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Re: Mathematical Logic
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Oh yeah - I thought it took a long time when I was loading it. My apologies!
If you google 'Further Pure 1 for OCR - Cambridge University Press' you
should find it.
(Or try http://www.cambridge.org/uk/catalogue/catalogue.asp?isbn=0521548985)
I'm not being paid - I think this series is brilliant. It contain all the
proofs that we philosophers enjoy! Also, because maths is built out of
axioms on top of axioms (kind of like a pyramid - hey, did anyone read 'The
Music of the Primes' by Marcus du Sautoy?), I keep on having to refer back
to earlier books in the series to understand how they can take the steps
they do. As this chapter on logic shows, even basic maths has interesting
stuff behind it.
Anyhow, hope you enjoy it!
Sam
----- Original Message -----
From: <A.M.Goldfinch@lse.ac.uk>
To: <samuelellison@hotmail.com>
Sent: Sunday, September 17, 2006 12:58 PM
Subject: RE: Mathematical Logic
Hi Sam,
It appears that the link you kindly provided isn't stable (ie it has how
expired). Could you provide me with the title of the book?
Cheers!
Andrew
________________________________
From: owner-bups-dis@purplepancake.com on behalf of Sam Ellison
Sent: Fri 08/09/2006 01:09
To: BUPS-DIS@bups.org
Subject: Re: Mathematical Logic
Hi,
For an online intro to proving mathematical statements - and the beauty and
elegance of a mathematical proof - surf to
http://www.cambridge.org/catalogue/catalogue.asp?isbn=0521548985&ss=sam
<http://www.cambridge.org/catalogue/catalogue.asp?isbn=0521548985&ss=sam>
and click 'view sample chapter'.
Sam
----- Original Message -----
From: Andrew Turner <mailto:ajturner.email@googlemail.com>
To:
Sent: Friday, August 25, 2006 2:22 PM
Subject: Re: Mathematical Logic
I took a module in mathematical logic and thoroughly enjoyed it - though I
haven't taken the exam yet due to the AUT action! I'd certainly recommend it
if you enjoy maths; some of the stuff covered was essentially an exercise in
doing trivial things in a complicated way, for instance proving arithmetical
statements. Other things were much less trivial; especially Godel's
incompleteness theorem. A particular favourite of mine being Rice's theorem.
As for books I found Bell & Machover 'A Course in Mathematical Logic'
helpful. it might be worth brushing up on set theory notation; but I picked
up most of what I needed to know more through necessity than supplementary
study.
Andrew Turner
(Yes...another Andrew)
On 8/25/06, A.M.Goldfinch@lse.ac.uk <A.M.Goldfinch@lse.ac.uk> wrote:
To reply to this message or start a new topic please email:
BUPS-DIS@bups.org
Hi Andrew,
Thanks for your detailed reply. I think mathematical logic is important for
one's intellectual development. I've been hearing about Godel's
incompleteness theorems for years; being able to prove his theorems would be
very satisfying.
I'll check out Hamilton and Boolos et al.
Best,
Another Andrew
________________________________
From: Andrew Bacon [mailto:andrew.bacon@lmh.ox.ac.uk ]
Sent: Thu 24/08/2006 19:26
To: Goldfinch,AM (ug)
Cc: BUPS-DIS@bups.org
Subject: Re: Mathematical Logic
Hi there Andrew,
I would strongly recommend mathematical logic if you are sure its your kind
of
thing! However, I am always wary of recommending it, because the
introductory
courses can be very dry. (Also, mathematical logic can sometimes be used to
talk about model theory, set theory, recursion theory all of which I would
highly recommend).
Basically my background is a degree in maths and philosophy. So in my first
year
I did logic taught by philosophers: propositional calculus, predicate
calculus
and soundness, completeness and compactness for both languages (with a
little
bit of philosophy of language). In the second year I basically did *exactly*
the
same syllabus again, but this time taught by the mathematics department. But
despite this, it was *very* different. The mathematician way is much more
pendantic and most of all fiddly, and I did not enjoy this particular course
very much (although its compliment, set theory, was probably my favourite
subject). However, this course is very important, and it paves the way for
the
interesting stuff that comes after. For example there are Gödel's
Incompleteness
theorems, or if you move towards model theory the Lowenheim-Skolem theorems.
Then of course it will be helpful if you want to get into set theory or the
philosophy of maths.
In terms of books, the Enderton is good, so is Hamilton 'Logic for
Mathematicians' (I think that's the name). Also 'Logic and Computability' by
Boolos, Jeffrey and Burgess is a nice read and it covers a lot.
Anyway, just check the syllabus to see what it says. It may well look
exactly
like the course you've done with the philosophy department but I can assure
you
it will still be worth doing. If it starts talking about the incompleteness
theorems, Gödel's constructible universe and so on, the jump might be a big
one.
Hope that helps,
Andrew
To reply to this message or start a new topic please email:
BUPS-DIS@bups.org
Has anyone on this list taken mathematical logic? If so, I'd be
interested to hear your experiences. In your experience, how much of a
conceptual leap was it from first-order predicate logic? Are there any
books you'd especially recommend (I have Enderton's classic 'A
Mathematical Introduction to Logic')? Are there any areas of mathematics
you'd recommend brushing up on before starting a mathematical logic
course? Which areas did you find most challenging? Would you recommend
mathematical logic?
Cheers.
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--
Andrew Bacon
Lady Margaret Hall
07830048336
http://users.ox.ac.uk/~lady1900
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