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How do we know the logic we use to logically infer is correct? What makes it correct? Why is "If X exists, then Y exists. X exists. Therefore Y exists." true?

  • Would anyone happen to know any books or other sources on this? – user265554 Oct 4 '15 at 20:18
  • We do not, in the end logical laws are no more than the part of our experience that proved most reliable. People using the inference you quote found that it always tested successfully when tried. But as Quine put it "no statement is immune to revision. Revision even of the logical law of the excluded middle has been proposed as a means of simplifying quantum mechanics; and what difference is there in principle between such a shift and the shift whereby Kepler superseded Ptolemy, or Einstein Newton, or Darwin Aristotle?". – Conifold Oct 4 '15 at 22:34
  • If your question is markedly different from the stack of others we've had on a similar topic, please edit your question to explain how what you're asking is distinct. – virmaior Oct 5 '15 at 0:25
  • See also the references into the answers to this post. – Mauro ALLEGRANZA Oct 5 '15 at 8:38
  • This is a very important question, it is a fundamental philosophical question. Should one object that it has a duplicate, since the answers the earlier question received were subpar? One good source is Michael Dummett's "The Logical Basis of Metaphysics" see the table of contents. Unfortunately that is not the best place to start for a beginner, I don't know what would be. – Johannes Oct 19 '15 at 8:42
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Logic like mathematics is based on an axiomatic system, it is a formal system. Therefore, it is producing immanently tautologous propositions out of itself by its axioms. I am not sure if there has been a Kolmogoroff of all systems of logic exemplifying the axioms, though.

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    Logic was in use long before axiomatic systems, and the logic of common reasoning isn't formal at all, formal logic only formalizes some aspects of it. Often badly, as in the case of the material conditional. – Conifold Oct 4 '15 at 22:30
  • I think it should be differentiated here: Yes, logic is trying to formalize semantics. But since Frege and Carnapp it is clear that these are not compatible. Although the axioms are not 100 ÷ clarified it should be clear that there must be some. Though mathematics can be used to characterize and describe empirical connections, it is in the end independent from it. I think logic is just the same. – Philip Klöcking Oct 5 '15 at 6:25

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