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The attempt to ground logic epistemically in any empirical discipline must fail, for these disciplines invariably presuppose the logical laws they are introduced to explain. Either logical laws need no epistemic foundation or they must be justified by a discipline at a different epistemic level from empirical science. 52 Husserl also rejected the psychologistic account of logical objects, the ideal terms of propositional meaning. To paraphrase his argument: the ancient description of logical laws as laws of thought had been nlisconstrued by the naturalists.

With the adoption of logical consistency as the criterion of mathematical validity, it became imperative to display mathematical theories in their most perspicuous logical form, to exhibit clearly their deductive structure and principles of inference. This revised assessment of the nature of mathematics was supported by the new mathematical methodology. Whatever heuristic importance intuition may have in the stage of original discovery, under the formalized approach it was not essential to mathematical demonstration and proof.

A calculus is a method of symbolic operation resting on a precise notation and explicit rules of formation and transformation. The rules determine which operations on the symbols are permissible and which are not. The only general restriction on a calculus is The Crisis of Philosophy 23 that its pattern of notational results admit of consistent interpretations. Boole did not adopt a fully conventionalist attitude toward his proposed algebra of logic. He accepted the transformation of propositions into propositional variables, but he argued that the rules for combining those variables must be based on the laws of the mind.

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