It 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 C, because the cases where A and B are the case can be disjoint from the cases where B and C are the case.
However, this does not prevent evidence from being transitive on particular occasions, and possibly on most occasions, namely whenever situations where A and B are the case are the same or mostly the same situations where B and C are the case.
For example, if someone speaks with me in a loud tone and with a red face, that is evidence that he is angry with me; and if he is angry with me, that is evidence that I have said or done something which offended him; and likewise speaking with me in a loud tone and with a red face is evidence that I have said or done something which offended him. In this case situations where A and B are the case, namely where someone is angry and speaking angrily with me, overlap a good deal with cases where B and C are the case, namely where the person is angry because I have offended him.
This is quite possibly the more common situation — namely that evidence is transitive in practice — and thus the likely reason why people tend mistakenly to conclude that evidence is always transitive.
2 thoughts on “Transitivity of Evidence Revisited”
Hey, you have an interesting blog but I don’t have any interesting comments on most of it, so I picked this post:
One subtle way this strikes in science is indices like GDP or IQ, where people try to aggregate complex realities into one number. Then the discussion about how “real” these indices are is basically a discussion about what kinds of evidence chains involving the index are transitive.
Thanks for the comment. Yes, that seems right.
I just now corrected the original statement here regarding how evidence can fail to be transitive, but you probably understood that even without the correction.