the direct and appropriate negative. The great aim of Aristotle is to mark out clearly what is the appropriate negative or Ἀπόφασις to each Κατάφασις (μία ἀπόφασις μιᾶς καταφάσεως, p. 17, b. 38), making up together the pair which he calls Ἀντίφασις, standing in Contradictory Opposition; and to distinguish this appropriate negative from another proposition which comprises the particle of negation, but which is really a new affirmative.
The true negatives ofhomo est justus — Omnis homo est justusare,Homo non est justus — Non omnis homo est justus. If you say,Homo est non justus — Omnis homo est non justus, these are not negative propositions, but new affirmatives (ἐκ μεταθέσεως in the language of Theophrastus).
Reviewing the treatise De Interpretatione, we have followed Aristotle in his first attempt to define what a Proposition is, to point out its constituent elements, and to specify some of its leading varieties. The characteristic feature of the Proposition he stated to be — That it declares, in the first instance, the mental state of the speaker as to belief or disbelief, and, in its ulterior or final bearing, a state of facts to which such belief or disbelief corresponds. It is thus significant of truth or falsehood; and this is its logical character (belonging to Analytic and Dialectic), as distinguished from its rhetorical character, with other aspects besides. Aristotle farther indicated the two principal discriminative attributes of propositions as logically regarded, passing under the names of quantity and quality. He took great pains, in regard to the quality, to explain what was the special negative proposition in true contradictory antithesis to each affirmative. He stated and enforced the important separation of contradictory propositions from contrary; and he even parted off (which the Greek and Latin languages admit, though the French and English will hardly do so) the true negative from the indeterminate affirmative. He touched also upon equipollent propositions, though he did not go far into them. Thus commenced with Aristotle the systematic study of propositions, classified according to their meaning and their various interdependences with each other as to truth and falsehood — their mutual consistency or incompatibility. Men who had long been talking good Greek fluently and familiarly, were taught to reflect upon the conjunctions of words that they habitually employed, and to pay heed to the conditions of correct speech in reference to its primary purpose of affirmation and denial, for the interchange of beliefs and disbeliefs, the communication of truth, and the rectification of falsehood. To many of Aristotle’s contemporaries this first attempt to theorize upon the forms of locution familiar to every one would probably appear hardly less strange than the interrogativedialectic of Sokrates, when he declared himself not to know what was meant by justice, virtue, piety, temperance, government, &c.; when he astonished his hearers by asking them to rescue him from this state of ignorance, and to communicate to him some portion of their supposed plenitude of knowledge.
Aristotle tells us expressly that the theory of the Syllogism, both demonstrative and dialectic, on which we are now about to enter, was his own work altogether and from the beginning; that no one had ever attempted it before; that he therefore found no basis to work upon, but was obliged to elaborate his own theory, from the very rudiments, by long and laborious application. In this point of view, he contrasts Logic pointedly with Rhetoric, on which there had been a series of writers and teachers, each profiting by the labours of his predecessors.1There is no reason to contest the claim to originality here advanced by Aristotle. He was the first who endeavoured, by careful study and multiplied comparison of propositions, to elicit general truths respecting their ratiocinative interdependence, and to found thereupon precepts for regulating the conduct of demonstration and dialectic.2
1See the remarkable passage at the close of the Sophistici Elenchi, p. 183, b. 34-p. 184, b. 9: ταύτης δὲ τῆς πραγματείας οὐ τὸ μὲν ἦν τὸ δὲ οὐκ ἦν προεξειργασμένον, ἀλλ’ οὐδὲν παντελῶς ὑπῆρχε — καὶ περὶ μὲν τῶν ῥητορικῶν ὑπῆρχε πολλὰ καὶ παλαιὰ τὰ λεγόμενα, περὶ δὲ τοῦ συλλογίζεσθαι παντελῶς οὐδὲν εἴχομεν πρότερον ἄλλο λέγειν, ἀλλ’ ἢ τριβῇ ζητοῦντες πολὺν χρόνον ἐπονοῦμεν.
