# Tagged Questions

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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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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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 ...
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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 ...
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### 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 ...
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### 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 ...
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### 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?
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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 ...
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### 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 ...
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### 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 ...
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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 ...