Topics Logic

Question If Laws of logic are true or hold in all contexts, how can there be more one law? Do the two versions of De Mogan's laws differ? If so. how? Does the law of excluded middle differ from the law of non contradiction and from either version of De Morgans laws? Enoch

Accepted:
September 22, 2012

Comments

Notice that the same question arises in math, where the laws also hold no matter what. Arithmetic contains commutative laws of addition and of multiplication, associative laws of addition and multiplication, a distributive law of multiplication over addition, etc. Are those laws different? Their representations on the page certainly look different.

I take it that you're asking, at bottom, how truths that hold in all possible worlds could count as distinct truths. The answer depends on how propositions are to be individuated, and here philosophers give various answers. On some theories, there's only one proposition that's true in all possible worlds, although there are indefinitely many sentences (some logical, some mathematical, some metaphysical) that express this single proposition. Other theories give a more fine-grained way of individuating propositions that allows for the existence of multiple propositions that are true in all possible worlds. You'll find more in this section of an SEP article; I recommend the whole article.