All human knowledge is false. As Popper said, we're all alike in our infinite ignorance.

So there's no shame in being wrong. But there is some sort of shame, even if you do it unintentionally, in trying to short-circuit arguments on principle and settling into a fixed, unchanging worldview.

We don't need certified true knowledge. We only ever have conjecture. But by criticism and experiment, we can remove some of the errors from our conjectures and therefore get closer to the truth.

Yes, they are human constructions, but that doesn't mean that they are false or meaningless just because they're human and humans are fallible. The point is, we only ever have fallible knowledge, we only ever trust propositions that are strictly false, even though they may contain knowledge.

Our mathematical knowledge is conjectural, just like our knowledge of physics. It's even more removed from our senses, because it's not true that the interior of our thoughts is more accessible to us than the world we perceive through our senses. Or the world that we perceive through our theories – like theories of the centre of the sun. We know lots about the centre of the sun, even though no one has ever perceived it, and perhaps no one ever will.

So mathematical truths are based on conjecture. What Gödel showed is that there is no firm ground underneath mathematical theories either. There's no way of proving that the standards of proof we currently use are perfectly rigorous.

How does this conception of conjectural knowledge apply to the multiverse interpretation of quantum mechanics? Is the particle that doesn't collapse or the collapse of the wave function that doesn't take place – is that now real in a separate universe? Can you explain simply to a layman what the reality of that looks like?

The fact is that there are experiments where one can show that individual quantum particles are strongly affected by something that is never seen. This is quite familiar in physics – even Newton postulated invisible forces that operated on the planets, though one can never perceive a force. And then in astronomy, in the early 20th century, we realised – well, before that, we realised that the stars are things like the sun. They're not dots like they seem in the sky. They are spheres, a million kilometres across of incandescent gas. And then we found that our galaxy isn't the only one in the universe.

And in quantum mechanics, we discovered that the world we see around us, the everyday world we see around us, or, in the laboratory, the photon that we see, is only one of many that are accompanying it. And they're all imperceptible to us, except in very specially contrived situations where they affect the photon that we do see. So that's Everettian quantum mechanics, I'd say, rather than an interpretation. There is only one interpretation, in my view, of quantum mechanics.