1See the remarkable passage at the close of the Sophistici Elenchi, p. 183, b. 34-p. 184, b. 9: ταύτης δὲ τῆς πραγματείας οὐ τὸ μὲν ἦν τὸ δὲ οὐκ ἦν προεξειργασμένον, ἀλλ’ οὐδὲν παντελῶς ὑπῆρχε — καὶ περὶ μὲν τῶν ῥητορικῶν ὑπῆρχε πολλὰ καὶ παλαιὰ τὰ λεγόμενα, περὶ δὲ τοῦ συλλογίζεσθαι παντελῶς οὐδὲν εἴχομεν πρότερον ἄλλο λέγειν, ἀλλ’ ἢ τριβῇ ζητοῦντες πολὺν χρόνον ἐπονοῦμεν.
2Sir Wm. Hamilton, Lectures on Logic, Lect. v. pp. 87-91, vol. III.:— “The principles of Contradiction and Excluded Middle can both be traced back to Plato, by whom they were enounced and frequently applied; though it was not till long after, that either of them obtained a distinctive appellation. To take the principle of Contradiction first. This law Plato frequently employs, but the most remarkable passages are found in the Phædo (p. 103), in the Sophista (p. 252), and in the Republic (iv. 436, vii. 525). This law was however more distinctively and emphatically enounced by Aristotle.… Following Aristotle, the Peripatetics established this law as the highest principle of knowledge. From the Greek Aristotelians it obtained the name by which it has subsequently been denominated, theprinciple, orlaw, oraxiom, ofContradiction(ἀξίωμα τῆς ἀντιφάσεως).… The law of Excluded Middle between two contradictories remounts, as I have said, also to Plato; though the Second Alcibiades, in which it is most clearly expressed (p. 139; also Sophista, p. 250), must be admitted to be spurious.… This law, though universally recognized as a principle in the Greek Peripatetic school, and in the schools of the middle ages, only received the distinctive appellation by which it is now known at a comparatively modern date.â€�The passages of Plato, to which Sir W. Hamilton here refers, will not be found to bear out his assertion that Plato “enounced and frequently applied the principles of Contradiction and Excluded Middle.â€� These two principles are both of them enunciated, denominated, and distinctly explained by Aristotle, but by no one before him, as far as our knowledge extends. The conception of the two maxims, in their generality, depends upon the clear distinction between Contradictory Opposition and Contrary Opposition; which is fully brought out by Aristotle, but not adverted to, or at least never broadly and generally set forth, by Plato. Indeed it is remarkable that the word Ἀντίφασις, the technical term for Contradiction, never occurs in Plato; at least it is not recognized in theLexicon Platonicum. Aristotle puts it in the foreground of his logical exposition; for, without it, he could not have explained what he meant by Contradictory Opposition. See Categoriæ, pp. 13-14, and elsewhere in the treatise De Interpretatione and in the Metaphysica. Respecting the idea of the Negative as put forth by Plato in the Sophistes (not coinciding either with Contradictory Opposition or with Contrary Opposition), see ‘Plato and the Other Companions of Sokrates,’ vol. II.ch. xxvii. pp. 449-459. I have remarked in that chapter, and the reader ought to recollect, that the philosophical views set out by Plato in the Sophistes differ on many points from what we read in other Platonic dialogues.
2Sir Wm. Hamilton, Lectures on Logic, Lect. v. pp. 87-91, vol. III.:— “The principles of Contradiction and Excluded Middle can both be traced back to Plato, by whom they were enounced and frequently applied; though it was not till long after, that either of them obtained a distinctive appellation. To take the principle of Contradiction first. This law Plato frequently employs, but the most remarkable passages are found in the Phædo (p. 103), in the Sophista (p. 252), and in the Republic (iv. 436, vii. 525). This law was however more distinctively and emphatically enounced by Aristotle.… Following Aristotle, the Peripatetics established this law as the highest principle of knowledge. From the Greek Aristotelians it obtained the name by which it has subsequently been denominated, theprinciple, orlaw, oraxiom, ofContradiction(ἀξίωμα τῆς ἀντιφάσεως).… The law of Excluded Middle between two contradictories remounts, as I have said, also to Plato; though the Second Alcibiades, in which it is most clearly expressed (p. 139; also Sophista, p. 250), must be admitted to be spurious.… This law, though universally recognized as a principle in the Greek Peripatetic school, and in the schools of the middle ages, only received the distinctive appellation by which it is now known at a comparatively modern date.â€�
The passages of Plato, to which Sir W. Hamilton here refers, will not be found to bear out his assertion that Plato “enounced and frequently applied the principles of Contradiction and Excluded Middle.â€� These two principles are both of them enunciated, denominated, and distinctly explained by Aristotle, but by no one before him, as far as our knowledge extends. The conception of the two maxims, in their generality, depends upon the clear distinction between Contradictory Opposition and Contrary Opposition; which is fully brought out by Aristotle, but not adverted to, or at least never broadly and generally set forth, by Plato. Indeed it is remarkable that the word Ἀντίφασις, the technical term for Contradiction, never occurs in Plato; at least it is not recognized in theLexicon Platonicum. Aristotle puts it in the foreground of his logical exposition; for, without it, he could not have explained what he meant by Contradictory Opposition. See Categoriæ, pp. 13-14, and elsewhere in the treatise De Interpretatione and in the Metaphysica. Respecting the idea of the Negative as put forth by Plato in the Sophistes (not coinciding either with Contradictory Opposition or with Contrary Opposition), see ‘Plato and the Other Companions of Sokrates,’ vol. II.ch. xxvii. pp. 449-459. I have remarked in that chapter, and the reader ought to recollect, that the philosophical views set out by Plato in the Sophistes differ on many points from what we read in other Platonic dialogues.
