Over the last couple of days I have realized that the laws of physics are rather more complex than they seem. The lovely equations like G = 8πT and F = Gmm′/r2 (with a different G in the two equations) seem to be an iceberg most of which is submerged in the icy waters of the foundations of mathematics where the foundational concepts of real analysis and arithmetic are defined in terms of axioms.
This has a curious consequence. We might think that F = Gmm′/r2 is much simpler than F = Gmm′/r2 + Hmm′/r3 (where H is presumably very, very small). But if we fill out each proposal with the foundational mathematical structure, the percentage difference in complexity will be slight, as almost all of the contribution to complexity will be in such things as the construction of real numbers (say, via Dedekind cuts).
Perhaps, though, the above line of thought is reason to think that real analysis and arithmetic are actually fundamental?
9 comments:
@Alex, Hi Dr. Pruss, I have got a question, I agree that there is necessary being existing, but how can we know it is God for certain? Why does necessary being has to be a mind and not a system of nature, maybe laws of nature?
By the way I am inspired by your work and I have been following you for nearly 6 months, I am grateful for what I have learned from your articles. Have a good day sir.
I think one must also acknowledge the "greater complexity than first appears" in another direction as well. If mathematical foundations are the base of the iceberg, the physical (observable) definitions of all the variables are the superstructure that must be put on top to turn a merely mathematical abstraction into a description of the concrete. E.g., a 3 dimensional vector could describe a real spatial direction in our universe or describe some feature of an abstract "space" based on some other system, like an economic data analysis or outputs from an electronic device. Without a set of definitions clearly mapping pronumerals to observables (or statistical facts about observables in QM), we don't have a Physics theory at all.
Thus, even without considering the problem of the qualia, a scientifically valid theory can never be strictly reducible to a TOE, with or without the necessary substructure to which Professor Pruss refers.
However, I think that when considering questions of complexity vs simplicity, it is reasonable to consider different levels separately and acknowledge that each level really is distinct, with its own "integrity of elegance", if that makes sense.
Thank you sir, I have a thought about this topic, if this necessary being is a mind, then it is basically god. Is there anyway to prove that necessary being is a mind. And I got a radical alternative for God as necessary being which is laws of reality, and this view says that laws can cause something or be the explanation of something so it can replace gor as necessary being. I am theist but I like certainty sir, so can we say that if there is a necessary being it is a immaterial mind?
HM: The laws of nature are not a plausible candidate for a necessary being. There is too much that looks random and arbitrary in the laws of nature--like the exact values of various constants, the number of dimensions of space, etc. It seems a lot more plausible that a mind chose the laws of nature.
Fr K:
Our theories do have this extra complexity, but I am not sure it affects the fundamental laws very much, because the fundamental laws will be formulated in terms of the fundamental (and indefinable) properties--say, charge.
Thank you Dr. Pruss, sorry for asking this on this post, I am new in this blog. You said that laws of nature is not a good candidate for a necessary being which I definitely agree but I've got this question, can something other than God be the necessary being like a necessary system(I call it necessary system, which I made it up but it is usually same as God but one of the differences between this system and God is this system does not have a mind or is not a mind), for last 1 year I am a bit skeptic about anything so I consider some of the lowest possibilities as they can happen, I think that God is more plausible than anything but I want to know it for certain sir, how can we be certain about necessay being is an immaterial mind?
By the way sorry for any misunderstandings Dr. Pruss, my main language is not English and I am sick these days so my brain does not function well these days.
Have a good day.
Dr. Pruss do you have any preferred arguments, articles about the gap problem, I have been searching for an argument and lot of them haven't satisfied me, I am looking for one that shows why necessary being has to be immaterial mind rather than a transcendent necessary being which is not mind but still can cause the universe, I would be very happ if you help me sir.(btw I agree on omnipotency for necessary being).
Hope you have a good day.
I think this might actually be a strong argument for Platonism. Given Platonism, there is one true mathematical structure, according to which F = Gmm′/r2 (hereafter F1) is simple and F = Gmm′/r2 + Hmm′/r3 (hereafter F2) is not. So F1 is much more probable given Platonism than F2. That is to say, Platonism actually predicts F1 rather than F2. The fact that more and more precise measurements continually confirm F1 over F2 means we keep getting evidence of Platonism.
Hi, I watched your videoes about Grim Reaper Paradox and Contingency Argument few months ago, can I ask you a question about the Gap Problem sir?
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