Modal Concepts

    The concept of necessity has logical connections with two others: possibility and impossibility.  A proposition is logically necessary if, and only if, its denial is logically impossible, and a proposition is logically possible if, and only if, it is not logically impossible.  So given any one of these three concepts, commonly called modal concepts, we can derive the other two.

    Modal arguments, or arguments that employ modal concepts, are tricky, sometimes very tricky indeed; and so, as a pedagogical device, 20th Century philosophers have worked out an elaborate language about possible worlds to help clarify some of the ambiguities and some of the fallacies in arguments that might look obviously valid to the unwary.

    Perhaps understandably, theology is an especially rich source of fallacious modal reasoning, though some of the most egregious examples of confusion arise in certain popular arguments for fatalism that make no use of theological concepts at all.  Here are two examples of how easy it is to fall into confusion; and as you examine the two arguments below, you might try to spot exactly where the confusion lies.

Argument I

(1a) If Smith is a bachelor at a time T, then necessarily Smith is unmarried at T.
(2a) But if necessarily Smith is unmarried at T, then it is not possible that Smith should be married at T.
(3a) And if it is not so much as possible that Smith should be married at T, then it never was and never will be within his power to be married at T.
(4a) Therefore, if Smith is a bachelor at a time T, then it never was and never will be within his power to be married at T.
Argument II
(1b) It is not possible (both that Smith should be a bachelor at T and that he should be married at T).
(2b) Therefore, if Smith should be a bachelor at T, then it is not possible that he should be married at T.
(3b) And if it is not so much as possible that Smith should be married at T, then it never was and never will be within his power to be married at T.
(4b) Therefore, if Smith should be a bachelor at a time T, then it never was and never will be within his power to be married at T.


    To those unfamiliar with such arguments, both of the above arguments may look distressingly valid, but in fact they are both invalid; the inference from (1b) to (2b) in Argument II, for example, illicitly transfers the impossibility of a conjunction to one of its individual conjuncts.  Exactly what this means and why such arguments are fallacious is one of the most important things you can learn in any philosophy class, particularly one in metaphysics.