perfectly appreciated. This is the individuality or totality of the attribute as predicate, which gives an entirely new and yet natural form of proposition and series of propositional forms. In regard to these, quantity is of no consequence; it falls out of consideration. § 406. This new classification of propositions is formally. legitimate, and is at the same time suitable to the actual facts of our experience and the needs of our thought. Taking Comprehension first as the basis of the whole, we have: A. All man is mortal (indivisible attribute or mark); .. Mortal is a mark of all man. E. No man is quadruped; . Quadruped is not a mark of any man. I. Some man is learned; .. Learning is a mark of some man. O. Some man is not learned ; .. Learning is not a mark of some man. U1. This man is artist; .. Artist is a mark of this man. U2. This man is not an assassin ; .. Assassin is not a mark of this man. In each predicate there is quality, not quantity. The judg ment is simple, natural, and easy; it is suitable to experience; it is simply convertible, and may be expressed in either form -as convertend or converse. To distinguish such propositional forms, we might call them-A Comp., E Comp., I Comp., O Comp., U Comp.1, U Comp.2 It is to be observed that the predicate (attribute) is taken in its whole comprehension, whether the judgment be affirmative or negative. When we say this man is not an assassin, we speak of the whole comprehension of the concept, as marked off from every other, either fuller or less in comprehension. We do not deny anything of him, except the complete whole essentially involved in the concept assassin. He may be homicide, or he may not; but this is neither (implicitly) affirmed nor denied in our judgment. § 407. In Extension, the following will be the scheme of forms: A1. All man is (some) mortal. These may be marked :-A Ex.1, A Ex.2; E Ex.1, E Ex.2; I Ex.; O Ex.1, O Ex.2; U Ex.1, U Ex.2. (a) The Port Royal Logicians were really the first to give effective prominence to the distinction between Extension and Comprehension in Notions and Propositions. But there are references to the distinction by other writers, before and after the date of the Port Royal Logic (1662). To say nothing meanwhile of the obvious references to the distinction in Aristotle himself, we have its apprehension and statement by Cardinal Cajetan in 1496.—(See Port Royal Logic, Introd. p. 33.) Collection of many is twofold; intensively, and thus the species is more collective, because it rather unites the adunata; extensively, and thus the genus is more collective, because many more fall under its unification (adunatione) than under the compass (ambitu) of the species. The species and genus are like generals-the one of which has a small army, but wholly unanimous; the other great, but of diverse factions. For that collects more intensively, this more extensively. Porphyry speaks of the extensive collection, and therefore says the genus is more collective. (Cajetanus in Porph. De Genere et Specie.) The species is in itself more one than the genus, since the species expresses a nature absolutely indivisible formally, whence it is called atoma; but the genus imports a nature divisible.-(Cajetanus in Porph. De Genere et Specie, quoted by Stahl, Regula Philosophicæ, Tit. xii. Reg. v., p. 381: London, 1672; first ed. 1635.) (b) Avicenna had said-Predication is of two sorts, either univocal or denominative. Socrates is a man, is univocal. Here there is true and univocal predication. Man is white, or man has whiteness,--this is denominative. Man is not said to be whiteness; as Socrates is said to be man. (Log., p. 3 v. B.; Prantl, ii. p. 325.) (c) The universal which Logic examines contains three things: the name, which expresses several things; the idea, which represents general things; and the nature, which is in several things.-(La Dialectique du Sieur de Launay, Dissert. iii. p. 72: Paris, 1673.) (d) Universale inest singulis inferiorum, et de illis potest prædicari, non secundum extensionem, seu universalitatem, sed secundum naturam tantum et comprehensionem. Ut tota essentia naturæ sensitivæ, secundum omnia attributa sua, est in singulis animalibus; non autem in tota extensione, quæ una cum convenientia eorum in quibus extendi tur, est forma universalis.