Varieties of Constructive Mathematics
Cambridge University Press (1987)
| Abstract | This is an introduction to, and survey of, the constructive approaches to pure mathematics. The authors emphasise the viewpoint of Errett Bishop's school, but intuitionism. Russian constructivism and recursive analysis are also treated, with comparisons between the various approaches included where appropriate. Constructive mathematics is now enjoying a revival, with interest from not only logicans but also category theorists, recursive function theorists and theoretical computer scientists. This account for non-specialists in these and other disciplines. | |||||||||
| Keywords | Constructive mathematics | |||||||||
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| Buy the book | $56.00 direct from Amazon Amazon page | |||||||||
| Call number | QA9.56.B75 1987 | |||||||||
| ISBN(s) | 0521318025 9780521318020 | |||||||||
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G. S. Ceĭtin (ed.) (1971). Five Papers on Logic and Foundations. Providence, R.I.,American Mathematical Society.
Richard L. Tieszen (2005). Phenomenology, Logic, and the Philosophy of Mathematics. Cambridge University Press.
Solomon Feferman, Relationships Between Constructive, Predicative and Classical Systems of Analysis.
Frank Waaldijk (2005). On the Foundations of Constructive Mathematics – Especially in Relation to the Theory of Continuous Functions. Foundations of Science 10 (3).
Hajime Ishihara & Satoru Yoshida (2002). A Constructive Look at the Completeness of the Space $\Mathcal{D} (\Mathbb{R})$. Journal of Symbolic Logic 67 (4):1511-1519.
H. Billinge (2000). Applied Constructive Mathematics: On Hellman's 'Mathematical Constructivism in Spacetime'. British Journal for the Philosophy of Science 51 (2):299-318.
Helen Billinge (2003). Did Bishop Have a Philosophy of Mathematics? Philosophia Mathematica 11 (2):176-194.
Laura Crosilla & Peter Schuster (eds.) (2005). From Sets and Types to Topology and Analysis: Towards Practicable Foundations for Constructive Mathematics. Oxford University Press.
Douglas Bridges & Steeve Reeves (1999). Constructive Mathematics in Theory and Programming Practice. Philosophia Mathematica 7 (1):65-104.
I. Loeb (2012). Questioning Constructive Reverse Mathematics. Constructivist Foundations 7 (2):131-140.
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