5.154 In an urn there are equal numbers of white and black balls (and no others). I draw one ball after another and lay them back again in the urn. Then by this experiment I can determine that the number of black balls drawn and the number of white balls drawn get nearer to one another as the drawing goes on.

*That* is therefore not a mathematical fact.

If I now say: It is as probable that I will draw a white ball as a black, then that means: All circumstances known to me (including laws of nature assumed as hypotheses) give to the occurrence of the one event no *more* probability than to the occurrence of the other. That is, they give – as can be easily gathered from the explanations above – to each the probability ½.

What I confirm by the experiment is that the occurrence of both events is independent of the circumstances with which I am no closer acquainted.

Since the first paragraph is entirely *a priori*, why is this not a mathematical fact? Is it logical? Empirical? And what circumstances is he talking about at the end? Obscure to me.

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