AND ON LOGIC IN GENERAL. 



sideration. Nevertheless, I cannot but hold the choice 

 and distribution of the modal forms to have been a 

 real lapse, as well in Aristotle as in his followers : and 

 it seems that the later philosophers of the middle 

 ages had come to something lilce the same conclusion. 

 Those who would see the modal system in its full 

 perfection of confusion, should, if they will trust 

 Crackanthorpe, consult the Jesuit Peter Fonseca, qui 

 totis quinque prolixis capitibus de Modalibus agens, im- 

 plicat se misere hitce spinis, nee tamen rem ipsam ullo 

 modo explicat, sed velut alter Sisyphus, versat saxum 

 sudans nitendo, neque proficit hilum: et propemodum 

 facit ut lector intelligendo nihil quidquam intelligat. 



The application of the ideas of necessary and im- 

 possible to universals, and of conting<>nt to particulars, 

 was a mistake. It made a truly metaphysical conclu- 

 sion the consequence of a mathematical form. Omnis 

 homo est animal, taken to bo a necessity because no 

 exception was ever noticed, might have been a con- 

 tingency: that is to say, it might have been, for 

 aught the logicians knew, not merely possible for the 

 Creator to have placed on earth — in a literal sense — 

 rational and accountable vegetables, which they ad- 

 mitted, but even possible within the limits of the 

 actual plan. And this mistake led to paralogisms. 

 Thus, it was affirmed that a syllogism with a modal 

 major might give a modal conclusion, though the 

 minor was not modally given, but categorically. Thus 

 from — It is necessary an animal should feel; every 

 man is animal ; they inferred it to be necessary a man 

 should feel. Here one particular modality of the 

 minor is tacitly assumed from its form : or else conclusio 

 sequitur partem deteriorem was strangely forgotten. In 

 what I have called the metaphysical form of the pro- 

 position, the question of necessity or contingency is 

 left open. As the intention of thought in the pre- 

 mises, so also in the conclusion: necessary or con- 

 tingent as the case may be. And any form may be 

 thought as necessary, or as contingent : thus the irre- 

 pugnance of two notions may be either, as well as 

 their repugnance. 



I was not at all aware, when I forwarded to the 

 Society on one day two papers so different in their 

 subjects as the present one and that on the beats of 

 imperfect consonances, that both had some relation to 

 the antagonism of the numbers 3 and 2. The in- 

 equality of 219 and 312 is the source of a great part 

 of the difficulties of temperament ; and it may be that 

 the ill success of the attempt to assimilate a ternary 

 and binary modo of subdivision was a large part of 

 the reason why a fair and consistent juxtaposition of 

 the mathematical and metaphysical forms of predica- 

 tion did not become a recognised part of logic. 



Addition to Postscript. In my second paper I took 

 some part of that distinction between extension and 

 intension which I have developed in the present paper. 

 On this point my eminent oi)ponent (Discussions, Ist 



ed. p. 643*, 2nd ed. p. 698), speaking of his own 

 maxim that "the predicate of the predicate is, with 

 the predicate, affirmed or denied of the subject," pro- 

 ceeds thus : " In fact, if this principle be not univer- 

 sally right, if Mr De Morgan be not altogether wrong, 

 my extension of the doctrine of Breadth and Depth, in 

 correlation, from notions to propositions and syllogisms, 

 has been only an egregious blunder." I do not rejoin 

 that of this I put myself upon the country, for two 

 reasons. First, because the last phrase is not one in 

 which I should like to join issue with such an oppo- 

 nent, alive or dead. Secondly, because there lurks in 

 the sentence I have quoted afallacia plurium descrip- 

 tionum, which prevents it from conveying no more 

 than the point at issue. Sir W. Hamilton's principle 

 is universally right, in its own meaning and in its 

 proper place ; but it is not contradictory of any thing 

 brought forward by me ; so that it does not make me 

 altogether wrong. No one can dispute the principle 

 when it is affirmed of qualities, distributed and sepa- 

 rately residing in their subjects of inhesion. The dif- 

 ference between me and my opponent begins when 

 he affirms or implies that his principle is, appertains 

 to, or is in any way connected with, or even opposed 

 to, the form of thought on which, from Aristotle 

 downwards, has been based the distinction between 

 extension and comprehension, denotation and conno- 

 tation, logical whole and metaphysical whole, or what- 

 ever it may be called. This true and ever-abiding 

 distinction is affirmed by Sir W. Hamilton, and denied 

 by me, to be identical with that drawn by himself be- 

 tween Breadth and Depth. And this is the point on 

 which issue is joined. 



Addition to note in Postscript. On this proposal 

 of Sturm's Leibnitz, who describes it, remarks that the 

 difference between a positive and privative terra, or, 

 what I call a term and its contrary, is of the matter 

 of the term and not of the form of the proposition. 

 Had ho said that the distinction is of the form of the 

 term, as distinguished from the form of the proposition, 

 he would have been right; but there would have been 

 no objection to take. Both Leibnitz and my critics 

 should have objected to contrapositive conversion as 

 material. But here, as in other cases, it is only the 

 now introduction which is material: the established 

 usage is formal. And this illustrates what I remarked 

 in my second paper, namely, that the opposition 

 really made is not of form to matter, but ot what 

 has been usually recognised as formal to that which 

 has not. 



It may be that the earliest attempt to augment the 

 Aristotelian moods was that of John Hospiniau (the 

 Genevan divine was Rodolph) mentioned by Leibnitz 

 as having appeared in a work published at Basle, 1560, 

 8vo. By pressing into the service indefinite and sin- 

 gular teims, and by admitting syllogisms of weakened 

 conclusion (as Cesaro in the second figure) Ho!=pinian 



