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  1.  50
    Nonstandard Set Theory.Peter Fletcher - 1989 - Journal of Symbolic Logic 54 (3):1000-1008.
    Nonstandard set theory is an attempt to generalise nonstandard analysis to cover the whole of classical mathematics. Existing versions (Nelson, Hrbáček, Kawai) are unsatisfactory in that the unlimited idealisation principle conflicts with the wish to have a full theory of external sets. I re-analyse the underlying requirements of nonstandard set theory and give a new formal system, stratified nonstandard set theory, which seems to meet them better than the other versions.
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  2.  41
    A Constructivist Perspective on Physics.Peter Fletcher - 2002 - Philosophia Mathematica 10 (1):26-42.
    This paper examines the problem of extending the programme of mathematical constructivism to applied mathematics. I am not concerned with the question of whether conventional mathematical physics makes essential use of the principle of excluded middle, but rather with the more fundamental question of whether the concept of physical infinity is constructively intelligible. I consider two kinds of physical infinity: a countably infinite constellation of stars and the infinitely divisible space-time continuum. I argue (contrary to Hellman) that these do not. (...)
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  3.  16
    Brouwer’s Weak Counterexamples and the Creative Subject: A Critical Survey.Peter Fletcher - 2020 - Journal of Philosophical Logic 49 (6):1111-1157.
    I survey Brouwer’s weak counterexamples to classical theorems, with a view to discovering what useful mathematical work is done by weak counterexamples; whether they are rigorous mathematical proofs or just plausibility arguments; the role of Brouwer’s notion of the creative subject in them, and whether the creative subject is really necessary for them; what axioms for the creative subject are needed; what relation there is between these arguments and Brouwer’s theory of choice sequences. I refute one of Brouwer’s claims with (...)
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    Enrico Martino, Intuitionistic Proof Versus Classical Truth: The Role of Brouwer’s Creative Subject in Intuitionistic Mathematics, Springer, 2018: Logic, Epistemology, and the Unity of Science, Vol. 42, Pp. 170 + XIII. ISBN 978-3-319-74356-1 EUR 93,59, 978-3-030-08971-9 EUR 93,59,ISBN 978-3-319-74357-8 EUR 74,96.Peter Fletcher - 2019 - Studia Logica 107 (4):845-851.
  5. Life Without Fear.Peter Fletcher - 1940 - Philosophical Review 49:91.
     
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