Re: Torkel Franzen on truth

On Wed, 19 Dec 2007 10:53:59 -0800 (PST), george <greeneg@xxxxxxxxxx>
wrote:


George knows very well by now that his views on many issues are
quite bizarre

hardly.

But they are - sometimes, george!


and idiosyncratic.

Well, unpopular, yes.

Well, not generally accepted, right... ;-)


Prof. Smith and I have been talking, for example, about the
intended model vs. the formal language. He is the one who
said that he didn't think formal languages should even be referred
to as a language. That is considerably less defensible than anything
*I* have ever said.

Well..., Alonzo Church [you know that guy?] also mentioned such a view,
in one of his papers. He writes:

"We distinguish between a /logistic system/ and a /formalized language/
on the basis that the former is an abstractly formulated calculus for
which no interpretation is fixed, and thus has a syntax and no
semantics; but the latter is a logistic system together with an
assignment of meanings to its expressions. [...]

In order to obtain a formalized language it is necessary to add to
these /syntactical rules/ of the logistic system, /semantical rules/
assigning meanings (in some sense) to the well-formed expressions of the
system."

(Alonzo Church, The Need for Abstract Entities, 1951)

[ Oh right, this is an ancient text and etc. etc. *sigh* ]


Insisting that mathematicians "usually" have an intended model to
begin with instead IS SILLY.

Nonsense. (Clearly historically most mathematical "theories" started out
_without_ being formalized as axiomatic systems. At least this is true
for _set theory_, as you certainly will know.)


WHERE DID THEY GET this model from?

Mathematical intuition?


F.

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