Freiling's axiom of symmetry ($\sf AS$) is known as a justification for falsity of Continuum Hypothesis. Freiling in his 1986 paper, Axioms of symmetry: throwing darts at the real number line, provides a "deemed intuitive" probabilistic argument for this axiom.

Question: I'm looking for mathematical and philosophical references that argue the intuition behind Freiling's axiom of symmetry, particularly those which question the acceptability of the intuition behind this axiom based on some mathematical or philosophical reasons, in order to figure out the main directions of criticism towards $\sf AS$.

  • $\begingroup$ This looks to me like a question about philosophy rather than mathematics. On the other hand it wouldn't surprise me if the logicians who hang around here will have some interesting things to say about it. $\endgroup$ – eric Jan 3 '16 at 16:55
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    $\begingroup$ As you'll be aware, there are already mathematical objections on the Wikipedia page. These seem to me to be pretty coherent and sensible, in the sense that you can see that they are in some sense valid objections. I don't know if you can expect more than this from a mathematical point of view -- it's not as if these objections can somehow be "dealt with" forcing the need to formulate more. That's why it felt like a philosophy question -- from the point of view of math objections it seemed to me that Wikipedia might well document what is essentially the last word on the matter. $\endgroup$ – eric Jan 3 '16 at 17:07
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    $\begingroup$ @eric The objections part in the Wikipedia article is my motivation for asking this question but I think it is so brief. $\endgroup$ – Morteza Azad Jan 3 '16 at 17:12
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    $\begingroup$ See Throwing Darts at a Ruler: Unpacking the Intuition Behind Freiling’s Axiom of Symmetry in particular section 3 of the paper. $\endgroup$ – Mohammad Golshani Jan 4 '16 at 5:20
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    $\begingroup$ See also Symmetry and the Brown-Freiling Refutation of the Continuum Hypothesis $\endgroup$ – Mohammad Golshani Jan 4 '16 at 5:27

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