I gave a description of how a Bayesian sees the difference between “X supports Y” and “X is consistent with Y” in our previous discussion. I don’t know if you saw it, you havn’t responded to it and you aren’t acting like you accepted it so I’ll give it again here:
“X is consistent with Y” is not really a Bayesian way of putting things, I can see two ways of interpreting it. One is as P(X&Y) > 0, meaning it is at least theoretically possible that both X and Y are true. The other is that P(X|Y) is reasonably large, i.e. that X is plausible if we assume Y.
“X supports Y” means P(Y|X) > P(Y), X supports Y if and only if Y becomes more plausible when we learn of X. Bayes tells us that this is equivalent to P(X|Y) > P(X), i.e. if Y would suggest that X is more likely that we might think otherwise then X is support of Y.
Suppose we make X the statement “the first swan I see today is white” and Y the statement “all swans are white”. P(X|Y) is very close to 1, P(X|~Y) is less than 1 so P(X|Y) > P(X), so seeing a white swan offers support for the view that all swans are white. Very, very weak support, but support nonetheless.
For a Popperian definition, you guys are allowed to criticise something right? In that case could we say that support for a proposition is logically equivalent to a criticism of its negation?
The whole ‘there is no positive support’ thing seems like an overreaction to the whole Cartesian ‘I can prove ideas with certainty thing’. I agree that certain support is a flawed concept, but you seem to be throwing the baby out with the bathwater by saying uncertain support is guilty by association and should be rejected as well.
Also, I’m a little incredulous here, do you really reject the policeman’s syllogism? Would you say he is wrong to chase the man down the road? If you encountered such a person, would you genuinely treat them as you would treat anyone else?
could we say that support for a proposition is logically equivalent to a criticism of its negation?
No. The negation of a universal theory is not universal, and the negation of an explanatory theory is not explanatory. So, the interesting theories would still be criticism only, and the uninteresting ones (e.g. “there is a cat”) support only. And the meaning of “support” is rather circumscribed there.
If you want to say theories of the type “the following explanation isn’t true: ….” get “supported” it doesn’t contribute anything useful to epistemology. the support idea, as it is normally conceived, is still wrong, and this rescues none of the substance.
The other issue is that criticism isn’t the same kind of thing as support. It’s not in the same category of concept.
Yes I really reject the policeman’s syllogism. In the sense of: I don’t think the argument in the book is any good. There are other arguments which are OK for reaching the conclusion (but which rely on things the book left unstated, e.g. background knowledge and context. Without adding anything at all, no cultural biases or assumptions or hidden claims, and even doing our best to not use the biases and assumptions built into the English language, then no there isn’t any way to guess what’s more likely).
If the Policeman’s argument is only valid in the light of background assumptions, why
would they need to be stated? Surely we would only need to make the same tacit assumptions to agree with the conclusions. Everyday reasoning differs from formal
logic in various ways, and mainly because it takes short cuts. I don’t think that invalidates
it.
I gave a description of how a Bayesian sees the difference between “X supports Y” and “X is consistent with Y” in our previous discussion. I don’t know if you saw it, you havn’t responded to it and you aren’t acting like you accepted it so I’ll give it again here:
For a Popperian definition, you guys are allowed to criticise something right? In that case could we say that support for a proposition is logically equivalent to a criticism of its negation?
The whole ‘there is no positive support’ thing seems like an overreaction to the whole Cartesian ‘I can prove ideas with certainty thing’. I agree that certain support is a flawed concept, but you seem to be throwing the baby out with the bathwater by saying uncertain support is guilty by association and should be rejected as well.
Also, I’m a little incredulous here, do you really reject the policeman’s syllogism? Would you say he is wrong to chase the man down the road? If you encountered such a person, would you genuinely treat them as you would treat anyone else?
I missed your comment. I found it now. I will reply there.
http://lesswrong.com/lw/3ox/bayesianism_versus_critical_rationalism/3uld?context=1#3uld
No. The negation of a universal theory is not universal, and the negation of an explanatory theory is not explanatory. So, the interesting theories would still be criticism only, and the uninteresting ones (e.g. “there is a cat”) support only. And the meaning of “support” is rather circumscribed there.
If you want to say theories of the type “the following explanation isn’t true: ….” get “supported” it doesn’t contribute anything useful to epistemology. the support idea, as it is normally conceived, is still wrong, and this rescues none of the substance.
The other issue is that criticism isn’t the same kind of thing as support. It’s not in the same category of concept.
Yes I really reject the policeman’s syllogism. In the sense of: I don’t think the argument in the book is any good. There are other arguments which are OK for reaching the conclusion (but which rely on things the book left unstated, e.g. background knowledge and context. Without adding anything at all, no cultural biases or assumptions or hidden claims, and even doing our best to not use the biases and assumptions built into the English language, then no there isn’t any way to guess what’s more likely).
If the Policeman’s argument is only valid in the light of background assumptions, why would they need to be stated? Surely we would only need to make the same tacit assumptions to agree with the conclusions. Everyday reasoning differs from formal logic in various ways, and mainly because it takes short cuts. I don’t think that invalidates it.