OLOFOS -Finitism versus Infinitism


21 novembre 2018



Raadzaal, Institute of Philosophy, Kardinaal Mercierplein 2

Rencontre avec Jan Heylen (KULeuven) organisée dans le cadre des séminaires OLOFOS "Formal methods towards scientific ontology"

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). His version of finitism is "apophatic finitism" (i.e. nothing can be said about the largest number). In this paper it is shown that one can use Van Bendegems own strategy to similarly conclude that no "truths" of finitism are lost to the infinitist. At this point the connection with negative theism will be made. 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. The first horn of the dilemma will be related to the Carnapian position in meta-metaphysics. The second second horn of the dilemma will be connected to the logical notion of duality. If time permits, I will discuss the prospects for a finitistic theory of truth.

The talk will be in English.