I'm currently trying to read into topos foundations for theories of physics and I wonder if we are really able to give a philosophical foundation for what a possible future theory of physics should satisfy.
There are interpretations of quantum mechanics, where the act of observation is just an entanglement between the wave function of the observer and the wave function of the object in observation, and while there still might be philosophical issues with this, I can make a lot of sense about it. Maybe I'm lacking in knowledge, phantasy or creativity, but I have a really hard time imagining a philosophical foundation of physics established before QM, which would integrate this entanglement interpretation, and I don't see how we can be sure that no future theory of physics with its accompanying mathematics will allow us to see reality, and especially the role of the observer or the praxis of information collection, in a completely different light again.
It's hard to formulate an objective question out of these ponderings, but maybe something along the lines of:
- Has there been pre-quantum philosophy of physics which was able to deal with the implications of QM?
- Are there current philosophies of the foundation of physics, whose proponents claim that they are not merely developing tools to help physicists overcome deeply internalized assumptions about the nature of reality, in order to increase their scope in the search of new theories, but that they are able to precisely outline the realm of where such a future theory of physics must lie in, so that we can make any sense of it?
- Out of the two scenarios described in the previous question, where does the topos approach fall into?
- Maybe this clarifies when I dive further into the topic, but is the topos approach motivated by our good experiences in the past of generalizing function arrows in
Setto arrows in another suitable category, or is there an intrinsic relation to physics, where one could argue that even without any knowledge of category theory, a very intelligent agent could have come up with this approach as a natural generalization from our current framework of physics?