438 



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



I now ask what is the real basis of this system ? It is formed on what I call the pepper- 

 box plan ; all and some are shaken out upon subjects and predicates in every possible way. 

 I am a decided advocate for this process, as a preliminary mode of collecting materials : and 

 I have now before me 512 modes of enunciation — and this only an instalment — obtained by 

 using the pepperbox with some of the pairs of correlative notions which are scattered 

 through the systems. It would have been well for logic if Aristotle had followed this plan. 

 But it is an error to assume that because certain junctions of correlative concepts give an 

 incomplete system, therefore the introduction of all the remaining junctions must complete 

 that system. Any person who makes this supposition may become liable to the remark made 

 by Hamilton upon Aristotle — and which I now make upon himself — that he commenced his 

 synthesis before he had completed his analysis. 



As soon as the distribution of 'all' and 'some' had been made, and also introduction of 

 the partitive sense of ' some', very slight attention would have shown that the enunciative 

 forms present an imperfect system of the kind which I called complex in my Formal Logic, 

 and terminally precise in my third paper. Contrary or privative terms being refused admis- 

 sion, it would have been seen that there are Jive terminally precise relations ; or rather, three 

 terminally precise, and two of which one terminal ambiguity is due to the refusal of priva- 

 tive terms, which refusal prevents statement of the relation in which one name stands to the 

 contrary of another. On the principle — which I will not argue further, for with great per- 

 sonal respect for its deniers, I tell them their denial is absurd — that no system of enuncia- 

 tion can be admitted to the name until it is as powerful at denial as at assertion, and at asser- 

 tion as at denial, five contradictions ought to have been introduced. The conjunctive proposi- 

 tions should have brought in their disjunctive denials; and the whole would then have stood 

 as follows. I use both Hamilton's language and my own; but the symbols are now to 

 express Aristotelian forms. 



1. All X is some Y : X toto-partially inclusive of Y : X a sub-identical of Y : X )o) Y, 

 conjoined of X) ) Y and X)) Y. The contradiction is 'Either X(.(Y or X((Y', 

 which I denote by X ( , ( Y. 



2. All X is all Y : X toto-totally inclusive of Y : X an identical of Y : X 1 1 Y, con- 

 joined of X ) ) Y and X ( ( Y. The contradiction is ' Either X (•( Y or X )•) Y', denoted by 

 X)),((Y. 



3. Some X is all Y : X parti-totally inclusive of Y : X a superidentical of Y : X («( Y, 

 conjoined of X ( ( Y and X ( • ( Y. The contradiction is ' Either ) • ) Y or X ) ) Y ', denoted 

 byX),)Y. 



4. Any X is not any Y : X toto-totally exclusive of Y : X an external of Y, X ) • ( Y. 

 The contradiction is X ( ) Y, which, as explained, should have been the partipartial negation, 

 ' Some X is not some Y' of Hamilton's system. 



[Mr Baynes (iVoc. 22, 1862) cheerfully accepts this syllogism 

 under the name I have given it, declares it valid, and will 

 defend it if it be "seriously assailed." This is hasty writing: 

 he means that he will defend what he supposes Hamilton to 



have meant, not what / suppose him to have let pass. But 

 what Mr Baynes takes for Hamilton's meaning needs no de- 

 fence ; what I suppose him to have passed cannot be seriously 

 assailed. December, 1862.J 



