nn's Type 1 and Type 2 processes? . . . . . . . . . . . . . . . . . 24 6 Final remarks 26 1 Two types of reality 1.1 Objective definiteness and objective indefiniteness Our thesis in this paper is that mathematics (including logic) can be used to attack the problem of finding a realistic interpretation of (standard Dirac-von-Neumann) quantum mechanics (QM). Mathematics itself contains a very basic duality that can be associated with two meta-physical types of reality: 1. the common-sense notion of objectively definite reality assumed in classical physics, and 2. the notion of objectively indefinite reality suggested by quantum physics. The problem of interpreting quantum mechanics is essentially the problem of making sense out of the notion of objective indefiniteness. The approach taken here is to follow the lead of the mathematics of partitions, first for sets (where things are relatively "clear and distinct") and then for complex vector spaces where the mathematics of full QM resides. There has long been the notion of subjective or epistemic indefiniteness ("cloud of ignorance") that is slowly cleared up with more discrimination and distinctions (as in the game of Twenty Questions). But the vision of reality that seems appropriate for quantum mechanics is objective or ontological indefiniteness. The notion of objective indefiniteness in QM has been most emphasized by Abner Shimony ([37], [38], [39]). From these two basic ideas alone - indefiniteness and the superposition principle - it should be clear already that quantum mechanics conflicts sharply with common sense. If the quantum state of a system is a complete description of the system, then a quantity that has an indefinite value in that quantum state is objectively indefinite; its value is not merely unknown by the scientist who seeks to describe the system. [37, p. 47] 2 The fact that in any pure quantum state there are physical quantities that are not assigned sharp values will then mean that there is objective indefiniteness of these quantities. [39, 