(MiG Tournament) Physical laws must conform to preconceptions of what is logical

Are mathematically-expressed physical laws complete? What is this debate about? In R1, Pro said, “I will be arguing that just because there exist theoretical models that work mathematically, they cannot be considered to represent actual reality if in doing so they would violate logic.” In my first response I said, “My position is that the only things that rule out a possible physical theory are (a) a contradiction within the theory itself or (b) a contradiction with observation.” The context of the debate underscores the resolution. We had a debate in which modern cosmology, called multiverse theory or string field theory was discussed. Theory is well-developed mathematically, but is currently not proved to be a correct description of how reality actually works. The theory includes concepts that seem incredible, such multiple universes that coexist in different dimensions as bubbles of time and space in a timeless backdrop. Pro argues, essentially, that even though the math works, we can rule out the theory on the grounds that reality must be logical and such a construct is illogical. Separately, others have argued that time cannot extend infinitely far into the past because it is illogical to suppose that an infinity can exist in reality. Again, the math works, but we are obliged to impose additional standards of logic. An old example is interesting because the supposed logic of reality cuts both ways. Is the universe infinite or finite? The logical argument that it is infinite is that if it were finite, there would then have to be something beyond the boundary. However, the argument that there can be no real infinity also applies; if real infinities are impossible, then the universe must be finite. Mathematics allows resolution in ways be cannot imagine: space itself is curved, so the universe can be both finite and yet have no boundary. Keep in mind that we agree that having a mathematical theory that agrees with present observations does not mean the theory is correct. In principle, many theories can agree with current observations, but might need modification when new data shows them limited. As a theory is found to agree with more and more observations, we become more confident of it's ability to make reliable predictions. Pro seems to distinguish between scientific laws and theories. There is no formal distinction. We now know that Newton's Laws of Motion are only approximations, while the Theory of Relativity is more broadly correct. All of science is tentative. It works in the domain where it has been tested. In summary, Pro's position is that a scientific theory can work mathematically, but there is an extra test of logic that lies outside of the math that must be applied before a scientific theory can be accepted. My position is that mathematically correct theories can be accepted without any additional tests, because being correct implies they are completely logical. Pro's Contentions Support the Con Position It is critical to my position that mathematical theories must conform to logic. Pro has been contending that, and I fully agree. Reality also conforms to logical axioms. Logical axioms are the part of logic that is taken as self evident, that things cannot simultaneously both exist and not exist and similar basic assertions. In reality there are physical laws that extend well beyond the logical axioms. These include the laws of motion, the laws of thermodynamics, and so forth. In the mathematical expression of physical laws, these are embodied as non-logical axioms. We demand that both reality and mathematical models of reality be logical overall, meaning that no contradictions can be demonstrated. At this point in the debate, I believe we have established that no theory can “work mathematically” if it violates logic. Logical axioms are universally true, and if a violation is shown by contradiction the mathematics are invalid. Non-logical axioms are defined for the particular type of mathematics (like algebra, calculus, or geometry), and if they are found to lead to a contradiction then the math is invalid. Of course, it's possible to make a mistake and formulate a bad theory, but the means of detecting the error is at hand. It suffices to show it contains a contradiction. In this debate, we have also established that new mathematical systems are invented as required to describe reality. Newton invented calculus to formulate the Laws of Motion, and so forth. This important, because it means that mathematical models can be made of anything occurs in reality. As Pro has insisted, math is logical and reality is logical. That's all that's needed. The interesting part of physical theories relate to the non-logical axioms. These are the postulated properties of the universe. They are expressed in mathematical form to facilitate testing the theory. It's possible that the axioms lead to contradictions within the theory, in which case the theory fails. It's also possible that the theory will contradict an observation of the physical world, in which case the theory fails because it does not work. Argument from Contingency P1. Mathematics is contingent upon logic. Yes, both the logical and non-logical axioms cannot lead to contradictions. There are many different sets of non-logical axioms. P2. The plausibility of physical theories relies upon mathematics. Yes, but this means that both finite and infinite universes are plausible, a multiverse containing bubbles of 3-dimensional space plus time is plausible, spontaneous events are plausible, and a steady-state universe in plausible. All are described by logically-correct mathematical theories. C1. Therefore the plausibility of physical theories is contingent upon logic. This only means that theories including logical contradictions are ruled out, and none of the theories at issue in this debate pose logical contradictions. Therefore contention supports the Con position that if a theory is mathematically correct, it is a plausible description of reality. Nothing external is required for it to be proved logical. Argument from Reality Yes, reality is logical and therefore nothing need be considered outside of a mathematically correct theory to describe reality. This supports the Con position. I think the Pro position confuses logical axioms with non-logical axioms. The logical axioms are the simple rules of logic. They apply universally to math and to reality, but they assert very little of interest. They say that A and B includes A, and other such basic things. They say nothing about whether time or space can be infinite. As I asserted at the outset, a mathematical theory of the universe is plausible if it is mathematically correct, meaning the combination of logical and non-logical axioms pose no contradictions, and it agrees with all of our observations of reality. That is all that is required, because it encompasses all that is relevant. I should clarify that my opening remark about not understanding each other was a joke. But it does reflect the sense of the debate that begs if we are talking about the same subject. I cannot see how Pro's arguments relate to there being something outside of mathematical models needed to describe reality, and Pro claimed I never argued that mathematical models are complete. As I said, it will keep readers alert.