568 FALLACIES. 



irreligion." It is briefly as follows: I thought of a thing yesterday; I 

 ceased to think of it; I think of it again to-day. I had, therefore, in my 

 mind yesterday an idea of the object ; I have also an idea of it to-day ; 

 this idea is evidently not another, but the very same idea. Yet an inter- 

 vening time elapsed in which I had it not. Where was the idea during 

 this interval? It must have been somewhere; it did not cease to exist; 

 otherwise the Idea I had yesterday could not be the same idea ; no more 

 than the man I see alive to-day can be the same whom I saw yesterday if 

 the man has died in the mean while. Now an idea can not be conceived to 

 exist any whei'e except in a mind ; and hence there must exist a Universal 

 Mind, in which all ideas have their permanent residence during the inter- 

 vals of their conscious presence in our own minds. 



It is evident that Berkeley here confounded sameness numero with 

 sameness specie, that is, with exact resemblance, and assumed the former 

 where there was only the latter ; not perceiving that when we say we have 

 the same thought to-day which we had yesterday, we do not mean the same 

 individual thought, but a thought exactly similar: as we say that we have 

 the same illness which we had last year, meaning only the same sort of illness. 



In one remarkable instance the scientific world was divided into two 

 furiously hostile parties by an ambiguity of language affecting a branch of 

 science which, more completely than most others, enjoys the advantage of 

 a precise and well-defined terminology. I refer to the famous dispute re- 

 specting the vis viva, the history of which is given at large in Professor 

 Playfair's Dissertation. The question was, whether the force of a mov- 

 ing body was proportional (its mass being given) to its velocity simply, or 

 to the square of its velocity: and the ambiguity was in the word Force. 

 "One of the effects," says Playfair, "produced by a moving body is pro- 

 portional to the square of the velocity, while another is proportional to the 

 velocity simply :" from whence clearer thinkers were subsequently led to 

 establish a double measure of the efliciency of a moving power, one being 

 called vis viva, and the other momentum. About the facts, both parties 

 were from the first agreed : the only question was, with which of the two 

 effects the term force should be, or could most conveniently be, associa- 

 ted. But the disputants were by no means aware that this was all; they 

 thought that force was one thing, the production of effects another ; and 

 the question, by which set of effects the force which produced both the 

 one and the other should be measured, was supposed to be a question not 

 of terminology, but of fact. 



The ambiguity of the word Infinite is the real fallacy in the amusing 

 logical puzzle of Achilles and the Tortoise, a puzzle which has been too 

 hard for the ingenuity or patience of many philosophers, and which no less 

 a thinker than Sir William Hamilton considered as insoluble ; as a sound 

 argument, though leading to a palpable falsehood. The fallacy, as Hobbes 

 hinted, lies in the tacit assumption that whatever is infinitely divisible is 

 infinite; but the following solution (to the invention of which I have no 

 claim) is more precise and satisfactory. 



The argument is, let Achilles run ten times as fast as the tortoise, yet 

 if the tortoise has the start, Achilles will never overtake him. For sup- 

 pose them to be at first separated by an interval of a thousand feet: when 

 Achilles has run these thousand feet, the tortoise will have got on a hun- 

 dred ; when Achilles has run those hundred, the tortoise will have run ten, 

 and so on forever : therefore Achilles may run forever without overtaking 

 the tortoise. 



