M Theory Lesson 100
But isn't that just what the physics has been telling us we must do? Lambek and Scott take the viewpoint that categorical logic treats logic pragmatically, as a part of ordinary mathematics, thus refuting logicism. Should logos theory refuse to accept this point of view? Recall that in M theory any useful logical statement has a physical meaning pertaining to a given experiment and its constraints. The numbers associated with logical statements (or rather diagrams) also take on a physical meaning (loosely speaking, a collection of measurements). Thus both logic and number theory should be derived from the physical principles of measurement, expressed as a higher dimensional topos theory.
There is a chicken-and-egg objection: that the formalism of higher toposes requires the mathematics of logic before acquiring a physical interpretation. However, since physics is undoubtedly guiding the axioms in question, this argument appears weak. Ironically, logicism in M Theory would be the ultimate in reductionism, despite the intuition of emergent schemes on different scales.
 J. Lambek and P.J. Scott, Introduction to higher order categorical logic, Cambridge U.P. 1986