2008/12/12 Thomas Dalton thomas.dalton@gmail.com:
Next, let's say that if A-B and B-C are connected, then A-C are too.
No. That's only generally true for equality relations.
Equivalence relations are not equality relations.
Actually, transitivity is a requirement for an equivalence relation. (In addition to symmetry (A~B => B~A) and reflexivity (A~A for all A).)
Ok, I used the wrong phrase, but it's still very much the case that the interlanguage relationship definitely isn't transitive, and he's assuming it is.