Graduate studies at Western
Philosophia 26 (3-4):279-319 (1998)
|Abstract||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||No keywords specified (fix it)|
|Categories||categorize this paper)|
|Through your library||Configure|
Similar books and articles
David Galloway (1999). Seeing Sequences. Philosophy and Phenomenological Research 59 (1):93-112.
Valeria Giardino (2010). Intuition and Visualization in Mathematical Problem Solving. Topoi 29 (1):29-39.
Jennifer Mensch (2011). Intuition and Nature in Kant and Goethe. European Journal of Philosophy 19 (3):431-453.
Yuri Cath (2012). Evidence and Intuition. Episteme 9 (4):311-328.
Mark McEvoy (2007). Kitcher, Mathematical Intuition, and Experience. Philosophia Mathematica 15 (2):227-237.
Colin Cheyne (1997). Getting in Touch with Numbers: Intuition and Mathematical Platonism. Philosophy and Phenomenological Research 57 (1):111-125.
Jennifer Wilson Mulnix (2008). Reliabilism, Intuition, and Mathematical Knowledge. Filozofia 62 (8):715-723.
Antony Eagle (2008). Mathematics and Conceptual Analysis. Synthese 161 (1):67–88.
Ernest Sosa (1996). Rational Intuition: Bealer on its Nature and Epistemic Status. Philosophical Studies 81 (2-3):151--162.
Richard Tieszen (1992). Kurt Godel and Phenomenology. Philosophy of Science 59 (2):176-194.
Added to index2009-01-28
Total downloads17 ( #78,173 of 738,458 )
Recent downloads (6 months)1 ( #61,778 of 738,458 )
How can I increase my downloads?