So abductive inference (IBE) is distinguished from enumerative induction. The former basically involves inverting deductive conditionals to generate hypotheses. So when asked why the grass is wet we immediately start coming up with deductive stories for how the grass might have gotten wet “It rained therefore the grass got wet”, “The sprinkler was on therefor the grass got wet” (note that the idea that explanans deductively entail explanandum is almost certainly false but this was the dominant position in philosophy of science when abductive inference was first discussed and a lot of times people don’t update their versions of IBE to take into account the, much better, causal model of explanation). Then the available hypotheses are compared and the best one chosen according to some set of ideal criteria. In contrast, enumerative induction involves looking at lots of particular pieces of evidence and generalizing “I’ve seen the grass be wet 100 times and 90 of those times it had rained, therefore it rained (with a 10% chance I’m wrong)”.
Now, the “ideal criteria” for an IBE differ from philosopher to philosopher but everyone worth their salt will include degree of consistency with past observation so IBE essentially subsumes enumerative induction. Usually the additional criteria are vaguer things like parsimony and generality. Now, since enumerative induction is about the frequency of observations it is more conducive to mathematical analysis and the Bayesian method. But the things IBE adds to the picture of inference aren’t things the Bayesian method has to ignore, you just have to incorporate the complexity of a hypothesis into its prior. But since objective Occam priors are the most confusing, controversial and least rigorous aspect of Bayesian epistemology there is room to claim that somehow our incorporation of economy into our inferences requires a vaguer, more subjective approach.
But that’s stupid. The fact that we’re bad Bayesian reasoners isn’t a rebuttal to the foundational arguments of Bayesian epistemology (though, those aren’t fantastic either). Your inferential method still has to correspond to Bayes’ rule or your beliefs are vulnerable to being dutch booked and your behavior can be demonstrated to be suboptimal according to your own notion of utility (assuming certain plausible axioms about agency).
That the authors say things like “If one wants to evaluate the probability that this world exists and there are infinitely many possibilities, n, then no matter how small a probability one assigns to each one, the sum will be infinite” suggests they are either unfamiliar with or reject an approach identifying the ideal prior with the computational complexity of the hypothesis (note that a strict enumerative inductive approach can be redeemed if facts about computational complexity are nothing more than meta-inductive facts about our universe(s)).
Whether one accepts that approach or not it plainly can’t be worse than relying on evolved, instinctual or aesthetic preference when picking hypotheses—which I assume is where they’re going with this. One needn’t apply an explicitly Bayesian method at all to reject God on IBE grounds. Theism plainly fails any economy criteria one would want- and I could go on about why but this comment needs to end.
Thanks for the comment; I think it aligns well with many of the rest of the comments as well. I actually would be interested to know what you mean by “fails any economy criteria.” I’m not familiar with that term.
An explanation is usually said to be economical if it is simple, general, elegant etc. In other words, whatever criteria you want to use in addition to ‘consistent with evidence’- this is mostly (entirely?) covered in these parts by discussing the complexity of the hypothesis. I’m just using it as a catch-all term for all those sorts of criteria for a good hypothesis. To make God seem like a ‘good’ hypothesis for something you need to pretty much invert your usual standards of inference.
Duh! In reading your response, it seems so simple, but for some reason when I read “economy” the first time, I just blanked as to what it would mean. I guess I’ve not been active enough around here lately. I understand, now. Complexity, more parts = lower probability by definition, Occam’s razor, etc.
I’m thinking your point is that any phenomenon’s explanation automatically decreases in economy when introducing beings and concepts vastly foreign to observation and experience. Would that be reasonably accurate?
So abductive inference (IBE) is distinguished from enumerative induction. The former basically involves inverting deductive conditionals to generate hypotheses. So when asked why the grass is wet we immediately start coming up with deductive stories for how the grass might have gotten wet “It rained therefore the grass got wet”, “The sprinkler was on therefor the grass got wet” (note that the idea that explanans deductively entail explanandum is almost certainly false but this was the dominant position in philosophy of science when abductive inference was first discussed and a lot of times people don’t update their versions of IBE to take into account the, much better, causal model of explanation). Then the available hypotheses are compared and the best one chosen according to some set of ideal criteria. In contrast, enumerative induction involves looking at lots of particular pieces of evidence and generalizing “I’ve seen the grass be wet 100 times and 90 of those times it had rained, therefore it rained (with a 10% chance I’m wrong)”.
Now, the “ideal criteria” for an IBE differ from philosopher to philosopher but everyone worth their salt will include degree of consistency with past observation so IBE essentially subsumes enumerative induction. Usually the additional criteria are vaguer things like parsimony and generality. Now, since enumerative induction is about the frequency of observations it is more conducive to mathematical analysis and the Bayesian method. But the things IBE adds to the picture of inference aren’t things the Bayesian method has to ignore, you just have to incorporate the complexity of a hypothesis into its prior. But since objective Occam priors are the most confusing, controversial and least rigorous aspect of Bayesian epistemology there is room to claim that somehow our incorporation of economy into our inferences requires a vaguer, more subjective approach.
But that’s stupid. The fact that we’re bad Bayesian reasoners isn’t a rebuttal to the foundational arguments of Bayesian epistemology (though, those aren’t fantastic either). Your inferential method still has to correspond to Bayes’ rule or your beliefs are vulnerable to being dutch booked and your behavior can be demonstrated to be suboptimal according to your own notion of utility (assuming certain plausible axioms about agency).
That the authors say things like “If one wants to evaluate the probability that this world exists and there are infinitely many possibilities, n, then no matter how small a probability one assigns to each one, the sum will be infinite” suggests they are either unfamiliar with or reject an approach identifying the ideal prior with the computational complexity of the hypothesis (note that a strict enumerative inductive approach can be redeemed if facts about computational complexity are nothing more than meta-inductive facts about our universe(s)).
Whether one accepts that approach or not it plainly can’t be worse than relying on evolved, instinctual or aesthetic preference when picking hypotheses—which I assume is where they’re going with this. One needn’t apply an explicitly Bayesian method at all to reject God on IBE grounds. Theism plainly fails any economy criteria one would want- and I could go on about why but this comment needs to end.
Thanks for the comment; I think it aligns well with many of the rest of the comments as well. I actually would be interested to know what you mean by “fails any economy criteria.” I’m not familiar with that term.
An explanation is usually said to be economical if it is simple, general, elegant etc. In other words, whatever criteria you want to use in addition to ‘consistent with evidence’- this is mostly (entirely?) covered in these parts by discussing the complexity of the hypothesis. I’m just using it as a catch-all term for all those sorts of criteria for a good hypothesis. To make God seem like a ‘good’ hypothesis for something you need to pretty much invert your usual standards of inference.
Duh! In reading your response, it seems so simple, but for some reason when I read “economy” the first time, I just blanked as to what it would mean. I guess I’ve not been active enough around here lately. I understand, now. Complexity, more parts = lower probability by definition, Occam’s razor, etc.
I’m thinking your point is that any phenomenon’s explanation automatically decreases in economy when introducing beings and concepts vastly foreign to observation and experience. Would that be reasonably accurate?