Discussion:
  1. Branden Fitelson (2008). Goodman's "New Riddle". Journal of Philosophical Logic 37 (6):613 - 643.
    First, a brief historical trace of the developments in confirmation theory leading up to Goodman's infamous "grue" paradox is presented. Then, Goodman's argument is analyzed from both Hempelian and Bayesian perspectives. A guiding analogy is drawn between certain arguments against classical deductive logic, and Goodman's "grue" argument against classical inductive logic. The upshot of this analogy is that the "New Riddle" is not as vexing as many commentators have claimed (especially, from a Bayesian inductive-logical point of view). Specifically, the analogy (...)
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2009-05-15
MLE seminar comments on Fitelson

Cross-posted from http://mleseminar.wordpress.com/

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You can find the handout for this week here. I thought this was a really good paper, and we didn’t find all that much to criticise in it. It was a bit frustrating not to hear more about Fitelson’s positive story, in particular about the bridge principle that he would endorse instead of the various versions of RTE that he criticises. He’s clearly saving the juicy stuff for his book.

In particular, I find it hard to see how he plans to steer a middle ground between the Carnap/Williamson-style ‘a priori priors’ version of objective bayesianism, and the subjective bayesian approach. My naive take on the matter is that you either think that there’s a unique correct set of priors or you don’t. Maybe these priors aren’t a priori knowable (contra the Carnap/Williamson approach), although it seems that a position like this would be committed to complete epistemic rationality being in principle unattainable.

I wasn’t sure how strongly Fitelson meant to criticise the subjective Bayesian’s RTE’. Although as it stands the principle is useless, presumbly the subjective Bayesian wants to find a principle which is extensionally equivalent to RTE’ but which is not useless, because it picks out K’ in a different and more illuminating way. Fitelson gives no argument that this will prove difficult.

Gonzalo pointed out an interesting consequence of Hempel’s confirmation theory – all propositions are equally confirmed simpliciter. Of course, what we are interested in is confirmation of propositions by particular other propositions; this just underlines that Hempel’s confirmation relation is a logical and not an epistemic relation.

Another observation Gonzalo made is that M is trivially false if we allow for properties like ‘being such that this grass is green’. ‘This grass is green’ confirms ‘all grass is green’; but obviously statements like ‘this grass is green and this grass is such that that grass is blue’ do not confirm ‘all grass is green’, as M says it should.