OK, got it, thank you. I have two doubts. (i) Why a belief with degree 1 is not affected by new information which is counter-evidence to that belief? Does it mean every belief with degree 1 I have now will never be lost/defeated/changed? (ii) The difference between what you call traditional epistemology and Bayesianism involves lots of things. I think one of them is their objectives - the traditional epistemologist and the Bayesian in general have different goals. The first one is interested in posing the correct norms of reasoning and other sources of beliefs (perception, memory, etc). The second one maybe is more interested in modelling rational structures for a variety of purposes. That being the case, the puzzles I brought maybe are not of interest for Bayesians - but that does not mean Bayesianism solve the question of what is the correct thing to do in such cases. Thanks for the link (I already know Harman's approach, which is heavily criticized by Conee and others).
(i) That remark concerns a Bayesian agent, or more specifically an agent who updates by conditionalization. It's a property of conditionalization that no amount of evidence that an agent updates upon can change a degree of belief of 0 or 1. Intuitively, the closer a probability gets to 1, the less it will decrease in its absolute value in response to a given strength of counterevidence. 1 corresponds to the limit at which it won't decreases at all from any counterevidence.
(ii) I'm well-aware that the aims of most epistemologists and most Bayesian philosoph...
I present here two puzzles of rationality you LessWrongers may think is worth to deal with. Maybe the first one looks more amenable to a simple solution, while the second one has called attention of a number of contemporary epistemologists (Cargile, Feldman, Harman), and does not look that simple when it comes to a solution. So, let's go to the puzzles!
Puzzle 1
At t1 I justifiably believe theorem T is true, on the basis of a complex argument I just validly reasoned from the also justified premises P1, P2 and P3.
So, in t1 I reason from premises:
(R1) P1, P2 ,P3
To the known conclusion:
(T) T is true
At t2, Ms. Math, a well known authority on the subject matter of which my reasoning and my theorem are just a part, tells me I’m wrong. She tells me the theorem is just false, and convince me of that on the basis of a valid reasoning with at least one false premise, the falsity of that premise being unknown to us.
So, in t2 I reason from premises (Reliable Math and Testimony of Math):
(RM) Ms. Math is a reliable mathematician, and an authority on the subject matter surrounding (T),
(TM) Ms. Math tells me T is false, and show to me how is that so, on the basis of a valid reasoning from F, P1, P2 and P3,
(R2) F, P1, P2 and P3
To the justified conclusion:
(~T) T is not true
It could be said by some epistemologists that (~T) defeat my previous belief (T). Is it rational for me to do this way? Am I taking the correct direction of defeat? Wouldn’t it also be rational if (~T) were defeated by (T)? Why ~(T) defeats (T), and not vice-versa? It is just because ~(T)’s justification obtained in a later time?
Puzzle 2
At t1 I know theorem T is true, on the basis of a complex argument I just validly reasoned, with known premises P1, P2 and P3. So, in t1 I reason from known premises:
(R1) P1, P2 ,P3
To the known conclusion:
(T) T is true
Besides, I also reason from known premises:
(ME) If there is any evidence against something that is true, then it is misleading evidence (evidence for something that is false)
(T) T is true
To the conclusion (anti-misleading evidence):
(AME) If there is any evidence against (T), then it is misleading evidence
At t2 the same Ms. Math tells me the same thing. So in t2 I reason from premises (Reliable Math and Testimony of Math):
(RM) Ms. Math is a reliable mathematician, and an authority on the subject matter surrounding (T),
(TM) Ms. Math tells me T is false, and show to me how is that so, on the basis of a valid reasoning from F, P1, P2 and P3,
But then I reason from::
(F*) F, RM and TM are evidence against (T), and
(AME) If there is any evidence against (T), then it is misleading evidence
To the conclusion:
(MF) F, RM and TM is misleading evidence
And then I continue to know T and I lose no knowledge, because I know/justifiably believe that the counter-evidence I just met is misleading. Is it rational for me to act this way?
I know (T) and I know (AME) in t1 on the basis of valid reasoning. Then, I am exposed to misleading evidences (Reliable Math), (Testimony of Math) and (F). The evidentialist scheme (and maybe still other schemes) support the thesis that (RM), (TM) and (F) DEFEATS my justification for (T) instead. So that whatever I inferred from (T) is no longer known. However, given my previous knowledge of (T) and (AME), I could know that (MF): F is misleading evidence. It can still be said that (RM), (TM) and (F) DEFEAT my justification for (T), given that (MF) DEFEAT my justification for (RM), (TM) and (F)?