Gödel, Escher, Brock, Part 2
Chatterbox continues to wrestle with the question of whether David Brock's lurid confessions might be true. As he explained yesterday, it all boils down to Kurt Gödel's Incompleteness Theorem, which translates paradoxical statements like "Everything I say is a lie" into the language of mathematics. With a little manipulation, though, the Brock Paradox can be rendered soluble. Or can it?
We take for our text a purported solution to the Liar's Paradox (as it was known to the Greeks) by David Tribble, a software engineer in Plano, Texas. Tribble works off the following version of the Liar's Paradox:
Epimenides is a Cretan.
Epimenides states, "All Cretans are liars."
Chatterbox thinks a fair summary of David Brock's article, "I Killed Anita Hill (I'm Sorry)," in the August issue of Talk and, very likely, the forthcoming book (Blinded by the Right) from which it is excerpted, would be as follows:
Brock is a conservative.
Brock states, "All conservatives are liars."
Using this template, we can now put the Talk piece through Tribble's solution, which assumes that there is more than one Cretan, and that Epimenides is a liar. In Tribble's proof, Chatterbox has substituted "Brock" for "Epimenides" and "conservatives" for "Cretans." Thus:
P. 1 Brock is a conservative.
P. 2 Brock is either a liar or a truth-teller.
P. 3 His statement is either true or false.
And now we start dropping in Tribble's assumptions:
P. 4 There is more than one conservative.
P. 5 Brock is a liar.
P. 6 Thus Brock's statement is false.
P. 7 Thus "All conservatives are liars" is false.
P. 8 Thus not all conservatives are liars.
P. 9 Thus some (one or more but not all) conservatives are not liars.
P. 10 Thus at least one (but not all) of them is a liar.
P. 11 Thus Brock, a conservative, could be a liar.
Problem: Although Brock was still describing himself as a conservative when he began his confessional jag three years ago, the subtitle of his forthcoming book, inconveniently, is The Conscience of an Ex-Conservative (a play on the title of a famous book by Barry Goldwater). Thus we need to reformulate the paradox as follows: