Tiegue Rodrigues
Claudio
valcarenghi
mssilva77
Rafael
fmmuller
Indexing the Preface Paradox
The paradox of the preface is all about rationality, simultaneously troubling and interesting.
You’ve got a set of propositions and respective evidence. An inconsistent superset is always possible at the same fallible degree of justification. These supersets are only an inference away from a contradiction. Yet simple inferences can transform between sets.
A series of rational steps leading to an irrational belief. Inconceivable!
Everyone should agree that, after the paradox is structured, belief revision is necessary. Consistency must be restored so that contradictions cannot be rationally deduced. Collecting more evidence, weakening or strenghtening justification. This is the way out. If conflicting evidence remains equally strong that’s a texbook case for belief suspension.
But the paradox is neither about justification nor probabilities. That comes afterwards, and preempting these evaluations does not help. How did we get in this situation in the first place?
What situation? You can say that irrational beliefs are okay, or that we got nowhere anyway, since rationally justified beliefs are skeptically unobtainable. Both views do ‘solve’ the paradox. Both views are also uninteresting, because that’s not what we are looking for, is it? But not irrelevant, they are telling rationality may be too vague. There is something wrong here, we just don’t know what.
The paradox is classically stated with propositions P = {p1,…,pN} supported by evidence E = {e1,…,eN}, plus the proposition P’, that “P is not entirely correct”, supported by equally strong E’. Individually, this is perfectly rational. The whole however, is inconsistent, and we are one inference away from explicit contradictions.
Naturally this partitions things into before/after incoherence. And the closure discussion is framed this way. Over what kinds of sets does rationality closure holds, where can rational inferences be made?
It may be, however, that the most productive questions are about which inferences are rational, and which are not. In cases where multiple inferences are needed in the paradox structure, it becomes clearer that irrationality is not introduced until partial inferences are made, regardless of the initial set consistency condition. It could be the deciding factor is not a property of the set, but the inference content. Rather, the lack of content in the inference. A natural consequence of this would be that partial inferences may be irrational.
But regardless of the particular results of the paradox, it is still of further interest. Rational disagreement occurs between two agents, A1 and A2, with equally strong justification. The interplay between the knowledge of an opposing epistemic peer and the sustainability of one’s initial justification is still controversial, mostly in how it relates which kinds of evidence to what precedence of justification.
However, to identify the paradox as a special case of rational disagreement, where A1 and A2 just happen to be the same agent, may be helpul. Firstly, it dispels any lingering doubts about conceptual disclosure. A1 and A2, being the same, share all evidence, all interpretation of such evidence, and all modes and contexts of inference. Yet they can still reach either opposable result. The idea that, given all these favorable conditions, there can be no disagreement, is moot.
Secondly, it means that a general solution to disagreements must handle this particular case as well. Blanket solutions like Steadfastness go further and faster into dogmatism, and the Conciliatory view falls dangerously closer to skepticism.
And thirdly, but still importantly, it may signal that a solution to disagreement problems rests less on evidence and simmetric evaluation, as currently debated, and more on rationality itself, as the paradox suggests.
Rafael, and 
lucas are discussing. 
lucas 3:37 pm on May 24, 2011 Permalink |
Hello man
Good job on this topic! But let me tell you what i think about it. I think there are two different questions, one relating to closure principles and what kind of inferences are warranted in this context, and another one relating to rationality of inconsistency as such. These are diferent questions, but even if we deny something like closure in the preface situation, still remains some problem.
lucas 4:04 pm on May 24, 2011 Permalink |
oh sorry, i pressured the button without wanting it!
But let me continue…
We must make two distinctions. The first one, i already mentioned : beetween closure principles, and the rationality of inconsistency. They are related, but are diferent topics. Even if we reject closure principle, still remain a second question : can be inconsistency rational and warranted, even with we reject closure principles in this particular case? But the most important point is another. The preface paradox it’s not It’s not about disagreement ( rational or not ) . I can’t find any meaning in something like ” John doe disagree with himself”, unless you just mean he has contradictory ( or inconsistency) beliefs. Other than a metaphorical way of saying than he has inconsistent beliefs, that’s hardly inteligible.
