The distinction that physics seems to have retained from the original intuition is that between a determinate and finite set of rules (or laws or universals of a particular kind) and an infinitely large set of potential descriptions.
First of all, I don’t think this is anthropologically accurate. I have seen a number of cases of (what appears to me to be) confusion in physics (and probably even more in philosophy) engendered by thinking of laws as rules in a sense more robust than what you describe here. I gave one example in this comment, and I could give others if you desire. The reason I brought up the effect of social cognition is that concepts have power. Someone may insist that by “rule” they really just intend the attenuated definition you’ve given, just as someone may insist that by “human” they literally just mean “featherless biped”, but when one tries to redefine established concepts in this way, the original conceptions have an insidious way of sneaking into one’s inferences. Someone tells you Natalie Portman has feathers, and you insist that this is conceptually impossible because she is human and humans are featherless bipeds.
Second, I don’t see how thinking of laws as rules is necessary to establish that the laws are finite. On my modification of Lewis’s view, the laws are the axioms (Lewis himself says “axioms and theorems”, but I think that’s clearly the wrong way to go) of the best deductive system, where “best” depends on some balance of simplicity and strength (and presumably some other virtues as well). These systems will at the least be recursively axiomatizable, and in most actual cases finitely axiomatizable. If not, your system will take a HUGE hit on the simplicity metric. So Lewis’s descriptive view itself gives warrant for constraining the set of laws. We don’t need help from prescriptive intuitions, as far as I can see.
As for the claims about the completeness of physical law, these might correctly characterize the expectations of physicists, but the expectations of physicists are not dispositive in this case. If you look at what’s actually going on in physics, it’s not at all clear that those expectations are being borne out. Our best current theories (such as the Standard Model) are effective field theories. There are two points to be made about this. First, it shows that non-fundamental theories, coarse-grained theories that are only valid when certain conditions hold, can (contrary to your claim in another comment) be accurate and precise enough within their domains of validity to be regarded as basically a complete description of that domain. You said in the other comment that this would be “miraculous”. In so far as the extreme unlikelihood of precise EFTs is a prediction of your viewpoint, it appears to have been disconfirmed.
Second, the prevalence of EFTs highlights the fact that we have no fundamental physical theory as of yet, no complete characterization of behavior at some fundamental level. At the moment, we can’t even rule out the possibility that there is no “fundamental level” in the ordinary sense. H. M. Georgi and others have suggested that physicists may need to give up the Grand Unified Theory model and instead think of themselves as discovering EFTs at ever higher energy scales on an infinite tower of effective theories that contain nonrenormalizable interactions (I might try to offer an accessible summary of some of the ideas here in a future post). I don’t endorse this perspective at all, but I don’t think one should be ruling out live scientific options (even unpopular ones) on purely metaphysical grounds.
First of all, I don’t think this is anthropologically accurate. I have seen a number of cases of (what appears to me to be) confusion in physics (and probably even more in philosophy) engendered by thinking of laws as rules in a sense more robust than what you describe here. I gave one example in this comment, and I could give others if you desire. The reason I brought up the effect of social cognition is that concepts have power. Someone may insist that by “rule” they really just intend the attenuated definition you’ve given, just as someone may insist that by “human” they literally just mean “featherless biped”, but when one tries to redefine established concepts in this way, the original conceptions have an insidious way of sneaking into one’s inferences. Someone tells you Natalie Portman has feathers, and you insist that this is conceptually impossible because she is human and humans are featherless bipeds.
Second, I don’t see how thinking of laws as rules is necessary to establish that the laws are finite. On my modification of Lewis’s view, the laws are the axioms (Lewis himself says “axioms and theorems”, but I think that’s clearly the wrong way to go) of the best deductive system, where “best” depends on some balance of simplicity and strength (and presumably some other virtues as well). These systems will at the least be recursively axiomatizable, and in most actual cases finitely axiomatizable. If not, your system will take a HUGE hit on the simplicity metric. So Lewis’s descriptive view itself gives warrant for constraining the set of laws. We don’t need help from prescriptive intuitions, as far as I can see.
As for the claims about the completeness of physical law, these might correctly characterize the expectations of physicists, but the expectations of physicists are not dispositive in this case. If you look at what’s actually going on in physics, it’s not at all clear that those expectations are being borne out. Our best current theories (such as the Standard Model) are effective field theories. There are two points to be made about this. First, it shows that non-fundamental theories, coarse-grained theories that are only valid when certain conditions hold, can (contrary to your claim in another comment) be accurate and precise enough within their domains of validity to be regarded as basically a complete description of that domain. You said in the other comment that this would be “miraculous”. In so far as the extreme unlikelihood of precise EFTs is a prediction of your viewpoint, it appears to have been disconfirmed.
Second, the prevalence of EFTs highlights the fact that we have no fundamental physical theory as of yet, no complete characterization of behavior at some fundamental level. At the moment, we can’t even rule out the possibility that there is no “fundamental level” in the ordinary sense. H. M. Georgi and others have suggested that physicists may need to give up the Grand Unified Theory model and instead think of themselves as discovering EFTs at ever higher energy scales on an infinite tower of effective theories that contain nonrenormalizable interactions (I might try to offer an accessible summary of some of the ideas here in a future post). I don’t endorse this perspective at all, but I don’t think one should be ruling out live scientific options (even unpopular ones) on purely metaphysical grounds.