646 Transactions. — Miscellaneous. 



respect analogous to that which we have for the truth of the 

 axioms of mathematics. 



Of necessary truths, properly speaking, the one unfailing 

 criterion is that they should always be truths in regard to 

 abstractions — never, in any case, truths in regard to concrete 

 realities. That the moon which I see above me is one, not 

 two, cannot be a necessary truth, no matter how certain I am 

 of it. I might, indeed, be under a not uncommon hallucina- 

 tion in affirming its unity ; but the proposition that " one is 

 not two " stands on altogether a different footing. One is not 

 two. Why ? Because it is by hypothesis one. It is this 

 intrusion of an assumption which can be contradicted which 

 makes possible a necessary truth, resting, as all such truths 

 do, on the law of contradiction. As, however, the current 

 confusion of thought with regard to abstraction is at the root 

 of much of the confusion of thought in regard to necessary 

 truth, it may be well at this point to endeavour to arrive at a 

 sound opinion with regard to the true nature of this important 

 mental process. 



In a j)aper read before this Society about two years ago on 

 "Professor Huxley's Metaphysics," I endeavoured to draw 

 attention to the crudity of the opinions in regard to the for- 

 mation of abstract conceptions expressed by that very Philis- 

 tine representative of English empiricism. With your per- 

 mission I will recapitulate a portion of what I then said : 

 "This mental operation" [abstraction]. Professor Huxley 

 says, "maybe rendered comprehensible by considering what 

 takes place in the formation of compound photographs — when 

 the images of the faces of six sitters, for example, are each 

 received on the same photographic plate for a sixth of the 

 time requisite to ta.ke one portrait. The final result is that 

 all those points in which the six faces agree are brought out 

 strongly, while all those in which they differ are left vague ; 

 and thus what may be termed a genuine portrait of the six, in 

 contradistinction to a specific portrait of any one, is produced." 

 Similarly he thinks, " In dreams one sees houses, trees, and 

 other objects, which are perfectly recognisable as such, but 

 which remind one of the actual objects as seen out of ' the 

 corner of the eye,' or the pictures thrown by a badly-focussed 

 magic-lantern. A man addresses us who is like a figure seen 

 by twilight, or we travel through countries where every feature 

 of the scenery is vague, the outlines of the hills are ill marked, 

 and the rivers have no defined banks. They are, in short, 

 generic ideas of many j)ast impressions of men, hills, and 

 rivers." Here it is plain enough that what is vague is 

 confounded with what is generic. One might as well 

 say tliat those of Turner's pictures which are success- 

 ful in conveying the effect of a hazy atmosphere are 



