A Topos Representation for Probabilities

In the topos approach to quantum theory, logical and non-instrumentalist concepts are fundamental while measurements, statistics and probabilities play a secondary role.
In a recent paper Isham and Doering show how it is possible to subsume purely quantum-theoretical aspects of probability by the logical aspects as provided by the topos approach. In this way probability concepts become secondary and derived from the logical, topos-internal aspects.
  • Aim: Give meaning to probabilities also in contexts in which the relative-frequency interpretation is not available.
  • Strategy: Replace probability measure with a collection of truth values.
  • Strategy: Replace probability measure with a collection of truth values.
  • Outcome: Probabilities interpreted as propensities/potentiality of a given event to occur. The mathematical context in which such propensities acquire meaning is the Heyting algebras of truth values.
A short summery of what is done in the paper can be found here