Rafael 4:33 pm on May 24, 2011 Permalink |
First, thanks for the comments!
Well, yes, the preface and disagreement are distinct problems, motivated very differently, and each brings many unique issues. But I think they share one issue: they both deal with equal strength opposable justification. The preface needs it, and disagreement wants it.
The disagreement discussion entertains the possibility that, with full disclosure, the apparent “equal strength” of the justification disappears, that perfectly balanced evidence cannot exist. It can, and in the preface it does.
You are also right that the preface isn’t about self agreement/disagreement. I’m not sure the disagreement discussion brings something to the preface. I think it’s the other way around.
elusivethoughts 8:26 pm on May 26, 2011 Permalink |
Hey Rafael,
Actually, I don’t think that it is correct to say about the preface paradox that each sentence in the book that ‘S’ reasonably (or justifiably) believes is believed with the same degree of justification (or as you said: “equal strength”). Likewise, I don’t think that it is correct to say, assuming closure, that the degree of justification that ‘S’ believes (C1&…&Cn) is the same degree of justification that ‘S’ has for believing ~(C1&…&Cn).
I just can’t see what the point is for talking about the “equal strength of the justification”, just because it doesn’t matter the the degree of justification each belief has. If a belief is considered rational, then it has already meet the threshold of justification required for it to be considered rational. And ‘S’ can have a rational belief that is more justified that another rational belief.
The same thing holds for the disagreement debate, it is not a problem of “equal strength” of the justification.
I hope that my speech might be useful somehow.
lucas 9:53 pm on May 26, 2011 Permalink |
Elusive is right . Both problems are about ” qualities”, not quantities or degrees. If we accept the conclusion of the preface paradox, what has been accepted is that inconsistency can be justified or rational. There’s no specification on the strenght of the justification.
Anyway, I don’t know how the rational desagreement issue could help the preface paradox. Maybe you’re saying that just because you bitte the bullet on the preface paradox, rational inconsistencys are ok on the desagreement issue. But that’s absurd! You can’t invoke the preface paradox to warrant inconsistency when it’s convenient to you.
Rafael 6:21 pm on May 27, 2011 Permalink |
The paradox is qualitative. It is qualitative because degrees of justification don’t help. They don’t help because they are equivalent. If they weren’t equivalent, they would help, and there would be no paradox.
A well researched preface applied to a book of coin flip statements isn’t a paradox. Research rationally defeats coin flips. Likewise, a well researched book doesn’t create a paradox when questioned by a coin flip. The problem becomes rationality when beliefs aren’t prima facie rejected because of lesser justification. That only works with the equal degrees.
That is to say, prefaces with unequal degrees have standard bayesian solutions, and aren’t paradoxes at all.
And when I mean equal, I mean equal between (C1&…&Cn) and~(C1&…&Cn), not between individual Cx.
And, again, I think it’s the paradox that helps with disagreement. It’s a well understood example of full disclosure.
Tiegue And His Elusive Thoughts 2:28 am on May 28, 2011 Permalink |
If S rationally believes (C1&…&Cn) the evidence or justification that S has for it is sufficient for it to be considered rational. Likewise, If S rationally believes ~ (C1&…&Cn) the evidence or justification that S has for it is sufficient for it to be considered rational. This is what makes things puzzling: the possibility of a rational or justified belief in an inconsistency or contradiction.
Solve the paradox is not a case of giving up one of the conjuncts because of a lack of justification, nor give up one of them simply because one is more justified than the other.
In this sense, it does not mean that the evidence (or justification) possessed by S for believing in each one of the conjuncts need to display the same degree of justification.
In the case of disagreement you have two different subjects that are considering contradictory contents, or propositions. While ‘A’ is saying ‘p’, ‘B’ is saying ~’p’.
Even if they are sharing the same body of evidence it does not mean that ‘A’ believes that ‘p’ with the same degree of justification that ‘B’ believes that ~’p’.
it would be possible that ‘B’ – despite the fact of accessing the same evidenve that ‘A’ – comes to believe ~’p’ by wishful thinking and not because of the relevant evidence.