Paradoxes

[Abhishek Makkar]

Lets discuss the paradoxes we know, let me start with the one i like the most:

I am lying.

-Abhishek

[Peter van de Riet]

My personal favorite is Bertrand's paradox. Whenever somebody is talking about random, I ask him/her about this one. This leads always to some nice discussions, which I like.

[fred rosenberger]

I like the one where Ben Casey meets James Kildare.

[Stan James]

Much of the math in Goedel, Escher & Bach went over my head or has since leaked out, but I think I remember that Goedel's contribution was to prove you can write "this is false" in any sufficiently expressive language, which shattered the hope of any complete and perfect number system. Does that sound right?

[fred rosenberger]

hmmm... i seem to recall something about any language will allow a paradox. you need a 'superset' (my term) language, or a meta-language to resolve them.

but that higher level one will then have paradoxes, so you need a meta-meta-language, and so on.

i think...

[Dave Lenton]

Originally posted by Fred Rosenberger:
hmmm... i seem to recall something about any language will allow a paradox. you need a 'superset' (my term) language, or a meta-language to resolve them.

I like it - it seems explaining the concept that new phrases are needed because the current ones are not sufficient required new phrases because the current ones are not sufficient. Recursion!