Hmm, maybe I need to reveal my epistemology another step towards the bottom. Two things seem relevant here.
I think you you SHOULD take your best model literally if you live in a human brain, since it can never get completely stuck requiring infinite evidence due to it’s architecture, but does have limited computation and doubt can both confuse it and damage motivation. The few downsides there are can be fixed with injunctions and heuristics.
Secondly, you seem to be going with fuzzy intuitions or direct sensory experience as the most fundamental. At my core is instead that I care about stuff, and that my output might determine that stuff. The FIRST thing that happens is conditioning on that my decisions matter, and then I start updating on the input stream of a particular instance/implementation of myself. My working definition of “real” is “stuff I might care about”.
My point wasn’t that the physical systems can be modeled BY math, but that they themselves model math. Further, that if the math wasn’t True, then it wouldn’t be able to model the physical systems.
With the math systems as well you seem to be coming from the opposite direction. Set theory is a formal system, arithmetic can model it using gödel numbering, and you can’t prevent that or have it give different results without breaking arithmetic entirely. Likewise, set theory can model arithmetic. It’s a package deal. Lambda calculus and register machines are also members of that list of mutual modeling. I think even basic geometry can be made sort of Turing complete somehow. Any implementation of any of them must by necessity model all of them, exactly as they are.
You can model an agent that doesn’t need the concepts, but it must be a very simple agent with very simple goals in a very simple environment. To simple to be recognizable as agentlike by humans.
Hmm, maybe I need to reveal my epistemology another step towards the bottom. Two things seem relevant here.
I think you you SHOULD take your best model literally if you live in a human brain, since it can never get completely stuck requiring infinite evidence due to it’s architecture, but does have limited computation and doubt can both confuse it and damage motivation. The few downsides there are can be fixed with injunctions and heuristics.
Secondly, you seem to be going with fuzzy intuitions or direct sensory experience as the most fundamental. At my core is instead that I care about stuff, and that my output might determine that stuff. The FIRST thing that happens is conditioning on that my decisions matter, and then I start updating on the input stream of a particular instance/implementation of myself. My working definition of “real” is “stuff I might care about”.
My point wasn’t that the physical systems can be modeled BY math, but that they themselves model math. Further, that if the math wasn’t True, then it wouldn’t be able to model the physical systems.
With the math systems as well you seem to be coming from the opposite direction. Set theory is a formal system, arithmetic can model it using gödel numbering, and you can’t prevent that or have it give different results without breaking arithmetic entirely. Likewise, set theory can model arithmetic. It’s a package deal. Lambda calculus and register machines are also members of that list of mutual modeling. I think even basic geometry can be made sort of Turing complete somehow. Any implementation of any of them must by necessity model all of them, exactly as they are.
You can model an agent that doesn’t need the concepts, but it must be a very simple agent with very simple goals in a very simple environment. To simple to be recognizable as agentlike by humans.