In the comments to this post on time preference, I pointed to a confusion in Ayn Rand's use of the example of "an immortal, indestructible robot" to show that only "life" makes the concept of "value" possible. Her basic idea was that an immortal, indestructible robot "would not be able to have any values; it would have nothing to gain or to lose; It could not regard anything as for or against it, as serving or threatening its welfare, as fulfilling or frustrating its interests. It could have no interests and no goals."
The problem here, as I see it, is the assumption that if you are immortal, then you would necessarily know this to be the case. The argument seems to rely not so much on being immortal, but in believing you are immortal. Suppose A has secretly been granted immortality, but he does not know it. Wouldn't he have values still, in Rand's paradigm? And what about mortal A who delusionally believes he is immortal? According to Rand, he would have no values (but this seems to be belied by experience--both insane, and sane, people, who believe in a version of immortality nevertheless seem to have values, even in Rand's loose sense; and they certainly demonstrate that they value things, when they act).
Re-reading Hoppe's A Theory of Socialism and Capitalism today, as is my wont, I notice Hoppe argues (p. 9) that one reason acting necessarily imposes costs is that we only have one body so can only do one thing a time with it. Regarding time, he notes:
And I would be restrained by scarcity in another respect as well: as long as this scarce resource "body" is not indestructible and is not equipped with eternal health and energy, but rather is an organism with only a limited life span, time is scarce, too. The time used up in pursuing goal A reduces the time left to pursue other goals.
Notice the similarity to the indestructible robot idea above. In this case, I think Hoppe is correct that our lives are finite and "The time used up in pursuing goal A reduces the time left to pursue other goals", which means that time is, indeed, scarce. This is one factor that enters into our decisions as real, live acting humans in the real world of time scarcity.
It seems to me that this is not only because our bodies are "not indestructible," but also because someone could never, even in principle, know that his body was indestructible. For even if one somehow were magically given immortality and lived from day to day unchanging for thousands of years, how could one be sure that this would last forever? So it seem to me that even if a person was truly immortal and indestructible, time would be scarce for him, since he would not know he was immortal.
Conversely, this would imply that religious people who claim to believe they will live forever in the afterlife either do not view time as scarce, or that they do not really believe what they claim to.
In this connection, see also Mises's comments on how the concept of action would apply to God:
Scholastic philosophers and theologians ... conceived an absolute and perfect being, unchangeable, omnipotent, and omniscient, and yet planning and acting, aiming at ends and employing means for the attainment of these ends. But action can only be imputed to a discontented being, and repeated action only to a being who lacks the power to remove his uneasiness once and for all at one stroke. An acting being is discontented and therefore not almighty. If he were contented, he would not act, and if he were almighty, he would have long since radically removed his discontent. For an all-powerful being there is no pressure to choose between various states of uneasiness; he is not under the necessity of acquiescing in the lesser evil. Omnipotence would mean the power to achieve everything and to enjoy full satisfaction without being restrained by any limitations. But this is incompatible with the very concept of action. ... The paradoxes are insoluble. Has the almighty being the power to achieve something which is immune to his later interference? If he has this power, then there are limits to his might and he is no longer almighty; if he lacks this power, he is by virtue of this fact alone not almighty. [emphasis added]
(See also the discussion of the theological implications of Mises's views here and here.)
