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Logical and mathematical truths differ from the empirical sciences in being necessary; they can be discovered *a priori* and in general can be proved (*contra* Quine). How is this possible? This problem is partly met by recognizing that the rational sciences are sciences of the possible. Only the mathematical structures that are instantiated in space‐time are existents. Furthermore, using the Entailment Principle, it is seen that only the logico‐mathematical axioms require truthmakers. We should recognize *laws* in these sciences, but laws that are necessary. Such laws will be truthmakers for truths about uninstantiated structures, for instance large infinite numbers. What is the source of these necessary laws? Perhaps it is a necessity in the nature of things.

*Keywords: *
logic;
mathematics;
W.V. Quine;
entailment principle;
mereology;
laws;
necessity

*Chapter.*
*1509 words.*

*Subjects: *
Philosophy of Mind

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