FOM: second-order logic is a myth

[Martin Davis]

At 09:27 PM 2/22/99 -0500, simpson at math.psu.edu wrote:

>
>Fair enough.  My proposal to call it `the logicist thesis' was a
>little off-base.  Let's call it `Hilbert's thesis', as originally
>proposed by Martin Davis.  Martin, where is the article in which you
>proposed it?  I was trying to remember where I read that ....
>

I think the only place it's in print is in the Barwise HANDBOOK in Barwise's
own initial article FIRST-ORDER LOGIC. (p. 41). I had argued, I no longer
remember when and where, that Hilbert's Thesis plus the requirement that the
declarative content of an algorithm for computing the truth value of a
relation LOGICALLY IMPLIES that that relation have the correct values
together IMPLY Church's Thesis.

By the way, I have given a lecture to lots of computer scientists with the
title IN DEFENSE OF FIRST ORDER LOGIC arguing with examples that instances
of new "logics" introduced in computer science are often dealt with more
handily and efficiently as first-order theories.

Martin