He begins the Analytica Priora by setting forth his general purpose, and defining his principal terms and phrases. His manner is one of geometrical plainness and strictness. It may perhaps have been common to him with various contemporary geometers, whose works are now lost; but it presents an entire novelty in Grecian philosophy and literature. It departed not merely from the manner of the rhetoricians and the physical philosophers (as far as we know them, not excluding even Demokritus), but also from Sokrates and the Sokratic school. For though Sokrates and Plato were perpetually calling for definitions, and did much to make others feel the want of such, they neither of them evinced aptitude or readiness to supply the want. The new manner of Aristotle is adapted to an undertaking which he himself describes as original, in which he has no predecessors, and is compelled to dig his own foundations. It is essentially didactic and expository, and contrasts strikingly with the mixture of dramatic liveliness and dialectical subtlety which we find in Plato.
The terminology of Aristotle in the Analytica is to a certain extent different from that in the treatise De Interpretatione. The Enunciation (Ἀπόφανις) appears under the new name of Πρότασις,Proposition(in the literal sense) orPremiss; while, instead of Noun and Verb, we have the wordTerm(Ὅρος), applied alike both to Subject and to Predicate.3We pass now from the region ofdeclaredtruth, into that ofinferentialorreasonedtruth. We find the proposition looked at, not merely as communicating truth in itself, but as generating and helping to guarantee certain ulterior propositions, which communicate something additional or different. The primary purpose of the Analytica is announced to be, to treat of Demonstration anddemonstrative Science; but the secondary purpose, running parallel with it and serving as illustrative counterpart, is, to treat also of Dialectic; both of them4being applications of the inferential or ratiocinative process, the theory of which Aristotle intends to unfold.
3Aristot. Analyt. Prior. I. i. p. 24, b. 16: ὅρον δὲ καλῶ εἰς ὃν διαλύεται ἡ πρότασις, οἷον τό τε κατηγορούμενον καὶ τὸ καθ’ οὗ κατηγορεῖται, &c.Ὅρος —Terminus— seems to have been a technical word first employed by Aristotle himself to designate subject and predicate as theextremesof a proposition, which latter he conceives as theintervalbetween thetermini—διάστημα. (Analyt. Prior. I. xv. p. 35, a. 12. στερητικῶν διαστημάτων, &c. See Alexander, Schol. pp. 145-146.)In the Topica Aristotle employs ὅρος in a very different sense — λόγος ὁ τὸ τί ἦν εἶναι σημαίνων (Topic. I. v. p. 101, b. 39) — hardly distinguished from ὁρισμός. The Scholia take little notice of this remarkable variation of meaning, as between two treatises of the Organon so intimately connected (pp. 256-257, Br.).
3Aristot. Analyt. Prior. I. i. p. 24, b. 16: ὅρον δὲ καλῶ εἰς ὃν διαλύεται ἡ πρότασις, οἷον τό τε κατηγορούμενον καὶ τὸ καθ’ οὗ κατηγορεῖται, &c.
