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Pierce's law works on the peculiarity of the truth table of implication, in which an implication is only false when the antecedent is true and the consequent is false. Implication is always true otherwise. We can show Pierce's law through reductio ad absurdum: For Pierce's law to be false, ((P → Q) → P) must be true and P false If P is false (p1), (P → Q) ...


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A misleading feature I observe in many textbooks on logic is that they restrict translations to and from natural language to a few strict patterns, upshot of which is a habit of interpretations bereft of the huge power of informal semantics, which, however, mathematicians freely enjoy (I have always thought that it would be very nice if the English language ...


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Short Answer Rationalism tends to rely on deductively certain methods to establish the truth. Empirical truths are probable to a degree. It is a rational fact that given the theory of numbers, any number can be composed of a product of unique primes raised to a power. But is an empirical method only that can determine which prime number was used to generate ...


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What about the "upward re-transmission of falsity". In empirical science we assume theories (hypotheses) T and deduce predictions: P. I.e. we have statements like T → P. Then we test the prediction P with empirical data (e.g. through an experiment). If the prediction is refuted by empirical evidence (it is falsified), we conclude that the theory T is ...


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