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Thank you for the examples. That shows that we are talking about different things. In all those examples, we are talking about a way to model them using rules e
by nanis 5y ago
Thank you for the examples. That shows that we are talking about different things. In all those examples, we are talking about a way to model them using rules enshrined in the _axiomatic_ foundations of probability. Things like, "given that the probability of X is p and the probability of Y is q and X and Y are independent events, probability of X and Y is p times q" etc.
That statement and the statements about the actual values of probabilities have no empirical content. Statements like "if there are 10 balls in an urn and three of them are red, the probability of pulling out a red ball is 30%" are _assumptions_ and they are not falsifiable. In practice, this simplifying assumption seems to have worked at least in making it easier think about certain phenomena and so we maintain that assumption, but it is an assumption nevertheless.
- leereeves 5y agoI disagree. Statements like "if there are 10 [well mixed and otherwise indistinguishable] balls in an urn and three of them are red, the probability of pulling out a red ball is 30%" are absolutely falsifiable. An experiment showing that this statement is false is certainly possible. You're right that these are mathematical models and therefore simplifications of reality, but they are useful mathematical models only if their predictions are empirically valid. And if anyone came up with a more empirically useful version of probability, they'd be famous even if mathematicians refused to accept it, because all the scientists, engineers, gamblers, actuaries, etc who rely on the predictions of probability would make it so.