MODAL LOGIC

We considered above (and in Appendix 1) the Paradox of Material Implication. This worries many philosophers, although teachers of first year logic are largely reconciled to and q is F.

But many people would expect it to be equivalent, not to its simply not being the case thatp is T and q is F, but to its being impossible thatp is T and q is F. For in that case, if p is true, it is impossible for q to be false, which seems to capture better the idea that q follows from p. This motivates us to look at the whole question of possibility and necessity, which are the subject of Modal Logic.

The basis of this extension of logic is the introduction of two more statement operators, not truth functional ones this time:

Actually each of these may be defined in terms of the other as follows:

The first says that something is necessarily the case iff it is impossible for it not to be the case; the second says that something is possibly the case iff it is not necessary for it to not be the case. These are logically equivalent, and we’ll take the first as a rule of inference for Modal Logic:

EXERCISE 24.2

24.3

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Source: Arthur R.T.W.. An Introduction to Logic: Using Natural Deduction, Real Arguments, a Little History, and Some Humour. Broadview Press,2016. — 456 p.. 2016

MODAL LOGIC

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