David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Ezio Di Nucci
Jack Alan Reynolds
Learn more about PhilPapers
Erkenntnis 68 (3):359 - 379 (2008)
Recent years have seen a growing acknowledgement within the mathematical community that mathematics is cognitively/socially constructed. Yet to anyone doing mathematics, it seems totally objective. The sensation in pursuing mathematical research is of discovering prior (eternal) truths about an external (abstract) world. Although the community can and does decide which topics to pursue and which axioms to adopt, neither an individual mathematician nor the entire community can choose whether a particular mathematical statement is true or false, based on the given axioms. Moreover, all the evidence suggests that all practitioners work with the same ontology. (My number 7 is exactly the same as yours.) How can we reconcile the notion that people construct mathematics, with this apparent choice-free, predetermined objectivity? I believe the answer is to be found by examining what mathematical thinking is (as a mental activity) and the way the human brain acquired the capacity for mathematical thinking.
|Keywords||Philosophy Logic Ethics Ontology Epistemology Philosophy|
|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
George Lakoff (1980/2003). Metaphors We Live By. University of Chicago Press.
George Lakoff & Rafael E. Núñez (2000). Where Mathematics Comes From How the Embodied Mind Brings Mathematics Into Being.
Derek Bickerton (1996). Language and Human Behavior. Seattle: University Washington Press.
Jacques Hadamard (1949). The Psychology of Invention in the Mathematical Field. Philosophy and Phenomenological Research 10 (2):288-289.
Keith J. Devlin (2000). The Math Gene How Mathematical Thinking Evolved and Why Numbers Are Like Gossip.
Citations of this work BETA
J. M. Dieterle (2010). Social Construction in the Philosophy of Mathematics: A Critical Evaluation of Julian Cole's Theory. Philosophia Mathematica 18 (3):311-328.
Similar books and articles
Mark McEvoy (2013). Experimental Mathematics, Computers and the a Priori. Synthese 190 (3):397-412.
Mark Colyvan (2011). Fictionalism in the Philosophy of Mathematics. In E. J. Craig (ed.), Routledge Encyclopedia of Philosophy.
James Franklin (1989). Mathematical Necessity and Reality. Australasian Journal of Philosophy 67 (3):286 – 294.
Nicolas D. Goodman (1991). Modernizing the Philosophy of Mathematics. Synthese 88 (2):119 - 126.
Mario Livio (2009). Is God a Mathematician? Simon & Schuster.
Anthony Birch (2007). Waismann's Critique of Wittgenstein. Analysis and Metaphysics 6 (2007):263-272.
Bertrand Russell (1919/1993). Introduction to Mathematical Philosophy. Dover Publications.
Christian Hennig (2010). Mathematical Models and Reality: A Constructivist Perspective. [REVIEW] Foundations of Science 15 (1):29-48.
Stewart Shapiro (1983). Mathematics and Reality. Philosophy of Science 50 (4):523-548.
Added to index2009-01-28
Total downloads45 ( #89,231 of 1,790,408 )
Recent downloads (6 months)9 ( #94,427 of 1,790,408 )
How can I increase my downloads?