On the Peirce's "balancing reasons rule" failure in his "large bag of beans" example

Details On the Peirce's "balancing reasons rule" failure in his "large bag of beans" example On the Peirce's "balancing reasons rule" failure in his "large bag of beans" example

2010-03-18

arxiv.org/abs/1003.3659v1

Mathematics

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10 pages, 1 figure

Scientific paper

Take a large bag of black and white beans, with all possible proportions considered initially equally likely, and imagine to make random extractions with reintroduction. Twenty consecutive observations of black make us highly confident that the next bean will be black too. On the contrary, the observation of 1010 black beans and 990 white ones leads us to judge the two possible outcomes about equally probable. According to C.S. Peirce this reasoning violates what he called "rule of balancing reasons", because the difference of "arguments" in favor and against the outcome of black is 20 in both cases. Why? (I.e. why does that rule not apply here?)

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