Questions tagged [paradoxes]

Paradoxes are arguments which contradict logic or common sense, often by using false and implicit premises.

A paradox is an argument that produces an inconsistency, typically within logic or common sense. Most logical paradoxes are known to be invalid arguments but are still valuable in promoting critical thinking. However some have revealed errors in logic itself and have caused the rules of logic to be rewritten. (e.g. Russell's paradox)

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Hilbert's hotel: why can't I repeat it infinitely many times?

I was wondering about the following: Suppose a new guest arrives and wishes to be accommodated in the hotel. We can (simultaneously) move the guest currently in room 1 to room 2, the guest currently in room 2 to room 3, and so on, moving …
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Is the Banach-Tarski paradox realistic? Why is Volume not an invariant?

Banach-Tarski says that given a glass ball, we can break it into two glass balls of equal volume to the original (plus other generalizations). The explanations I have found for this paradoxical notion is that volume is not an invariant when we do…
MT_
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For x < 5 what is the greatest value of x

It can't be $5$. And it can't be $4.\overline{9}$ because that equals $5$. It looks like there is no solution... but surely there must be?
Tom
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What exactly is the paradox in Zeno's paradox?

I have known about Zeno's paradox for some time now, but I have never really understood what exactly the paradox is. People always seem to have different explainations. From wikipedia: In the paradox of Achilles and the Tortoise, Achilles is in a…
Improve
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Help me to understand the potato paradox

From wiki - Fred brings home $100$ kg of potatoes, which (being purely mathematical potatoes) consist of $99\%$ water. He then leaves them outside overnight so that they consist of $98\%$ water. What is their new weight? The surprising answer is…
Mr.Banks
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Thomson's Lamp and the possibility of supertasks

The Thomson's Lamp paradox: A mad scientist owns a desk lamp. It begins in the toggled on position. The scientist toggles the lamp off after one minute, then on after another half-minute. After a quarter-minute the lamp is toggled off, then the…
user14069
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The condemned philosopher paradox. Can someone explain it to me?

the following paradox is a variation of the Barber Paradox, I don't quite understand why this is a paradox so I'd like to hear you tell why, please. There was a philosopher who had committed a crime (for example, he stared at a King's espouse)…
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Why is the Hilbert-Bernays paradox paradoxical?

The Hilbert-Bernays Paradox is produced by defining h as '(the referent of h) + 1'. Why is this a paradox? It seems strange to believe that we could define h in terms of itself. I suspect I'm missing some context, but I can't find anything else…
Casebash
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If I ask a person if they can say "no" and they say "no", is this a paradox?

If I ask a person if they can say "no" and they say "no", is this a paradox? If they answer "no" it means they can't say "no", but they just said it
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Achilles without tortoise

I am Achilles, and, with no tortoise in front of me, I start running on a straight line. The $1$st metre, I cover in $1/2$ second. The $2$nd metre in $1/4$ second. The $3$rd metre in $1/8$ second. The $n$-th metre in $1/2^n$ second, $n = 1,2,3,……
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Balls and Urn Paradox

So, I came across the following paradox: At $1$ minute before noon, put in balls $1 \sim 10$ and take out ball number $1$. At $1/2$ minute before noon, put in balls $11\sim20$ and take out ball number $2$ and so on. How many balls are there at…
Peter
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If supposing that a statement is false gives rise to a paradox, does this prove that the statement is true?

The title pretty much says it all: If supposing that a statement is false gives rise to a paradox, does this prove that the statement is true? Edit: Let me attempt to be a little more precise: Suppose you have a proposition. Furthermore, suppose…
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How to ensure that you haven't run into a paradox proving a theorem e.g. by proof by contradiction?

While preparing some lecture notes for next semester and going back to basics (set theory and proof strategies) I came along the following simple question which is about proving theorems in general but exemplified here by the proof by…
vonjd
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Self-referential paradox

In some legal documents, we read, "this page is intentionally left blank." Since this text is written on this page, the page is not really blank. Is there a mathematical formulation for this paradox? I thought this was similar to Russell's paradox,…
zeynel
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Is this Simpson’s Paradox?

In January, there were 2,700 new sign ups, and 3,500 who opt out. As at end January, there are 60,000 customers in our database. In February, there were 3,400 new sign ups and 4,300 who opt out. As at end February, there are 59,100 customers in our…
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