Posers and Puzzles
09 Apr 05
09 Apr 05
This will give you something to think about.
Suppose someone makes the claim that "All crows are black." If just three or four black crows are seen, that claim is weakly confirmed. But if millions are seen, it strongly confirms it. Now this can easily transfered into the logically equivalant form, "All non-black objects are not crows." But does that mean that seeing a yellow caterpillar, or a purple cow helps prove that "All crows are black?"
I believe so. What do you think?
09 Apr 05
Originally posted by ark13I agree that it also helps build the proof that "all crows are black". I base this on this logic: to prove all crows are black, we need to either show that 1. all crows are black (obviously) or 2. all non-black objects are not crows.
This will give you something to think about.
Suppose someone makes the claim that "All crows are black." If just three or four black crows are seen, that claim is weakly confirmed. But if millions are seen, it strongly confirms it. Now this can easily transfered into the logically equivalant form, "All non-black objects are not crows." But does that ...[text shortened]... , or a purple cow helps prove that "All crows are black?"
I believe so. What do you think?
There are probably a whole lot more non-black objects than there are crows (so #2 is probably not the best way to go), but the number is finite. So seeing one does help build (at least a little bit) the case that all non-black objects are not crows. In that sense, it does help the proof.
although you could probably also argue that there are so many non-black objects that no one could possible see and classify them all, so that seeing one non-black object doesn't help you get to the full proof. Still, seeing the non-black non-crow object doesn't disprove the claim that all crows are black, and so in that sense it may strengthen the claim that all crows are black.
It's a good question...never really thought about it that way...i'm sure the arguments could go deeper and deeper down a bottomless pit...
09 Apr 05
Originally posted by ark13It would provide further evidence, but help to "prove" nothing.
This will give you something to think about.
Suppose someone makes the claim that "All crows are black." If just three or four black crows are seen, that claim is weakly confirmed. But if millions are seen, it strongly confirms it. Now this can easily transfered into the logically equivalant form, "All non-black objects are not crows." But does that ...[text shortened]... , or a purple cow helps prove that "All crows are black?"
I believe so. What do you think?
11 Apr 05
Originally posted by PalynkaYes, realistically, it's impossible to prove that all non-black objects aren't crows, but that's not the point. If the law to be proved was instead "All crows in my room are black." Then that could be translated to, "All non-black objects in my room aren't crows." And that could be proven realively easily. It's not the fact that it's impossible to find all non-black objects that's of interest. It's whether or not the finding of one increases the chance of the law being true.
Actually, the paradox is that this line of reasoning leads you to conclude that nothing is "provable" through evidence alone.
It is impossible to confirm that all non-black objects are not crows, therefore it is impossible to prove that all crows are black.
🙄
11 Apr 05
Originally posted by ark13But then you are changing the situation. In your new case, there's no need for samples as the whole universe (your room) is being considered.
Yes, realistically, it's impossible to prove that all non-black objects aren't crows, but that's not the point. If the law to be proved was instead "All crows in my room are black." Then that could be translated to, "All non-black objects in my room aren't crows." And that could be proven realively easily. It's not the fact that it's impossible to ...[text shortened]... f interest. It's whether or not the finding of one increases the chance of the law being true.
In your original case, the relevant elements in the universe (the crows) are a very very small group in a near infinite number of elements. If in fact we consider them infinite, then mathematically it would not prove anything. They are indeed finite but there is such a residual effect that it is almost zero.
It's a bit like 1-0,999999(9)...=0. Mathematically this is true, yet, IMO, it falls under the same paradox.
11 Apr 05
Originally posted by ark13But you keep changing your argument.
Yes, realistically, it's impossible to prove that all non-black objects aren't crows, but that's not the point. If the law to be proved was instead "All crows in my room are black." Then that could be translated to, "All non-black objects in my room aren't crows." And that could be proven realively easily. It's not the fact that it's impossible to ...[text shortened]... f interest. It's whether or not the finding of one increases the chance of the law being true.
11 Apr 05
It IS possible, but not probable, that it can be proven that all crows are black (or not), since the number of crows is finite. Finding all of them though is improbable.
The corollary (correct word?) is not probable or possible, since the number of non-crow objects is NOT finite, as argued earlier. In the entire universe, their are an infinite number of objects. However, if we restrict our space to Earth alone, then yes, the second argument helps "prove" the first.
A layman to statistical thinking,
alcra
11 Apr 05
Originally posted by AlcraFinding all crows would prove that all non-black objects are not crows, because you accounted for ALL the crows.
It IS possible, but not probable, that it can be proven that all crows are black (or not), since the number of crows is finite. Finding all of them though is improbable.
The corollary (correct word?) is not probable or possible, since the number of non-crow objects is NOT finite, as argued earlier. In the entire universe, their are an infinite number of obj ...[text shortened]... es, the second argument helps "prove" the first.
A layman to statistical thinking,
alcra
11 Apr 05
Much I marvelled this ungainly fowl to hear discourse so plainly,
Though its answer little meaning, little relevancy bore;
For we cannot help agreeing that no living human being
Ever yet was blessed with seeing bird above his chamber door,
Bird or beast upon the sculptured bust above his chamber door,
With such name as "Nevermore."
12 Apr 05
Originally posted by BowmannI'm not changing my argument. In fact, I wasn't aware I had an argument. This whole time I've been trying to clarify this problem and simply play the devil's avdocate. When I gave the example with my room, it was an oversimplification. But if we consider the universe to have a finite amount of objects, it is truly the same as the initial problem. I only asked, would finding a non-black, non-crow object slightly (however small) increases the likelyhood that the law, "All crows are black," is true. And if the universe, as my room, has a finite amount of "stuff" then I believe this to be true. And it seems that most people agree with this.
But you keep changing your argument.