A few points:
1. Whatever the chance that the future (or rather our role in it) simply won’t exist, that should be discounted directly by the relevant probability of extinction. That said, while I do worry about asteroids, I take this probability to be relatively small over the next five hundred years.
2. Our uncertainty about the future is good reason for performing an expected value calculation, but it does not provide additional reason for time discounting. It will shape the p’s that go into the expected value calculation.
3. Austrians and Knightians may believe that our uncertainty about the future is deeply radical and that the entire expected value calculation is meaningless.
I am closer to a Bayesian myself. But even if we take the Knightian view at face value, it does not diminish the importance of the future. Whether or not we call expected value calculations "scientific" or "stupid," we still need to make choices about the future. A woman might think "I simply can’t imagine what sort of man I might marry." He might even be some hitherto unimagined extraterrestrial being. But her parents should still set aside some money for the possible ceremony.
To make the uncertainty stronger and more general, perhaps the parents think "We have *no* idea what will happen with our daughter, marriage or not. Perhaps she will sell kitchen equipment, perhaps she will be turned into a sweet potato." In any case there is no general reason for the parents to think they should save less rather than more. The potential outcome might require a very large expenditure on their part.
Some of my technically inclined readers are already thinking about the
third derivative of the utility function and the precautionary motive
for saving. The intuition is this: if the effect of your savings is very uncertain, you might either eschew savings altogether ("who knows what it will bring?"), or you might feel a need to save all the more. The third derivative will determine which is the correct decision, and this is not a matter of the discount rate per se.
4. The party analogy: Let’s say you have no idea who will show up at the party (or what the future will look like). How can you buy the food until you know whether the guests are Hindu, Muslim, or whatever. Fair enough, perhaps we should wait. But given the uncertainty, we might want to set aside more savings for future contingencies, and not spend all the money today.
Let’s consider this "third derivative" business in a little more detail. When does radical uncertainty justifiably mean the future should be ignored? A Christian might believe that he should not save up for Rapture. Perhaps Rapture, once it comes, will be so different and so unexpected in its nature that current precautions simply were not worth making. Odds are your mutual fund won’t make it into heaven (or hell?). Fair enough.
Alternatively, let’s say you are worried about an avian flu pandemic, but you don’t have a good idea what such a pandemic would look like. You probably still should buy more bottled water, not less, and pickle more kimchee, not less.
The practically-minded can debate which of these two cases more closely resembles global warming.