No matter what you say I will continue to stubbornly insist on using the most logical meaning.

Logic has little, if not anything, to do with language. I, on the other hand, see the logic of the other side: this is a deictic pronoun referring to that which is close to the speaker, as opposed to that by the hearer and yon by a third person who is neither ego or tu. If it's humpday, and somebody (not Mr ThePook nor zmjezhd) says this Tuesday, it makes sense that s/he is referring to the day before, not that one six days out (or seven as the Romans counted, they being a logical people, too). I don't see what the fuss is, as long as the person doing the reckoning does so consistently. That way I don't get into squabbles over whether soda is pop or coke.

The funny thing is that next is an archaic superlative form of nigh, so when somebody says next Tuesday, they literally and etymologically mean the closest Tuesday to the day they are speaking of.

Ceci n'est pas un seing.