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Is it true that a fundamental axiom of logical reasoning is that reality doesn't contradict? Can someone explain why this assumption is a reasonable starting point if true or what a more accurate fundamental axiom is if false?

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    Hi, welcome to Philosophy SE. Traditionally, there are three fundamental "laws of thought", you can read about them in Wikipedia. This site is more suitable for more specific and pointed questions that come up after general reading. – Conifold Nov 13 '19 at 8:36
  • There is certainly meaningful work on contradiction-permitting logics - see paraconsistent logic. – Noah Schweber Nov 14 '19 at 0:09
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    This is why a mathematician should marry a mathematician. If you work with people then it is best to get used to the excluded middle, and see Noah’s comment. – Gordon Nov 14 '19 at 2:56
  • How would you form a coherent picture of the world (set of rules) without excluding contradictions? Of course once you have a coherent picture, then you can handle a closer look at things that (seem to) contradict. – christo183 Nov 15 '19 at 6:49
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You're talking about the law of non-contradiction. A can't be both A and not A at the same time and in the same sense. It's a reasonable starting point because thought is impossible without it.

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  • Paraconsistent logic would disagree. – Noah Schweber Nov 14 '19 at 0:08
  • Paraconsistent logic doesn't assert that contradictions are true. – user18800 Nov 14 '19 at 3:51
  • The 'law' of contradiction has no bearing on 'thought'. Without it there might be no system of logic, which system has nothing to do with reality. The law of contradiction is an artificial construct which makes language games possible. It has nothing to do with reasoning, philosophy or any questions about reality. CMS – Charles M Saunders Nov 14 '19 at 14:30
  • If the law of non-contradiction were false, thought would be the same as non-thought, reason the same as non-reason, and language games the same as non-language games. – user18800 Nov 14 '19 at 16:09

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