2

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?

user265554
  • 367
  • 2
  • 11
  • Would anyone happen to know any books or other sources on this? – user265554 Oct 04 '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quantum mechanics; and what difference is there in principle between such a shift and the shift whereby Kepler superseded Ptolemy, or Einstein Newton, or Darwin Aristotle?*".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 04 '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 05 '15 at 00:25
  • See also the references into the answers to this [post](http://math.stackexchange.com/questions/1429071/logic-reality). – Mauro ALLEGRANZA Oct 05 '15 at 08:38
  • 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 08:42
  • @Johannes I understand that there probably is not a book for beginners on this subject since it's such a fundamental one. What should one begin to read about / study so it would be one day possible for him to understand, for example, The Logical Basis of Metaphysics? – user265554 Oct 19 '15 at 08:45
  • Read an introduction to logic, an introduction to philosophy of language, and then an introduction to philosophy of logic. And after the basics see for example the book: "The Concept of Logical Consequence: An Introduction to Philosophical Logic" (Matthew W. McKeon). IEP also has good introductory articles like this: http://www.iep.utm.edu/logcon/ . – Johannes Oct 19 '15 at 09:31
  • @Johannes I don't know how much experience you have with different books on the subject, but how would this set of books sound for the three introductory books? On logic - Introduction to Logic by Gensler. On philosophy of language - The Philosophy of Language by Martinich. On philosophy of logic - An Introduction to Philosophical Logic by Grayling. – user265554 Oct 19 '15 at 12:05
  • I think Matinich's book is an anthology, so not the best choice. I have not seen Gensler's book.Grayling's book looks promising. I have a post here that contains some suggestions: https://philosophy.stackexchange.com/questions/23857/why-is-it-so-difficult-to-write-good-philosophy-textbooks. – Johannes Oct 19 '15 at 12:33
  • @Johannes Thank you! I'm pretty sure I'll find some good books from that post (: – user265554 Oct 19 '15 at 12:40

1 Answers1

1

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.

Philip Klöcking
  • 13,015
  • 3
  • 39
  • 69
  • 1
    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 04 '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 05 '15 at 06:25