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A little bit of context, I'm running into a problem (from my eyes). It seems to me that the amount of logical possibilities that arise from premises exponentially increases to a point that the normal laws of thought are insufficient guidelines for reasoning, and because of this I think what is needed is a stricter logical system from what we already have which in a predictive manner filters out possibilities which don't meet a certain standard, I was hoping that this is already something that's been tried or fulfilled so that maybe I could build on it. Apologies if the question is stupid.

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    I think it's a good question, but could be improved with an example or two, and perhaps a description of the desired end state. Because it shouldn't be too hard to filter possibilities as long as the criteria are clear. Commented yesterday
  • Bayesianism and its razored idealized cousin Solomonoff induction (AIT) are the usual logic of science whereof possibilities abound, yet they don't predict how possibilities arise from premises in a relevant way, you need something like trace equivalence which will lead you to monads & comonads of Leibnizian monadology... Commented yesterday

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You seem to be asking if there's a system that tells us not only which inferences are valid, but which inferences are useful. The answer is that no such system has been discovered yet. We know this because every academic in the world would be interested in such a system, so if it existed, it would be famous.

Our best general tool for predicting how possibilities will branch out, filtering out possibilities that aren't useful, and guiding reasoning is human intuition.

We've made various attempts at approaching, matching, or exceeding humans' abilities to filter out possibilities, in one field or another; those attempts are usually called "artificial intelligence."

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One can derive all of modern physics from the relativity principle logically (assuming that we include branches of mathematics like geometry and calculus into "what can be done logically"). That is, indeed, exponential growth. We do, of course, not even have to go there. Standard natural number theory meets that threshold, already.

If we reduce our premises to the axioms of group theory and the generator of the trivial group, then all we will ever get is the identity element and trivial concatenations of group axioms applied to the identity element, which all result in the identity element.

Since one can give trivial corner cases for either end of this question, then the only question left is if one can always come up with premises and logical derivation rules that reproduce a finite or infinite set of pre-defined (logically consistent) conclusions and nothing else and that satisfy the formal criterial for a "logic system". Let's assume that's the case, what did we win? At best we got ourselves a special kind of compression algorithm for our conclusion set, but since that was a random choice to begin with we didn't learn anything.

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    How do you get quantum field theory from relativity? Sure you can complexify groups. But why would you do that? Note there are some beautiful answers: physics.stackexchange.com/questions/141354/… but it comes down to asthethics imo Commented yesterday
  • @MoreAnonymous By applying Wigner's insight (I am just guessing that it was his, others may have known this before him) that "Quantum mechanics is the unitary representation theory of the Poincare group.". That is where all the talk about Lie groups and specifically SU(n) comes from. It's not a matter of aesthetics at all. Math gives us all the answers here... the real problem is that it gives us way more answers than nature is willing to accept. Nature has made one choice (at the current moment) and we don't know why it's that one and not something else. Commented yesterday
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    I think the furthest you can get is general relativity from the principle of relativity alone but QM/QFT is a different beast. Why the heck would God (I am using this metaphorically) postulate non unitary time evolution (Born rule) when we measure something vs when we don't is a mystery to me. Commented yesterday
  • @MoreAnonymous We don't use the Born rule in QFT. QFT is a scattering theory with plane waves in and plane waves out and the only relevant measurements are the locally conserved Lie charges (in flat spacetime energy, momentum, angular momentum and things like lepton number etc. for U(1)xSU(2)xSU(3)). The Born rule is a hack in non-relativistic theory that explicitly asserts what is supposed to be measurable (the non-relativistic theory doesn't know spin, for instance) by defining the absorption spectrum of the measurement system in an ad-hoc way (i.e. not from symmetries). Commented yesterday
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    @Syed you can redefine locality to say information can't travel faster than the speed of light. In other words there is no way i can use entangled pairs to send a message faster than the speed of light. Commented yesterday

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