Metaphysics

Causal Necessity: Pragmatic Investigation of the Necessity by Brian Skyrms

By Brian Skyrms

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It is my contention, against these ironic dismissals, that a suitably modified ‘Pythagorean’ option would be uniquely able, having clarified what ‘mathematics’ is about, to resolve Badiou’s problems and to offer a thoroughly immanentist and demystified metaphysical worldview. An uncrossable boundary between the domains of physics and mathematics has often been expounded by Badiou himself. Let me quote at length some rare passages where Badiou directly addresses the problem of the relationship between the two: [i]n the final analysis, physics, which is to say the theory of matter, is mathematical.

Axiom of set existence or the void set: there is a set (and this is the void set). 1. Axiom of Extensionality: if two sets have the same elements (members), they are equal; 2. Axiom of the Power Set: for every set x there is a set P(x) whose elements are all the subsets of x. (a Subset being any set y which is part of the set x that groups together some elements of x); 3. Axiom of Infinity: there is an infinite set; 4. Axiom of Replacement: if the set x exists, the set y, obtained by replacing one by one each element of x with another element, also exists; 5.

Can we wholeheartedly accept Badiou’s ontology? My answer is no, for it presents some major problems. As I will explain in the next chapter, what I take to be the major problem lies in its inability to offer a precise account of the relationship between the ontological and the empirical. How are non-ontological ‘situations’ to be understood? Is the common Badiouian exemplification of situations within one of the four fields of philosophical conditions to be understood as a mere analogy or is there something deeper than a structural similarity between, say, the ‘situation’ of the French Revolution or that of Galilean science and the ontological One?

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