Ὅρος —Terminus— seems to have been a technical word first employed by Aristotle himself to designate subject and predicate as theextremesof a proposition, which latter he conceives as theintervalbetween thetermini—διάστημα. (Analyt. Prior. I. xv. p. 35, a. 12. στερητικῶν διαστημάτων, &c. See Alexander, Schol. pp. 145-146.)
In the Topica Aristotle employs ὅρος in a very different sense — λόγος ὁ τὸ τί ἦν εἶναι σημαίνων (Topic. I. v. p. 101, b. 39) — hardly distinguished from ὁρισμός. The Scholia take little notice of this remarkable variation of meaning, as between two treatises of the Organon so intimately connected (pp. 256-257, Br.).
4Analyt. Prior. I. i. p. 24, a. 25.
4Analyt. Prior. I. i. p. 24, a. 25.
The three treatises — 1, Analytica Priora, 2, Analytica Posteriora, 3, Topica with Sophistici Elenchi — thus belong all to one general scheme; to the theory of the Syllogism, with its distinct applications, first, to demonstrative or didactic science, and, next, to dialectical debate. The scheme is plainly announced at the commencement of the Analytica Priora; which treatise discusses the Syllogism generally, while the Analytica Posteriora deals with Demonstration, and the Topica with Dialectic. The first chapter of the Analytica Priora and the last chapter of the Sophistici Elenchi (closing the Topica), form a preface and a conclusion to the whole. The exposition of the Syllogism, Aristotle distinctly announces, precedes that of Demonstration (and for the same reason also precedes that of Dialectic), because it is more general: every demonstration is a sort of syllogism, but every syllogism is not a demonstration.5
5Ibid. I. iv. p. 25, b. 30.
5Ibid. I. iv. p. 25, b. 30.
As a foundation for the syllogistic theory, propositions are classified according to their quantity (more formally than in the treatise De Interpretatione) into Universal, Particular, and Indefinite or Indeterminate;6Aristotle does not recognize the Singular Proposition as a distinct variety. In regard to the Universal Proposition, he introduces a different phraseology according as it is looked at from the side of the Subject, or from that of the Predicate. The Subject is, or is not, in the whole Predicate; the Predicate is affirmed or denied respecting all or every one of the Subject.7The minor term of the Syllogism (in the first mode of the first figure) is declared to be in the whole middle term; the major is declared to belong to, or to be predicable of, all and every the middle term. Aristotle says that the two are the same; we ought rather to say that each is the concomitant and correlate of the other, though his phraseology is such as to obscure the correlation.
6Ibid. I. i. p. 24, a. 17. The Particular (ἐν μέρει), here for the first time expressly distinguished by Aristotle, is thus defined:— ἐν μέρει δὲ τὸ τινὶ ἢ μὴ τινὶ ἢ μὴ παντὶ ὑπάρχειν.
6Ibid. I. i. p. 24, a. 17. The Particular (ἐν μέρει), here for the first time expressly distinguished by Aristotle, is thus defined:— ἐν μέρει δὲ τὸ τινὶ ἢ μὴ τινὶ ἢ μὴ παντὶ ὑπάρχειν.
7Ibid. b. 26: τὸ δ’ ἐν ὅλῳ εἰναι ἕτερον ἑτέρῳ, καὶ τὸ κατὰ παντὸς κατηγορεῖσθαι θατέρου θάτερον, ταὐτόν ἐστι — ταὐτὸν,i.e.ἀντεστραμμένως, as Waitz remarks in note. Julius Pacius says:— “Idem re, sed ratione differunt ut ascensus et descensus; nam subjectum dicitur esse vel non esse in toto attributo, quia attributum dicitur de omni vel de nullo subjectoâ€� (p. 128).
7Ibid. b. 26: τὸ δ’ ἐν ὅλῳ εἰναι ἕτερον ἑτέρῳ, καὶ τὸ κατὰ παντὸς κατηγορεῖσθαι θατέρου θάτερον, ταὐτόν ἐστι — ταὐτὸν,i.e.ἀντεστραμμένως, as Waitz remarks in note. Julius Pacius says:— “Idem re, sed ratione differunt ut ascensus et descensus; nam subjectum dicitur esse vel non esse in toto attributo, quia attributum dicitur de omni vel de nullo subjectoâ€� (p. 128).
