In this paper we intend to argue that: (1) the question `True V or not True V' is central to both the philosophical and mathematical investigations of the foundations of mathematics; (2) when posed within a framework in which set theory is seen as a science of objects, the question `True V or not True V' generates a dilemma each horn of which turns out to be unacceptable; (3) a plausible way out of the dilemma mentioned at (2) is provided by an approach to set theory according to which this is considered to be a science of structures.
Oliveri, G. (2016). True V or not True V, That is the Question. In F. Boccuni, A. Sereni (a cura di), Objectivity, Realism, and Proof (pp. 143-164). Dordrecht : Springer International Publishing [10.1007/978-3-319-31644-4_9].
True V or not True V, That is the Question
OLIVERI, Gianluigi
2016-01-01
Abstract
In this paper we intend to argue that: (1) the question `True V or not True V' is central to both the philosophical and mathematical investigations of the foundations of mathematics; (2) when posed within a framework in which set theory is seen as a science of objects, the question `True V or not True V' generates a dilemma each horn of which turns out to be unacceptable; (3) a plausible way out of the dilemma mentioned at (2) is provided by an approach to set theory according to which this is considered to be a science of structures.
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