Finitism versus Infinitism: No "truths'' are lost

Jan Heylen


No "truths" of infinitism with respect to natural numbers (i.e. there are infinitely many natural numbers) are lost, says Van Bendegem, who defends strict finitism with respect to natural numbers (i.e. there are only finitely many natural numbers). In this paper it is shown that one can use Van Bendegem's own strategy to similarly conclude that no "truths" of finitism are lost to the infinitist. It will be further argued that, as a consequence, the debate between finitist and infinitist is not about the truth beyond the "truths'' or that the "truths" are not adequate representations of the ontological commitments of the two frameworks.


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