Necessary truth

Modal logic is intended to represent arguments involving essentially the concepts of necessity and possibility. Some preliminary comments about the idea of necessity, therefore, won't go amiss. There is a long philosophical tradition of distinguishing between necessary and contingent truths. The distinction is often explained along the following lines: a necessary truth is one which could not be otherwise, a contingent truth one which could; or, the negation of a necessary truth is impossible or contradictory, the negation of a contingent truth possible or consistent; or, a necessary truth is true in all possible worlds (pp. 188ff. below), a contingent truth is true in the actual but not in all possible worlds. Evidently, such accounts aren't fully explanatory, in view of their ‘could (not) be otherwise’, ‘(im)-possible’, ‘possible world’. So the distinction is sometimes introduced, rather, by means of examples: in a recent book (Plantinga 1974 p. 1) ‘7 + 5 = 12’, ‘If all men are mortal and Socrates is a man, then Socrates is mortal’ and ‘If a thing is red, it is coloured’ are offered as examples of necessary truths, and ‘The average rainfall in Los Angeles is about 12 inches’ as an example of a contingent truth.

The distinction between necessary and contingent truths is a metaphysical one; it should be distinguished from the epistemological distinction between a priori and a posteriori truths.