The definition given of a Syllogism is very clear and remarkable:— “It is a speech in which, some positions having been laid down, something different from these positions follows as a necessary consequence from their being laid down.� In aperfectSyllogism nothing additional is required to make the necessity of the consequence obvious as well as complete. But there are alsoimperfectSyllogisms, in which such necessity, though equally complete, is not so obviously conveyed in the premisses, but requires some change to be effected in the position of the terms in order to render it conspicuous.8
8Aristot. Anal. Prior. I. i. p. 24, b. 18-26. The same, with a little difference of wording, at the commencement of Topica, p. 100, a. 25. Compare also Analyt. Poster. I. x. p. 76, b. 38: ὅσων ὄντων τῷ ἐκεῖνα εἶναι γίνεται τὸ συμπέρασμα.
8Aristot. Anal. Prior. I. i. p. 24, b. 18-26. The same, with a little difference of wording, at the commencement of Topica, p. 100, a. 25. Compare also Analyt. Poster. I. x. p. 76, b. 38: ὅσων ὄντων τῷ ἐκεῖνα εἶναι γίνεται τὸ συμπέρασμα.
The term Syllogism has acquired, through the influence of Aristotle, a meaning so definite and technical, that we do not easily conceive it in any other meaning. But in Plato and other contemporaries it bears a much wider sense, being equivalent to reasoning generally, to the process of comparison, abstraction, generalization.9It was Aristotle who consecrated the word, so as to mean exclusively the reasoning embodied in propositions of definite form and number. Having already analysed propositions separately taken, and discriminated them into various classes according to their constituent elements, he now proceeds to consider propositions in combination. Two propositions, if properly framed, will conduct to a third, different from themselves, but which will be necessarily true if they are true. Aristotle calls the three together a Syllogism.10He undertakes to shew how it must be framed in order that its conclusion shall be necessarily true, if the premisses are true. He furnishes schemes whereby the cast and arrangement of premisses, proper for attaining truth, may be recognized; together with the nature of the conclusion, warrantable under each arrangement.
9See especially Plato, Theætêt. p. 186, B-D., where ὁ συλλογισμὸς and τὰ ἀναλογίσματα are equivalents.
9See especially Plato, Theætêt. p. 186, B-D., where ὁ συλλογισμὸς and τὰ ἀναλογίσματα are equivalents.
10Julius Pacius (ad Analyt. Prior. I. i.) says that it is a mistake on the part of most logicians to treat the Syllogism as including three propositions (ut vulgus logicorum putat). He considers the premisses alone as constituting the Syllogism; the conclusion is not a part thereof, but something distinct and superadded. It appears to me that thevulgus logicorumare here in the right.
10Julius Pacius (ad Analyt. Prior. I. i.) says that it is a mistake on the part of most logicians to treat the Syllogism as including three propositions (ut vulgus logicorum putat). He considers the premisses alone as constituting the Syllogism; the conclusion is not a part thereof, but something distinct and superadded. It appears to me that thevulgus logicorumare here in the right.
In the Analytica Priora, we find ourselves involved, from and after the second chapter, in the distinction of Modal propositions, the necessary and the possible. The rules respecting the simple Assertory propositions are thus, even from the beginning, given in conjunction and contrast with those respecting the Modals. This is one among many causes of the difficulty and obscurity with which the treatise is beset. Theophrastus and Eudemusseem also to have followed their master by giving prominence to the Modals:11recent expositors avoid the difficulty, some by omitting them altogether, others by deferring them until the simple assertory propositions have been first made clear. I shall follow the example of these last; but it deserves to be kept in mind, as illustrating Aristotle’s point of view, that he regards the Modals as principal varieties of the proposition, co-ordinate in logical position with the simple assertory.
11Eudemi Fragmenta, cii.-ciii. p. 145, ed. Spengel.
11Eudemi Fragmenta, cii.-ciii. p. 145, ed. Spengel.
Before entering on combinations of propositions, Aristotle begins by shewing what can be done with single propositions, in view to the investigation or proving of truth. A single proposition may beconverted; that is, its subject and predicate may be made to change places. If a proposition be true, will it be true when thus converted, or (in other words) will its converse be true? If false, will its converse be false? If this be not always the case, what are the conditions and limits under which (assuming the proposition to be true) the process of conversion leads to assured truth, in each variety of propositions, affirmative or negative, universal or particular? As far as we know, Aristotle was the first person that ever put to himself this question; though the answer to it is indispensable to any theory of the process of proving or disproving. He answers it before he enters upon the Syllogism.
