In one sense you can’t use evidence to argue with a prior, but I think that factoring in computational resources as a cost would have put you on the wrong side of a lot of our discoveries about the Universe.
Could you expand that with examples? And if you can’t use evidence to argue with a prior, what can you use?
I’m thinking of the way we keep finding ways in which the Universe is far larger than we’d imagined—up to and including the quantum multiverse, and possibly one day including a multiverse-based solution to the fine tuning problem.
The whole point about a prior is that it’s where you start before you’ve seen the evidence. But in practice using evidence to choose a prior is likely justified on the grounds that our actual prior is whatever we evolved with or whatever evolution’s implicit prior is, and settling on a formal prior with which to attack hard problems is something we do in the face of lots of evidence. I think.
I’m thinking of the way we keep finding ways in which the Universe is far larger than we’d imagined
It’s not clear to me how that bears on the matter. I would need to see something with some mathematics in it.
The whole point about a prior is that it’s where you start before you’ve seen the evidence.
There’s a potential infinite regress if you argue that changing your prior on seeing the evidence means it was never your prior, but something prior to it was.
You can go on questioning those previous priors, and so on indefinitely, and therefore nothing is really a prior.
You stop somewhere with an unquestionable prior, and the only unquestionable truths are those of mathematics, therefore there is an Original Prior that can be deduced by pure thought. (Calvinist Bayesianism, one might call it. No agent has the power to choose its priors, for it would have to base its choice on something prior to those priors. Nor can it priors be conditional in any way upon any property of that agent, for then again they would not be prior. The true Prior is prior to all things, and must therefore be inherent in the mathematical structure of being. This Prior is common to all agents but in their fundamentally posterior state they are incapable of perceiving it. I’m tempted to pastiche the whole Five Points of Calvinism, but that’s enough for the moment.)
You stop somewhere, because life is short, with a prior that appears satisfactory for the moment, but which one allows the possibility of later rejecting.
I think 1 and 2 are non-starters, and 3 allows for evidence defeating priors.
Could you expand that with examples? And if you can’t use evidence to argue with a prior, what can you use?
I’m thinking of the way we keep finding ways in which the Universe is far larger than we’d imagined—up to and including the quantum multiverse, and possibly one day including a multiverse-based solution to the fine tuning problem.
The whole point about a prior is that it’s where you start before you’ve seen the evidence. But in practice using evidence to choose a prior is likely justified on the grounds that our actual prior is whatever we evolved with or whatever evolution’s implicit prior is, and settling on a formal prior with which to attack hard problems is something we do in the face of lots of evidence. I think.
It’s not clear to me how that bears on the matter. I would need to see something with some mathematics in it.
There’s a potential infinite regress if you argue that changing your prior on seeing the evidence means it was never your prior, but something prior to it was.
You can go on questioning those previous priors, and so on indefinitely, and therefore nothing is really a prior.
You stop somewhere with an unquestionable prior, and the only unquestionable truths are those of mathematics, therefore there is an Original Prior that can be deduced by pure thought. (Calvinist Bayesianism, one might call it. No agent has the power to choose its priors, for it would have to base its choice on something prior to those priors. Nor can it priors be conditional in any way upon any property of that agent, for then again they would not be prior. The true Prior is prior to all things, and must therefore be inherent in the mathematical structure of being. This Prior is common to all agents but in their fundamentally posterior state they are incapable of perceiving it. I’m tempted to pastiche the whole Five Points of Calvinism, but that’s enough for the moment.)
You stop somewhere, because life is short, with a prior that appears satisfactory for the moment, but which one allows the possibility of later rejecting.
I think 1 and 2 are non-starters, and 3 allows for evidence defeating priors.
What do you mean by “evolution’s implicit prior”?