Blanshard on Implication and Necessity #3

This post is about Mr. Blanshard’s critique of strict implication as posited by C. I. Lewis.

Professor Lewis “would agree that when p implies q materially or formally this gives no assurance that q is deducible from p, nor does it give us what we usually mean by implication. He believes that his own system of ‘strict implication’ gives us both. This relation he defines as follows (the symbol stands for ‘strictly implies’ and  for ‘possible’ or ‘self-consistent’): p  q. = .   (p  q); that is, ‘ “p strictly implies q” is to mean “It is false that it is possible that p should be true and q false” or “The statement ‘p is true and q false’ is not self-consistent.” When q is deducible from p, to say “p is true and q is false” is to assert, implicitly, a contradiction” (385).

Note: is not the symbol in Blanshard’s book, but I couldn’t find how to use his and is often used to mean imply.

“There is no doubt that this sense of ‘implies’ is far nearer to the ordinary meaning than the previous senses. It no longer asks us to say anything so alien to common usage as that every true proposition implies every other, or that every false proposition implies all conceivable propositions; it is far more critical and selective” (385)

“Take an instance. ‘If anything is red, then it is extended.’ This, I think, is a fair example of implication in an ordinary sense. Now when we say that anything’s being red implies that it is extended, it is our meaning this, that if we denied that it was extended we whould also have to deny that it was red? I do not think so. I agree, of course, that when p implies q, to deny q does commit us to denying p also; I agree that in such a case to affirm p and deny q would be inconsistent. … When I say that p implies q, I am saying that a certain relation holds between them. The inability to insert not-q consistently instead of q is not the same as that relation, but something that holds in virtue of it” (386-7).