Abstract
Until now quantum logics has been first-order, but physics requires higher-order logics. We construct a natural higher-order languageQ for quantum physics.Q is a finitistic logic based on Peano set theory and Grassmann algebra. Higher-order predicates are identified with their extensions, higher-rank sets. QAND and QOR (the AND and OR ofQ) are naturally noncommutative but reduce to the commutative lattice operations for the first-order part of the language. We form higher-order predicates and sets by a setting operator similar to Peano'st that forms a simple extensort Ψ = }Ψ} from any extensorΨ. In a note added in proof, we correctQ so that a bond like {{α, β}} between two fermionsα andβ is a quasiboson, as the application to lattice chromodynamics strongly suggests.
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