MENTAL STATES AND PROCESSES. 91 



Mr. Romanes illustrates his contention by a reference 

 to mathematics, which demonstrates for us with especial 

 clearness the great value of symbols. We are told,* 

 ** Man begins by counting things, grouping them visibly 

 \i.e. by the Logic of Recepts]. He then learns to count 

 simply the numbers, in the absence of things, using his 

 fingers and toes for symbols. He then substitutes 

 abstract signs, and Arithmetic begins." But no man 

 could begin really counting the simplest things unless 

 he already possessed the idea of number ; and, as Mr. 

 Romanes truly says, " before the idea of number can rise 

 at all," a distinct power of intellectual conception must be 

 present.! The very essence of "counting" is nujnerical 

 distinction. To suppose that a man could voluntarily 

 begin to count, without any idea of such distinction, is 

 absurds But men, like animals, may "group objects 

 visibly" without counting. To separate objects in groups 

 — were they in groups which accidentally had definite 

 numerical relations — without any regard to their number, 

 could never be counting. To suppose that a man by 

 " not counting " could learn to count, or that he could 

 acquire the idea of " number " by performing actions 

 wherein he took no note of real numerical relations, 

 is to add absurdity to absurdity. He could not possibly 

 take note of any numerical relations without having the 

 idea of numerical relation, that is, without possessing 

 very abstract ideas and having already an intellectual 

 nature. We dwell on this point because it is a good 



t For what is implied in the idea of "number," see "On Truth," 

 p. 241. 



