Blanshard on Implication and Necessity #2

This post is about Mr. Blanshard’s critique of formal implication.

“We turn, then, to formal implication. Our hopes rise as we do, for Mr. [Bertrand] Russell describes it as ‘a much more familiar notion’ which as a rule is really in mind even when material implication is mentioned. But these hopes sink again as we learn what formal implication means. ‘Formal implication is a class of material implications; it asserts that in every case of a certain set of cases material implication holds. … In the statement ‘Socrates is a man implies Socrates is mortal’ we have the expression of a material implication. In the statement ‘If anything is a man then it is mortal’ we have the expression of a formal implication …”

“Now as an account of necessity do we find here any advance? Certainly not so far as concerns the items summarized. Each statement of  a implying  a,  b implying  b, etc., is merely a factual statement that  a and  a (the truth of  a and the falsity of  a), etc. do not occur together. And we have seen there is no necessity there. Does it appear then in review by which we take in all the items as a glance? No again. If the connection of p with q in some one case falls short of being necessary, that same connection does not become so merely holding in all cases.”

“We begin to see, then, in what such logic involves us. It cuts us off altogether from the knowledge of universal truth” (381-2).

“The ignoring of necessity on the part of what is offered as logic, where if anywhere one would expect to find necessary connection, is a legitimate ground of dissatisfaction with the newer logistic disciplines … Stripped of its symbolism and regarded in bare logical essentials, this is the well worn atomism of Hume and Mill. There are no necessary propositions, only statements of class inclusion. There are no necessary inferences; what look like these are statement of exceptionless conjunction” (383).

“When he [the formalist] says ‘triangles have internal angles equal to 180 degrees’, does he mean ‘no triangles do in fact lack this characteristic'? If this is all he means, he has no reason to be surprised if he finds a triangle tomorrow with half or twice that number; there never was any must in the case; the new fact is merely one to be noted, and added to his collection. … Indeed extensional logic has here reversed the true order of priority; it is only because we have a prior insight into the nature of the triangle and what this nature involves that we can be so sure about particular cases. When we say a implies b, we surely mean that a in virtue of being a rather than c or d, implies b; the implication is bound up with intension. And we are clear that in the intension or content upon which thought is directed, we find connections far more intimate than the de facto togetherness to which material and formal implication are both restricted.” (384-5).