Caklile. — Oil Necessary Truth. 6i9 



cannot enclose a space" is not equivalent to saying, "These 

 two lines which I judge to be straight cannot enclose a 

 space." That, so far from being necessary, would probably 

 not even be true. "What it is equivalent to is plainly this : 

 " If these two lines are straight they cannot enclose a space." 

 Mr. Mill shows himself occasionally to be aware of the exist- 

 ence of such assumptions behind every general conception. 

 He tells us, for nistance, that in naming''' " we create an 

 artificial association between attributes and a certain combi- 

 nation of articulate sounds." This means that for the pur- 

 poses of thought and intercourse we agree that the particular 

 colour we know as green shall have the name "green." It is 

 plain, then, that if we afterwards proceed to say that the 

 name " green" is equally applicable to some other colour, such 

 as blue, we break our convention, we sublate our hypothesis, 

 and we involve ourselves in as unmistakable a logical con- 

 tradiction as it is possible to conceive. 



Similarly, if w'e are asked, "On what sort of evidence does 

 the truth of the axiom which affirms that things which are 

 equal to the same thing are equal to one another rest?" we 

 need not hesitate to reply, "On the law of contradiction." 

 Professor Bain thinks not. He claims for it, alone among the 

 axioms, the character of being a generalisation from expe- 

 rience.! " Equality," he says, " is properly defined as innne- 

 diate coincidence." If it is, why, then, might not the term 

 "coincidence" be used convertibly wdth the term "equality"? 

 It is plain enough that it could not. If we predicate equality 

 of two lines we do not mean that the}' do coincide, but that 

 they possess that attribute whereby they would, if superim- 

 posed, coincide. The coincidence of two lines would be a 

 matter of fact to which no necessary propositions could ever 

 apply. Their equality is a matter of abstraction, to which 

 such propositions are alone applicable. Coincidence is given 

 by sense, and sense only, and is open to the intelligence of all 

 beings possessed of sight and touch. Equality is learned 

 through sense, of course, but by thought, and is probably quite 

 beyond the intellectual grasp of the Bushman or the Dammara. 

 We cannot use the term " equal " intelligibly without knowing 

 that the equals of equals are equal, any more than we can use 

 the term "black" intelligibly without knowing that what is 

 black is black. Suppose we try to realise the meaning of the 

 negative of the proposition that the equals of equals are equal. 

 We suppose ourselves measuring off any definite length from 

 one line, and then the same length from another line. We 

 then try to put it to ourselves, "Perhaps these lengths, after 



* Ex. Ham. Phil., 4fch ed., p. 394. 



t " Mental and Moral Science," ed. 3, p. 187. 



