Boolean indeterminacy solutions to the problems of material constitution

Abstract This paper offers uniform, unified solutions to the three problems of material constitution, i.e., the Puzzle of the Statue and the Clay (the modal version), the Puzzle of the Ship of Theseus, and the Problem of the Many. The solutions are based on the single idea that there is much indeterminacy in the material world. The solution to the first puzzle states that there is only one object in the sculptor’s studio whose modal profile is largely indeterminate. The solution to the second puzzle states that while the Original Ship survives the changes either as the Repaired Ship or as the Reassembled Ship, it is indeterminate which one. The solution to the third puzzle states that while the cat on the mat is identical with one of the many precise catlike objects on the mat, it is indeterminate which one. The metaphysical-mathematical theory behind these solutions is spelled out, according to which all propositions, properties, and relations are in reality Boolean-degreed, including the numerical identity relation, and the indeterminacy of a proposition is identified as the proposition’s involving an intermediate Boolean degree between Truth (or 1) and Falsity (or 0).