448 



Mr DE morgan, ON THE SYLLOGISM, No. V. AND 



Now Hamilton, who could not read in any other than the cumular sense, and who 

 was possessed of the quantified predicate not merely as that which could be, and ought to be, 

 but as that which is and must be, — asserted (IX. ii. 263), positively for this occasion only, 

 that his great leader' talked " nonsense." He misconceived the nature of the falsehood 

 imputed to a universal predicate : he thought that Aristotle's objection to ' every man is 

 every living being' arose out of horses and dogs, rats and mice, &c., not being men. He 

 charges the founder of logic [sic notus Ulysses?) with rejecting a logical form on the ground 

 of certain matter making it false. To the last he could not see that the Aristotelian proposi- 

 tion attributes the whole predicate to every example of the subject: to the last he fixes on 

 Aristotle the ' all man is all animal', of the modern school, the erroneous translation of ' Omnis . 

 homo est omne animal' And he totally omits to notice Aristotle's assertion that not one pro- 

 position of the form ' Every A is every B ' can be true : from which, on his plan of interpreta- 

 tion, he ought to have accused his master of denying the existence of co-extensive terms. 



Mr Baynes's work (HI.) gives links which had long been dropped in the history of 

 this discussion : and its author is a decisive instance of the manner in which Hamilton's 

 teaching made cumular quantity the only one known in the history of logic, and the only one 

 which can result from scientific analysis. The ambiguity which misled Hamilton seems to 

 have come into general discussion by the sixteenth century: for by that time, taking tlie 

 common belief that only man can laugh, the disputants had completely substituted '■Omnis 

 homo est omne risibile' for Aristotle's instance, as placing the true issue in clearer light. They 

 then asserted, in plain and rational terms, that every man is not every laugher, for each man 

 is only one. Mr Baynes calls this " the inconceivably inconsequent ground that if all man is 

 all risible, then necessarily each man is all risible." Here omnis homo is translated all man, 

 and made to mean all men. Mr Baynes proceeds thus "...to take a parallel example (one. 



' " The whole doctrine of the non-quantitication of the 

 predicate is only another example of the passive sequacity of 

 the logicians. They follow obediently in the footsteps of their 



great master He prohibits once and again the annexation 



of the universal predesignation to the predicate. For why, he 

 says, such predesignation would render the proposition absurd; 

 giving as his only example and proof of this, the judgment, — 



All man is all aiiimal Yet this nonsense (be it spoken with 



all reverence of the Stagirite) has imposed the precept on the 

 systems of Logic down to the present day" (ix. ii. 26S). 

 Again (ix. ii. 29fi), Hamilton declares that "a general rule or 

 postulate of logic Is, — That in the same logical unity (propo- 

 sition or syllogism), the same term or quantification sliould 

 not be changed in import." Hence he infers that if in "All 

 man is all risible" the first all be distributive, so is the second. 

 Hamilton may lay down this postulate for himself and those 

 who like it : but there never was such a postulate in logic. 

 On the contrary, the universal practice, down to our own time, 



implies that in ' Every man is ', all that follows the word is 



is predicated of each man. If we say ' some men are twenty 

 men' the obvious falsehood drives us to metaphor: some men 

 have each the power of twenty. But Hamilton would have it 

 that it has been postulated that this proposition means a literal 

 truth; i.e. this man is one, that man another, &c. — a certain 



some making up twenty. It may be so understood by postu- 

 lation : but it never has been. 



But though the charge against Aristotle is a mere miscon- 

 ception of his meaning, Hamilton fell into the very error 

 of which he accused his leader, namely, that of rejecting a 

 form because certain 7n«//er falsifies it. He is speaking (vi. 

 627*) of the use of any in affirmatives. "Now, let us try 'any' 

 as an affirmative: — 'Any triangle is any trilateral.' This is 

 simple nonsense : for we should thus confound every triangle 

 with every other, pronouncing them all to be identical. Nor, 

 in fact, does Mr I>e Morgan attempt this. He wisely omits 

 the form. But what an omission!" I pass over the last 

 assertion with the observation that the very first proposition in 

 the table here criticised is "Any one X is any one Y": 

 these words are followed by ''giving there is but one X and 

 one Y, and X is Y." What I have here to do with is Hamil- 

 ton's distinct rejection of the form because it is false as applied 

 to plural notions. It is false that "any triangle is any trilate- 

 ral": he who makes this assertion " confounds every triangle 

 with every "other"; that is, asserts the existence of only one 

 triangle. And it is false that " every animal is a man": but 

 this does not compel the rejection of " Every X is Y " from 

 the forms of enunciation, on the ground of the instance declar- 

 ing horses and dogs to be men. 



