The Nature of Necessity

THE distinction between necessary and contingent truth is as easy to recognize as it is difficult to explain to the sceptic's satisfaction. Among true propositions¹ we find some, like

(1) the average annual rainfall in Los Angeles is about 12 inches that are contingent, while others, like

(2) 7+5 = 12

or

(3) If all men are mortal and Socrates is a man, then Socrates is mortal

that are necessary.

But what exactly do these words--'necessary' and 'contingent' --mean? What distinction do they mark? Just what is supposed to be the difference between necessary and contingent truths? We can hardly explain that p is necessary if and only if its denial is impossible; this is true but insufficiently enlightening. It would be a peculiar philosopher who had the relevant concept of impossibility well in hand but lacked that of necessity. Instead, we must give examples and hope for the best. In the first place, truths of logic--truths of propositional logic and first order quantification theory, let us say--are necessary in the sense in question. Such truths are logically necessary in the narrow

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