Re: Torkel Franzen on truth

On Dec 18, 3:36 am, Peter_Smith <ps...@xxxxxxxxx> wrote:
We start off working in everyday mathematics.

You don't even know what that means.

You are beginning by presuming the existence of an intended model.

That is just not the way it's generally done any more.

Wanting maximal rigour
and absolute clarity, we reflect on our practices, and regiment our
informal mathematical language, and regiment chunks of our everyday
mathematics into nicely disciplined axiomatic systems.

That is the BEGINNING, NOT THE END, of the process.

We construct,
for example, the regimented theory most of us call first-order PA.

Almost nobody more than 10 years younger than you ever did any
such thing. The rest of us STARTED with PA. It embodies the basic
things we know, at first-order, about this realm.

This theory is as semantically contentful as the informal inchoate
theory we started off with,

No, it isn't, and more to the point, PURELY BY VIRTUE OF BEING
a first-order syntactic theory, IT IS NOT semantically contentful AT
ALL.

The completeness theorem is fundamentally a proof that first-order
semantics SIMPLY DOESN'T EXIST.
.

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