I am going to be brief, but there is still much confusion on this grand philosophical dispute, which started when Brad DeLong, as is his wont, said innocently enough about a renowned philosopher: “Thomas Nagel is not smarter than we are–in fact, he seems to me to be distinctly dumber than anybody who is running even an eight-bit virtual David Hume on his wetware.”
I’m not going to recapitulate the whole controversy. But at least some people misunderstood what Steve Landsburg was doing in his response to DeLong. So let me spell out just that subset of the dispute:
(1) In his critique of Nagel, Brad DeLong didn’t merely say, “I find Nagel’s particular argument for the powers of pure reasoning to be a bad example, or to be improperly conducted.” No, he actually said:
Thus Thomas Nagel’s insistence that we need a theory of consciousness that accounts for our reason’s ability to become an instrument of transcendence that grasps objective reality–that insistence falls apart like an undercooked blancmange…Any theory that provided such an account of reason becoming an instrument of transcendence and offering guarantees of grasping objective reality would be hopelessly, terribly, laughably wrong….
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… [Bold added.]
(2) Steve Landsburg took the above passages to mean that DeLong was claiming “that pure reason can never be a source of knowledge,” and Steve explicitly said that perhaps that wasn’t DeLong’s claim. (However, looking at the block quote above, where DeLong is saying we need to run things by the physicists first, he sure does seem to believe that there’s no such thing as knowledge about objective reality, that you can access via pure reason.) So, if that were indeed DeLong’s claim, Steve refutes him thus, with a list of facts about objective reality that you can only obtain via pure reasoning:
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 so on.
Those who are familiar with the methodological works of the Austrian School will recognize that we are here butting up against Immanuel Kant’s categories of knowledge. (Here’s a link that lays out the basics, though I haven’t read it carefully so maybe the writer here is sloppy. But upon a quick glance it looks OK.)
Kant’s system had a two-fold distinction, between analytic/synthetic and a priori/a posteriori. Here are my dumbed-down paraphrases, which a real philosopher in the Kantian tradition may not like: “Analytic” means you can determine the truth or falsity just by analyzing the terms and their definitions. “Synthetic” means the truth value corresponds to something about objective reality, something “out there” and not just coming from human conventions in terminology. “A priori” means you don’t need in your proof to appeal to experience. “A posteriori” means your argument for the bit of knowledge does make an appeal to past sensory experience. Here’s a quick example of how *I* (not necessarily all philosophers and presumably not Brad DeLong) would populate the categories:
Synthetic A Posteriori statements: The sun is hot. (True.) Brad DeLong is very civil. (False.)
Analytic A Posteriori statements: [Empty set. I thought I came up with an example when I was teaching at Hillsdale but David Gordon vetoed it.]
Analytic A Priori statements: A bachelor has no wife. (True.) A bachelor has a wife. (False.)
Synthetic A Priori statements: Every natural number is the sum of four squares. (True, since I trust Landsburg.) All true statements in arithmetic can be proved within an axiomatic system. (False, and I’m sure Landsburg will bite my head off for saying this ungrammatically.)
In Human Action, Mises said economic principles were a priori. However, I don’t think he actually took a stand on whether they were synthetic or analytic. Hans Hoppe in this essay (which I think is really powerful) said they were synthetic, and that Mises’ action axiom solved the mind-body problem. (The guy was productive, what can we say. That’s why they named an Institute after him.)