PIRSA:13120060 Scientific Series Quantum Foundations

DOI10.48660/13120060

Series: Quantum Foundations

deJonghe, R. (2013). Rebuilding Mathematics on a Quantum Logical Foundation. Perimeter Institute. https://pirsa.org/13120060

deJonghe, Richard. Rebuilding Mathematics on a Quantum Logical Foundation. Perimeter Institute, Dec. 10, 2013, https://pirsa.org/13120060 

@misc{ pirsa_PIRSA:13120060,
  doi = {10.48660/13120060},
  url = {https://pirsa.org/13120060},
  author = {deJonghe, Richard},
  keywords = {Quantum Foundations},
  language = {en},
  title = {Rebuilding Mathematics on a Quantum Logical Foundation},
  publisher = {Perimeter Institute},
  year = {2013},
  month = {dec},
  note = {PIRSA:13120060 see, \url{https://pirsa.org}}
}

Abstract

It is not unnatural to expect that difficulties lying at the foundations of quantum mechanics can only be resolved by literally going back and rethinking the quantum theory from first principles (namely, the principles of logic). In this talk, I will present a first-order quantum logic which generalizes the propositional quatum logic originated by Birkhoff and von Neumann as well as the standard classical predicate logic used in the development of virtually all of modern mathematics. I will then use this quantum logic to begin to build the foundations of a new ``quantum mathematics'' --- in particular a quantum set theory and a quantum arithmetic --- which has the potential to provide a completely new mathematical framework in which to develop the theory of quantum
mechanics.

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