> I think that this is not quite true: ... No it is. It is quite true that mathematical impossibility is mathematical and has nothing to do with the real world

> I think that this is not quite true: ... No it is. It is quite true that mathematical impossibility is mathematical and has nothing to do with the real world. > ... but it applies only to mathematical models; that is, models cannot exhibit the behaviour. This doesn't prevent the real world from exhibiting that behaviour, but it does mean that, if the real world exhibits that behaviour, then the model is inaccurate. You are talking about the validity of a mathematical model (with respect to a real world phenomena). That is a completely different notion. Mathematically impossible means that, using the rigors of a mathematical proof, a contradiction is reached starting from the original mathematical assumptions. You started with math and ended with math. No real world involved. > [quantum mechanics and gravity] First of all, you're not making your life easier by defending your point using the argument of incompatibility of quantum mechanics and gravity. And second of all, again you're mixing validity of a mathematical model as applied to observed phenomena, with the notion of mathematical impossibility. If the theory of quantum mechanics and the theory of gravity are incompatible and each on its own is unable to explain all of the observed physical world, that means both are likely inaccurate (rather incomplete) models of reality and we need a new model (maybe string theory) to explain the physical world.