Space and Symmetries in Max Black's Argument

(Metaphysics and Ontology, English)

ne of the most popular comments on the Principle of the Identity of Indiscernibles (PII) is Max Black's article (1952) written in a manner of dispute between A -- the supporter of PII -- and B who tried to reject it. In one of the arguments B asks to imagine the universe that contains nothing but two exactly similar pure-iron spheres of the diameter of one meter, with this same color, temperature etc. He claims that they are a counterexample of PII. Moreover, he argues that this reasoning works also with all symmetrical objects (e.g. with two mirror-reflected Napoleons) and mentions point and axis reflections. The goal of this talk is to provide rigorous definitions and mathematical background for this considerations, which will allow to present that B was wrong.

B's considerations seem to be rather unclear. Fistly, he does not provide definition of the space in his argument. I will consider several possibilities equipped with mathematical description, e.g. some versions of absolute and relational spaces: oriented, non oriented and non orientable ones with different numbers of dimensions. After the analysis of their symmetries it will turn out that for some of them B's argument does not work. In order to prove my statement I will provide my own variants of the argument in different spaces. The majority of them takes advantage of the notion of incongruent counterparts naively defined in famous Kant's argument (1768). I will provide their rigorous definition (that refers to isometry and rigid motion) that will allow to show on mathematical ground which pairs: spaces and objects, fails to support B's view and indicate the reason of such situation. Finally, I will provide some more complicated variants of the argument (e.g. two hands on Movius strip) that are contradictory to PII.

This considerations will show that B's argument is incorrect in some cases; the mathematical background will explain the reason of this failure. Considering different spaces is interesting, because it may lead to the conclusion that although PII can be rejected in B's ideal universe, it works perfectly in our physical reality -- depending on the nature of our space.

Chair: Markus Hierl

Time: 14:00-14:30, 12 September 2018 (Wednesday)

Location: SR 1.006

Marta Emilia Bielińska

(Jagiellonian University, Poland)

Marta Emilia Bielińska is an undergraduate student in Interfaculty Individual Studies in the Humanities (main division: Philosophy) and Studies in Mathematics and Natural Sciences (main division: Theoretical Physics) at Jagiellonian University in Cracow. She is interested in philosophy of physics (especially in context of symmetries and orientation of space), metaphysics of modalities and temporal logic.

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