The rules which he lays down on the subject have passed into all logical treatises. They are now familiar; and readers are apt to fancy that there never was any novelty in them — that every one knows them without being told. Such fancy would be illusory. These rules are very far from being self-evident, any more than the maxims of Contradiction and of the Excluded Middle. Not one of the rules could have been laid down with its proper limits, until the discrimination of propositions, both as to quality (affirmative or negative), and as to quantity (universal or particular), had been put prominently forward and appreciated in all its bearings. The rule for trustworthy conversion is different for each variety of propositions. The Universal Negative may be converted simply; that is, the predicate may become subject, and the subject may become predicate — the proposition being true after conversion, if it was true before. But the Universal Affirmative cannot be thus converted simply. It admits of conversion only in the manner called by logiciansper accidens: if the predicate change places with the subject, we cannot be sure that the proposition thus changed will be true,unless the new subject be lowered in quantity from universal to particular;e.g.the proposition, All men are animals, has for its legitimate converse not,Allanimals are men, but only,Someanimals are men. The Particular Affirmative may be converted simply: if it be true that Some animals are men, it will also be true that Some men are animals. But, lastly, if the true proposition to be converted be a Particular Negative, it cannot be converted at all, so as to make sure that the converse will be true also.12
12Aristot. Analyt. Prior. I. ii. p. 25, a. 1-26.
12Aristot. Analyt. Prior. I. ii. p. 25, a. 1-26.
Here then are four separate rules laid down, one for each variety of propositions. The rules for the second and third variety are proved by the rule for the first (the Universal Negative), which is thus the basis of all. But how does Aristotle prove the rule for the Universal Negative itself? He proceeds as follows: “If A cannot be predicated of any one among the B’s, neither can B be predicated of any one among the A’s. For if it could be predicated of any one among them (say C), the proposition that A cannot be predicated of any B would not be true; since C is one among the B’s.�13Here we have a proof given which is no proof at all. If I disbelieved or doubted the proposition to be proved, I should equally disbelieve or doubt the proposition given to prove it. The proof only becomes valid, when you add a farther assumption which Aristotle has not distinctly enunciated, viz.: That if some A (e.g.C) is B, then some B must also be A; which would be contrary to the fundamental supposition. But this farther assumption cannot be granted here, because it would imply that we already know the rule respecting the convertibility of Particular Affirmatives, viz., that they admit of being converted simply. Now the rule about Particular Affirmatives is afterwards itself proved by help of the preceding demonstration respecting the Universal Negative. As the proof stands, therefore, Aristotle demonstrates each of these by means of the other; which is not admissible.14
13Ibid. p. 25, a. 15: εἰ οὖν μηδενὶ τῶν Β τὸ Ἀ ὑπάρχει, οὐδὲ τῶν Ἀ οὐδενὶ ὑπάρξει τὸ Β. εἰ γὰρ τινι, οἷον τῷ Γ, οὐκ ἀληθὲς ἔσται τὸ μηδενὶ τῶν Β τὸ Ἀ ὑπάρχειν· τὸ γὰρ Γ τῶν Β τί ἐστιν.Julius Pacius (p. 129) proves the Universal Negative to be convertiblesimpliciter, by aReductio ad Absurdumcast into a syllogism in the First figure. But it is surely unphilosophical to employ the rules of Syllogism as a means of proving the legitimacy of Conversion, seeing that we are forced to assume conversion in our process for distinguishing valid from invalid syllogisms. Moreover theReductio ad Absurdumassumes the two fundamental Maxims of Contradiction and Excluded Middle, though these are less obvious, and stand more in need of proof than the simple conversion of the Universal Negative, the point that they are brought to establish.
13Ibid. p. 25, a. 15: εἰ οὖν μηδενὶ τῶν Β τὸ Ἀ ὑπάρχει, οὐδὲ τῶν Ἀ οὐδενὶ ὑπάρξει τὸ Β. εἰ γὰρ τινι, οἷον τῷ Γ, οὐκ ἀληθὲς ἔσται τὸ μηδενὶ τῶν Β τὸ Ἀ ὑπάρχειν· τὸ γὰρ Γ τῶν Β τί ἐστιν.
