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?
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.
Another solution to the later problem may be paraconsistent logic, where LEM is maintained, but untrue does not always mean false.
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.
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.
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.
Sorry, it's the internet encyclopedia of philosophy
by Sriparna 8 years ago
What is the difference between logical thinking and creative thinking?Logical thinking and creative thinking are two different things. What do you think the difference is? Was Sherlock Holmes logical or creative while he solved mysteries? Would love to read your perspectives.
by Kathryn L Hill 7 years ago
...furthermore, He is behind the logical aspect of the world. In other words, He invented logic! We merely discovered / uncovered it!
by aka-dj 11 years ago
It seems to come up so often, as if faith and logic were mortal enemies. Can you please explain why you see it that way? If you see the opposite, why?Quite frankly, I have NO problem with it.
by marinealways24 11 years ago
Is your belief based on faith, logic, or both?Can a person be logical if they have an illogical belief or faith?
by aka-dj 9 years ago
So many Atheists and Agnostics refute faith/religion with living by logic and reason. But, to be really honest, it is totally impossible.What do you say?
by sibtain bukhari 7 years ago
There is no scientific and logical evidence of self existence of universe, therefore,only logical conclusion is the creator of universe not proving its self existence .
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