196 Mr DE morgan, ON THE SYLLOGISM, No. Ill, 



syllogism. The common form seems to make the whole prove no more than must have been 

 proved in establishing the part. It is only an appearance : but there is substantial neglect in 

 omitting to notice that the syllogism, as logical, has nothing to do with the sort of vindication 

 under which its premises are advanced. If there be a logical necessity that every Y is Z, then 

 X being Y, X is Z. Let the necessity be from a priori deduction, let it be the imperfect 

 necessity of induction of the past made deduction of the future, or let it be the a. posteriori 

 necessity of a complete induction, the syllogism is one and the same act of mind in all cases. 

 The full mathematical form includes all these cases, and shews their inclusion. 



The above forms leave only a contingent place for the additional propositions which 

 enter when the predicate is quantified by postulation of every distribution of all and some. 

 It may come out that X and Y are identical in extent : this is one case of A. It mtist 

 come out that some X is not some Y, unless X and Y be singular and identical. The 

 first is to be referred to the forms of terminal precision, the second to a notion antecedent 

 to propositional enunciation, and connected with the purposes and distinctions of nomenclature. 



XIV. The idea of enumeration of individuals does not afford the most satisfactory 

 basis for a doctrine of logical quantity which shall put the counter wholes, mathematical and 

 metaphysical, into complete correlation. 



In the mathematical whole, the logicians often conceal enumeration by speaking of ewtent 

 instead of number : not ' every man is one of the animals,' but 'All man is part of animal.' Very 

 strange is it to a beginner to hear of the extent of the term man, and of parts of that extent, 

 as if the notion were capable of continuous accretion, and each new birth put a little bit more 

 man into the extent. To me, when I first heard this language, it seemed as if the notion man 

 had been treated after the manner of a dish of potatoes de-individualised by being skinned and 

 then mashed together. There is perhaps in the geometrical idea some help towards the ex- 

 pression of class as a unit, because number is connected with the notion of partition in a closer 

 way than area. Still, the attribute compounded of attributes does not seem at once, and 

 without effort, to correlate with the class aggregated of classes. 



If we subdivide a class into four others, there is an amount of information in the four, as 

 four, which we are not conscious of when we see four attributes in an individual object. If 

 the worthy Jesuit Gaspar Schott had announced that the number of beatified existences on 

 whose aid man could rely was the 256th power of 2, there would have been an intelligible basis 

 of comparison with other things: how many to each man, what reduction by probable increase 

 of population in a given time, &c. would be matters of approximation for an actuary. But 

 when Schott announced 2^^ as the number of graces and glories of the Virgin, no comparison 

 could well exist within the limits of attractive speculation. For aught we can say, there may 

 be 2^ distinct powers in human reason, developed or undeveloped. 



In classification, we know that we arrive at a true infima species, the individual : for from 

 the individual we start, and therefore to the individual we can regress. But in an attribute 

 we begin with the compound ; and our knowledge of simple substances is not yet attained, far 

 less our atomic theory. In the case of a simple perception, as white, we may just distinguish 

 brightness and tint, but we can go no further : the pr'sm which decomposes the cause does not 

 decompose the effect, does not give separate perceptions of which we were perceptively con- 



