Mathematical Objectivity: Truth and Independence

(Logic/Philosophy of Mathematics, English)

he absolute security provided by mathematical proof has to face some limits, mainly: axioms and undecidable sentences (Gödel, Goodstein or the Continuum Hypothesis). Over the decades there have been a large number of attempts to justify such sentences employing concepts as coherence, simplicity or consequence. However, these attempts are inconclusive. Not only does the quest for justification remain open, the very possibility of this justification is an open problem too: are sentences as the Continuum Hypothesis objective matter?

The objective of the talk is to discuss how Wright's (1992) criteria for objectivity apply in the context of mathematical foundations (set theory). Specifically, the availability of a minimalist and classical truth predicate, one defining a maximally consistent set of sentences as extension, for set theory will be assessed. This point, semantic realism, is tied with metaphysical realism. Also, the behaviour of this predicate inside of a plural context (multiversism) will be analysed. Since truth acts as a criterion for choice theories, is semantic realism a good criterion for objectivity inside of a plural ontology of mathematics?

Key words: objectivity, truth, undecidability, multiversism, set theory

Chair: Katia Parshina

Time: 14:40-15:10, 09. September 2022 (Friday)

Location: SR 1.006

Ismael Ordonez Miguens

(University of Santiago de Compostela, Spain)

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