643 research outputs found
Review of: C. Cellucci, Is mathematics problem solving or theorem proving?, Found. Sci. 22 (2017), no. 1, 183—199
No full textThe author contrasts two philosophical conceptions of mathematics: problem solving versus theorem proving. The former is related to the analytic method and the latter to the axiomatic method. He traces the distinction back to Greek philosophy and highlights the critical role of Hilbert in the controversy. He argues that the analytic method should be preferred in view of Gödel's incompleteness theorems and because it accords better with the work methods of mathematicians. He finally suggests that the appeal of the axiomatic method lies in the fact that justification and well-organised presentation are valuable from a didactic perspective
Neo-Fregeanism naturalized. The role of the one-to-one correspondence in numerical cognition
No full textRips et al. argue that the construction of math schemas roughly similar to the Dedekind/Peano axioms may be necessary for arriving at arithmetical skills. However, they neglect the neo-Fregean alternative axiomatization of arithmetic, based on Hume's principle. Frege arithmetic is arguably a more plausible start for a top-down approach in the psychological study of mathematical cognition than Peano arithmetic. © 2008 Cambridge University Press
A physicalist reinterpretation of ‘phenomenal’ spaces
No full textThis paper argues that phenomenal or internal metrical spaces are redundant posits. It is shown that we need not posit an internal space-time frame, as the physical space-time suffices to explain geometrical perception, memory and planning. More than the internal space-time frame, the idea of a phenomenal colour space has lent credibility to the idea of internal spaces. It is argued that there is no phenomenal colour space that underlies the various psychophysical colour spaces; it is parasitic upon physical and psychophysical colour spaces. The argumentation is further extended to other sensory spaces and generalised quality spaces. © Springer 2006
[Review of: H.G. Callaway (2008) Meaning without analyticity. Essays on Logic, Language and Meaning]
No full textReview of: S. Pollock, The significance of a categoricity theorem for formal theories and informal beliefs.In: Objectivity, realism, and proof, 319–344, Boston Stud. Philos. Hist. Sci., 318, Springer, 2016.
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