Changes

<p>The proposition that the diagonal is incommensurable has stood in the textbooks from time immemorial without ever being assailed and I am sure that the most modern type of mathematician holds to it most decidedly.  Yet it seems quite absurd to say that there is any objective practical difference between commensurable and incommensurable.</p>

<p>The proposition that the diagonal is incommensurable has stood in the textbooks from time immemorial without ever being assailed and I am sure that the most modern type of mathematician holds to it most decidedly.  Yet it seems quite absurd to say that there is any objective practical difference between commensurable and incommensurable.</p>

<p>Of course you can say if you like that the act of expressing a quantity as a rational fraction is a piece of conduct and that it is in itself a practical difference that one kind of quantity can be so expressed and the other not.  But a thinker must be shallow indeed if he does not see that to admit a species of practicality that consists in one's conduct about words and modes of expression is at once to break down all the bars against the  

<p>Of course you can say if you like that the act of expressing a quantity as a rational fraction is a piece of conduct and that it is in itself a practical difference that one kind of quantity can be so expressed and the other not.  But a thinker must be shallow indeed if he does not see that to admit a species of practicality that consists in one's conduct about words and modes of expression is at once to break down all the bars against the nonsense that pragmatism is designed to exclude.</p>

nonsense that pragmatism is designed to exclude.</p>

<p>What the pragmatist has his pragmatism for is to be able to say:  here is a definition and it does not differ at all from your confusedly apprehended conception because there is no practical difference.  But what is to prevent his opponent from replying that there is a practical difference which consists in his recognizing one as his conception and not the other?  That is, one is expressible in a way in which the other is not expressible.</p>

<p>What the pragmatist has his pragmatism for is to be able to say:  here is a definition and it does not differ at all from your confusedly apprehended conception because there is no practical difference.  But what is to prevent his opponent from replying that there is a practical difference which consists in his recognizing one as his conception and not the other?  That is, one is expressible in a way in which the other is not expressible.</p>