If it's possible for a cat to be alive and dead at the same time, or for a particle to be in two places at the same time, would that show there are at least some things about which one couldn't rely on "Either P or not P" as a sound step in reasoning?

Why is the sorites problem a "paradox"? Isn't it fundamentally a problem of definition?

Is it possible to employ a truth predicate or truth set (set of all true propositions) in ordinary first order logic?

Mustn't there be a counterexample to any statement that's a generalisation, because if there weren't a counterexample the statement would be a matter of fact and not a generalisation?

This is a question about pure logic. There are two theries: Theory A and Theory B. Theory A assumes AssumptionA. Theory B assume AssumptionB. The two assumptions are mutually exclusive: if AssumpionA then not AssumptionB and vice versa. I believe that a philosophical result is that Theory A and Theory B cannot prove anything about each other. All you can do is preface each result with the assumption. For example, if Theory A proves X and Theory B proves Y, then we can say "If AssumptionA, then X" and "If AssumptionB then Y". Who first proved this? Where is it documented? Eugene

When you ask why people believe in logic, it seems to me that the commonest answer is, "It works." But that answer seems problematic to me; how do you know it won't stop working? I guess what I'm asking is -- are logical laws nothing more than empirical regularities, models of how things behave? Are logical laws any different from empirical laws? Is there any stronger reason to have faith in logic apart from the fact that it works and has always worked?

My one distinguishing feature is that I don't have a distinguishing feature - paradox?

Some people define some things (which they truly may be or are) Impossible. 'Impossible' has a humane meaning in itself. But... If 'something' is really impossible... then why can you think that? If something is impossible... then why did the neurons in your brain have that thought? It must've been impossible for them to think of something which is not possible.

Does an universal affirmative (A) premise entail a particular affirmative (I) one? I mean "All men are mortal" entails "Some men are mortal" or not? This is somehow confusing. Since, if you think that in a relation with set theory, it is impossible for (I) not to be entailed by (A). (A) intuitively entails (I). However, when looking at the opposition of square and applying, for example, tree method to prove the entailment, it results that (A) does not entail (I).

In an answer to a question, Stephen Maitzen wrote, "if one's argument depends on controversial premises, then one ought to improve the argument by finding less controversial premises that imply one's conclusion." Am I mis-reading what he wrote? Does it come across to others as "one starts with the desired conclusion and then works backwards to develop premises that would support the desired conclusion." ? There may be evidence from recent psychological studies (e.g., Kahneman's Thinking Fast and Slow that indicate that our minds actually do work in this manner. However, I was under the impression that philosophers generally reason by starting with premises that seem reasonable, and then using logic to determine where those premises lead. His statement perhaps indicates a different path.