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Showing posts with the label statistical inferences

Resolving the lottery paradox without abolishing Venn Diagrams

  Yesterday I wrote about the lottery paradox, the epistemological crux of some of my recent reading. I refer you back to yesterday's post if you come to this not knowing what the term means. I will proceed today presuming that you know.  Now, clearly, part of what makes the paradox ... paradoxical is the rule of conjunction. This is the idea that if A is known and B is known then it follows that A + B is known. Or, in a weaker alternative statement: if A is rationally believable and B is rationally believable then A + B is rationally believable.  After all, why can we not simply say that "it is true that my ticket is a loser and I can know that this is true by considering the laws of probability"? One reason I can't say that with a clean logical conscience is that if I can say it of my own ticket I can say it of any one of the thousand (or however many) others that were sold. And if I can do THAT, then by the principle of conjunction I can say that all the tickets ar...