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To the memory of John D. TrimmerThis paper assesses the impact of disjunctive facts on the quantum logic read off procedure. The purpose of the procedure is to transfer a significant quantum structure to a set of propositions; its first step is an attempt to discover that structure. Here I propose that disjunctive facts as traditionally conceived have blocked the procedure at its first step and have therefore subverted the best-known attempts to read off quantum logic. Recently however Allen Stairs has proposed a view of disjunctive facts which re-establishes the possibility of reading off quantum logic. Both the traditional conception and Stairs’ revision of disjunctive facts are interesting in their own right, independent of quantum propositional logic. Too many things are called ‘quantum logic’. The term is disentangled and notation is fixed in this preliminary step which relies on basic lattice theory.

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Schrödinger's argument about a “cat penned up in a steel chamber” is a timely challenge to those concerned with the philosophy of quantum theory; the argument prompts difficult decisions about correlated quantum mechanical systems, locality, reality and completeness. Here Schrödinger's own text is reproduced and, in view of the text, several plausible axioms and formal rules are chosen. Then, beginning with the axioms and using the rules, a contradiction is derived. This result establishes that Schrödinger's argument can be viewed as a paradox, a derivation of a contradiction from plausible assumptions. A final section of the paper refines the paradox and treats two possible resolutions as representative of a watershed issue in the foundations of quantum mechanics.Comments concerning the method of formalization were provided when I applied the method to the Einstein-Podolsky-Rosen argument (1978).