1
vote
0answers
33 views

Why is time important in the Ross-Littlewood paradox?

I have read many defferent versions of the Ross-Littlewood Paradox. This post: Fun quiz: where did the infinitely many candies come from? This post: Paradox: increasing sequence that goes to $0$? ...
3
votes
2answers
230 views

Leibniz' Law and that good old riddle

There exists a Theory of Identity in mathematical logic. I've encountered it for the first time in Principia Mathematica by Alfred North Whitehead and Bertrand Russell (1910). Quote: "This definition ...
3
votes
2answers
135 views

Understanding: Axiom of Specification and Russell's Paradox: there is no universe?

Following Halmos's Naive Set Theory, Russell's Paradox emerges from using the axiom of specification (that for every set $A$ and property $\phi$ there exists a set $Y$ whose elements are those ...
4
votes
3answers
287 views

How can any statements be proven undecidable?

As I understand it, undecidability means that there exists no proofs or contradictions of a statement. So if you've proved $X$ is undecidable then there are no contradictions to $X$, so $X$ always ...
2
votes
1answer
287 views

Russell Paradox and set theories

The Russell paradox arise in the Cantor set theory, but it can be avoided in the $ZF$ and in $NGB$ axiomatic set theory. Are there other axiomatic set theories in which this paradox can be avoided? ...
6
votes
2answers
363 views

Are there any non-self-referential statements that cannot be assigned a truth value?

Statements like A) A is false. or B1) B2 is true. B2) B1 is false. cannot be assigned a truth-value due to their ...