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?
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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