But notions like explanatory power & scientific methodology can only come into play after making the prior choice to believe in the existence of things to which they apply?
I don't think that you should reject skepticism but fully embrace it: reject the idea that you were ever entitled to belief without priors. Assign probabilities and confidence parameters to all of your statements, make them conditional, and you are good to go.
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Taking my sense-data scepticism as example then, do you mean something like: H=“My observations are in fact observations of a real universe” e=“I observe things” p(H)=The prior probability p(e)=Nearly 1 p(e|H)=Also nearly 1 p(H|e)=tobecalculated & plug into Bayes equation?
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I realise that where I was going with this is already written up at the final para of https://plato.stanford.edu/entries/induction-problem/#BaySub … : “The simple, and obvious, criticism of the Bayesian method is that the prior (before knowledge of any evidence) probabilities … are arbitrary. The Bayesian response…
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