ORIGIN OF SOME GENERAL ERRORS. 823 



cup should have a different shape from one of metal ; why a 

 cup of hammered metal should be distinct from a molded one ; 

 and why vessels of other materials should have their specific 

 forms. 



I have intimated that many of our most common associations 

 arise from impressions that have acted upon us from our youth. 

 The nature of these impressions is conditioned on the experiences 

 of the generations that have preceded us. In other words, these 

 traditions play an important part in our aesthetic impressions. 

 The Greeks employed in their marble temples motives that dated 

 from a distant epoch when building was done with wood. A 

 diversion from these rules would have produced an unpleasant 

 impression on the Greeks, and would have been contrary to the 

 " style." Our case is not different. All of our ornamental motives 

 are derived from time-honored traditions ; and our aesthetic sat- 

 isfaction in them continues unharmed by the reflection that in 

 many cases they are no longer adapted to present conditions. 



We meet errors of a similar class on scientific ground. Take, 

 for example, the paradox of Zeno the Eleatic, concerning Achilles 

 and the tortoise. The swift Achilles, it supposes, can never over- 

 take the tortoise, because a distance intervenes between them, 

 and he will have to run for a certain time before the distance 

 is reduced by half, another length of time to reduce it to a 

 quarter, to an eighth, and so on to infinity. More time is re- 

 quired to reduce the rest of the distance by half, and the number 

 of these possible parcels is infinite; hence Achilles will never 

 catch up with the tortoise. Now, since we know that he will 

 overtake it, wherein is the sophism ? It is not in any real con- 

 tradiction between the laws of our thought and experience ; but a 

 typical error is involved, in which thought, moving in a way that 

 generally leads to the truth, is at fault in the special case. It is 

 true, in ordinary cases, that when we continue adding indefinitely 

 new intervals to any interval of time, the sum of all will be infi- 

 nite. This fact, generally valid, in the particular case leads our 

 judgment to a false conclusion. The special feature in the prob- 

 lem is that if parcels of time, infinite in number, diminish accord- 

 ing to certain laws, their sum will not be infinite, but may be very 

 small. "We do not have to be accomplished in mathematics to 

 comprehend the sophism and find its solution. Every one knows 

 that we can divide a length of one metre into a half metre plus a 

 quarter, plus an eighth, etc., of a metre, and thus obtain an infinite 

 number of factors, the sum of which, however, shall always be 

 within a metre. The general error involved in the discussions of 

 this sophism is also a typical one, for it originates in the predomi- 

 nance in our consciousness of the general law, with the non- 

 association of the particular case. The phenomenon is therefore 



