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The purpose of this paper is to show that the mathematics of quantummechanics (QM) is the mathematics of set partitions (which specifyindefiniteness and definiteness) linearized to vector spaces, particularly inHilbert spaces. That is, the math of QM is the Hilbert space version of themath to describe objective indefiniteness that at the set level is the math ofpartitions. The key analytical concepts are definiteness versus indefiniteness,distinctions versus indistinctions, and distinguishability versusindistinguishability. The key machinery to go from indefinite to more definitestates is the partition join operation at the set level that prefigures at thequantum level projective measurement as well as the formation ofmaximally-definite state descriptions by Dirac's Complete Sets of CommutingOperators (CSCOs). This development is measured quantitatively by logicalentropy at the set level and by quantum logical entropy at the quantum level.This follow-the-math approach supports the Literal Interpretation of QM--asadvocated by Abner Shimony among others which sees a reality of objectiveindefiniteness that is quite different from the common sense and classical viewof reality as being "definite all the way down."

Follow the Math!: The mathematics of quantum mechanics as the mathematics of set partitions linearized to (Hilbert) vector spaces