Metaphysics & mathematics

Edward Feser, An open letter to Heather MacDonald:

Now I have claimed – as a great many other thinkers, both secular and religious, would claim – that philosophy, and in particular the branch of philosophy called metaphysics, is another form of inquiry which is both rational and at least in part non-empirical. It can be thought of as being similar to both empirical science and mathematics in some respects, and different from both in other respects. Like empirical science, metaphysics often begins with things we know via observation. But like mathematics, it arrives at conclusions which, if the reasoning leading to them is correct, are necessary truths rather than contingent ones, truths that could not have been otherwise. That doesn’t mean that the metaphysician is infallible, any more than the mathematician is. It means instead that if he has done his job well, he will (like the mathematician) have discovered truths about the world that are even deeper and more indubitable than the most solid findings of empirical science.

1) The last sentence takes sides in a debate within mathematical philosophy as to the nature of mathematics. A minor point, but I think not trivial.

2) I don’t grant that metaphysics is very analogous to mathematics at all.* There is a reason that powerfully predictive sciences such as physics use mathematics in preference to verbal reasoning. Humans are really bad at reasoning without the formal structure of mathematics. Really bad. Mathematics straitjackets human cleverness, and prevents one from slowly inching toward their preferred conclusion through a sequence of plausible, if not definite, chain of propositions.

Natural science & mathematics know progress. We cede to them pride of place in intellectual disciplines precisely because we see their fruit all around us.  The method of mathematical proof is so robust that Euclid’s The Elements is still used as a textbook today because it is of more than historical interest.  And yet mathematics does move on at the same time, the elementary techniques learned by most students in the natural sciences (e.g., introductory calculus) are no longer of great intellectual interest.

Note: I do on occasion enjoy reading pre & early modern metaphysicians, but only because of their relevance to the history of thought.

* On second thought, perhaps it is analogous. When I was last interested in philosophical apologetics I would run into a fair amount of logical notation. But, the relation is similar to that of particle physics and social physics (i.e., a quantitative understanding of the dynamics of human societies).  I hope that one day social physics can add some genuine value, but it is not even a shadow of what particle physics is.