Evidence and logical implication can be compared; we can say that logical implication is conclusive evidence, or that evidence is a sort of weak implication.
Evidence is commutative. If A is evidence for B, B is evidence for A. But logical implication is not; if A implies B, B does not necessarily imply A. However, even in the case of implication we can say that if A implies B, B is evidence for A.
Implication is transitive. If A implies B, and B implies C, then A implies C. We might be tempted to think that evidence will be transitive as well, so that if A is evidence for B, and B is evidence for C, A will be evidence for C. But this is not necessarily the case; this sort of thinking can lead to believing that the evidence can change sides. Attempting to make evidence transitive is like trying to draw a conclusion from a syllogism without any universal terms; if A is evidence for B, then some B cases are A cases, but not necessarily all of them; if every B case were an A case, then A would imply B, not merely be evidence for it. So if A is evidence for B, and B for C, then some C cases are B cases, and some B cases are A cases; but we cannot conclude that any C cases are A cases. A and C may very well be entirely disjoint. Thus the theory of evolution, taken as given, is evidence that transitional fossils between man and ape can be found; and the finding of such a transitional fossil is evidence for the (completely implausible) theory that some fossils have been preserved from every kind of organism that has ever inhabited the earth. But the theory of evolution taken as given does not provide evidence for the completely implausible theory; rather, the theory of evolution and the completely implausible theory would refute one another, at least if we are also given a little bit of background knowledge.
2 thoughts on “Evidence and Implication”
[…] more probable that the next crow I see will be black. But this does not follow, since this would be attempting to apply transitivity to evidence. The probability of “I see a black crow today”, given that “I see a black crow tomorrow,” […]
[…] was earlier shown that evidence in general is not transitive. The reason given was that if A is evidence for B, and B for C, A is not necessarily evidence for […]