David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Ezio Di Nucci
Jack Alan Reynolds
Learn more about PhilPapers
British Journal for the Philosophy of Science 49 (3):425-450 (1998)
To what extent can constructive mathematics based on intuitionistc logic recover the mathematics needed for spacetime physics? Certain aspects of this important question are examined, both technical and philosophical. On the technical side, order, connectivity, and extremization properties of the continuum are reviewed, and attention is called to certain striking results concerning causal structure in General Relativity Theory, in particular the singularity theorems of Hawking and Penrose. As they stand, these results appear to elude constructivization. On the philosophical side, it is argued that any mentalist-based radical constructivism suffers from a kind of neo-Kantian apriorism. It would be at best a lucky accident if objective spacetime structure mirrored mentalist mathematics. the latter would seem implicitly committed to a Leibnizian relationist view of spacetime, but is it doubtful if implementation of such a view would overcome the objection. As a result, an anti-realist view of physics seems forced on the radical constructivist.
|Keywords||No keywords specified (fix it)|
|Categories||categorize this paper)|
Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
|Through your library|
References found in this work BETA
No references found.
Citations of this work BETA
Karin Katz & Mikhail Katz (2012). A Burgessian Critique of Nominalistic Tendencies in Contemporary Mathematics and its Historiography. Foundations of Science 17 (1):51-89.
Vladimir Kanovei, Karin U. Katz, Mikhail G. Katz & Mary Schaps (2015). Proofs and Retributions, Or: Why Sarah Can’T Take Limits. Foundations of Science 20 (1):1-25.
Similar books and articles
Thomas Benda (2008). A Formal Construction of the Spacetime Manifold. Journal of Philosophical Logic 37 (5):441 - 478.
John Earman & John Norton (1987). What Price Spacetime Substantivalism? The Hole Story. British Journal for the Philosophy of Science 38 (4):515-525.
Joseph K. Cosgrove (2011). On the Mathematical Representation of Spacetime. New Yearbook for Phenomenology and Phenomenological Philosophy 11:154-186.
Robert DiSalle (1992). Einstein, Newton and the Empirical Foundations of Space Time Geometry. International Studies in the Philosophy of Science 6 (3):181 – 189.
Vincent Lam (2007). The Singular Nature of Spacetime. Philosophy of Science 74 (5):712-723.
B. Kerkhove & J. P. Bendegem (2012). The Many Faces of Mathematical Constructivism. Constructivist Foundations 7 (2):97-103.
Robert Disalle (1995). Spacetime Theory as Physical Geometry. Erkenntnis 42 (3):317-337.
H. Billinge (2000). Applied Constructive Mathematics: On Hellman's 'Mathematical Constructivism in Spacetime'. British Journal for the Philosophy of Science 51 (2):299-318.
Jill North (2009). The “Structure” of Physics. Journal of Philosophy 106 (2):57-88.
Added to index2009-01-28
Total downloads43 ( #94,398 of 1,793,090 )
Recent downloads (6 months)1 ( #463,661 of 1,793,090 )
How can I increase my downloads?