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logical necessity

When something is logically necessary, it is true by definition. These can also be called analytic truths. If we can prove that something is true because "it could not be otherwise," then it is logically necessary. The statement is true with an absolute degree of certainty.

A similar concept is that of empirical necessity. Facts that are empirically necessary could have been otherwise in some possible world (they're not logically impossible). But our world didn't turn out that way and although the alternative state of affairs might be unlikely, it is not impossible.

An example of logical necessity is the statement that "All bachelors are unmarried." This statement is necessarily true because that is how we define the word bachelors, as men who are unmarried. True mathematical statements also are logically necessary. For example 3+3 must equal 6. It's not an accident that it equals 6, and it's not possible that in some alternative world 3+3 would equal 38. A proposition is logically necessary if it is not logically possible for it to be false. Therefore a logically necessary proposition cannot be debated. It is often thought that analytic statements must be logically necessary (see analytic statements).

--Jesse Clayton


PhilosophyOnline, "Rationalism: Empirical and Logical Necessity."
URL = http://www.philosophyonline.co.uk/tok/rationalism4.htm

Alex Rosenberg. Philosophy of Science: A Contemporary Introduction. Routledge, 2000.