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?