452 FALLACIES. 



vis viva, the history of which is given at large in Pro- 

 fessor Playfair's Dissertation. The question was whe- 

 ther the force of a moving 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 Play fair 

 " produced by a moving body is proportional 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 efficiency 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, associated. But 

 the disputants were by no means aware that this was 

 all; they thought that force was one thing, the pro- 

 duction 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 

 among others of Dr. Thomas Brown, who considered 

 the sophism as insoluble; as a sound argument, 

 though leading to a palpable falsehood; not seeing 

 that .such an admission would be a reductio ad ab- 

 surdum of the reasoning faculty itself. 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. 



