# In the dunce’s corner …

I’m spending a bit of quality time in the dunce’s corner, having dashed off a ‘solution’ to a problem in propositional calculus (yes propositional calculus, for heaven’s sake) over at math.stackexchange and got it quite wrong. And as fate would have it, I was off-line for a while, staying over with my aged mother, so couldn’t quickly delete it. Ho hum. So much for totting up “reputation points” eh?

OK: here’s the problem for you (from Enderton’s Math Logic book): let # be the three-place connective such that #(A, B, C) is true so long as the majority of A, B, C are true. Show that {#, ¬} is not an expressively adequate set of connectives.

Knowing I’m quite capable of that sort of thing makes the business of doing a final read of  Gödel 2 for thinkos a bit fraught. Even at this last minute stage I’ve found a silly omission. Ah well ….

Still, there are mistakes and mistakes. I had occasion a couple of days ago to look at James Robert Brown’s Philosophy of Mathematics where he makes a complete hash of understanding why the Intermediate Value Theorem is non-trivial (no, a diagram does not cut it). I was wondering about whether to bang on about that here, when — by one of those coincidences — I came across the ever-excellent T.W. Körner‘s Companion to Analysis where he takes a sideswipe at Brown: “The author cannot understand the problems involved in proving results like the intermediate value theorem and has written his book to share his lack of understanding with a wider audience.” Körner than proceeds to give a presentation which should be enough for most readers to work out (at least some of) what’s gone so wrong in Brown’s discussion. Job done.

This entry was posted in Logic. Bookmark the permalink.