So I read DeLong as arguing Nagel is wrong because he thinks reason gives us some kind of transcendental access to objective truth. He writes (paraphrasing Nagel): "My mind is in immediate contact with the rational order of the universe!... I abandon the belief that I am going south-southwest because my reason's transcendent grasp of objective reality makes me know with certainty that it could not possibly be true!"
It is the foundationalism of Nagel's approach to reason that bothers DeLong, not the mere fact that he used reason!
Landsburg doesn't address this criticism at all. He simply notes that we reason about things that we have no empirical access to (unlike the sun rising, which we reason about and then observe). He provides a list:
"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..."
And then gives us five more along the same lines.
Right to all of them (I'm trusting Landsburg on Zorn and a few others I don't know myself). Landsburg shows we reason abstractly too.
So? What's his point exactly? Does he think Brad DeLong doesn't think we reason abstractly? Or that reason is useless? I guess that's what Landsburg is arguing, but I've never seen Brad say anything like that.
And what does Landsburg think of the claim that this list is just a set of results that we get out of applying the rules of word games that we've developed? They are "right" and "true" in the context of the logic of that word play (the rules of mathematics that we set up, etc.) but not in any objective sense outside of that word play. Except, of course, insofar as that word play seems very useful for describing the universe, whether you're a physicist or an economist. But once we get into description of the universe, of course, we move into the territory of our frail faculties (as if some of our mathematical brains weren't frail enough!) and we are still not connecting to any "objective" or "transcendent" reality.
Landsburg heroically stakes the claim that internally consistent logical structures like mathematics have "right" and "wrong" answers.
So who exactly disagrees with that?
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