The “Lewis proviso”: thoughts on the role of metaphysics and the possible role/relation concerning mathematics

David Lewis has a phrase which goes something like “we [as philosophers] should be on the side of physics, but not take sides within physics”.

 This is a very noble and difficult position to have; but face it; we will be dead in a hundred years, and scientific developments will continue as always. My eye is on Kant here; Kant’s transcedental aesthetic fails because of a little thing called non-euclidean geometry. Kant believed that our belief that space was infinite and boundless is a priori necessary…hmm, ‘fraid not Immanuel.

Despite this; I think metaphysics is very important; and we need to accomodate for scientific developments as much as we can. Metaphysics isn’t science (contrary to some philosophers in my department); but the two are supposed to depict the same world of experience (metaphysics of a world of experience? That would sound absurd to many!)

Let me give a paradigm case in Mathematics:

We grant that some of the oldest platitudes in mathematics are true; like Pythagoras Theorem; or (almost entirely all of) Euclid’s elements; yet during the time these mathematical truths were thought of and agreed upon, they believed in superstitious absurdities, socially deleterious nonsense and things which are just plain false! Pythagoras the philosopher may have been wrong; Leibniz the philosopher may have been wrong. But Leibniz the Mathematician, Newton, the Mathematician, Pythagoras the Mathematician…were hitting on a reality so beyond their contemporamous knowledge of empirical science and theoretical physics that they went beyond knowledge and hit upon the realm of indisputable truths and platitudes; the so-called “book” that Erdos referred to. [Destre]

Perhaps Destre has just shot me in the foot; Destre referred to Mathematics as the paradigm science of reason over experience…NOT metaphysics. Destre sometimes suggests there isn’t a real different; or rather, that one should survive, and not the other…and he doesn’t think mathematics is ever going to die…

I’m optimistic that metaphysics is possible. Kant (rightly) points out the thirst for knowledge that humans have, so thirstful that we are too pretentious for our own good to even come close to fulfilling those pretentions. The Kantian programme I am okay with; despite that; I think the Lewis Proviso should assert two things

  1. The independence of Metaphysics from Empirical Science
  2. The openness of Metaphysics to be refined or not contradict, or not make assertions regarding the domain/discourse of Empirical science

But here are some hard questions I can’t answer:

  1. Is metaphysics superior to mathematics?
  2. Is mathematics a reduction of metaphysics to its fundamental primitives?
  3. What is the relation to metaphysics and logic; and better still; metaphysics to mathematics? (corollorary question: mathematics and logic)
  4. Kant’s ultimate question: Is metaphysics possible?

These are all hard questions



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