Tuesday, March 24, 2009

YES

It’s been a while since a five minute talk could make me relate to someone else’s predicament faster than you say chocolate. Vincent referred to domestic dramas today as they manifest themselves through frustration and exasperation. As he suggested, any father would be bound to be at least baffled if his son answered “yes” when asked: “do you want ice-cream or chocolate?” Making a distinction between inclusive disjunction (that which remains true if either or both of its arguments are true) and exclusive disjunction (that which is true if only one, but not both, of its arguments are true, and is false if neither or both are true) Vincent concluded that, logically, whereas he clearly went the exclusive way – intending for his son to pick one of the two things – his son’s affirmative answer to an either/or question suggested inclusiveness. According to Vincent’s logic, his son would have preferred both.

That maybe so, but if you ask me there are other possibilities. For instance, I’m willing to stake a winning bet on the following proposition: what Vincent’s son said yes to is chocolate. Not ice-cream, and not both. How do I know this, one would like to know? By making recourse to precedence. Here’s an example taken also from the private sphere. In my family both my sister and I do what Vincent’s son does all the time, answer yes (or no) to an either/or question. In our convoluted brains, yes always refers to the last word mentioned in the string, not to all, and not to some other things in the middle. Vincent should try it. I can disclose, however, that the practice drives people up the wall, so I won’t recommend it. Especially not when one is past 40.

Now I actually wonder why neither my sister nor myself grew out of it, especially since our mother was also a logician. So logically speaking there is no explanation, unless we want to axiomatize undecidability. (Ok, I can’t resist so here it comes: there is some logic with a finite frame property that is undecidable (“maybe one or the other”). I like Urquhart’s proposition that for any subset X of ω there exists a logic Ax with the finite frame property, such that Ax has the same “degree of unsolvability as X.” Basically this means that if one answers an either/or question with a yes, no, or even a maybe - which, btw, Vincent anticipates his son might also do one day - one shows a preference for spatial logics that allows for incomplete structures. In other words, one departs from the binary structure of the crossroad (nicely represented on Vincent's chest)).


Finally, however, if I wouldn’t win the bet the logical way, I would still win it because of aesthetics. Choosing chocolate over ice-cream is a sign of good taste – and way exclusive – so to Vincent’s son, I would say this: welcome to the club.

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