Brad DeLong appears to argue here that because pure reason once led him, Brad Delong, to an incorrect conclusion about which direction he was facing, it follows that pure reason can never be a source of knowledge.
(If that’s not his point, then the only alternative reading I can find is that Thomas Nagel is guilty of choosing a poor example to illustrate a point that DeLong would rather ridicule than refute.)
It would be too too easy to make a snarky comment about how we’ve known all along about Brad DeLong’s tenuous relationship with reason. Instead, here, for the record is a list of ten facts, of which I am willing to bet that DeLong is aware of at least 7 — none of them, as far as I can see, accessible to humans via anything but pure reason:
1) The ratio of the circumference of a (euclidean) circle to its radius is greater than 6.28 but less than 6.29.
2) Every natural number can be uniquely factored into primes.
3) Every natural number is the sum of four squares.
4) Zorn’s Lemma is equivalent to the Axiom of Choice (given the other axioms of Zermelo-Frankel set theory).
5) The realization of a normally distributed random variable has probability greater than .95, but less than .96, of lying within two standard deviations of the mean.
6) If p and q are odd prime numbers then the equations x^2 – q = p y and x^2 – p = q y are either both solvable in integers or both unsolvable in integers, unless p and q both leave remainders of 3 when divided by 4, in which case exactly one of them is solvable in integers.
7) If the Peano axioms are consistent, there are true statements about arithmetic that do not follow logically from them (and ditto for any other system of axioms).
8) The Peano axioms are consistent.
9) Every continuous function from the unit disk to itself has a fixed point.
10) The Heisenberg Uncertainty principle follows from the properties of the Fourier transform.
DeLong concludes with this:
And I cannot help but think that only a philosophy professor would believe that our reason gives us direct access to reality. Physicists who encounter quantum mechanics think very differently…
Really? How would you deduce the uncertainty principle from anything but pure reason? How does he think Dirac predicted the positron?
Hat tip to Bob Murphy who called this to my attention. Gene Callahan comments here.
Edited to add: A more pointed Gene Callahan post is here.