On Physics Borrowing from Mathematics and Metaphysics

The first inquiry into nature began in opposition to metaphysics. Aristotle took it on himself to show that a science of nature was possible, contra Plato and Parmenides. In order to found the science, Aristotle had to borrow various terms which belong to metaphysics. When these terms are used in the context of physics, the terms are natural, and not metaphysical (the “act” and “potency” used in the definition of motion are borrowed, but in physics they only extend to mobile being, not to being as such).

The second inquiry into nature began in opposition to Aristotle’s physics. The metaphyscial objections of Parmenides no longer bothered anyone, and so no one particularly cared about borrowing various metaphysical terms to explain natural things. The interest was instead on extending the scope of mathematical physics, which advances by borrowing truths from mathematics. When used in the context of the science of nature, the truths are natural, and not mathematical, as Aristotle himself showed in the second book of his physics.

(in calling these two approached “first” and “second” I am stateing a purely contingent fact. It simply happened that one science developed before the other. The two inquiries into nature are so distict that Galileo could have very well written before Parmenides. There is nothing in mathematical accounts that make them dependent on previous metaphysically-borrowed accounts. One does not need to know about matter and form and causes in order to measure the rate of a free fall.)

In both cases, the benefit and the danger of borrowing is the same: certitude. Mathematics and metaphysics are characterized by a certitude that is simply not possible to attain about natural things as such. Both mathematics and metaphysics deal with immobile things, but nature is essentially mobile. Nature cannot exist apart from a part that is unintelligible to us. The certitude of both goes bad in different ways: on the one hand, we cannot spin out all truths about natural things simply by meditating on their definitions, on the other hand we cannot imagine that nature is really nothing but the clarity of mathematical formulae and laws. Both borrowed sciences confer a benefit that the other one fails to provide: metaphysics allows us to say some really unchangeable and categorical statements, but only about nature in general; mathematics gives us an operable and predictive knowledge of the concrete things in nature, but only a hypothetical knowledge.

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3 Comments

  1. alan said,

    July 27, 2008 at 10:09 pm

    Nature is not “essentially mobile”. Ens mobile is more properly ‘ens in quantum mobile’ for every mobile presupposes an immobile substrate. Nor is physical being outside of being–the being common to substance and the categories is, according to Aquinas, the *subject matter* of metaphysics, and God is the *principle* of the subject matter. Cf. Thomas’s Commentary on Boethius’s De trinitate. If, as you seem to suggest, being as such were unintelligible prior to the discovery of immobile being, then ‘being’ in the premises of the proofs for the existence of God would mean ‘material being’. Since nothing can be in the conclusion of a syllogism that isn’t in the premises, God would be “material being” which is absurd. Further, act and potency divide being. That we discover this in material being does not make material being unintelligible precisely as being. It is true that in the Summa contra gentiles I, 12, St. Thomas writes that: “For, as it is said in the Metaphysics IV, if there is no knowable substance higher than sensible substance, there will be no science higher than physics.” This doesn’t say that God is naturally known prior to our knowledge of the being common to substance and the categories, it says that were there no substance higher than sensible substance there could be no metaphysical science. This is precisely the inference that is required if there is a metaphysical demonstration for the existence of God as cause of the being common to substance and the categories…

  2. a thomist said,

    July 28, 2008 at 4:08 am

    This is a real puzzler. As far as I can figure out, you think that when I said “Physics first developed in opposition to metaphysics” I meant that Physics involved the denial of metaphysics, or that it was completely unrelated to it. You say “if, as you seem to suggest, being as such were unintelligible prior to the discovery of immobile being…” I must be suggesting this in a very mysterious way, since the whole point of that paragraph and even the post was to show that physics can borrow from metaphysics to attain a great deal of its certitude, which presupposes the intelligibility of being, right?

    This borrowing need not be straightforeward and simple. We can use parts of another science without recognizing them as such, we can develop an entire science and then realize that parts of it are better placed in another science, we can develop different parts at different times, etc. It’s simply not the case that we develop every scince from the beginning using only principles proper to the science. It’s messier than that. Aristotle’s great genius was for seeing where everything belonged. He used act, potency (for example) in physics, but he gave no treatment of them as such in physics, but in book IX of the Metaphysics.

  3. alan said,

    July 28, 2008 at 12:19 pm

    In re: “since the whole point of that paragraph and even the post was to show that physics can borrow from metaphysics to attain a great deal of its certitude, which presupposes the intelligibility of being, right?”

    I am happy to discover, then, that I have misunderstood! Because I am in utter agreement that certain of the judgments in the Physics are implicitly and actually of metaphysical import.

    So, three cheers for your fine clarification!


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