Constructivist Foundations 7 (2):141-149 (2012)

Authors
Jean Paul Van Bendegem
Vrije Universiteit Brussel
Abstract
Context: Strict finitism is usually not taken seriously as a possible view on what mathematics is and how it functions. This is due mainly to unfamiliarity with the topic. Problem: First, it is necessary to present a “decent” history of strict finitism and, secondly, to show that common counterarguments against strict finitism can be properly addressed and refuted. Method: For the historical part, the historical material is situated in a broader context, and for the argumentative part, an evaluation of arguments and counterarguments is presented. Results: The main result is that strict finitism is indeed a viable option, next to other constructive approaches, in mathematics. Implications: Arguing for strict finitism is more complex than is usually thought. For future research, strict finitist mathematics itself needs to be written out in more detail to increase its credibility. In as far as strict finitism is a viable option, it will change our views on such “classics” as the platonist-constructivist discussion, the discovery-construction debate and the mysterious applicability problem . Constructivist content: Strict finitism starts from the idea that counting is an act of labeling, hence the mathematician is an active subject right from the start. It differs from other constructivist views in that the finite limitations of the human subject are taken into account
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Debunking, Supervenience, and Hume’s Principle.Mary Leng - 2019 - Canadian Journal of Philosophy 49 (8):1083-1103.
On the Coherence of Strict Finitism.Auke Alesander Montesano Montessori - 2019 - Kriterion - Journal of Philosophy 33 (2):1-14.

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