David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
Philosophia 26 (3-4):279-319 (1998)
Great intuitions are fundamental to conjecture and discovery in mathematics. In this paper, we investigate the role that intuition plays in mathematical thinking. We review key events in the history of mathematics where paradoxes have emerged from mathematicians' most intuitive concepts and convictions, and where the resulting difficulties led to heated controversies and debates. Examples are drawn from Riemannian geometry, set theory and the analytic theory of the continuum, and include the Continuum Hypothesis, the Tarski-Banach Paradox, and several works by GÃ¶del, Cantor, Wittgenstein and Weierstrass. We examine several fallacies of intuition and determine how far our intuitive conjectures are limited by the nature of our sense-experience, and by our capacities for conceptualization. Finally, I suggest how we can use visual and formal heuristics to cultivate our mathematical intuitions and how the breadth of this new epistemic perspective can be useful in cases where intuition has traditionally been regarded as out of its depth
|Keywords||Philosophy Philosophy Epistemology Ethics Philosophy of Language Philosophy of Mind Philosophy of Science|
|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
No citations found.
Similar books and articles
David Galloway (1999). Seeing Sequences. Philosophy and Phenomenological Research 59 (1):93-112.
Ernest Sosa (1996). Rational Intuition: Bealer on its Nature and Epistemic Status. Philosophical Studies 81 (2-3):151--162.
Antony Eagle (2008). Mathematics and Conceptual Analysis. Synthese 161 (1):67–88.
Jennifer Wilson Mulnix (2008). Reliabilism, Intuition, and Mathematical Knowledge. Filozofia 62 (8):715-723.
Colin Cheyne (1997). Getting in Touch with Numbers: Intuition and Mathematical Platonism. Philosophy and Phenomenological Research 57 (1):111-125.
Mark McEvoy (2007). Kitcher, Mathematical Intuition, and Experience. Philosophia Mathematica 15 (2):227-237.
Yuri Cath (2012). Evidence and Intuition. Episteme 9 (4):311-328.
Jennifer Mensch (2011). Intuition and Nature in Kant and Goethe. European Journal of Philosophy 19 (3):431-453.
Valeria Giardino (2010). Intuition and Visualization in Mathematical Problem Solving. Topoi 29 (1):29-39.
Richard Tieszen (1992). Kurt Godel and Phenomenology. Philosophy of Science 59 (2):176-194.
Added to index2009-01-28
Total downloads23 ( #84,199 of 1,410,301 )
Recent downloads (6 months)1 ( #155,456 of 1,410,301 )
How can I increase my downloads?