Moving down the same trajectory as in my previous post (see here), I’d like to once again articulate why our use of quantum set theory is important in conjunction with Laruelle, Deleuze, and Badiou.
Since at this plateau we are becoming-mathematicians, let us read a quick introductory summary of the practicality of set theory follows (see here):
The purpose of set theory is not practical application in the same way that, for example, Fourier analysis has practical applications. To most mathematicians (i.e. those who are not themselves set theorists), the value of set theory is not in any particular theorem but in the language it gives us. Nowadays even computer scientists describe their basic concept – Turing machines – in the language of set theory. This is useful because when you specify an object set-theoretically there is no question what you are talking about and you can unambiguously answer any questions you might have about it. Without precise definitions it is very difficult to do any serious mathematics.
Furthermore, to apply the “quantumness” aspect to what we have revealed, we find that Ernesto Rodriguez succinctly makes note of the practicality of quantum set theory in his 1984 dissertation abstract:
The work of von Neumann tells us that the logic of Quantum Mechanics is not Boolean. This suggests the formulation of a quantum theory of sets based on quantum logic much as modern set theory is based on Boolean logic. In the first part of this dissertation such a Quantum Set Theory is developed. In the second part, Quantum Set Theory is proposed as a universal language for physics. A Quantum Topology and the beginnings of a Quantum Geometry are developed in this language. Finally, a toy model is studied. It gives indications of possible lines for progress in this program. (see here)