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From: bph@buengc.BU.EDU (Blair P. Houghton)
Newsgroups: comp.ai,sci.philosophy.tech
Subject: Re: How to dispose of naive science types (short)
Message-ID: <535@buengc.BU.EDU>
Date: 24 Jul 88 23:36:25 GMT
References: <483@cvaxa.sussex.ac.uk> <794@l.cc.purdue.edu> <488@aiva.ed.ac.uk> <1496@crete.cs.glasgow.ac.uk> <531@ns.UUCP>
Reply-To: bph@buengc.bu.edu (Blair P. Houghton)
Followup-To: comp.ai
Organization: Boston Univ. Col. of Eng.
Lines: 64

In article <531@ns.UUCP> logajan@ns.UUCP (John Logajan x3118) writes:
>gilbert@cs.glasgow.ac.uk (Gilbert Cockton) writes:
>> logajan@ns.UUCP (John Logajan x3118) writes:
>> >unproveable theories aren't very useful.
>
>> most of your theories [...] will be unproven,
>> and unproveable, if only for practical reasons.
>
>Theories that are by their nature unproveable are completely different from
>theories that are as of yet unproven.  Unproveable theories are rather
>special in that they usually only occur to philosophers, and have little to
>do with day to day life.  You went on and on about unproven theories but failed
>to deal with the actual subject, namely unproveable theories.
>
>Please explain to me how an unproveable theory (one that makes no unique
>predictions) can be useful?
>

Rudy Carnap wrote _The Logical Syntax of Language_ in 1937.  In it
he described the development of an all-encompassing, even recursive
syntax that could be used to implement logic without bound.

One of the simplest examples of unproveability is the paradox

"This sentence is false."

It drives you nuts if you analyze it semantically; but, it's blithering
at a very low level if you hit it with logic:  call the sentence S;
the sentence then says 

"If S then not-S."

Even a little kid can see that such a thing is patent nonsense.

The words in the sentence--the semantics--confuse the issue; while
both sentences say exactly the same thing in different semantics.

Carnap's thesis in the book was of course that the logic of communication
is in the syntax, not the semantics.

I'm correcting myself: now that I look at it, the paradox really says

"S = not-S."

Carnap's mistake (what makes him horribly obscure these days) is
that he did all of this amongst a sea of bizarre symbolic definitions
designed as an example of the derivation of his syntactical language;
but he did it, and it's a definition of _everything_ necessary to
carry on a logical calculus without running into walls of description.
It even defines itself without resorting to outside means; sort of
like writing a C compiler in C without ever having to write one in
assembly, and running it on itself to produce the runnable code.
Of course, the computer is a semantic thing...

I would hope some stout-hearted scientists would apply this sort of thing
to unproveable theories; we might find out about god, after all.

				--Blair
				  "To be, or not to be;
				   that requires one TTL gate
				   at a minimum, but you could
				   do it with three NAND-gates,
				   or just hook the output
				   to Vcc."