Whether in primitive tribes or the most technologically advanced 21st-century cities, human beings are born with the facility to reason. It requires rational analysis to stalk an animal, just as it does to decide which utility company offers the best deal. So why is it that we are prone to act irrationally, to be persuaded by bad arguments and led by cynical leaders?

This is the question that, in so many words, Steven Pinker seeks to answer in his new book. Pinker, the Harvard cognitive psychologist, is the author of a number of chunky works that have grown steadily more popular, and perhaps more polemical, in their approach. From disentangling the mysteries of cognition and how we learn grammar, he moved on to making the case that humanity is growing less violent in The Better Angels of Our Nature.

That book stirred plenty of controversy, and the affable Pinker has become an increasingly disparaged figure by those who see him as a white male product, and defender, of the scientific establishment. Among other things, Rationality is also a response to these critics, a reaffirmation of critical thinking against the encroachments of critical theory.

As he writes: “Fashionable academic movements like postmodernism… hold that reason, truth and objectivity are social constructions that justify the privilege of dominant groups.” Pinker’s line is that while we may never definitely establish objective truth, objective truth nonetheless exists, and our best means of getting closest to it is through rational understanding.

But what does rationality actually mean? Essentially, it amounts to a set of rules and tools that help us to eliminate bias, bigotries, phobias, superstitions and what Pinker calls the “cognitive illusions” that stand between us and our clearest perception of reality. Among these tools are systems of logic, probability and empirical reasoning.

Just the mention of such phrases brings to mind Star Trek’s Mr Spock – the archetype of the dry and humourless slave to rational thought. Pinker is neither dry nor humourless. And while his jokes may not be exactly rib-ticklers, he knows that what we find funny is often nothing more than clever inversions of logic. Or as the critic Clive James once put it, a sense of humour is just common sense, dancing.

Reason has never been as sexy as emotion, and our romantic side will always back the passionate over the rational. Yet even Romeo, as Pinker notes, citing the psychologist William James, had to employ his rational mind to find a way to overcome the obstacles placed between himself and Juliet.

As Pinker points out, rationality is really just a means of getting what we want, thus even the most irrational people are capable of making rational choices. Where things become difficult is when our brains, which have evolved to seek mental shortcuts, lead us astray – a fate that regularly visits even the sharpest of minds.

To illustrate this tendency, Pinker outlines some classic traps and fallacies. My favourite is the three door choice that used to feature in a US gameshow. Behind one of the doors was a car and behind the other two a goat. After the contestant selected a door, the host would open one of the other remaining two doors, revealing a goat. Then the contestant would be offered the opportunity to change her choice of door.

Most contestants stayed with their original choice, assuming it was a 50-50 deal – an assumption made by even some notable mathematicians. But they were wrong. Changing to the other door improves the contestant’s chance of winning the car from one in three to one in two. We struggle to compute that basic fact of probability. But imagine that there were a thousand doors, and you chose one, and then 998 were opened to reveal goats. Would you still stick with your original choice, rather than opt for the other unopened door?

How does a gameshow brain-teaser have any application in real life? Because we jump to wrong conclusions all the time, by relying on habit and intuition, and by fearing change. The anti-vaccine movement, says Pinker, is a case in point. It focuses on extremely rare reactions to vaccines and ignores the far more common consequences of not taking a vaccine.

The same goes for the rise of populism. Someone such as Donald Trump lies and contradicts himself almost every time he opens his mouth, yet his emotional pull often “trumped” his logical shortcomings.

It’s hard to argue against Pinker’s own logic, yet there will always be a ghost in the machine, those urges and instincts that serve to distort reality. We are hugely more likely to die while driving than while flying, yet this knowledge does little, if anything, to ease the fear of nervous flyers. In the end, though, rationality is all we have to prevent the world from descending into chaos or tyranny. You can’t argue against it – other than by rational means, which would be self-defeating. Nonetheless, it wouldn’t be rational to underestimate the lure of the irrational.

• Rationality: What It Is, Why It Seems Scarce, Why It Matters by Steven Pinker is published by Allen Lane (£25). To support the Guardian and Observer order your copy at guardianbookshop.com. Delivery charges may apply