[FOM] philosophical literature on intuitionism

Thomas Forster T.Forster at dpmms.cam.ac.uk
Sat Oct 18 19:30:54 EDT 2008

Thanks to all who replied.  (And apologies for being so tardy - i
fired off individual emails to thank people for suggestions but my
mailer sent them to fom instead and Martin intercepted them on the
grounds that they were personal communications not intended for the
list).  I append a compendium of suggestions that may be helpful to
people (a large majority on this list, i suspect) whose position wrt
constructivism in mathematics is the same as mine; that is to say 
to people who are well aware of the important difference between
constructive and classical proof but who do not see that difference 
as a reason for believing that classical proof is in any way suspect.
(If you want a label for this position you might like the word 
`cohabitationist' used by my erstwhile Cambridge colleague Tom Baldwin).  
There may of course be such reasons, and it is in the philosophical 
writings of constructivists that one might expect to find them.  
Hence my request.

(Another - quite specific - reason i have for interest in the
philosophical motivation for constructivism is that - and in this i 
am probably not like most list members - i have to teach logic to
philosophy students.  One thing those students might be interested in
is the Quinean problem of *radical translation*.  The communication
difficulty between classical and constructive logicians isn't
normally thought of as radical translation problem a la Word and
Object, but there is no reason why it shouldn't be.  The negative
interpretation gives the constructive logician a way of reading the
utterances of the classical logician as things that are sensible and
true; in the other direction possible world semantics gives the
classical logician a way of making sense of the constructive denial of
T non D - inter alia.  They do not delude themselves that the possible
world semantics is what constructive logicians actually *mean*.  If 
I am to make better use of the pedagogical opportunity afforded by 
the teaching of constructive logic to my philosophy students to make 
a point about Radical Translation then i should try to arm myself  
with a clear picture of what the constructivists do in fact think.)

It is indeed possible, as Dirk van Dalen says, to ask google and
thereby discover a complete bibliography.  The result would be an
embarras de richesse: what we want is a place to *start*. In any 
case, for those of us who do not read Dutch (such as your humble
correspondent - despite (i) having had a father who was a fluent 
Dutch speaker, and (ii) having done a stint as a Ph.D student in 
Brussels!)  the thought of trying to read Brouwer in the original is
deeply frightening.  In fact I have been given conflicting advice
about the advisability of trying Brouwer even in translation.  It
seems he is rather Kantian - and not all of us can read Kant easily.


One obvious source is Dummett, but people who know more about this
than i do say that Dummett's take on these matters is eccentric and
that he is not a good place to start.

The most recommended points of departure seem to be

Mark van Atten, "On Brouwer" in the Wadsworth Philosophers Series.
2004 (95pp).  This gets rave citations

So does van Atten's SEP entry on the history of intuitionistic logic
(Also got lots of references.)

Mancosu: *From Brouwer to Hilbert* was recommended by several people.

van Stigt, W., 1990, Brouwer's Intuitionism, Amsterdam: North-Holland.
Brouwer's Intuitionism<http://projecteuclid.org/DPubS/Repository/1.0/Disseminate?view=body&id=pdf_1&handle=euclid.rml/1204834908>

Brouwer's Cambridge Lectures on Intuitionism, ed. by D. van Dalen, Cambridge U press 1981

- Hesseling, D., 2003, Gnomes in the Fog. The Reception of Brouwer's
Intuitionism in the 1920s, Basel: Birkhäuser.

Dirk van Dalen's two volume MYSTIC, GEOMETER, AND INTUITIONIST: THE  
LIFE OF L.E.J.BROUWER (Oxford 1999 for Vol.1) 

Intuitionism, An Introduction, by A. Heyting, North Holand, 1956

Dummett [1975] The Philosophical Basis for Intuitionistic Logic. 
in Truth and Other enigmas..

Dummett on a theory of meaning and its impact on logic" in:
B.M. Taylor (ed), Michael Dummett, Contributions to Philosophy, pp
117-65, Martinus Nijhoff Publishers, Dordrecht, 1987.  (Panu adds:
Especially for some issues with Dummett and Prawitz, see also
"Conceptions of truth in intuitionism":

Dirk van Dalen home page:
is recommended as a source

Also Wim Feldman.

URL:  www.dpmms.cam.ac.uk/~tf; 
DPMMS ph: +44-1223-337981; 
mobile in UK +44-7887-701-562; 
mobile in US: +1-412-818-1316; 
mobile in NZ +64-210580093.

More information about the FOM mailing list