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Questions tagged [paradox]

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Request for papers regarding Blackwell's solution to the two envelope problem

I am researching the two-envelope problem. In particular, I am working with the variant in which the chooser tries to pick the envelope with more money in it with a greater than 50% accuracy, having ...
Mathguy2718's user avatar
1 vote
0 answers
118 views

Logic which depends on the point of view / perspective? (Semantic space of logic)

I am not sure if this question is appropriate for MO, since I have only a basic understanding of Boolean logic, and am maybe not qualified to ask questions beyond that, but still I will try to write ...
mathoverflowUser's user avatar
-2 votes
2 answers
144 views

Greedy euclidean tour expansion - a case of unexpected hanging?

In the euclidean plane an common heuristic for the TSP is to start with the convex hull of the point set and then successively integrate as the next point and insertion position the combination that ...
Manfred Weis's user avatar
  • 12.7k
11 votes
2 answers
2k views

Can linear logic be used to resolve unexpected hanging/surprise examination paradox?

In the Unexpected Hanging Paradox, the prisoner tries to narrow down their date of execution using seemingly sound logical reasoning. They instead arrive at a contradiction. When the paradox is ...
wlad's user avatar
  • 4,853
4 votes
0 answers
377 views

Do you know any deep paradoxes or controversial hypothesis in category theory similar to those we have in set theory?

There is a lot of non-obvious and controversial topics and questions in set theory. From its begining in the first half of 20th century it have generated many paradoxes. For example there are ...
user3048747's user avatar
-3 votes
1 answer
311 views

What is a good formalization of this classic math puzzle? [closed]

Here is a classic math olympiad problem (but this is NOT my question!): Each of the girls A and B tells the teacher a positive integer but neither of them knows the other's number. The teacher writes ...
Martin Weidner's user avatar
0 votes
0 answers
189 views

What known paradoxes are associated with having a type-level tuple indexed by all ordinal numbers?

By a type-level tuple $t(f)$ that captures a function $f$, it is meant a relation that is definable by a stratified formula that assigns to $t(f)$ the same type it assigns to each element of the ...
Zuhair Al-Johar's user avatar
3 votes
1 answer
452 views

Put 10 balls in the jar then randomly take 1 out. Do it infinitely many times. Find the probability of resulting in an empty jar [closed]

The original discussion (in Chinese): https://www.zhihu.com/question/58702489 The original problem was from an probability theory exam. The problem is translated as: Assume an infinitely large jar ...
Liwei Cai's user avatar
13 votes
0 answers
1k views

Has anyone read/debunked Yessenin-Volpin–Hennix “Beware of the Gödel-Wette paradox”?

A student recently asked me about the status of a 2001 arXiv post, Beware of the Gödel-Wette paradox!, by Alexander Yessenin-Volpin (aka Esenin-Volpin and several other transliterations) and Catherine ...
Peter LeFanu Lumsdaine's user avatar
4 votes
2 answers
583 views

Avoiding reflexive paradox in set theory

I am an amateur mathematician, and certainly not a set theorist, but there seems to me to be an easy way around the reflexive paradox: Add to set theory the primitive $A(x,y)$, which we may think of ...
Richard Thrasher's user avatar
8 votes
5 answers
810 views

Positive results coming from paradoxes

Many examples comes to mind, the most famous being the Gödel's theorems viewed as formalisations of the Liar's paradox. I just realised that the proof of non-calculability of Kolmogorov complexity is ...
6 votes
5 answers
1k views

How to tell a paradox from a "paradox"?

Russell's paradox showed that naive set theory leads to a contradiction. This was something that was taken seriously and caused a lot of work. Now, Banach–Tarski paradox is arises from a result that a ...
user avatar
21 votes
3 answers
5k views

James-Stein phenomenon: What does it mean that a James-Stein estimator beats least squares estimator?

Background James-Stein estimator and Stein's phenomenon, as described in Wikipedia are rather counterintuitive and amazing. It is claimed that if one wants to estimate the mean $\Theta$ of Gaussian ...
Alexander Chervov's user avatar
10 votes
1 answer
3k views

Applications of Banach-Tarski Paradox to Probability Theory?

I was just curious, since the B-T paradox is a measure theoretic result, if there are any consequences of this paradox in probability theory? Also, is there is a way of stating the B-T paradox in the ...
Matt Calhoun's user avatar