I never questioned your statement that there could be systems in which the normal (classical)equivalency between a statement and its contrapositive did not hold: I only questioned the obviousness of the of your claim that any system that did not include the law of excluded middle and double negation elimination axioms would invariably us to “quickly get to rejection of equivalence of the contrapositive.” (Well, that and whether “if you love something, [then] set it free” was even a proposition. I still say that it is not). Basically, my argument was that since the two axioms did not appear to me to be required to prove the equivalence of a statement and its contrapositive within classical logical, it might be possible to construct a rational system without those axioms that still supports proposition-contrapositive equivalency. I’m not convinced that it IS possible; I’m just not yet convinced that it IS NOT possible.

That said, I enjoyed the diversion, and particularly appreciate the book links!

Back to Arlo: I imagine the (missing) caption in the last panel as saying, “Earlier…”