Joined: Jan. 2006
|Quote (Reciprocating Bill @ Oct. 18 2009,08:17)|
|Therefore it seems to me that information regarding the crackedness of 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.|
Information about crackedness is superfluous only when you already know that the marble is red. †If you don't yet know the color, crackedness is still salient. †A cracked marble cannot falsify the hypothesis. †An uncracked marble might turn out to be blue, thus falsifying the hypothesis.
|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.
What's happening in your scenario is that you're essentially drawing twice: you look at a marble -- that's the first draw -- and if it's red, you remove it from the truck -- that's the second draw. †The first draw establishes that the marble is red, reducing the number of possible disconfirmations by one. †It therefore strengthens the hypothesis. †The second draw is irrelevant, since we now know that the marble cannot disconfirm the hypothesis.
|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.|
That's right. †Once we know that an object is a banana, further observation cannot strengthen the hypothesis that all ravens are black. (I love that sentence.) †But determining that the object is a banana -- or more precisely, determining that the object is not a raven -- does strengthen the hypothesis. †
|But, at least vis bananas versus ravens, that level of ignorance is implausible.|
It's implausible only if you already know something about the object. †Seeing an object, hearing an object, touching an object, or learning the location of an object are all observations that tell you something about the object.
If I ask you whether object X is a raven, but give you no other information about object X, then you have no way of reliably delivering the correct answer.
I should add that even if you do have information about the object, further observations can still be relevant. †If you know that a particular object is in the produce section of your local grocery store, but you haven't observed it yet, you will sensibly conclude that it is far more likely to be a banana than a raven, but there is still a finite probability that it is a raven, and a smaller but still finite probability that it is a non-black raven. Observing that it is, in fact, a banana therefore strengthens the hypothesis that all ravens are black, though by a very small amount.
And the set of natural numbers is also the set that starts at 0 and goes to the largest number. -- Joe G
Please stop putting words into my mouth that don't belong there and thoughts into my mind that don't belong there. -- KF