One of the few things that I really appreciate having encountered during my study of philosophy is the Gettier problem. Paper after paper has been published on this subject, starting with Gettier's original "Is Justified True Belief Knowledge?" In brief, Gettier argues that knowledge cannot be defined as "justified true belief" because there are cases when people have a justified true belief, but their belief is justified for the wrong reasons.
For instance, Gettier cites the example of two men, Smith and Jones, who are applying for a job. Smith believes that Jones will get the job, because the president of the company told him that Jones would be hired. He also believes that Jones has ten coins in his pocket, because he counted the coins in Jones's pocket ten minutes ago (Gettier does not explain this behavior). Thus, he forms the belief "the person who will get the job has ten coins in his pocket."
Unbeknownst to Smith, though, he himself will get the job, and further he himself has ten coins in his pocket that he was not aware of-- perhaps he put someone else's jacket on by mistake. As a result, Smith's belief that "the person who will get the job has ten coins in his pocket" was correct, but only by luck.
While I don't find the primary purpose of Gettier's argument particularly interesting or meaningful (much less the debate it spawned), I do think Gettier's paper does a very good job of illustrating the situation that I refer to as "being right for the wrong reasons." This situation has important implications for prediction-making and hence for the art of rationality as a whole.
Simply put, a prediction that is right for the wrong reasons isn't actually right from an epistemic perspective.
If I predict, for instance, that I will win a 15-touch fencing bout, implicitly believing this will occur when I strike my opponent 15 times before he strikes me 15 times, and I in fact lose fourteen touches in a row, only to win by forfeit when my opponent intentionally strikes me many times in the final touch and is disqualified for brutality, my prediction cannot be said to have been accurate.
Where this gets more complicated is with predictions that are right for the wrong reasons, but the right reasons still apply. Imagine the previous example of a fencing bout, except this time I score 14 touches in a row and then win by forfeit when my opponent flings his mask across the hall in frustration and is disqualified for an offense against sportsmanship. Technically, my prediction is again right for the wrong reasons-- my victory was not thanks to scoring 15 touches, but thanks to my opponent's poor sportsmanship and subsequent disqualification. However, I likely would have scored 15 touches given the opportunity.
In cases like this, it may seem appealing to credit my prediction as successful, as it would be successful under normal conditions. However, I think we perhaps have to resist this impulse and instead simply work on making more precise predictions. If we start crediting predictions that are right for the wrong reasons, even if it seems like the "spirit" of the prediction is right, this seems to open the door for relying on intuition and falling into the traps that contaminate much of modern philosophy.
What we really need to do in such cases seems to be to break down our claims into more specific predictions, splitting them into multiple sub-predictions if necessary. My prediction about the outcome of the fencing bout could better be expressed as multiple predictions, for instance "I will score more points than my opponent" and "I will win the bout." Some may notice that this is similar to the implicit justification being made in the original prediction. This is fitting-- drawing out such implicit details is key to making accurate predictions. In fact, this example itself was improved by tabooing[1] "better" in the vague initial sentence "I will fence better than my opponent."
In order to make better predictions, we must cast out those predictions that are right for the wrong reasons. While it may be tempting to award such efforts partial credit, this flies against the spirit of the truth. The true skill of cartography requires forming both accurate and reproducible maps; lucking into accuracy may be nice, but it speaks ill of the reproducibility of your methods.
[1] I greatly suggest that you make tabooing a five-second skill, and better still recognizing when you need to apply it to your own processes. It pays great dividends in terms of precise thought.
Sure. And (C) is unachievable in practice if one is updating one's information state sensibly from sensible priors.
I am uncertain what you mean to convey in this example by the difference between a "world state" (e.g., ASH or AST) and an "information state" (e.g. p("ASH")=0.668).
The "world state" of ASH is in fact an "information state" of p("heads")>SOME_THRESHOLD, which is fine if you mean those terms to be denotatively synonymous but connotatively different, but problematic if you mean them to be denotatively different.
Yes, agreed that this is strictly speaking unachievable, just as "I know for absolutely certain that the coin is heads" was.
That said, I'm not sure what it means for a human brain to have "I know for absolutely certain that the coin is almost surely heads" as a distinct state from "I am almost sure the coin is heads," and the latter is achievable.
Works for me.
And now you've lost me again. Of course there are real physical reasons why certain information states are not possible... e.g., my brain is incapable of representing certain thoughts. But I suspect that's not what you mean here.
Can you give me some examples of the kinds of cases you have in mind?
Actually, I meant p("heads") = 0.999 or something.
No, I meant: "I know for absolutely certain that the coin is heads". We agree that this much you can never know. As for getting close to this, for example having the information state (D) where p("heads") = 0.99999... (read more)