[FOM] mathematics as formal

[Alex Blum]

Steven Ericsson-Zenith wrote:

>On Mar 25, 2008, at 1:27 PM, rgheck wrote:
>  
>
>>I thought logic was the study of such things as validity. It's no
>>convention that, if it's true that p and also true that q, then it's
>>true that p and q. It may be due to convention that the word "if"  
>>means
>>if, etc. (Then again, it may not be.) But that's an entirely different
>>matter, and it is of no concern to logic.
>>    
>>
>
>In my view the notion of validity applies only to convention. That is,  
>the subject of validity is convention, and the question of whether the  
>convention is absolute, true and complete is of interest but it is a  
>separate matter.
>  
>
It is clearly a matter of convenion what 'true' , 'and', and 'valid' 
mean but surely given what they do mean, it is necessarily true that if  
p and q are both true then p is true. Or, that if p and q have both been 
proved then p has  been proved. Just imagine the contrary in either 
case. And if validity is a matter of convention what of inconsistency? 
For if p is valid not-p is inconsistent.
Alex Blum