Sigh. Glancing through Chapter 22 of my Gödel book late last night, my eye was caught by a sentence on p. 197. I stared in disbelief. It says that ACA0 is the second-order theory you get when you restrict the φ(x) we can substitute into the Comprehension Scheme to those which lack second-order quantifiers. That’s fine. But there in four black and white words it also says — as if it is the same thing — that the φ(x) must belong to LA (the language of first-order arithmetic). Which is of course plain wrong. The φ(x) might contain second-order free variables/parameters.
Aaargghh! How on earth did that stray false clause get in? Checking an earlier version of the book, it wasn’t there: so it must have been a later ‘helpful’ addition!
The psychology of this kind of “thinko” (I can hardly plead that it is a typo!) is intriguing. How is it possible to write, and then no doubt let pass on another reading or two, something you know perfectly well to be false? Sigh.
1 thought on “Staring in disbelief …”
Hi Peter. I know how painful these things are, but reading your post I couldn’t help being reminded of this: http://www.youtube.com/watch?v=Bak28KYLIgc
The psychology of thinkos is certainly intriguing. What’s particularly interesting is how one’s ability to spot them shoots up once they are in print and uncorrectable. One reads with quite a different eye.