What is the difference between a fact and an inferences?

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The main problem with trying to compare "fact" and "inference" is that it is an odd pairing. Logicians or communication theorists distinguish between "premises" and "inferences", where a premise is an initial proposition assumed and an inference something that may be derived by performing logical operations on one or more premises.

The term fact (normally used in a rather imprecise popular form) refers not to the logical status of a proposition as a premise or an inference, but rather to some element of correspondence with external reality. The distance from New York City to Los Angeles might be a fact. The time it takes to drive from one to the other can be arrived at empirically (by driving from one to the other to find out how long it takes) or by inference, based on calculations of distance and speed. Thus the claim that "it takes X hours to drive from NYC to LA" can be either a statement of empirical fact or an inference, depending on how you arrived at the claim.

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