Do all the non-contradicted-by-evidence ideas gain equal probability (so they are always tied and i don’t see the point of the “probabilities”), or differential probability?
EDIT: I’m guessing your answer is you start them with different amounts of probability. after that they gain different amounts accordingly (e.g. the one at 90% gains less from the same evidence than the one at 10%). but the ordering (by amount of probability) always stays the same as how it started, apart from when something is dropped to 0% by contradicting evidence. is that it? or do you have a way (which is part of induction, not critical argument?) to say “evidence X neither contradicts ideas Y nor Z, but fits Y better than Z”?
Different hypotheses (= models) can gain different amounts of probability. They can start with different amounts of probability, too, of course.
to say “evidence X neither contradicts ideas Y nor Z, but fits Y better than Z”?
Of course. That’s basically how all statistics work.
Say, if I have two hypotheses that the true value of X is either 5 or 10, but I can only get noisy estimates, a measurement of 8.7 will add more probability to the “10” hypothesis than to the “5″ hypothesis.
They get identical probabilities—if their prior probabilities were equal.
If (as is the general practice around these parts) you give a markedly bigger prior probability to simpler hypotheses, then you will strongly prefer the simpler idea. (Here “simpler” means something like “when turned into a completely explicit computer program, has shorter source code”. Of course your choice of language matters a bit, but unless you make wilfully perverse choices this will seldom be what decides which idea is simpler.)
In so far as the world turns out to be made of simply-behaving things with complex emergent behaviours, a preference for simplicity will favour ideas expressed in terms of those simply-behaving things (or perhaps other things essentially equivalent to them) and therefore more-explanatory ideas. (It is at least partly the fact that the world seems so far to be made of simply-behaving things with complex emergent behaviours that makes explanations so valuable.)
I do, but more or less only to the extent that they will make potential different predictions. If two models are in principle incapable of making different predictions, I don’t see why should I care.
so e.g. you don’t care if trees exist or not? you think people should stop thinking in terms of trees and stick to empirical predictions only, dropping any kind of non-empricial modeling like the concept of a tree?
Isn’t it convenient that I don’t have to care about these infinitely many theories?
why not?
Since there is an infinity of them, I bet you can’t marshal critical arguments against ALL of them :-P
you can criticize categories, e.g. all ideas with feature X.
I think you’re getting confused between actual trees and the abstract concept of a tree.
i don’t think so. you can’t observe entities. you have to interpret what entities there are (or not – as you advocated by saying only prediction matters)
you can criticize categories, e.g. all ideas with feature X
How can you know that every single theory in that infinity has feature X? or belongs to the same category?
you can’t observe entities
My nervous system makes perfectly good entities out of my sensory stream. Moreover, a rat’s nervous system also makes perfectly good entities out if its sensory stream regardless of the fact that the rat has never heard of epistemology and is not very philosophically literate.
or not
Or not? Prediction matters, but entities are an awfully convenient way to make predictions.
Do all the non-contradicted-by-evidence ideas gain equal probability (so they are always tied and i don’t see the point of the “probabilities”), or differential probability?
EDIT: I’m guessing your answer is you start them with different amounts of probability. after that they gain different amounts accordingly (e.g. the one at 90% gains less from the same evidence than the one at 10%). but the ordering (by amount of probability) always stays the same as how it started, apart from when something is dropped to 0% by contradicting evidence. is that it? or do you have a way (which is part of induction, not critical argument?) to say “evidence X neither contradicts ideas Y nor Z, but fits Y better than Z”?
Different hypotheses (= models) can gain different amounts of probability. They can start with different amounts of probability, too, of course.
Of course. That’s basically how all statistics work.
Say, if I have two hypotheses that the true value of X is either 5 or 10, but I can only get noisy estimates, a measurement of 8.7 will add more probability to the “10” hypothesis than to the “5″ hypothesis.
what do you do about ideas which make identical predictions?
They get identical probabilities—if their prior probabilities were equal.
If (as is the general practice around these parts) you give a markedly bigger prior probability to simpler hypotheses, then you will strongly prefer the simpler idea. (Here “simpler” means something like “when turned into a completely explicit computer program, has shorter source code”. Of course your choice of language matters a bit, but unless you make wilfully perverse choices this will seldom be what decides which idea is simpler.)
In so far as the world turns out to be made of simply-behaving things with complex emergent behaviours, a preference for simplicity will favour ideas expressed in terms of those simply-behaving things (or perhaps other things essentially equivalent to them) and therefore more-explanatory ideas. (It is at least partly the fact that the world seems so far to be made of simply-behaving things with complex emergent behaviours that makes explanations so valuable.)
I don’t need to distinguish between them, then.
so you don’t deal with explanations, period?
I do, but more or less only to the extent that they will make potential different predictions. If two models are in principle incapable of making different predictions, I don’t see why should I care.
so e.g. you don’t care if trees exist or not? you think people should stop thinking in terms of trees and stick to empirical predictions only, dropping any kind of non-empricial modeling like the concept of a tree?
I don’t understand what this means.
The concept of a tree seems pretty empirical to me.
there are infinitely many theories which say trees don’t exist but make identical predictions to the standard view involving trees existing.
trees are not an observation, they are a conceptual interpretation. observations are things like the frequencies of photons at times and locations.
Isn’t it convenient that I don’t have to care about these infinitely many theories?
Since there is an infinity of them, I bet you can’t marshal critical arguments against ALL of them :-P
I think you’re getting confused between actual trees and the abstract concept of a tree.
I don’t think so. Human brains do not process sensory input in terms of ” frequencies of photons at times and locations”.
why not?
you can criticize categories, e.g. all ideas with feature X.
i don’t think so. you can’t observe entities. you have to interpret what entities there are (or not – as you advocated by saying only prediction matters)
Why not what?
How can you know that every single theory in that infinity has feature X? or belongs to the same category?
My nervous system makes perfectly good entities out of my sensory stream. Moreover, a rat’s nervous system also makes perfectly good entities out if its sensory stream regardless of the fact that the rat has never heard of epistemology and is not very philosophically literate.
Or not? Prediction matters, but entities are an awfully convenient way to make predictions.