Fred

Dude, were you by any chance referring to this article? "Our Cultural Value-Deprivation" (published in The Voice of Reason) is referenced; specifically, Ayn Rand's approval of Chomsky's method of arguing against Skinner: Footnote 3 of that article is also relevant.

I believe the relevant article is "The Question of Scholarships" from The Voice of Reason. The idea is that you can morally accept scholarships or grants coming from taxpayer money only if you are not an advocate of taxation.

Primary source: Introduction to Objectivist Epistemology. You'll want to check out the appendix sections on mathematics and the philosophy of science. I can barely get through a page of this book without rolling on the floor, it's so good. I recall some tantilizing ideas in OPAR about the relationship between mathematics and concept-formation. Ron Pisaturo and Glenn Marcus have written some outstanding articles on the philosophy of mathematics. Mr. Pisaturo lists the articles on his website. Highly recommended. Leonard Peikoff and David Harriman are doing exciting work on induction in physics, book forthcoming. Have I missed anything?

CF's explanation of Goedel's theorem is good. More concisely, the incompleteness theorem (as strengthened by Rosser) states that any formal system including first-order arithmetic is either inconsistent or incomplete. CF is also correct to point out that the Goedel sentence does not actually say "I am false," as in the liar's paradox, but rather: "I am not a theorem of the present formal system." Or: "I am not a consequence of the axioms and rules of inference you have chosen." Because of the clever machinery he introduces to accomplish the self-reference, Goedel seems to sidestep our objections to the liar's paradox. I studied this theorem two years ago as the culmination of a course in mathematical logic -- before I was familiar with the Objectivist epistemology. Due to its importance for the theory of computation, I plan to revisit it in the near future. (I am currently scrutinizing a closely related topic, the undecidability of the halting problem.) Like Heisenberg's "uncertainty principle," Goedel's infamous theorem may well be a true statement about reality which is merely widely misinterpreted due to bad philosophy.

I'm glad you brought this up, Tom. The liar's paradox warrants special attention. A proposition cannot be both true and false at the same time, because a contradiction cannot exist. But, as David's example demonstrates, there's such a thing as a bad proposition. The proposition in question is invalid because it is detatched from reality. To what does "this statement" refer? Coming to grips with self-reference is crucial for my research into the foundations of mathematics and computer science. For instance, the liar's paradox is the basis for Goedel's incompleteness theorem.

Thanks for the welcome, Ash. I plan to contact ARI soon; I'm hoping to start the club along with the spring semester. It's great to have all this help!

Hi gang. I've been lurking for a couple of weeks, and I like what I see. I'm a doctoral student at Georgia Tech. My field is operations research. If you've never heard of OR, just think "math that Dagny Taggart would use" -- for example, to determine a train schedule which satisfies customer demand at minimum cost. Operational problems can get really complex, and many billions of dollars are riding on methods for the solution of various types of problems. I finished an undergraduate degree in mathematics from Duke last year. It was at Duke that I first heard about Objectivism. The first couple of years I was kind of gradually coming around to it, and then 9/11/01 really woke me up: ideas matter; bad ideas kill. From then on I was involved with Duke Objectivists (ably led by Alex Epstein, who you may recognize as a writer for ARI and TIA). Interests of mine relevant to this group include: (Re-)starting an Objectivist club here at Georgia Tech. (It seems that a previous club ran out of steam around 1998.) Applying Objectivism to mathematics and (partly by extension) to theoretical computer science. I'm also a classical pianist, and I'd love to talk about music.