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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 Set to 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?
  • The point of philosophy of physics is not to guess what distant future might bring, but to conceptually organize and clarify the current physics, and sketch out promising options for its extensions. Einstein was influenced by Mach's philosophy in transitioning from classical physics to relativity, for example, and Bohr was involved with the Vienna circle of philosophers in developing his observer-dependent view of QM. For current developments, see e.g. Rickles's philosophical primer on quantum gravity. – Conifold Oct 17 '19 at 9:22
  • @Conifold could there possibly be a distinction between philosophy of physics and philosophy of the foundations of physics? Because the question in that linked article, what is a thing, seems to address rather the latter than the former. – fweth Oct 17 '19 at 9:29
  • The latter is a subset of the former. But when it comes to figuring out how current foundational theories (like general relativity and quantum field theory) can be unified and extended, one has no choice but to confront foundational issues head on. This is what Rickles covers for quantum gravity, and the topos approach is a particular proposal in that direction. However, if you are looking for some timeless a priori foundations of once and future physics, the kind that Plato or Kant believed in, that is no longer believed or pursued by many. – Conifold Oct 17 '19 at 9:35
  • OK, I see, thank you! – fweth Oct 17 '19 at 9:38
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    I edited your title to make it sound less prejudicial, I think it was the reason for the downvote. You can roll back the edit, or change it further. – Conifold Oct 17 '19 at 9:44
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What you're talking about is metaphysics.

Has there been pre-quantum philosophy of physics which was able to deal with the implications of QM?

Yes. It is not 'philosophy of physics' but simply philosophy. It may be called the Perennial philosophy or non-dualism. It endorses a neutral metaphysical theory. This easily deals with QM as is explained by Ulrich Mohrhoff in his book The World According to Quantum Mechanics.

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?

See answer to previous question. The philosophy of the Upanishads is capable of explaining QM and it was endorsed by Erwin Schrodinger for this reason among others, so perhaps you could read some of his writing. He spent forty years trying to persuade his peers.

I feel that physicists are bound in end to come around to Mohrhoff and Schrodinger's view, and wonder why even today so few philosophers do so. It's not as if someone has had a better idea. Perhaps it's 'not-invented-here' syndrome.

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