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

Accepting preconceptions rejects most of the modern physics proved true The debate is about “preconceptions of what is logical.” For example, Pro believes that it is not possible for an actual infinity to exist because for such to exist would be illogical. Pro claims a scientific theory allows space or time to extend to infinity must be rejected without regard to other evidence of the truth of the theory. I gave several examples of scientific theories that appear to deny logic. “Logic” seems to demands that one can always go faster, yet the speed of light is an upper limit. It seems if space were bounded there would have to be something beyond the boundary, and hence no possibility of space being finite. Science nonetheless proved theories that defy apparent logic are true. So the problem for the Pro position is to determine what appears to defy logic from what actually defies logic. Pro did not respond to my examples with claims of their being within the bounds of our ordinary logic, nor did he deny the well-established science of them being true. Pro cites Hilbert's paradox as an example of a preconception of logic that ought to trump any physical theory involving countable infinity. However, Pro's reference [R4.2] says. “[Hilbert's paradox and the like] demonstrate a paradox not in the sense that they demonstrate a logical contradiction, but in the sense that they demonstrate a counter-intuitive result that is provably true...” Thus Pro is asserting that if something is counter-intuitive but provably true, it must be rejected nonetheless. Much of modern physics –virtually all of relatively and quantum physics-- is counter-intuitive but provably true. Relativity and quantum physics are both mathematically consistent and verified as accurately modeling the real world. Pro makes a distinction between a potential infinity and an actual infinity. There is no such distinction known to mathematics. Mathematics is invented to describe the real world, as Newton invented calculus to derive the laws of motion, yet no mathematician or scientist has invented a mathematics that deal with actual infinities. The distinction is no more than than the bounds of human intuition. Consider calculus, which depends upon the limits of infinitesimally small quantities as they approach zero. We do not insist upon a distinct actual calculus in which the limits are never reached and then demand that the laws of motion be rewritten with actual calculus. Nor do we reject the laws of motion on the grounds that calculus fails a test of intuition. Resolving Zeno's Paradox of Motion depends upon an actual infinity. Ssuppose a very fast runner—such as mythical Atalanta—needs to run for the bus. Clearly before she reaches the bus stop she must run half-way, as Aristotle says. There's no problem there; supposing a constant motion it will take her 1/2 the time to run half-way there and 1/2 the time to run the rest of the way. Now she must also run half-way to the half-way point—i.e., a 1/4 of the total distance—before she reaches the half-way point, but again she is left with a finite number of finite lengths to run, and plenty of time to do it. … And now there is a problem, for this description of her run has her traveling an infinite number of finite distances, which, Zeno would have us conclude, must take an infinite time, which is to say it is never completed. [4. http://plato.stanford.edu...] To simply walk across a room, an actual infinity of decreasing finite distances must be traversed. It is done without a problem. Perhaps calculus students have just not developed the intuition to appreciate the truth underlying the infinitesimals of calculus? I don't think that's the case. Mathematics is accepted because it is both logically consistent and useful. The paradox of Hilbert's Hotel is that all of the infinite number of rooms are full, yet there is room for infinitely more guests. We have no intuition about how that works, but it obeys the rules of logic. Mathematics using the concepts of infinity work to provide results that accurately describe the real world; If we adopt the resolution, we must reject most of modern physics despite it's having been proved true. The correct approach is to not impose preconceived notions of what is “logical,” meaning intuitive, but rather to rely entirely upon actual logic. This allows counter-intuitive theories to stand or fall on their merits and not upon limits of human intuition. Any logical theory ought to be allowed We insist that both the real world and mathematical models of the real world obey logical axioms. Logical axioms are basic logical principles, such as (A and B) must contain A. A mathematical system, such as calculus or geometry, combines logical axioms with non-logical axioms. A non-logical axiom is like the associative rule for integer mathematics. The combination of logical and non-logical axioms cannot be proved to be self-consistent, but it can be disproved by finding even a single case that leads to violation of a logical axiom. Pro spent much effort in R2 and R3 arguing that mathematics has this high level of logical certainty. He's right, it does. That supports relying upon it as the basis of physical modeling. To form a theory of physical science mathematics must be tied real world. Since mathematics is logical and the real world is logical, mathematics can always be derived to model the real world. Mathematics includes statistical models that allow the world to be described without it being deterministic. Mathematics is only a tool for describing the world, but once a mathematical system is formulated it can be tested for logical consistency. With the mathematical systems at hand, physical theories are formed that attempt to accurately model the real world. Physical theories require knowledge of the real world. If the mathematical model of the real world disagrees with an observation, the theory is proved wrong. We have a great deal of data about how the physical world behaves and scientists work to make mathematical models that agree with all that is known. A theory that agrees with all that is known can then be used to predict new results. Validation of the results derives from consistency of new observations with predictions of the theory. The reason that any mathematically valid theory ought to be allowed as plausible scientific theory is because such theories have a high certainty of obeying the logical axioms and also being logically consistent. Rejecting theories on grounds that they are counter-intuitive limits science to what humans can imagine. It would reject much of modern physics already proved true. Of course, we agree theories must always be proved consistent with observed data, and proving part of a theory does not prove all of it. Debate Issues Pro set out In R1 to prove, “.. 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.” He then argued in R2 and R3 that mathematical models are logical and that they describe a real world that is logical. In those rounds, he did not give a single example nor did he argue how a theoretical model that works mathematically can fail represent reality. His example, Hilbert's Hotel Paradox, and accompanying argument were presented in R4. But Pro's debate rules given in R1 say that no new arguments can be presented in R4. I rebutted the new argument –being counter-intuitive is not a logical paradox-- but I could have just pointed out that only the Con case had been supported in R2 and R3, and that Pro had not made a prima facie case at that point. The resolution is negated.