I've just read a fascinating essay by primatologist Frans de Waal, Primates and Philosophers. (It's the Archbishop of Canterbury who leaps to my mind on hearing the phrase 'primate morality', but of course the title refers to the kinds of hairy primates who are our evolutionary ancestors rather than the kind who run the church.)
De Waal wants to have a go at those who argue that human morality is a cultural overlay on a nature which is amoral – he calls this 'veneer theory' and links it to TH Huxley amongst others. Part of the book consists of replies by angry veneer theorists (not that they accept the description). However, the philosophical spat is less interesting than de Waal's observations on the behaviour of the primates – chimps and capuchin monkeys – he has observed carefully for years. I found his argument that human morality ihas evolved from our inherent nature as social apes very persuasive. It's consistent with other work on the evolution of reciprocal altruism eg Axelrod's Evolution of Cooperation. To me it suggests a way of reconciling the assumption of self-interest common to economics and evolutionary studies with observations about how people in fact behave: self-interest in this sense does not equate to selfishness.
One of the other features of the essay that fascinated me is de Waal's frequent reference to Adam Smith and my hero David Hume, whose theorising about human nature and the moral sentiments which characterise it he sees as consistent with the findings of primatologists. There has always been much mutual borrowing between economics and evolutionary theory. Darwin read Malthus as well as Hume and Smith, Marx and Veblen borrowed from Darwin; more recently John Maynard Smith's evolutionarily stable strategy concept came from game theory. Paul Krugman years ago gave a terrific speech on this interchange. Long may it continue. Both are natural sciences which seek to explain human behaviour and ultimately I think they'll converge, and cognitive science along with them.