Conditionals, Causation and Necessity
by Dennis J. Darland
January 11, 2009
Last revised 11.01.2009 12.12 time
Copyright © 2009 Dennis J. Darland


First, although the material conditional, which is defined truth functionally (i.e. extensionally) is useful, it is not adequate to the meaning of implication. For example, supposing one believes

(x)(f(x) ⇒ g(x))

(which by the way is not the logical form laws really have.) If this were just something which were just accidental (That is there were no relation to connect f and g other stronger than an extensional one.) then there could be no reason to infer that such a relation would hold on the future from the fact that it has in the past. But we use such relations in everyday life (and in science - though not so simple) all the time. Even Quine, who wanted to eliminate these intensional relations, himself was trying to define meaning in terms of dispositions to behavior. Such dispositions themselves are such relations which must be understood intentionally, not just extensionally. C. I. Lewis has good reasoning on this subject - I have started into An Analysis of Knowledge and Valuation. I think one criterion of the intensional conditional is that we are willing to infer new cases of the such laws from old ones - there could be no reason to make such inferences if there were only extensional meanings. It may be that meaning of the conditional may be definable through axioms even though it cannot be defined truth functionally. In such axioms, it would not be true that

¬ p ⇒ (p ⇒ q)


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