[Freddy]

I enjoyed this video and thought some of you might be interested too.

[ivan.moony]

I was thinking about Russel's Paradox in terms of my language that should be able to describe any other language. The solution boils down to the time of checking of does the set contain itself. If it's before that time, the set contains itself. If it's after that time, the set doesn't contain itself. Excluding the time from the equation generates the paradox.

From another point of view, expressing the paradox in terms of logical predicates, if S(s, x) means that x is in set s, writing the questionable set yields: (~ S(s, s)) <-> S(s, s), which is a provable contradiction. This judgement is simply contradictory, without any special logic treatment. If there was a programming language based on logic, it would throw compile time error when reading this line of code.

And that empty set (representing zero, I think) reminds me of falsity (which can't be true because it's a falsity). Maybe similar relation holds for the set from Russel's Paradox. Maybe that set represents a falsity. Like a set of all paradoxical sets. Is there such a set? If there is, is it the same set as a set of all falsities?

[MagnusWootton]

The set of all sets that dont contain themselves, is not a paradox.