Paradoxes

I have recently been reading 2 books by Bertrand Russell – his autobiography, and his Introduction to Mathematical Philosophy. The former is fairly interesting; I find it nice to be reminded that even fantastic academics/thinkers are human and have ‘issues’ [innit].

Having said that, these are not always so usual…I’m also reading “Phantoms in the brain” by V.S. Ramachandran [alternative title “The Man who Mistook His Foot for a Penis”] and there’s a great quote in which Crick (of DNA fame) asks Ramachandran for advice on making his book more accessible to the lay person:
“I say, Rama,” Crick said with exasperation, “the trouble is, I don’t know any lay people. Do you know any lay people I could show the book to?”

What a long aside. So the latter is quite interesting but largely stuff I know but in a wordier format which doesn’t really suit me anymore but might be useful when I forget these things. The autobiography has just passed Russell’s first mention of his struggle with paradoxes, specifically a version of the ‘liar paradox’.

By coincidence I happened to pick out a book (Vagueness & Contradiction by Roy Sorensen; less coincidental) and a particular page in this book (more coincidental) pointing out Russell had originally made an error in his transcription of this paradox, one which was later corrected (by a guy who noticed the error quoted in The Man Who Loved Only Numbers…the trail of books gets ever longer :D). The error was as follows:

1a) The 2nd statement is false
2a) The 1st statement is false

In the version I have the paradox is:

1b) The 2nd statement is true
2b) The 1st statement is false

If 1a is true then 2a is false. If 2a is false then 1a is true. [no paradox]
If 1a is false then 2a is true. If 2a is true then 1a is false. [no paradox]

If 1b is true then 2b is true. If 2b is true 1b is false. [paradox]
If 1b is false then 2b is false. If 2b is false 1b is true. (if 1b is true then…) [paradox]

1a and 1b are interesting because it seems perverse to arbitrarily assign different truth values (i.e. truth or falsehood) to two tokens (instances) of the same sentence in the absence of a good reason. But 1b and 2b are a proper paradox (propa innit…doing this makes it more accessible right?) in that, it is absolutely not clear how one might solve the problem. Now, I’d love to offer up a succinct thesis as to the solution to this problem…but although I do have ideas (evolutionary epistemology to name drop, oh hohoho how we chortle :p) I have neither succinct ideas nor a proof so I can’t…but err, well I haven’t blogged in a while and this is one of a few things that I’ve thought about and which coexists with the things one might put on a blog. I might put up some paradoxes with solutions (so not real paradoxes) at some point because they also interest me :).

Unfortunately my reading is interrupted by that whole work thing I’m doing, so I actually wrote most of this blog last week I just didn’t get around to finishing it until now…hohum. At some point I'm sure I'll get to Russell's whole issue about books containing all the books (but what book {insert shock face} may contain that book, and that book and that book...)...I dunno if you call it philosophy or maths (or 'dull shit that no one cares about')...I quite like it sometimes :).