Date: Feb 15, 2013 9:56 AM
Author: Jesse F. Hughes
Subject: Re: infinity can't exist
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!