SOPhiA 2019

Salzburgiense Concilium Omnibus Philosophis Analyticis

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Programme - Talk

Beyond Infinity; Dialethism and the Ontology of the Transfinite
(Logic & Philosophy of Mathematics, English)

The main purpose of my talk is to present essential parts of my masters-dissertation "Beyond Infinity; The Epistemology and Ontology of the Transfinite". Hereby, I will focus on the discussion of classical paradoxes of set theory, as well as their canonical axiomatic solutions and the persistent problems related to these solutions.
The idea of iterative set construction in axiomatic systems like ZFC- or NBG-set theory, leads to problematic consequences, which are mainly the result of the rejection of unrestricted comprehension and Cantor's initial philosophical idea of a domain principle. Whereby, the rejection of these fundamental principles has led e.g. to the problem, that axiomatic systems, in the form of ZFC, are fundamentally restricted in their language and not capable of consistently talking about themselves.
These observations inspired radical interpretations, in which (some) all-sets are considered as "dialethia", which are bearers of contradictory properties. This metaphysical assumption makes set theory to a paraconsistent project and following to a possible foundation of mathematics in general within the broader domain of paraconsistent mathematics.
Accordingly, my talk focuses on the critical representation of these dialethic solutions as well as a comparison to potential alternatives.

Chair: Fabian Heimann
Time: 18:20-18:50, 18 September 2019 (Wednesday)
Location: SR 1.007

Simon Graf 
(University of Graz, Austria)

Simon Graf is prior to completing his MA in Philosophy at the Karl-Franzens-University of Graz, with a certificated Master specialization in History and Philosophy of Science. Accordingly, his research interests focus on Philosophy of Science, Philosophy of Mathematics, Epistemology, Philosophy of Mind as well as Technology Ethics.

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