3
votes
3answers
142 views

Paradoxes in Logic

What is it that makes something a paradox? It seems to me that paradoxes are just, in many cases, misunderstandings about the properties some object can have and so misunderstandings about ...
3
votes
2answers
186 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 ...
4
votes
4answers
275 views

The set of all things. A thing itself?

If the universe is the set of all things. Does it contain itself? In other words is it a thing itself? I know its a stupid question, but it really grinds my gears. Thanks! Edit 8.12 Okey, someone ...
4
votes
0answers
91 views

Relationship between paradoxes in logic and geometry/topology

Though I've been reading for years, this is my first question here. Believe it or not, I've tried the search feature- apologies if this is a duplicate. The main point of this post can be summarized ...
1
vote
2answers
257 views

Russell's Paradox

Many of you know such paradox... " $\exists y \forall x (x \in y \Longleftrightarrow \Phi(x)$" for any function $\Phi(x)$ substitute $x \notin x$ for $\Phi(x)$ Then by existential instantiation ...
1
vote
3answers
118 views

Paradoxes without self-reference?

Most paradoxes involves self-reference, the only exception known to me is Yablo's paradox, however it is still debated if it is really without self-reference. So, I was wondering, are there other ...
10
votes
3answers
167 views

Problems with using logic to study logic

Does using logic as a tool to study logic itself lead to problems/paradoxes? Similarly to how self-referencing sentences sometimes make no sense, e.g. This statement is false. When we try to study ...
6
votes
2answers
267 views

How to formalize this paradox?

A friend gave me this problem (in the "blue box") An interesting fact about the number $2$. How many times the number $2$ appears in this text? It appears $2$ times. Well I see the ...
7
votes
6answers
869 views

What is a paradox in mathematics?

I was reading some of these "mathematical paradoxes", and trying to understand why the list presents only counterintuitive mathematical results. Is there room in mathematics for logical paradoxes?
15
votes
11answers
2k views

Logic nonsense/paradox

I'm not sure if this is a paradox or a nonsense or neither of both. Anyway this is the "problem" if we can call it like that: A: B is True B: A is False How can ...
4
votes
3answers
262 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 ...
6
votes
2answers
354 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 ...
2
votes
3answers
470 views

Classifying Types of Paradoxes: Liar's Paradox, Et Alia

The well-known Liar's Paradox "This statement is false" leads to a recursive contradiction: If the statement is interpreted to be true then it is actually false, and if it is interpreted to be false ...
1
vote
0answers
89 views

Paradox of a set being twice as big as another one [duplicate]

Possible Duplicate: Card doubling paradox I don't know how to resolve the following paradoxon: Assume two finite sets A, B, one being twice as big than the other, but you don't know which. ...
25
votes
8answers
7k views

Why is “the set of all sets” a paradox?

I've heard of some other paradoxes involving sets (ie, "the set of all sets that do not contain themselves") and I understand how paradoxes arise from them. But this one I do not understand. Why is ...