Julius Pacius (p. 129) proves the Universal Negative to be convertiblesimpliciter, by aReductio ad Absurdumcast into a syllogism in the First figure. But it is surely unphilosophical to employ the rules of Syllogism as a means of proving the legitimacy of Conversion, seeing that we are forced to assume conversion in our process for distinguishing valid from invalid syllogisms. Moreover theReductio ad Absurdumassumes the two fundamental Maxims of Contradiction and Excluded Middle, though these are less obvious, and stand more in need of proof than the simple conversion of the Universal Negative, the point that they are brought to establish.
14Waitz, in his note (p. 374), endeavours, but I think without success, to show that Aristotle’s proof is not open to the criticism here advanced. He admits that it is obscurely indicated, but the amplification of it given by himself still remains exposed to the same objection.
14Waitz, in his note (p. 374), endeavours, but I think without success, to show that Aristotle’s proof is not open to the criticism here advanced. He admits that it is obscurely indicated, but the amplification of it given by himself still remains exposed to the same objection.
Even the friends and companions of Aristotle were not satisfied with his manner of establishing this fundamental rule as to the conversion of propositions. Eudêmus is said to have given a different proof; and Theophrastus assumed as self-evident, without any proof, that the Universal Negative might always be converted simply.15It appears to me that no other or better evidence of it can be offered, than the trial upon particular cases, that is to say, Induction.16Nothing is gained by dividing (as Aristotle does) the whole A into parts, one of which is C; nor can I agree with Theophrastus in thinking that every learner would assent to it at first hearing, especially at a time when no universal maxims respecting the logical value of propositions had ever been proclaimed. Still less would a Megaric dialectician, if he had never heard the maxim before, be satisfied to stand upon an allegedà priorinecessity without asking for evidence. Now there is no other evidence except by exemplifying the formula, No A is B, in separate propositions already known to the learner as true or false, and by challenging him to produce any one case, in which, when it is true to say No A is B, it is not equally true to say, No B is A; the universality of the maxim being liable to be overthrown by any one contradictory instance.17If this proof does not convince him, no better can beproduced. In a short time, doubtless, he will acquiesce in the general formula at first hearing, and he may even come to regard it as self-evident. It will recall to his memory an aggregate of separate cases each individually forgotten, summing up their united effect under the same aspect, and thus impressing upon him the general truth as if it were not only authoritative but self-authorized.
15See the Scholia of Alexander on this passage, p. 148, a. 30-45, Brandis; Eudemi Fragm. ci.-cv. pp. 145-149, ed. Spengel.
15See the Scholia of Alexander on this passage, p. 148, a. 30-45, Brandis; Eudemi Fragm. ci.-cv. pp. 145-149, ed. Spengel.
16We find Aristotle declaring in Topica, II. viii. p. 113, b. 15, that in converting a true Universal Affirmative proposition, the negative of the Subject of the convertend is always true of the negative of the Predicate of the convertend;e.g.If every man is an animal, every thing which is not an animal is not a man. This is to be assumed (he says) upon the evidence of Induction — uncontradicted iteration of particular cases, extended to all cases universally — λαμβάνειν δ’ ἐξ ἐπαγωγῆς, οἷον εἰ ὁ ἄνθρωπος ζῷον, τὸ μὴ ζῷον οὐκ ἄνθρωπος· ὁμοίως δὲ καὶ ἐπὶ τῶν ἄλλων.… ἐπὶ πάντων οὖν τὸ τοιοῦτον ἀξιωτέον.The rule for the simple conversion of the Universal Negative rests upon the same evidence of Induction, never contradicted.
16We find Aristotle declaring in Topica, II. viii. p. 113, b. 15, that in converting a true Universal Affirmative proposition, the negative of the Subject of the convertend is always true of the negative of the Predicate of the convertend;e.g.If every man is an animal, every thing which is not an animal is not a man. This is to be assumed (he says) upon the evidence of Induction — uncontradicted iteration of particular cases, extended to all cases universally — λαμβάνειν δ’ ἐξ ἐπαγωγῆς, οἷον εἰ ὁ ἄνθρωπος ζῷον, τὸ μὴ ζῷον οὐκ ἄνθρωπος· ὁμοίως δὲ καὶ ἐπὶ τῶν ἄλλων.… ἐπὶ πάντων οὖν τὸ τοιοῦτον ἀξιωτέον.
