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I'm looking preferably for any survey articles on constructivism in the Philosophy of Mathematics - including Intuitionism in the tradition of Brouwer.

Hopefully such an article(s) will cover:

  1. Motivation (for mathematical and philosophical) for constructivism/intuitionism

  2. The main proponents of the view (including their differing stances) and a tracing of its development since Brouwer

  3. An exposition of the main components of constructivism/intuitionism in the context of the Philosophy of Mathematics

  4. Notable objections and substantiations of them

  5. Potential for future work, including modern reconstructions of the theory

Rather than a list of articles for each point - a lot of which I already have - I'm hoping someone can point me towards a full expository reference covering all of these thoughts.

Thanks

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    To get a modern idea I strongly recommend to read the introduction of the HoTT book: ncatlab.org/nlab/show/…
    – Urs Schreiber
    Commented Mar 5, 2014 at 15:34
  • I second the HoTT suggestion. Also if you can read Russian, there is an excellent survey by Albert Dragalin called Mathematical Intuitionism: Introduction to Proof Theory.
    – Hunan Rostomyan
    Commented Mar 6, 2014 at 18:40
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    @HunanRostomyan - there is an english translation published by American Mathematical Society in 1988.
    – Mauro ALLEGRANZA
    Commented Mar 8, 2014 at 15:37
  • A maybe useful link to a 1973 article by Graham Priest ( see page 118 of the original paper version) grahampriest.net/publications/papers/#1973 ( A Bedside Readers Guide to the Conventionalist Philosophy of Mathematics, with J. Bell and et. al., 115–132. Proc. Bertrand Russell Memorial Logic Conference, Denmark 1971, Leeds, 1973.)
    – Floridus Floridi
    Commented Nov 18, 2020 at 8:39

1 Answer 1

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A good point to start with is SEP; see the entries on Intuitionism in the Philosophy of Mathematics and Constructive Mathematics.

Of course, if you want some book references, following @Paul Ross suggestion, I will add :

Errett Bishop, Foundations of constructive analysis (1967)

Errett Bishop & Douglas Bridges Constructive Analysis (1985)

Michael Beeson, Foundations of constructive mathematics (1985).

All of them deal with the "mathematical side" and not with the philosophical.

About this one, see :

Michael Dummett, Elements of Intuitionism (2nd ed, 2000).

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  • The SEP article on Constructive Mathematics is written by Douglas Bridges, who is a very reputable source on the current state of the field. He's also given a good introductory lecture on the subject, with slides available at masfak.ni.ac.rs/cmfp2013/Nis%20lecture%20170113.pdf .
    – Paul Ross
    Commented Mar 5, 2014 at 15:31
  • @Mauro Many thanks - the SEP articles seem to be very thorough.
    – Mathmo
    Commented Mar 29, 2014 at 0:50

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