Logic

I am learning about the principle of noncontradiction ~(p^~p). I can see that this would work if we assume that 'p' can only be true or false. Why should I make this assumption. I can see a lot instances where we need more than 2 truth values (how people feel about the temperature of a room, for instance could have an infinite number of responses, and all would be true because the proposition is based on subjective experiences). What is this type of logic called? If this is a possible logic then can't someone argue that everything is this way?

Comments

Your example about the room temperature doesn't seem to support the idea that we need more than two truth-values, because you classify everyone's responses as true. Instead, the example raises the question of how to interpret the people in the room: as disagreeing with each other because they're making incompatible claims ("It's cold"; "It's not cold") or as only apparently disagreeing with each other because they're making compatible claims ("It feels cold to me"; "OK, but it doesn't feel cold to me").

Standard logic (often called "classical" logic) has just two truth-values. Many-valued logics are nonstandard logics that contain anywhere from three to infinitely many truth-values -- in the latter case, all of the real numbers in the closed interval [0,1], with '0' for 'completely false' and '1' for 'completely true'. You'll find lots of detailed information in this SEP entry.

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