The rule for the simple conversion of the Universal Negative rests upon the same evidence of Induction, never contradicted.
17Dr. Wallis, in one of his acute controversial treatises against Hobbes, remarks upon this as the process pursued by Euclid in his demonstrations:— “You tell us next that an Induction, without enumeration of all the particulars, is not sufficient to infer a conclusion. Yes, Sir, if after the enumeration of some particulars, there comes a general clause,and the like in other cases(as here it doth), this may pass for a proofe till there be a possibility of giving some instance to the contrary, which here you will never be able to doe. And if such an Induction may not pass for proofe, there is never a proposition in Euclid demonstrated. For all along he takes no other course, or at least grounds his Demonstrations on Propositions no otherwise demonstrated. As, for instance, he proposeth it in general (i. c. 1.) —To make an equilateral triangle on a line given. And then he shows you how to do it upon the line A B, which he there shows you, and leaves you to supply:And the same, by the like means, may be done upon any other strait line; and then infers his general conclusion. Yet I have not heard any man object that the Induction was not sufficient, because he did not actually performe it in all lines possible.â€� — (Wallis, Due Correction to Mr. Hobbes, Oxon. 1656, sect. v. p. 42.) This is induction byparity of reasoning.So also Aristot. Analyt. Poster. I. iv. p. 73, b. 32: τὸ καθόλου δὲ ὑπάρχει τότε, ὅταν ἐπὶ τοῦ τυχόντος καὶ πρώτου δεικνύηται.
17Dr. Wallis, in one of his acute controversial treatises against Hobbes, remarks upon this as the process pursued by Euclid in his demonstrations:— “You tell us next that an Induction, without enumeration of all the particulars, is not sufficient to infer a conclusion. Yes, Sir, if after the enumeration of some particulars, there comes a general clause,and the like in other cases(as here it doth), this may pass for a proofe till there be a possibility of giving some instance to the contrary, which here you will never be able to doe. And if such an Induction may not pass for proofe, there is never a proposition in Euclid demonstrated. For all along he takes no other course, or at least grounds his Demonstrations on Propositions no otherwise demonstrated. As, for instance, he proposeth it in general (i. c. 1.) —To make an equilateral triangle on a line given. And then he shows you how to do it upon the line A B, which he there shows you, and leaves you to supply:And the same, by the like means, may be done upon any other strait line; and then infers his general conclusion. Yet I have not heard any man object that the Induction was not sufficient, because he did not actually performe it in all lines possible.� — (Wallis, Due Correction to Mr. Hobbes, Oxon. 1656, sect. v. p. 42.) This is induction byparity of reasoning.
So also Aristot. Analyt. Poster. I. iv. p. 73, b. 32: τὸ καθόλου δὲ ὑπάρχει τότε, ὅταν ἐπὶ τοῦ τυχόντος καὶ πρώτου δεικνύηται.
Aristotle passes next to Affirmatives, both Universal and Particular. First, if A can be predicated of all B, then B can be predicated ofsomeA; for if B cannot be predicated of any A, then (by the rule for the Universal Negative) neither can A be predicated of any B. Again, if A can be predicated of some B, in this case also, and for the same reason, B can be predicated of some A.18Here the rule for the Universal Negative, supposed already established, is applied legitimately to prove the rules for Affirmatives. But in the first case, that of the Universal, it fails to provesomein the sense ofnot-allorsome-at-most, which is required; whereas, the rules for both cases can be proved by Induction, like the formula about the Universal Negative. When we come to the Particular Negative, Aristotle lays down the position, that it does not admit of being necessarily converted in any way. He gives no proof of this, beyond one single exemplification: If some animal is not a man, you are not thereby warranted in asserting the converse, that some man is not an animal.19It is plain that such an exemplification is only an appeal to Induction: you produce one particular example, which is entering on the track of Induction; and one example alone is sufficient to establish the negative of an universal proposition.20The converse of a Particular Negative is not in all cases true, though it may be true in many cases.
18Aristot. Analyt. Prior. I. ii. p. 25, a. 17-22.
18Aristot. Analyt. Prior. I. ii. p. 25, a. 17-22.
19Ibid. p. 25, a. 22-26.
19Ibid. p. 25, a. 22-26.