■ - AND ON THE LOGIC OF RELATIONS. ' 339 



the very notion of equation demand the identity of A and A to be conceded ? just as much 

 does the very notion of identification demand the equality of A and A to be conceded. We 

 can think of nothing but what has some attributes which have quantity ; and the very notion 

 of identity, demanding identity of all attributes, demands equality of quantity in those which 

 have quantity. On what definition, then, of form is ' equal of equal is equal' declared material, 

 while ' identical of identical is identical' is declared formal ? 



In choosing the instance of equality, a very near relation of identity, I am rendering 

 but a poor account of my own thesis. I maintain that there is no purely and entirely formal 

 proposition except this: — 'There is the probability a that X is in the relation L to Y.' 

 Accordingly, I hold that the copula is as much materialised, when for L we read identify, 

 as when for L we read grandfather. The mere notion of materiality, like that of quantity 

 (see my last paper), non suscipit magis et minus. And I hold the supreme form of syllo- 

 gism of one middle term to be as follows; — There is the probability a that X is in relation 

 L to Y ; there is the probability fi that Y is in relation M to Z ; whence there is the 

 probability a/3 that X has been proved in these premises to be in relation L of M to Z. 

 Here is nothing but formal representation, that is, expression of form without particular 

 specification of matter. I now proceed to something of a less controversial character. 



Any two objects of thought brought together by the mind, and thought together in 

 one act of thought, are in relation. Should any»one deny this by producing two notions 

 of which he defies me to state the relation, I tell him that he has stated it himself: he 

 has made me think the notions in the relation of alleged impossibility of relation; and has 

 made his own objection commit suicide. Two thoughts cannot be brought together in 

 thought except by a thought : which last thought contains their relation. 



All our prepositions express relation, and indeed all our junctions of words: but the 

 preposition of is the only word of which we can say that it is, or may be made, a part 

 of the expression of every relation; though the same thing may nearly be said of the 

 preposition to. When relation creates a noun substantive, of is unavoidable : if A by 

 its relation to B be C, it is a C of B. A volume might be written on the idiom of 

 relation : but it would be of the matter, not of the form, of the subject. I add a few 

 desultory remarks, because some readers would hardly, from the symbols themselves, form 

 a notion of the wide extent of thought which the symbols embrace. 



When two notions are components in one compound, as white and ball in the phrase 

 white ball, we have one of the many cases in which the relation is not made prominent, 

 and the compound, as a whole, is the notion on which thought fixes. So little is the 

 relation thought of that its introduction may produce unusual idioms. In speaking of 

 the appurtenance of white to ball, we have the whiteness of the ball, which is idiomatic : 

 but in speaking of the appurtenance of the ball to the white, we have the rotundity of 

 the white, which is not familiar, though intelligible. Here we are sensible of a difl^culty 

 which usage puts in the way of logic: language hesitates at realising notions which are 

 not objectively called things. The metaphysical distinction of the ball being a substance, 

 of which the whiteness is an inherent accident, is extralogical : all we have to do with 

 is the junction in one notion of matter, roundness, and whiteness. Whether whiteness and 



