= 27d567bc2d48d9f40e9ccc20ea370b15)
MrMind comments on Mixed Reference: The Great Reductionist Project - Less Wrong
You are viewing a comment permalink. View the original post to see all comments and the full post content.
= 783df68a0f980790206b9ea87794c5b6)
Loading…= b715d02e85f7b3b4ae65ca3d3e450868)
Subscribe to RSS Feed
Powered by Reddit
= f037147d6e6c911a85753b9abdedda8d)
You are viewing a comment permalink. View the original post to see all comments and the full post content.
Comments (353)
Just as mental gymnastics, what if instead we would be able to reduce physics and logic to magical reality fluid? :)
Anyway, for the "logic from physics" camp the work of Valentin Turchin seems interesting (above all "The cybernetic foundation of mathematics"). Also of notice the recent foundational program called "Univalent foundation".
I don't think you can reduce logic to anything else, since you would need to use logic to perform the reduction.
Well, since nobody have done that yet, we cannot be sure, but for example a reduction of logic to physics could look like this: "for a system built on top of this set of physics laws, this is the set of logical system available to it", which would imply that all the axiomatic system we use are only those accessible via our laws of physics. For an extreme seminal example, Turing machine with infinite time have a very different notion of "effective procedure".
How would one show the above, or even build up a system on top of physical laws without using logic?
I have (at the moment) no idea.
It's clear that such a demonstration needs to use some kind of logic, but I think that doesn't undermine the (possible) reduction: if you show that the (set of) logic available to a system depends on the physical laws, you have shown that our own logic is determined by our own laws. This would entail that (possibly) different laws would have granted us different logics. I'm fascinated for example by the fact that the concept of "second order arithmetical truth" (SOAT) is inacessible by effective finite computation, but there are space-times that allow for infinite computation (and so system inhabiting such a world could possibly grasp effectively SOATs).