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