Socrates Is Mortal Essay

The roots of modern logic go back to the syllogistic logic of Aristotle. If "All men are mortal" and "Socrates is a man", then you can correctly conclude that "Socrates is mortal". In this form of reasoning terms such as "mortal" are assumed to have an agreed upon definition and propositions such as "Socrates is mortal" are either true or false.

In classical logic every proposition is either true or false; this is the principle of bivalence. From this principle you can prove the law of the excluded middle, namely "P or not P". These are subtly different; the principle of bivalence is a property of the logic itself while the law of the excluded middle is a true proposition in the logic that works for any proposition P.

It seems reasonable that Socrates is either mortal or he is not mortal. Even if you agree that skepticism is a proper philosophical attitude, why bother being

That's not a problem in intuitionistic logic. You can always assume that a predicate is decidable as a premise and see what the consequences would be. If you want you can assume that all predicates are decidable and get the same results as classical logic. You have the option to make that choice, it is not forced on you by the logic. Classical logic does not allow you that choice.

YOU DON'T GIVE UP THAT MUCH

Many proofs don't rely on the law of the excluded middle. The philosophical problems come about when predicates are undecidable or when statements are made about infinite sets of things. Much of the time these aren't problems. In intuitionistic logic the law of the excluded middle is actually valid and provable in restricted setting such as decidable predicates over finite sets. The point is that being skeptical about the law of the excluded middle is a focused change. It does not mean being skeptical when someone says, "When I flip a coin I either get a heads or I don't."

IT'S OKAY TO NOT