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When you have an proof that A -> B and indications that A is true, you have two choices: - Accept that B is also true - Accept that A is false despite the indi
by rocqua 7y ago
When you have an proof that A -> B and indications that A is true, you have two choices:
- Accept that B is also true
- Accept that A is false despite the indications.
In a Bayesian way of thinking you compare which of these has a higher prior and pick that one. (Glossing over the fact that 'accept X is true' is not quite a Bayesian thing to say)
- nabla9 7y agoThat changes nothing because you assume A has higher prior and the other guy assumes -B has higher prior. When someone rejects the premise priors, you Bayesian reasoning does not help.
- rocqua 7y agoIt helps explain the paradox that the same evidence leads to differing conclusions.
- danharaj 7y agoWhat you described is not essentially different. It's the same phenomenon with {0, 1} (classical) and [0,1] (bayesian). What makes bayesian reasoning interesting is its dynamics, how does evidence change beliefs? But does it even make sense to talk about posteriors associated with classical deduction?
- gwern 7y agoIt's hard to say how Bayesian reasoning really works with classical logic (which is true of all statistical approaches), but you can set up plausible Bayesian models where you do get 'backfire' or 'polarization' effects in which people update in different directions based on the same observation because of the different models/priors they hold: https://www.gwern.net/docs/statistics/bayes/2007-bullock.pdf https://www.gwern.net/docs/statistics/bayes/2007-bullock.pdf http://papers.nips.cc/paper/3725-bayesian-belief-polarization.pdf http://papers.nips.cc/paper/3725-bayesian-belief-polarizatio...
- rocqua 7y agoI was thinking of Bayesian here as a contrast to Frequentist, not as a form of logic with uncertainty.