The argument from desire is an evidential argument, arguing for the existence of god from the empirical observation that we desire a relationship with Him and the further assumption that none of our desires are without objective foundation. It should not be confused with the argument from desire fallacy, which argues that god exists because we desire it; the argument from desire is a valid, albeit unsound, argument - the problem is with its assumptions, not with its deductive reasoning (well, at least not with the first deduction). Incidentally Proxima Centauri desires to meet friendly aliens. None of this proves that aliens exist or, if they do, that they are friendly.
The argument can be traced back at least to C.S. Lewis, but it is perhaps worthwhile to phrase the argument as posed by Peter Kreeft:
- A1 Every natural, innate desire in us corresponds to some real object that can satisfy that desire.
- A2 But there exists in us a desire which nothing in time, nothing on earth, no creature can satisfy.
- T1 Therefore there must exist something more than time, earth and creatures, which can satisfy this desire.
- T2 This something is what people call "God" and "life with God forever."
It is unfortunate that C.S Lewis never internalized the ramifications of evolution, for he understood its basics but failed to realize that it undermined his momentous apologetics. In this case, contemplating on the nature of cognition by biological means reveals that not only does (A1) not follow, but indeed that it is precisely the opposite - generally, our desires are aimed not at real objects but rather towards non-existent abstract qualities that we find in the existing objects. This is due to the limited computing resources at our disposal; it is far more efficient to develop the cognitive machinery to identify certain features and seize on them than to conduct a thorough and complete analysis of what is desirable and what is the reality before us (indeed, this is impossible). The result is that there are always, inherently, so-called "supernormal stimulai" - objects that will be more appealing than any existing natural object, as they will incorporate these desirable abstracts in extended forms. The most famous example is perhaps the attractiveness of smooth skin, and the other ideals of beauty that no woman (or man) can rise up to. Supernormal stimuli are real. If no real supernormal stimulus exists we can imagine one.
We want friends who are wise, powerful, loving and will support us through life’s crises. Polytheists imagine many different gods and goddesses who specialize in helping with different types of problems. Roman Catholics pray to different saints similarly. Christians think as Monotheists a large part of the time. They imagine a god who is all wise, all powerful and all loving. There is no reason beyond wishful thinking why their imaginary friend should exist and the Problem of evil suggests such an entity is unlikely or impossible.
We want to be young, active and healthy as long as possible. We evolved that wish because it helped motivate our ancestors to try and survive and to look after their health. There are physical limits to how long we can live therefore we want life after death.
The specific desire of A2 is not specified, and can vary. Whatever it is, objects (or situations, etc.) will be found that will alleviate it - but not completely satisfy it. Complete content is rare, and at best temporary. Instead, we will continue to seek in vain for supernormal stimulai. We will continue to seek "more beauty, more desirability, more awesomeness, more joy", a better and more perfect world than our ancestral environment. We evolved to handle the stress of not having everything we want. While we are looking for things that are better than what we’ve got our lives have purpose and meaning. If we get too much of what we want life can become empty and meaningless.
References and Notes
- See Peter Kreeft's site, 
- Then again, Lewis was perhaps not an adamant believer in biological evolution. See 
- See, for example, Wikipedia
- For an experimental example of these kinds of supernormal preference, see Aesthetic phenomena as supernormal stimuli: The case of eye, lip, and lower-face size and roundness in artistic portraits, Marco Costa, Leonardo Corazza, Perception, 2006, volume 35, pages 229-246