Date: Wed, 27 May 1998 11:33:10 +0100
From: jim <jmd-AT-dasein.demon.co.uk>
Subject: Re: Math/Metaphysics


In message <1CA69E22EC-AT-pluto.aum.edu>, Christopher Honey
<ch1745-AT-pluto.aum.edu> writes
>I really don't know much about symbolic logic (except for one class a 
>few years ago on it) and it's relationship to math, which is part of 
>which, but I'd always been told that math is part of logic.  I'd 
>never really questioned it, except so far as to ask whether this was 
>just philosophers dealing with insecurities about the claims to truth 
>of math, however, I'd be happy to hear more about that, or if you 
>know any basic works dealing with it (preferably more recent than 
>Scotus), even though it's a little outside of the scope of this list.
>
>Christopher Honey
>Dept of History
>AUM
>
>
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Pardon, folks, the following post is more in the nature of a book list than
anything that should be posted, but it responds to the above.

Christopher,
for a really rice book that will give you the historical background for the current
debates, I'd recommend Stephen Korner's book (I can't remember the title,
Intro to Phil of Math, I think). But it covers the postions FROM which the
current debates arise, so it is now of mostly of historical value.

For the Logical Positivists' quasi-Logicists position and the epistemological
advantages of it, you can look at Ayer's classic, Logic, Language, and Truth
(maybe, Language, Truth and Logic; anyway, it's some permutation of these
three words).
(Also Bill Craig (the "Craig" of "Craig's Theorem" had a piece called "The
Replacement of Auxiliary Expressions" published in the Phil Rev, in which a
very powerful argument is presented for reductionism; the response to the
position is that the initial 'definitional identifications" can't be achieved; this piece
gave Reductionism a real big push).

Arend Heyting had a beautiful piece called Intuitionism (written in the form of a
dialogue). 

There is a new book out entitled Phil of Math and the Hist of Math, edited by
Patricia Kitcher (MAYBE) (I can't remember: my problem is that I will be away
from my books and study for about a year -- they are in Japan; I'm in England
and Europe (sometimes) enjoying the rain (yuck)....).

Of course, one of the classics in the area is the anthology edited by Benaceraff
and Putnam (I heard that it's been recently re-issued with ammendments).

Anything that Hartry Field writes in this area is very important (his new book,
Science Without Numbers). Also Charles Chihara has a good book; and you
might want to look at Hao Wang's stuff and at Godel's Collected Works
(friends tell me that V.3 was just been published, and that it is a very nice
collection; I haven't seen it yet).

There's also an old, very short paperpack by "somebody" Newman and
"somebody somebody" somebody else entitled Godel's Proof; it's a popularized
treatment that's so-so.

And Ray Smullyan's introductory stuff is always esoteric tremendous fun, but of
outstanding quality of thought. He's an exceptionally astute philosopher, with a
very deep grasp of Godel's work (as deep as his incredibly long, beautiful
flowing white hair is long (unless he got it cut, of course)).

I'd be sceptical of Stephen Penrose's arguments, which stem from an old
argument by Lukacs (if I remember correctly), which rest on a misunderstanding
of Godel (one which Putnam has pointed out);  remember correctly)), and
would read Hofstader's Godel, Escher and Bach only FOR FUN.

John Searle's Mind's Brains and Science is great (first presented over the BBC
in the Reith Lecture Series, about ten years ago (there was a lot of excitement
here in London then: everyone was curious how well the dialectic between him
and Colin McGinn would go ...)).

Of course, Hubert Dreyfus (What's Computers Still Can't Do (as well as the
earlier, What Computers Cant Do (I think this was written with his brother who
teaches Electrical Engineering at Berkeley also).
Terry Winograd's and Fernando Flores's old book, Understanding Computers
and Cognition (Winograd was the one to design URDLU, the first
'sophisticated' language understander; he now does courses on Heidegger at
Stanford).

There's a lot of technical stuff: Hartley Rogers, Stephen Kleene, but, the best
intro book to the technically precise material (I think) is Martin Davis's book:
Computability and Undecidability (Dover now has got a copy out which is
cheap and has the important appendix which Davis later added to the first
publication). It is written with a very rare clarity and, so, makes for easy
reading, believe it or not; like any 'math/logic' text you read it with a paper and
pencil in hand (Lewis Carrol's advice).

Anyway, those books are for a healthy diet on the problems.
enjoy,

jim


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