Well, kind of. To be precise, my argument consists of two parts, reasoning from the anti-Platonist assumption that we are capable of logical/mathematical reasoning because it approximates rules for the behavior of physical objects: if I take one apple and then another, then remove the first, then I only have one apple (note that a thorough justification of this, like "because the apple I remove has to be one of the two I put together" requires a logical deduction and thus could not be counted upon if logical rules don't apply). The first part of the argument is to establish that these rules are not just local tendencies of physical nature like that things fall down. Here, I argue that we only evolved to comprehend these rules in a fairly small patch of spacetime but now have the capabilities to observe a vastly larger patch, so if the rules under consideration were to vary we should be able to observe that variation or it would truly be a vast coincidence. If we exclude that possibility because of its low probability then mathematical/logical laws have to at least be physical laws, meaning at least merely properties universal in the physical universe. Here, the second part of the argument comes in, starting from the assumption that mathematical laws are physical laws and bringing in the observation that the driving force of theoretical physics since at least Faraday was the unification of seemingly separate physical laws by exhibiting them as aspects of the same law. In fact, we are at this point pretty well on our way to unifying all physical laws (in a closer sense that would exclude mathematical laws) into one, which is formally given by a mathematical structure, basically a map from the universe into the four-dimensional sphere (that is a bit of an oversimplification, of course). If we now assumed mathematical/logical laws were physical, then we would have two sets of physical laws, very different in character: one properly physical law, which is basically a mathematical structure, and a couple of logical/mathematical laws (I really should invent a term for this, let's say logico-mathematical) laws that would only even give meaning to the properly physical law. That might actually be incoherent, but one could conceivably find a way to make sense of it (though it would be very weird), I'm not sure. But my actual argument is that such a situation would go against the tendency for unification of physical laws I outlined above. Meanwhile, the situation makes perfect sense if we turn it around and assume that the physical universe is a mathematical structure and that thus physical laws are actually mathematical as well. In that case, the entire physical universe is an object in a mathematical "universe" (formally speaking something like an ∞-topos), let's call it T, equipped with a map into the 4-sphere, which induces its physical laws as mathematical structure, and logic as we know it holds in the physical universe because it is the internal logic of the surrounding mathematical universe T. Of course, T itself is an object of a larger mathematical "universe" (formally an (∞, 1)-category) and its internal structure is induced by its position in that universe and so on. That chain never reaches an endpoint, basically due to size issues induced by Russell's paradox, but it does have something close to a fixed point in the ∞-category of (small) ∞-categories, which, up to size issues, contains itself. But that is another story that is not that relevant here.
Less versed in philosophy so lets see if I understand;
Because Mathematical Laws Don't change they must be at least physical laws but all physical laws can only be described mathematically thus what ever math 'is' it is foundational
That's right for the most part. However, the last part of my argument isn't about whether it would be possible to have a set of "properly" physical laws and another set of "mathematical" physical laws describing the former since that could conceivably be made sense of by some analytic philosopher. Rather, I'm saying that, since we assume that we can unify all physical laws (and have for the most part done so), we have to do the same with mathematical and physical laws if we assume mathematical laws are physical. But we can only do that if we assume a further mathematical background.
So is your argument that the perenniality of mathematics indicates it is the underlying structure of the universe?
Thanks for subscribing!
Well, kind of. To be precise, my argument consists of two parts, reasoning from the anti-Platonist assumption that we are capable of logical/mathematical reasoning because it approximates rules for the behavior of physical objects: if I take one apple and then another, then remove the first, then I only have one apple (note that a thorough justification of this, like "because the apple I remove has to be one of the two I put together" requires a logical deduction and thus could not be counted upon if logical rules don't apply). The first part of the argument is to establish that these rules are not just local tendencies of physical nature like that things fall down. Here, I argue that we only evolved to comprehend these rules in a fairly small patch of spacetime but now have the capabilities to observe a vastly larger patch, so if the rules under consideration were to vary we should be able to observe that variation or it would truly be a vast coincidence. If we exclude that possibility because of its low probability then mathematical/logical laws have to at least be physical laws, meaning at least merely properties universal in the physical universe. Here, the second part of the argument comes in, starting from the assumption that mathematical laws are physical laws and bringing in the observation that the driving force of theoretical physics since at least Faraday was the unification of seemingly separate physical laws by exhibiting them as aspects of the same law. In fact, we are at this point pretty well on our way to unifying all physical laws (in a closer sense that would exclude mathematical laws) into one, which is formally given by a mathematical structure, basically a map from the universe into the four-dimensional sphere (that is a bit of an oversimplification, of course). If we now assumed mathematical/logical laws were physical, then we would have two sets of physical laws, very different in character: one properly physical law, which is basically a mathematical structure, and a couple of logical/mathematical laws (I really should invent a term for this, let's say logico-mathematical) laws that would only even give meaning to the properly physical law. That might actually be incoherent, but one could conceivably find a way to make sense of it (though it would be very weird), I'm not sure. But my actual argument is that such a situation would go against the tendency for unification of physical laws I outlined above. Meanwhile, the situation makes perfect sense if we turn it around and assume that the physical universe is a mathematical structure and that thus physical laws are actually mathematical as well. In that case, the entire physical universe is an object in a mathematical "universe" (formally speaking something like an ∞-topos), let's call it T, equipped with a map into the 4-sphere, which induces its physical laws as mathematical structure, and logic as we know it holds in the physical universe because it is the internal logic of the surrounding mathematical universe T. Of course, T itself is an object of a larger mathematical "universe" (formally an (∞, 1)-category) and its internal structure is induced by its position in that universe and so on. That chain never reaches an endpoint, basically due to size issues induced by Russell's paradox, but it does have something close to a fixed point in the ∞-category of (small) ∞-categories, which, up to size issues, contains itself. But that is another story that is not that relevant here.
Less versed in philosophy so lets see if I understand;
Because Mathematical Laws Don't change they must be at least physical laws but all physical laws can only be described mathematically thus what ever math 'is' it is foundational
That's right for the most part. However, the last part of my argument isn't about whether it would be possible to have a set of "properly" physical laws and another set of "mathematical" physical laws describing the former since that could conceivably be made sense of by some analytic philosopher. Rather, I'm saying that, since we assume that we can unify all physical laws (and have for the most part done so), we have to do the same with mathematical and physical laws if we assume mathematical laws are physical. But we can only do that if we assume a further mathematical background.