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Thomas Aquinas is famous for making his 5 arguments for the existence of God. Arguably the weirdest of them is the Argument from Degrees.

As far as I understand it, the basic premise of the Argument from Degrees is "If there are two things that have some property to a higher and a lesser degree, there has to be a thing that has that same property to the maximal possible degree.". But isn't that implying that the Third Law of Thermodynamics is false? I mean, let's say the property in question is coldness. Some things are more cold than others. But, per the Third Law of Thermodynamics, there cannot be a maximally cold thing, the temperature of 0 Kelvins cannot exist.

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  • Yes. For another example, let me define f(x) = -x for any positive real number x, and f(x) = -1 for x <= 0. There is no real number x that maximizes f(x); you can get as close to 0 as you wish but never reach it.
    – causative
    Jun 20 at 21:27
  • The third law only precludes reaching absolute zero by thermodynamic means, because it is approached asymptotically. It can, in principle, be achieved by other means, as far as we know. Moreover, the "asymptotic approach" is a mathematical fiction, arbitrarily small deviations are physically meaningless. Aquinas is talking about concretely realizable properties rather than artifacts of mathematical models. His premise can be countered, but this is not a good example.
    – Conifold
    Jun 20 at 23:36

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Technically, there is no direct contradiction because the two principles operate in distinct domains: metaphysical properties versus physical temperature. The argument from degrees is akin to the concept of completeness in mathematics, but the "things" in your quote, "If there are two things that have some property to a higher and a lesser degree, there has to be a thing that has that same property to the maximal possible degree," refer to properties in a metaphysical or qualitative sense such as goodness or truth.

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