Of course, you can say the idea of “justification” doesn’t really carve reality at the joints once you adopt a Bayesian epistemology. You just select a large-enough probability space to contain events you care about, start with your prior, make sure you are capable of updating, and then you just update. Who needs any “justification”? Just run the math, bro.[3]
Alternatively, you can also simply abandon Bayesianism entirely in favor of another theory that builds on top of it (which I get the impression is the approach you endorse?)
I admit I am a bit inconsistent about how I use the term “Bayesian”; sometimes I use it to point to the “classic Bayesian picture” (like Dogmatic Probabilism here and Reductive Utility here). However, I think the core idea of Bayesian philosophy is subjective probability, which I still think is quite important (even within, say, infrabayesianism). Granted, I also think frequentist notions of probability can be useful and have an important role to play (EG, in the theory of logical induction).
Anyway, I think there’s something right about “justification doesn’t carve reality at its joints”, but I think stopping at that would be a mistake. Yes, I think justification works different ways in different contexts, and the seeming paradox of the regress argument comes mostly from conflating the “trying to convince someone else” context with the “examining your own beliefs” context. However, I do think there’s something interesting going on with both of those notions of justification, and it seems potentially fruitful to examine them rather than throw them out. “Just run the math” only works if you’re not in the business of examining your beliefs (eg, the faith you have in the math) or justifying said math to others.
I admit I am a bit inconsistent about how I use the term “Bayesian”; sometimes I use it to point to the “classic Bayesian picture” (like Dogmatic Probabilism here and Reductive Utility here). However, I think the core idea of Bayesian philosophy is subjective probability, which I still think is quite important (even within, say, infrabayesianism). Granted, I also think frequentist notions of probability can be useful and have an important role to play (EG, in the theory of logical induction).
Anyway, I think there’s something right about “justification doesn’t carve reality at its joints”, but I think stopping at that would be a mistake. Yes, I think justification works different ways in different contexts, and the seeming paradox of the regress argument comes mostly from conflating the “trying to convince someone else” context with the “examining your own beliefs” context. However, I do think there’s something interesting going on with both of those notions of justification, and it seems potentially fruitful to examine them rather than throw them out. “Just run the math” only works if you’re not in the business of examining your beliefs (eg, the faith you have in the math) or justifying said math to others.