[FOM] philosophical literature on intuitionism
William Tait
williamtait at mac.com
Thu Oct 23 14:29:35 EDT 2008
On Oct 16, 2008, at 8:09 PM, mark van atten wrote:
> Bill Tait Thu Oct 16 11:31:57 EDT 2008 wrote:
>
>> Of course, this subjectivist element in Brouwer's theory can be
>> eliminated and the theory of choice sequences can be tamed--- this
>> is done in the Kleene-Vesley paper on intuitionistic analysis and
>> in Dummett's book on intuitionism.
>
> No so-called elimination theorem has ever been produced for the
> general notion of choice sequence; only for very specific classes. The
> creating subject is wholly free to generate sequences that fall
> outside of them.
I did not mention any 'elimination theorems' in my posting, and I
agree completely with this part of what Mark wrote. I merely wanted to
point out that a part of intuitionistic mathematics can, like Bishop-
style constructive mathematics, be formulated without reference to the
creating subject. For me, that part of intuitionistic/constructive
mathematics is well-motivated although not absolutely compelling. I
was suggesting that the other part, involving 'objects' (choice
sequences) that do essentially involve the creating subject, motivated
Thomas Forster's "dream up" question. From Thomas' response (Oct 18),
it seems that I was wrong about this and that he was referring to
constructive mathematics generally. But I do think that a discussion
of the distinctively Brouwerian element of intuitionistic math would
be interesting.
In Weyl's version of intuitionism is there such an essential reference
to the creating subject? My impression is that there is not, at least
in "On the new foundational crisis of mathematics", but I haven't
gone back to check.
Incidentally, I possess lecture notes "Inleiding tot de
Intuitionistische Wiskunde", for a course by Heyting in 1952-3, edited
by Johann de Iongh. I got them when I was a student in Amsterdam in
1954-5. They are typed in Dutch with symbols drawn in by hand. There
doesn't seem to be much more than is in Heyting's book *Intuitionism:
An Introduction*, but my now almost nonexistent Dutch does not admit
of accurate skimming. I expect that there are other copies of the
notes around, but I mention mine just in case. (I don't think these
notes were mentioned by anyone in listing the literature on
intuitionism.)
Bill Tait
More information about the FOM
mailing list