Logic and Arithmetic
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At least since the time of Aristotle, logic has occupied a central place in the field of philosophy, and, interestingly enough, it was with a study on the nature of logic that the entire phenomenological movement began. Up to this point we have focused upon the nature of judgments — positive and negative, contingent and necessary, material and formal, synthetic and analytic — and, of course, the corresponding ontology and epistemology. As we turn now to consider the nature of logic we are not leaving the sphere of judgments and their corresponding ontology, but we are in fact further considering (at least in large part) special relationships between judgments, for instance, the way in which one or more judgments can imply or entail another judgment. And just as judgments posit states of affairs which exist prior to our acts of judging, so too Reinach finds that the ultimate laws of logic are, for the most part, general laws governing the connections between states of affairs.
KeywordsLogical Modality Ordinal Number Correspondence Theory Ontological Modality Pure Logic
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