SOPhiA 2018

Salzburgiense Concilium Omnibus Philosophis Analyticis

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Programm - Vortrag

Pluralities, Sets and Indefinite Absolutism
(Philosophy of Mathematics, Englisch)

Assume that we can quantify over everything there is. Accept further unrestricted plural comprehension, so we can take a trivial condition (such as 'x = x') to get the universal plurality of every object there is. If there are at least two things, we get from the plural version of Cantor's theorem that there are more pluralities than objects. So, there is no injective mapping from pluralities to objects. But, if you accept universal singularization, there is a unique object (for example a set) for each distinct plurality. Thus, there is an injective mapping from pluralities into objects. This is inconsistent!
Assuming that the plural version of Cantor's theorem is unproblematic, there are three ways of avoiding this inconsistency. The two more common responses are to deny either the possibility of absolute generality or universal singularization. The former position leads to what is called generality relativism, defended by for example Kit Fine. The latter position is to is called definite absolutism, defended by for example Timothy Williamson.
In recent work, Salvatore Florio and Oystein Linnebo have defended the third option, restrict the plural comprehension scheme, a position that may be called indefinite absolutism. The indefinite absolutist faces the challenge of answering the question of what pluralities there are in a non-arbitrary manner. The strategy of Florio and Linnebo is to develop for plural logic something similar to an idea from set theory known as ''limitation of size''. The resulting theory is named ''critical plural logic''.
Is the use of a conception from set theory to justify critical plural logic legitimate? I show how this use might be problematic given that we want to use plural logic to illuminate set theory. I argue that this way of justifying restrictions on plural comprehension introduces the need for more care in laying out the explanatory relationships between set theory and plural logic.

Chair: Sara Ayhan
Zeit: 14:40-15:10, 12. September 2018 (Mittwoch)
Ort: SR 1.005

Hans Robin Solberg
(University of Oslo, Norwegen)

I am from Oslo, Norway. I have just finished a master's degree in philosophy at the University of Oslo, supervised by Oystein Linnebo and Peter Fritz, on the topic of set theoretic pluralism. My BA is also in philosophy with a minor in linguistics. Fall 2018 I will start my studies towards a DPhil at the University of Oxford.

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