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True V or not True V, that is the question. (English) Zbl 1436.03061

Boccuni, Francesca (ed.) et al., Objectivity, realism, and proof. FilMat studies in the philosophy of mathematics. Cham: Springer. Boston Stud. Philos. Hist. Sci. 318, 143-164 (2016).
Summary: 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.
For the entire collection see [Zbl 1351.00011].

MSC:

03A05 Philosophical and critical aspects of logic and foundations
03E30 Axiomatics of classical set theory and its fragments
03E99 Set theory
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