I am convinced, but cannot prove, that time does not exist. I mean that I am convinced that there is a consistent way of thinking about nature, that makes no use of the notions of space and time at the fundamental level. And that this way of thinking will turn out to be the useful and convincing one.
I think that the notions of space and time will turn out to be useful only within some approximation. They are similar to a notion like "the surface of the water" which looses meaning when we describe the dynamics of the individual atoms forming water and air: if we look at very small scale, there isn't really any actual surface down there. I am convinced space and time are like the surface of the water: convenient macroscopic approximations, flimsy but illusory and insufficient screens that our mind uses to organize reality.
In particular, I am convinced that time is an artifact of the approximation in which we disregard the large majority of the degrees of freedom of reality. Thus "time" is just the reflection of our ignorance.
I am also convinced, but cannot prove, that there are no objects, but only relations. By this I mean that I am convinced that there is a consistent way of thinking about nature, that refers only to interactions between systems and not to states or changes of individual systems. I am convinced that this way of thinking nature will end up to be the useful and natural one in physics.
Beliefs that one cannot prove are often wrong, as proven by the fact that this Edge list contains contradictory beliefs. But they are essential in science and often healthy. Here is a good example from 25 centuries ago: Socrates, in Plato's Phaedon says:
"... seems to me very hard to prove, and I think I wouldn't be able to prove it ... but I am convinced ... that the Earth is spherical."
Finally, I am also convinced, but cannot prove, that we humans have an instinct to collaborate, and that we have rational reasons for collaborating. I am convinced that ultimately this rationality and this instinct of collaboration will prevail over the shortsighted egoistic and aggressive instinct that produces exploitation and war. Rationality and instinct of collaboration have already given us large regions and long periods of peace and prosperity. Ultimately, they will lead us to a planet without countries, without wars, without patriotism, without religions, without poverty, where we will be able to share the world. Actually, maybe I am not sure I truly believe that I believe this; but I do want to believe that I believe this.