I don't see the advantage of treating states of knowledge as arbitrary complex numbers (quantum amplitudes) rather than real numbers on the closed interval [0,1] (probabilities).
I think that for there to be an advantage of one type or another, you have to have some kind of goal or cost functional in mind. If you're talking about survival, belief propagation, etc., then it certainly is often advantageous to encode large, unwieldy descriptors of states of knowledge down into probabilities.
There are different types of knowledge that we categorize things into. What comes to my mind is the difference between a conclusion drawn by investigating axioms of logic and conclusions drawn from empirical evidence. When facing the claim that, &...
I am reading through the sequence on quantum physics and have had some questions which I am sure have been thought about by far more qualified people. If you have any useful comments or links about these ideas, please share.
Most of the strongest resistance to ideas about rationalism that I encounter comes not from people with religious beliefs per se, but usually from mathematicians or philosophers who want to assert arguments about the limits of knowledge, the fidelity of sensory perception as a means for gaining knowledge, and various (what I consider to be) pathological examples (such as the zombie example). Among other things, people tend to reduce the argument to the existence of proper names a la Wittgenstein and then go on to assert that the meaning of mathematics or mathematical proofs constitutes something which is fundamentally not part of the physical world.
As I am reading the quantum physics sequence (keep in mind that I am not a physicist; I am an applied mathematician and statistician and so the mathematical framework of Hilbert spaces and amplitude configurations makes vastly much more sense to me than billiard balls or waves, yet connecting it to reality is still very hard for me) I am struck by the thought that all thoughts are themselves fundamentally just amplitude configurations, and by extension, all claims about knowledge about things are also statements about amplitude configurations. For example, my view is that the color red does not exist in and of itself but rather that the experience of the color red is a statement about common configurations of particle amplitudes. When I say "that sign is red", one could unpack this into a detailed statement about statistical properties of configurations of particles in my brain.
The same reasoning seems to apply just as well to something like group theory. States of knowledge about the Sylow theorems, just as an example, would be properties of particle amplitude configurations in a brain. The Sylow theorems are not separately existing entities which are of themselves "true" in any sense.
Perhaps I am way off base in thinking this way. Can any philosophers of the mind point me in the right direction to read more about this?