If you can't make your mind up, we'll never get started

What in the past was a digression in a post that may never see light of day has now been broken out into something of its own, the better to display something or other. It concerns Thompson's argument that Hume's famous argument that a sequence of instrumental wantings can't go on forever is defective, which is a funny argument, or anyway, contains some funny bits. It involves a stone being pushed from α to ω, and thereby also intermediary points β, γ, δ, and so on, each successive point being halfway between ω and the one that came before. Of this chain of pushings he observes that an interlocutor and I might together forge a potentially infinite sequence of perfectly legitimate questions and answers, Why?.

One way to react to this is to note that even on some fearsomely optimistic assumptions, such as that each combined asking-and-answering takes three seconds, that there is no gap between exchanges, that Thompson and his interlocutor do nothing else for all their born days, and that their born days number 95 years, then they will reach the asking-and-answering following which no further question can be posed, nor answer made, since both parties are dead, stone dead, without even having engaged in one billion exchanges (20*60*24*365.25*95 = 999,324,000), and that, furthermore, if the initial distance through which the object is pushed is one meter, then after only 116 iterations they will be haggling about distances smaller than the Planck length, and, well, far be it from me to say that it is impossible or incoherent to want to move an object through a distance of 10E-36 meters, but it is certainly a strange thing to want, and I suspect that if you find yourself disposed to evince it, you are being used in the illustration of some philosophical thesis or other, and should seek redress. Maybe this is merely uncharitable, since clearly Thompson doesn't really mean that he can engage in a potentially infinite sequence of oral performances, not really really; maybe, on the other hand, it's some kind of disreputable biologism and dispensible to the sort of analysis he's engaged in. (But I don't think so.)

I'm sure there are other ways to react to it as well, but the more I read it over the less sure I am of what's supposed to be going on.

Comments

[Daniel Lindquist]

What's this argument from? It sounds amazing.

[Ben Wolfson]

It's in "Naïve Action Theory", which by your own account you recently read! It's in the section headed "Excursus: Hume's Argument for Final Ends Queried" (pp 113–15 if you've got the book).

[Ben Wolfson]

No, wait, that was "The Representation of Life".

[Daniel Lindquist]

Right, "Naive Action Theory" is something I need to read this weekend.

I don't even know what the third part of the book is called, and I don't have it in PDF (only inferior .doc form). I suspect it won't get read anytime soon.