Experimental mathematics

Erkenntnis 68 (3):331 - 344 (2008)
The rise of the field of “<span class='Hi'>experimental</span> mathematics” poses an apparent challenge to traditional philosophical accounts of mathematics as an a priori, non-empirical endeavor. This paper surveys different attempts to characterize <span class='Hi'>experimental</span> mathematics. One suggestion is that <span class='Hi'>experimental</span> mathematics makes essential use of electronic computers. A second suggestion is that <span class='Hi'>experimental</span> mathematics involves support being gathered for an hypothesis which is inductive rather than deductive. Each of these options turns out to be inadequate, and instead a third suggestion is considered according to which <span class='Hi'>experimental</span> mathematics involves calculating instances of some general hypothesis. The paper concludes with the examination of some philosophical implications of this characterization.
Keywords Philosophy   Logic   Ethics   Ontology   Epistemology   Philosophy
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References found in this work BETA
James Franklin (1987). Non-Deductive Logic in Mathematics. British Journal for the Philosophy of Science 38 (1):1-18.
Mark Steiner (1978). Mathematical Explanation. Philosophical Studies 34 (2):135 - 151.
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