-(Goveanus, Logica Elenetica, Disp. x. p. 128: Dublinii, 1683.) There are explicit and intelligent notices of the distinction in Hutcheson, Log. Comp, pp. 24, 25 (ed. 1754); in William Duncan's Elements of Logick, I. iv. § 2; Kirwan, Logick, i. p. 41 (1807). With all this, the doctrine has remained comparatively unfruitful until our own day. § 408. The table of propositional forms given by Hamilton is defective, in so far as it does not specially provide a form for Singulars. The form which is the nearest approach to this is AfA, but this is not adequate, and does not mark out the Singular either properly or without ambiguity. The following scheme may be given as a complete and specific statement of Categorical Propositional forms: Affirmative I. X is Y. Singular Definite, Comprehensive only, in two forms. (a) Newton is the author of the Principia. Concrete. (b) Veracity is the harmony between expression and conviction. Abstract. II. All X is all Y. Definite Omnitude-Double,-cor- III. All X is (some) Y. Definite Omnitude-Single. V. Some X is (some) Y. Negative X is not Y. I. Newton is not the author of the Principia. II. Any X is not (any) Y. III. Any X is not (some) Y. V. Some X is not (some) Y. No. I. is in Comprehension alone; No. II. is in Extension alone. All the others may be read both in Extension and in Comprehension. In the latter, the predicate is taken as indivisible and unquantified. If the predicate Y be taken as a class, we have an Extensive Proposition; if it be taken as a mark or indivisible attribute, we have a Comprehensive Proposition, and that in both cases, whether Affirmative or Negative. 327 CHAPTER XXV. QUANTIFIED PREDICATE-HISTORICAL NOTICES. $409. The history of opinions regarding the legitimacy or the opposite of quantifying the predicate is one in itself of much interest, and it has acquired importance from its bearing on the logical theories of Hamilton, Thomson, and De Morgan, and other recent developments in formal logic. So far as Aristotle is concerned, the principle of quantifying the predicate was rejected by him, when he had the doctrine expressly before him.1 On other occasions, Aristotle may be regarded as having proceeded on the legitimacy of the doctrine, and thus accepted it in practice. This is seen especially in his treatment of the formal Inductive Syllogism.2 The great body of logicians, since the time of Aristotle, have been content to acquiesce in Aristotle's rejection of a quantified predicate, and generally for the reasons he has given, which are by no means cogent or satisfactory.3 The notices hitherto given of writers favourable to the doctrine of a Quantified Predicate, either in theory or in assumption in practice, are to be found mainly in Hamil ton's Logic, and in Mr Baynes' New Analytic of Logical Forms.* Neither Prantl nor Ueberweg has given adequate attention to this point in their historical references. Mr Baynes, in the New Analytic, published in 1850, refers to certain names as recognising the doctrine in theory or in De Int., c. vii. §§ 2-4 c. x. An. Prior., i. 1 See Categories, ii. § 1, v. § 7. c. xxvii. § 9. An. Post., i. c. xii. § 10. 2 See below, p. 449 et seq. 3 For a statement and criticism of Aristotle's views, see Hamilton, Logic, iv. Appendix g, p. 298 et seq. New Analytic, App. i. p. 81. practice. The first is Laurentius Valla (1408-1457), in his De Dialectica, libri. iii. The references are to the edition at Paris of 1530, though the work was probably first published much earlier. Following Valla, is Ambrosius Nolanus in his Castigationes adversus Averroem: Venetiis, 1517. Then, Jodocus Isenacensis, or Jodoc Trutfeder of Eisenach, who was the instructor in philosophy of Luther, by no means a sympathetic pupil,—and who died in 1519. His work is Summulæ Totius Logica, 1501. In England we have Joshua Oldfield, in his Essay towards the Improvement of Reason, 1707; and there is a reference to Godfrey Ploucquet, Fundamenta Philosophia Speculativa, 1759. Thynne, in his notes to Walker's Compendium of Logic, the Trinity College, Dublin, text-book of the time, makes applications of the doctrine. Hamilton refers to authorities for and against the principle, among the former Titius, Ars Cogitandi (1721), and Ploucquet. His reference to Titius is, however, very incomplete.2 § 410. Valla recognises the principle alike theoretically and practically, though he cannot be said to have carried it out with anything like scientific development or precision. He adduces a number of instances of express quantification in ordinary language, for his criticisms of the approved logical doctrines of his day were made chiefly from a grammatical standpoint. There is universality in the predicate in such expressions as these-Nego aliquem esse beatum. Aliquem is here equivalent to ullum. Veto ullum intrare; prohibeo quemquam loqui. Then he recognises the equivalence of subject and predicate in such expressions as the lion roars (rugit), the horse neighs (hinnit), man laughs (ridet). The predicate here is coextensive with the subject, and precisely convertible.* Valla's doctrine acquires its importance from his application of it to the Conversion of Propositions. His doctrine on this point proceeds on the postulate of an express quantification of the predicate, and is perhaps the earliest application of it to this subject, affording at the same time a legitimate and useful simplification of the ordinary logical rules. 1 There is a later edition-Laurentii Valle Romani dialecticarum dispu tationum libri tres eruditiss. Opera Joannis Noviomagi castigati diligenter— Coloniæ, 1541. 2 See Logic, iv. Appendix g., and below, p. 334. 3 De Dial., ii. c. xxix. See above, pp. 257, 310. 4 De Dial., ii. xxii. |