The brutal attack in Woolwich has prompted in me thoughts of how wickedness, allied to the "truth" of religious belief, can lead men to heinous acts. For it is this sense of having access to the truth that makes religion the dangerous phenomenon that it so often is. Most of the terrible things human beings do to each other originate in a sense of moral conviction.

We call it evil – and rightly so – but from the perspective of the perpetrator, the experience of being in this place is exactly the opposite: it feels like being right. And feeling right is one of the most powerful alibis for wickedness.

Religion is not unique in generating this dangerous sense of rightness. But, precisely because it is in the business of right and wrong on the grand scale, it makes this mistake more frequently. In contrast, the relativism of "you do your thing and I do mine" seems like a benign alternative – though it can create the opposite failure of indifference. WB Yeats was surely right: when "the blood-dimmed tide is loosed … the best lack all conviction, while the worst are full of passionate intensity."

But the better alternative is not to give up on the idea of truth but to be continually suspicious that one has some sort of privileged access to it. The insightful American author Kathryn Schulz has made a powerful case for the importance of wrongness. We are conditioned, she argues, into thinking that being wrong is a product of laziness, stupidity or moral failure. It is one of the most basic things we learn as a child. When our maths test comes back covered in the teacher's disparaging red ink, with more crosses than ticks, then this is bad. Being wrong is thus intuited as some deep failure and so we are discouraged from pressing ourselves with the possibility that we are. We will do almost anything not to admit we are wrong – thus we live in denial, "trapped in a bubble of our own sense of rightness", as Schulz puts it.

But the fear of being wrong is also a fear that separates us from so much about what it is to be human. Schulz quotes Augustine: "Fallor ergo sum." I err therefore I am. Amusingly, I'm pretty sure that Augustine never said this (Schulz got it wrong, or I have just got it wrong), though the sentiment is entirely Augustinian. Because we are not God, we get things wrong. If religions understood this better, it would be a much safer phenomenon. Yet those who say "maybe" and "I'm not sure" are often classed a deficient in their belief.

When others see the truth differently, we go through three stages of contention. First, we assume they do not have access to the same information, Second, if we discover that they do, we assume they are being thick and don't understand what this information means. And thirdly, if they are evidently not thick, then we assume that they are motivated by something self-serving or wicked. Debates between believers and non-believers often have something of this character. If you see things differently, you are either ignorant, stupid or evil.

But there is a problem here. Some actions inspired by belief are, rightly, described as evil. If we give up any confidence in our access to truth, what basis can we have for making any moral claim? Edmund Burke had an interesting suggestion: "Perhaps truth may be better than peace. But as we have scarcely ever the same certainty in the one that we have in the other, I would, unless the truth were evident indeed, hold fast to peace, which has in her company charity, the highest of virtues."

Wickedness is a crime against peace not a crime against truth.

Twitter: @giles_fraser

• Comments for this article will be not be switched on