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I think the mathematics is a subject that should not hesitate to question any of it's old truths, as it enjoys the status of being foundation of the truth for most other sciences.

However, I'm seeing the tolerance of questioning on the math forums to be just as low as any other forum.

Of course, mathematicians are also humans and susceptible for making quick judgements based on shortcut criteria and their own intuitive beliefs. However, these strategies, some times, fail to meet the expectations for ensuring truth in such foundational layer of human knowledge.

One example is the responses and reactions received by my post, which seem solely based on quick judgements, without much thought.

A poster thinks it may not belong to mathematics, as it talks about multiple and seemingly contradictory truths. He/she might be hoping that mathematics is not a place for new paradoxes.

I want to request the community to keep this place with high appetite or tolerance for questioning.

Mathematics is a wild beast that feeds on the veracity emerging from the free and public debate, but not on approvals and endorsements handed out from behind the closed doors of the clubs. Sorry, I was a bit disappointed.

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I do not consider myself qualified to evaluate probability questions that have a flavor akin to that of Bertrand's paradox. But I would like to point out that the MO community has long been 'intolerant' of certain types of questions, and for good reason. These include 'questions' which purport to demonstrate that infinite sets lead to inconsistencies, or that uncountable sets lead to inconsistencies. They also include attempts to prove the Riemann Hypothesis, or Goldbach's conjecture. Such topics tend to be "crank magnets", and as professional mathematicians have long known, engaging with cranks can get to be extremely tiresome and distracting. I think the history of sci.math has shown where such things can take us, if tolerated and un-moderated.

Again, I am not lumping your particular question with those types of questions, and I'll have to leave it for others to judge its merits. I am merely answering to your general call for high levels of tolerance at MO for questioning the foundations of mathematics: unless such inquiries are conducted at a very high professional level, then the answer is sorry, but the community discourages those types of questions, for reasons given above.

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    $\begingroup$ I suggest mentioning that the scope of MathOverflow is more narrow, attempting to be question and answer rather than discussion and exploration. Further, the questions should be relatively brief in scope, referring to a step in a proof rather than a whole page of a proof. Gerhard "Shorter Relevant Posts Are Preferred" Paseman, 2019.01.12. $\endgroup$ – Gerhard Paseman Jan 12 at 16:37

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