Topics Logic

Question What is the difference between a conclusion that is "necessarily true, but not false" vs. "necessarily false, but not true"? They seem the same to me or is the answer based on probability? In the same light, what is the difference between "probably not necessarily false" and "probably but not necessarily true"? Thank you, Joe

Accepted:
August 21, 2014

Comments

Hello, Joe. Except for the difference in truth-values, I see no interesting difference between your first two descriptions. "Necessarily true, but not false" is a redundant description, because any proposition that's necessarily true is ipso facto not false and in fact couldn't have been false (indeed, that's what "necessarily true" means in this context). The second description is also redundant, because any necessarily false proposition is ipso facto not true and couldn't have been true. As far as I can see, probability has nothing to do with those two descriptions. In these cases, the word "necessarily" is being used in what's often called a modal sense.

The second pair of descriptions does concern probability. Any proposition that's "probably but not necessarily false" is more likely than not false but not certain to be false: the proposition has a probability greater than 0 but less than 0.5, on a scale of 0 to 1. Any proposition that's "probably but not necessarily true" has a probability of more than 0.5 but less than 1, on a scale of 0 to 1. In these cases, the word "necessarily" is being used in what's often called an epistemic sense, where it means "certainly".