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Should we accept the law of the excluded middle as a logical principle?

  1. PhiMaths ATB profile image60
    PhiMaths ATBposted 5 years ago

    Should we accept the law of the excluded middle as a logical principle?

    The law of the excluded middle says that either p or ~p is always the case, and is a basic principle of classical logic, but there are those that deny that it should always be accepted. Thoughts?

  2. SidKemp profile image95
    SidKempposted 5 years ago

    I think it should not always be accepted. I see two cases in practical life where it is very useful not to do so, and both arise in relation to philosophical systems not based in classical logic.

    One is in the Buddhist Madhyamika philosophy, which has a strong influence on Zen. It's fundamental principle is p -> ~p (p, therefore not-p), that is, if anything is true, it's opposite is also true. The entire Diamond Sutra is based on this logic, and it is a very freeing tool for those who know how to meditate with it and apply it to prevent becoming rigid about one's own ideas.

    The other is the result of Goedel's incompleteness theorem, one of the two events in the early 20th Century that created a breakdown of the belief that everything could be explained by classical logic and physics. Goedel demonstrated that any complete system that could describe the real number system (or anything more complicated) could be then shown to contradict itself. Every true statement could also be proven false. He showed that the solution produced by Whitehead (the theory of logical types) did not solve the problem. Most philosophers since then have avoided facing the issue by not creating complete systems. I prefer complete systems which contradict themselves, as I am influenced by Zen and Madhyamika philosophy.

    1. PhiMaths ATB profile image60
      PhiMaths ATBposted 5 years agoin reply to this

      Another solution to the later problem may be paraconsistent logic, where LEM is maintained, but untrue does not always mean false.

    2. SidKemp profile image95
      SidKempposted 5 years agoin reply to this

      Can you give me a reference introducing me to paraconsistent logic? And another is the work of Charles Sanders Peirce, focusing on abduction rather than deduction.

    3. PhiMaths ATB profile image60
      PhiMaths ATBposted 5 years agoin reply to this

      The IEP entry on paraconsistent logic is a good start. Mark Colyvan and Graham Priest also have a lot to say about this (and Colyvan also has many of his papers available on-line).

      I hadn't thought of C.S. Pierce - worth looking into definately.

    4. SidKemp profile image95
      SidKempposted 5 years agoin reply to this

      What is EIP? My brother's dissertation addressed this aspect of Peirce's work, "The Effect of Temporal Causal Content on Reasoning with Categorical Syllogisms" Steven M. Kemp, Ph,D., UNC Psychology, 1993. See also classical rhetoric as alt. logic.

    5. PhiMaths ATB profile image60
      PhiMaths ATBposted 5 years agoin reply to this

      Sorry, it's the internet encyclopedia of philosophy
      Sounds interesting.

 
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