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Rupert wrote:
> Edward Nelson, on the other hand, has done
> some interesting research about certain weak axiomatic theories in
> arithmetic, which may embody his stance. See his book "Predicative
> Arithmetic".
Thanks. I just downloaded it for free as a PDF file. And the first
chapter of his unfinished book on IST too. Do you have any other
recommendations?
What do you think of the system Shaughan Lavine gives in his
'Understanding The Infinite'? (I've read some high praise for this
book.) I only saw the book briefly, so I didn't have a chance to ponder
his system. But ab initio in my thinking about this, I can't imagine
how an ultrafinitist can give a truly rigorous axioimatization in which
there is largest natural and block us from adding 1 to that largest
natural (the paradox of the heap, as it were). But, of course, I need
to study the systems to see for myself, since otherwise my questions
are uninformed.
And, aside from that one chapter by Nelson, do you know of a good
explanation (rigorous but not so difficult that it starts with advanced
concepts).of axioms for IST? I saw a book by Alain Robert but it's not
what I'd like; it's more of sketchbook of ideas than it is a tight
theorem by theorem treatment. And some of the other books I found in
the QA299 section of the library jump right into more advanced stuff
way too fast for me.
MoeBlee
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