Land of Diskgrinder: November 2006

Saturday, November 04, 2006

edited the depression, a cold front for a warm back

well, I edited this peice of navel-gazing (as opposed to naval-grazing, which is eating ship lawns), as it was deeply black-dog in outlook (that fucker bit my heels for a whole year) and ultimately unrewarding, either for you (dear reader) or me (cheap writer). Damn, you only get that joke if you were born before the Singularity

Cod philosophy. For the following I will remind you of: self referencing sentences; the Epimenides' paradox; Russell's paradox; and maybe a bit of Cantor's diagonal argument vs. Jazz Butcher (though not yet).

Self reference: this statement refers to itself
Epimenides: this statement is false
Russell: what set does the set of all sets that don't contain themselves belong to?
Cantor Jazz Butcher: some infinities are bigger than others; when one gets up, goes out of the room, it gets replaced by another

So I have two self-referencing questions, the answers to which are always yes or no because they ask if something has a property (and that's the only choice you get), but the trick is that they ask if they themselves have a particular property - for example "is this question written in English?". 1 is the definition of yes; 2 is the pathological (in the epiminedes/russell sense) definition of no

is the answer to this question affirmative? - answer yes, and the question answers itself, in a way that can't get more affirmative
is 'the answer to this question negative? - answer no and you're lying, answer yes and you're wrong

2 is more interesting because I could always answer no to 1, but 2 circles recursively. Then I'll enumerate the set of all questions and show that there's always one question not numbered (not in the set of all questions, but still a question). Haven't worked this bit out yet, which is where Cantor comes in. Can't quite work out whether I'm taking the piss here. "Is it sugar?"