tsig
Posts: 339
Joined: Aug. 2006
|
| Quote (Reciprocating Bill @ Oct. 18 2009,10:17) | Keiths/Ravemo
There seems to be a bit of sleight of hand in the Ravens/Marbles example to which intuition also objects, and I'd be interested in your thoughts on same. (I'm thinking aloud).
Consider the marbles. In your example you drew a marble from the truck and found that it was a non-cracked red marble. That supplied incremental evidence for the proposition that all blue marbles are cracked because there is now one less opportunity for disconfirmation of the cracked-blue hypothesis.
However, suppose you draw more red marbles and some are cracked. Each draw of a cracked red marble also reduces by one the number of opportunities for disconfirming the cracked-blue hypothesis. Therefore it seems to me that information regarding the crackedness or red marbles (or the yellowness of bananas) is entirely superfluous - drawing any red marble will do, cracked or not, and we needn't observe whether is is cracked.
Knowing that any draw of a red marble (cracked or not) increases the probability that our cracked-blue hypothesis is correct to an equal degree, and having time to kill, we proceed to draw only red marbles. Per above, we needn't observe whether they are cracked. We simply remove them and discard. With every removal our excitement grows, as with each (per the logic above) it is becoming more likely that all blue marbles are cracked. Ultimately we are left with an unknown quantity of blue marbles, only. We can't be sure every blue marble is cracked, but the probability of same has incrementally increased, because the number of possible disconfirming observations is reduced.
Something is obviously wrong with the above. Having removed all red marbles from the truck we are no closer to knowing whether all blue marbles are cracked than before we started. What has happened (still thinking aloud) is that when we are able to select marbles on the basis of color, a deliberate draw of a red marble is not observation with relevance to the cracked-blue hypothesis, and therefore does not reduce the pool of such possible observations by one. A given draw is in the pool of observations relevant to that hypothesis - one that could possibly disconfirm the cracked-blue hypothesis - only so long as the we draw marbles blindfolded. Similarly, vis ravens and non-ravens, a given observation of an object remains in the the class of observations that are potentially relevant to the black-raven hypothesis (therefore, upon making it, reducing the pool of observations by one) only so long as we remain ignorant of whether or not the object is a raven prior to making the observation. But, at least vis bananas versus ravens, that level of ignorance is implausible.
What am I missing? |
Your marbles?/
(it had to be said)
ETA: and I see it was...with pictures:p
|
