# An Epistemological Derivation of Quantum Logic

**Source**: https://www.maths.tcd.ie/report_series/abstracts/tcdm0001.html
**Parent**: https://www.maths.tcd.ie/research/papers/

**An Epistemological Derivation of Quantum Logic** 

This paper deals with the foundations of quantum
mechanics. We start by outlining the characterisation, due to Birkhoff and
Von Neumann, of the logical structures of the theories of classical
physics and quantum mechanics, as boolean and modular lattices respectively.
We then derive these descriptions from what we claim are basic properties
of any physical theory - i.e. the notion that a quantity in such a theory
may be analysed into parts and that the results of this analysis may be
treated in languages with an underlying boolean structure. We shall see
that in the course of constructing a model of a theory with these
properties different indistinguishable possibilities will arise
for how the elements of the model may be named, that is to say different
possibilities arise for how they can be associated with points from Set.
Taking a particular collection of possibilities gives the usual boolean
lattice of the propositions of classical physics. Taking all possibilities
- in a sense, the set of all things that may be described by physical
theories - gives the lattice of quantum mechanical propositions. This
gives an interpretation of quantum mechanics as the complete set of such
possible descriptions, the complete physical description of the world.