
Re: infinity can't exist
Posted:
Feb 15, 2013 9:56 AM


fom <fomJUNK@nyms.net> writes:
> Here is where my complexity when interpreting > Aristotle's remarks arise: > > Something like > > x=y > > is called informative identity. > > But, within a formal proof, one can never > write that as an assumption. In a formal > proof, one begins with true sentences and > ends with true sentences. So all the > metalogical analysis of meaning outside > of a deduction is "armchair quarterbacking" > whereas what happens in a proof is > "regulation time".
I'm afraid I have no idea what you mean here. Natural deduction proofs involve assumptions all the darned time. For instance, one may begin the proof that sqrt(2) is irrational by: Assume that a and b are natural numbers such that (a/b)^2 = 2.
Now, given what you say below (snipped, since I don't really understand what you're getting at and have no comment), it may be that you think such a statement involves quantifiers and so is an exception to the rule you state above. But, honestly, there is *NOTHING* in the usual presentation of natural deduction that entails an equation cannot be taken as an assumption.
Do you think that these comments of yours are widely accepted or original?
 "Often times, when [...] looking for a sense of adventure, I'd doodle with math equations. Often too, when pressures of regular life were really bothering me, I'd go for the adventure of fiddling with math."  James S. Harris, a man of many mathematical adventures!

