The Many Faces of Mathematical Constructivism
Bart Van Kerkhove & Jean Paul Van Bendegem
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Abstract
Context: As one of the major approaches within the philosophy of mathematics, constructivism is to be contrasted with realist approaches such as Platonism in that it takes human mental activity as the basis of mathematical content. Problem: Mathematical constructivism is mostly identified as one of the so-called foundationalist accounts internal to mathematics. Other perspectives are possible, however. Results: The notion of “meaning finitism” is exploited to tie together internal and external directions within mathematical constructivism. The various contributions to this issue support our case in different ways. Constructivist content: Further contributions from a multitude of constructivist directions are needed for the puzzle of an integrative, overarching theory of mathematical practice to be solved.
Key words: mathematical constructivism, conceptualism, internalism vs externalism, meaning finitism, mathematical practice
Citation
Van Kerkhove B. & Van Bendegem J. P. (2012) The many faces of mathematical constructivism. Constructivist Foundations 7(2): 97–103. http://constructivist.info/7/2/097
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