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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.

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Dinesh Does Cosmology

Dinesh D’Souza has discovered the Anthropic Principle, after reading an article in Discover magazine.

It’s nothing we haven’t seen before, just more God-of-the-gaps:  “Here’s something we’re having real trouble understanding. Must be the hand of God!” Dinesh does not follow through with any of the further inquiries that arise in an unbeliever’s mind, e.g.:

  • Which God? Thor? Vishnu? Allah? Unkulunkulu?
  • Why only one God?
  • Who fine-tuned Him?
  • How come He waited a quarter million years to intervene in human history?
  • Is it your recommendation that these cosmologists cease their inquiries and their theorizing, shut up their labs, sell their equipment on eBay, and sign up for Divinity School? I mean, since the answers to their questions are already known? Will you make this recommendation in public? Or is it your intention to just sit there with a knowing smile on your face while the cosmologists pursue their futilities, until the day when they finally throw up their hands, say “Gosh dang it, you believers were right all along — it’s the hand of God!” and mail off for the Div. School application forms?
  • Etc., etc.


Dinesh’s piece does, though, illustrate that other gap that plagues us:  the gap between the curious, skeptical thought style of the empiricist (Wow, the universe sure is a weird place! Wonder if we’ll ever understand this? Good luck to those guys trying to figure it all out!) and the person of faith (Those guys are blind fools fumbling in the dark! It was all revealed to us long ago! Why can’t they see?)

That gap is at least as challenging as figuring out why the Fine Structure Constant is what it is and not some other number.

My own view of the Anthropic Principle is awestruck wonder at the inexplicable fact that my legs reach so precisely from my hips to the floor. What if they were an inch shorter?


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