FOM: Books, foundations, intuitionism, NF

[Vaughan Pratt]

From: Neil Tennant
>The whole interest in Dummett's meaning-
>theoretic justification of intuitionism is that it gets away from the
>earlier solipsistic motivation that Brouwer had. Dummett's argument for
>intuitionism is based, rather, on the *publicity* of communication, and
>the so-called Manifestation Requirement. The MR is that grasp of meaning
>should be able to be made manifest in the appropriate exercise of
>recognitional capacities relating to the use of sentences.

From: Harvey Friedman Mon 2/2
>You seem to suggest that there is a coherent view of intuitionism -
>different than Godel, Heyting, and Brouwer. I would like to see you explain
>*carefully* what this is without sending us to papers and books. If it is
>good, it can explained on the fom, at least enough so that one can get a
>feel for it.

From: Neil Tennant Wed 3/4
>Harvey more than anyone else knows just about everything worth knowing
>about the technical interrelationships between classical and
>intuitionsitic formal systems---so I hesitate to undertake the
>challenge with anything like a hope that anything I say will strike
>him as new or useful. On the other hand, he appears to be issuing a
>genuine invitation to make a philosophical case of which he professes
>an honest innocence. This places a rather onerous responsibility on
>one rash enough to forego royalties... but I'll try to do my
>best. That is, I shall try [in a SUBSEQUENT mailing] to state as
>succinctly as I can what exactly the Dummettian case is for revision
>of logic to (something in the neighbourhood of) intuitionistic logic.

This fascinating thread is close to the heart of fom's identity crisis
(independently of whether Steve and Harvey are willing to acknowledge
it has one), and I am therefore keen to see Tennant's promised precis
of Dummett's case.

For myself I fully support the thesis that intuitionistic logic is no less
meaningful a logic than classical, as I hope my recent postings in this
thread made clear (but my support could have been phrased more crisply).

I don't however see the idea of intuitionism as meaningful as originating
with Dummett, but rather with Heyting and Goedel.  (I would even include
Brouwer had his mysticism not covered his tracks so thoroughly as to
place his case beyond my limited competence to defend.)

I also don't see intuitionistic logic as the end of the line in that
progression.  *The* end of the line is linear logic, there is nothing
beyond it in the same sense that, going in the other direction, there
is nothing beyond classical logic.  Classical and linear logic are the
endpoints in a spectrum of logics that range from the logic of pure
separation to its dual logic of pure connection.  Intuitionistic logic
lives within that interval, close to the classical end.

Vaughan Pratt