God is being reinvented by atheists. It's an unexpected phenomenon. Martin Seligman, the psychologist responsible for the surge of interest in happiness, talks of never being able to get on with the God of the Christians. However, he speculates about a deity that will emerge in time: "I am optimistic that God may come at the end," he has written.

Or there's the theoretical biologist, Stuart Kaufmann. His reflections on evolution lead him to suggest that "the unfolding of the universe … appears to be partially beyond natural law" and hence he is "happy to accept this natural creativity in the universe as a reinvention of 'God'."

The work of the author and journalist Robert Wright is caught up in this movement. Much as evolution seems directed towards growing physiological complexity, he detects moral progress in the evolution of humanity. It's an insight supported by game theory. Very roughly, some activities we see in nature are zero-sum: one player wins, and the other must lose. There is no progress in that. However, some activities are non-zero-sum: it is possible to devise outcomes that are win-win. In such situations, to put it crudely, people can afford to be nice to each other. Seen as a force of history, that leads to an increase in compassion and the creation of the moral ideal of universal love. In his new book, The Evolution of God, Wright links that to Jewish, Christian and Muslim explorations of the divine. He believes his method points to a synthesis of faith and science, one that transcends contemporary antagonisms.

He even leaves open the possibility that the God of Abraham, Isaac and Jacob exists, though he's more inclined to the view that "God" is a creation of the human imagination, if one to be valued not dismissed; without "God", he suggests, our moral sensibilities would be indistinguishable from those of beasts. He comes closest to affirming a transcendent force for the good when exploring the work of Philo of Alexandria. This Jewish thinker envisaged a principle running through the cosmos, which he called the Logos. That abstract conception of God suits Wright's game theory, and its cost-benefit analysis: he calls Philo's Logos "the divine algorithm".

Wright is a searcher. His interviews with prominent writers on religion, online at meaningoflife.tv, would only be done by someone who is open-minded. But for all that, the narrow prism through which he views the history of religion – this compassion calculus – is distorting.

One obvious question to ask is whether humanity makes moral progress anyway. Stalin, Mao and Hitler don't warrant a mention in his book, and neither does the policy of the nuclear states in the west, that rests our security not on universal brotherhood but mutual annihilation. Wright would presumably answer that these features of the 20th century are aberrations, deviations along the path that nonetheless winds towards a better world. But is it really adequate to think of the Holocaust as an aberration? Surely, it's a fearful reminder of what humanity is persistently capable of.

For Wright to be right, theology must progress too. Hence, he presumes that primitive religion is, well, primitive. But does that stand up? The cave paintings of our Paleolithic ancestors have impressed some of the 20th century's most sophisticated artists. A spiraling trajectory of change seems at least as plausible as a linear course of development. That must be why we keep reading Plato and Confucius too.

To put it another way, Wright's thesis would fall foul of Karl Popper's critique of what he called pseudo-science. A pseudo-science is a theory that can accommodate any datum you care to throw at it; hence the Holocaust would be counted as an aberration not a falsification of moral progress. Alternatively, it is a historicist theory, claiming to summarise the past, understand the present, and so predict the future. Popper rejected historicism since it inevitably tells a partial tale of what's happened, and anyway, ignores the crucial feature of the human story, namely that our efforts at self-understanding are always scuppered by what is uncertain and wayward.

There are internal inconsistencies that cause Wright to trip up too. For example, he affirms that the human mind has been "designed" by evolution to harbour beliefs not because they are true, but because they adaptively advantageous. So can we affirm that evolutionary psychology itself is true? Evidence alone would not be enough, since it's the often deluded human mind that must interpret what game theory purports to tell us.

Sometimes the non-zero-sum analysis just looks silly as well. An example of this is Wright's explanation of Saint Paul's embrace of moral universalism, that in Christ there is "neither Jew nor Greek, slave nor free, male nor female." Wright describes it as crucial to Paul's "business model". It allowed anyone to sign up to his new product – Christianity – and so created a network effect much like that exploited by Microsoft's Windows: the more people installed his theological system into their lives, the more advantages accrued to everyone. Wright appears to recognize the Monty Pythonesque nature of this analysis when he nervously concedes that it is "somewhat speculative".

It's telling that he admits he has no theology, for all that he writes about God. Because Thomas Aquinas would have helped him. The great 13th-century theologian anticipated a number of the problems associated with the scientific study of religion. He observed that when we do, say, physics, we can first know what we are talking about, namely the cosmos, and so can second make progress in how to talk about it. However, when it comes to God, we're not sure what we're talking about and so constantly fail with the second step. "Whatever way we have of thinking of him is a way of failing to understand him as he really is," he wrote. That's presumably why, way back in Moses' time, God would only say "I am that I am."

That's quite an admission from a man who spent his whole life searching for ways of "thinking of him". Incidentally, it applies even if you think God is no more than a product of the human imagination; it's inherent in the concept of God. But perhaps, as Wright continues with his search, he'll find time for some theology too. I would be glad to read him then, as now.