AND THE PROBABILITIES OF AUTHORITY AND ARGUMENT. 383 



respect to convertible propositions. Thus, as to convertible propositions, i, PC, T, SCT are all of 

 the same effect: as to inconvertible propositions, T, SCT, SP and SC. 



There is a point which developes itself very strongly when we come to consider the transforma- 

 tions upon instances; namely, the distinction between the assertion of a proposition sul)jectively and 

 objectively. The former mode is that which is always presumed : but in actual use of logic the 

 distinction must be drawn. 



When we say. Every X is Y, as a proposition with meaning, and with or without truth as the 

 case may be, we treat neither X nor Y as having any other existence except that which our minds 

 give them: but we imply that if X have any such other existence, so lias ]'. But the syllogism 

 "X) Y and Y) Z therefore X) Z" is not valid merely by understanding A' and Z to be taken in 

 the conclusion as in the premises. The middle term must exist: not necessarily objectively, but it 

 must have a positive existence. It is no syllogism to say that A" is Y, if there be such a thing, and 

 Y (if &c.) is Z ; therefore X is Z. And yet there is no offence against any of the ordinary rules of 

 logic: the middle term is strictly middle; it is " Y, on the condition that F exists" in both. Thus 

 " Homer was a perfect poet (if ever there were one) ; a perfect poet (if &c.) is faultless in morals ; 

 therefore Homer was &c." The premises will sometimes be admitted ; but they do not prove the 

 conclusion : the proper conclusion is a dilemma, " Either Homer was faultless in morals, or there 

 never was a perfect poet." The existence here spoken of is objective : but the same thing applies to 

 purely subjective cases. The terms of the conclusion may be conditional : but inference requires 

 that the middle term should be unconditional. Every X (if ever X existed) is Y ; every Y is Z (if 

 ever Z existed) : therefore every X (if ever X existed) is Z (if ever Z existed). This is a good 

 syllogism : but Y is here absolute. 



When the syllogism can be converted into another, having for its middle term the contrary of 

 the first middle term, the same absolute existence must be claimed for the contrary. And here again 

 I remind the reader that the absolute existence spoken of is existence within the universe of the pro- 

 positions Thus X ) Y and Y) Z give X) Z, or y ) w and z) y give z) w. A positive existence 

 is then required both for F and y. There is an extreme case; y may not exist, that is, F may 

 contain the universe; but then F and Z are identical, and the conclusion X) Z is identical with 

 X )Y and z)x contains nothing. 



Whatever sort of existence is spoken of is tacitly claimed for the terms of a proposition by the 

 proposition itself: the refusal of this claim, or the denial by assertion of non-existence, being a dis- 

 tinct thing from denial by contradiction. A certain meadow (the universe of the proposition) is 

 flooded during the hay-harvest: the proposition "No part of the crop that was not flooded was 

 not saved" (of the form ,x . y) means logically that all wiiich was not flooded || was saved, that all 

 which was not saved (| was flooded, and that part may have been both flooded and saved. Some 

 reflexion (for want of habit of dealing with triple negatives makes the proposition rather complicated) 

 will shew that a person who is apt to think objectively of propositions, as all do who are not trained 

 in logical considerations, is much more likely to require the insertion of tlie words (//" «?(//) in two 

 places (jl) than he would be if the proposition were presented in the more simple form, "All the dry 

 crop was saved." Probably such a person would not require the conditional words here, merely 

 because he would take it that the proposition asserts that some was dry: reserving the right to deny 

 by non-existence if there were none. 



I suppose it is hardly necessary to remark that, in propositions, asserted as true, the same sort 

 of existence is claimed for both terms : for instance, that there is no objective first term with a sub- 

 jective second one. In such a proposition as "he is good" we may certainly say that "good" by 

 itself is a purely subjective notion ; a state of tlie mind in regard to an external object. But good 

 is not the term of the proposition ; it is he (an external object) is one of these external objects to which 

 the mind attaches the idea of good. I can conceive opposition to this : what I say is that the oppo- 

 nition is not to me, but to the universal maxims of technical logic. For all writers admit that I'A' 

 necessarily follows from XY: which caiuiot be if }' he a name of the state of the iiiin<l and A' of an 



