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.


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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 Mar 5 '14 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 Mar 6 '14 at 18:40
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    @HunanRostomyan - there is an english translation published by American Mathematical Society in 1988. – Mauro ALLEGRANZA Mar 8 '14 at 15:37

Simply use 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).

  • 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 Mar 5 '14 at 15:31
  • @Mauro Many thanks - the SEP articles seem to be very thorough. – Mathmo Mar 29 '14 at 0:50

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