Read it, it´s good.
Read it, it´s good.
will do, thanks.
That was interesting.
What´s your solution? I know you have one, so spit it out. ;-)
Universal statements are statements about the universe, not just black ravens or white ravens. Sighting of a non-black (and/or non-white) non-raven increases your knowledge of this entire universe, and hence confirms the hypothesis.
well, that was the first point of the article. But that is trivial. I asked about the paradox.Cut&paste:ADDENDUMVery well, you might say, but maybe every sighting of a non-black non-raven really does confirm, even if only to an infinitessimal degree, the hypothesis that all ravens are black. After all, if we could, somehow, check every non-black object in the universe, and if none of them were ravens, our statement that all ravens are black would be proved.Just so. Maybe my blue shirt does reinforce, even if only to some tiny degree, the hypothesis that all ravens are black. But if so, then it must also reinforce – to the same degree – a completely contradictory statement, namely, the hypothesis that all ravens are white. After all, my shirt is a non-white non-raven . . . .
__) well, that was the first point of the article. But that is trivial. I asked about the paradox.
Those two statements appear paradoxical only because of the way they are expressed.
"Those two statements appear paradoxical only because of the way they are expressed."
What do you mean more specificly? Which sentences/words are you thinking about that could be expressed differently to avoid the paradox?
Maybe ``Reinforcing'' or ``confirming'' isn't the right word to describe sighting of a non-black non-raven. If you could check every object in the universe, then sighting of a non-black non-raven means only one less object to examine about the universe. You can't confirm the hypothesis until you examine all the elements that constitute the universe (or you can falsify the hypothesis once you encounter an counter example). It's not really a gradual process in the sense that the likelihood of the hypothesis' being true increases with every observation of an element. Still, one less element to go is a kind of progress toward the final confirmation (or falsification), for both ``all ravens are black'' and ``all ravens are white.''
The troubling part is that the statement just says that (1) some elements constituting the universe are predicated as being raven and all of them are also black. It doesn't say (2) which element(s) constituting the universe is predicated as being black raven (i.e. where in the universe black ravens are, which portion of the universe in terms of xyz coordinate black ravens are occupying) or (3) how many elements are predicated as being black raven (i.e. how many ravens exist in the universe). Sighting of a non-black non-raven does contribute to the inquiries of the latter two kinds. Each singular statement about an element of the universe is a qualitatively significant piece of information for them. For example, if the universe consists of only 3 elements, space A, space B, space C, observing that A is non-black non-raven means that this universe is at least not such a universe that A is black raven, or that this universe is at least not such a universe that it contains three black ravens. For the first kind of statement, however, each singular statement on its own carries no qualitative significance unless it is of a counter example.
"You can't confirm the hypothesis until you examine all the elements that constitute the universe "
This is impossible, so that´s why hypothesis only can be falsified or "reinforced", not 100% "proven".
"It's not really a gradual process in the sense that the likelihood of the hypothesis' being true increases with every observation of an element."
That´s exactly what logic says it is (even if it´s really miniscule reinforcement for every observed element)
I´m not sure I understood your explenation though.
__) This is impossible, so that's why hypothesis only can be falsified or "reinforced", not 100% "proven".
That is the premise the author of the article added later: ``Very well, you might say, but maybe every sighting of a non-black non-raven really does confirm, even if only to an infinitessimal degree, the hypothesis that all ravens are black. After all, if we could, somehow, check every non-black object in the universe, and if none of them were ravens, our statement that all ravens are black would be proved.'' Unless this premise stands and you can examine every element (or raven) that constitutes the universe, the hypothesis will never be ``confirmed.''
__) That´s exactly what logic says it is
Well, it isn't, so the two hypotheses appear paradoxical. Gradual confirmation isn't really confirming anything. Nor does the contrapositive. I am questioning exactly in what sense sighting of a non-black non-raven is claimed to be ``reinforcing'' the hypothesis.
(1) Sighting of a falsifying instance (non-black raven) directly and qualitatively disproves the hypothesis. (2) Sighting of a confirming instance (black raven) and (3) of an instance neither confirming nor falsifying (non-black non-raven), on the other hand, are of a totally different nature. They obviously can't prove the hypothesis qualitatively. But do they really ``reinforce'' the hypothesis in the sense that they gradually increase the chance of the hypothesis' being correct?
Suppose that there exists only one raven in the universe. You could observe as many non-black non-raven objects in the universe as you want. Now, what kind of influence do such observations, individually or all together, have on the likelihood of the only raven's being black? Even if you have observed every other element that constitutes the universe, whether the very last element will turn out to be black raven or not is not dependent of the outcome of those observations.
Sighting of black ravens and non-black non-ravens only increases the general *knowledge* about the universe, knowledge about the portions of the universe that are not necessarily related to portions that are ravens.
Another example: Suppose that the universe is a finite space consisting of only 5 elements. Each element has 1/5 chance of taking one of the following forms: black raven, white raven, human, rock, and empty space. Once you discovered what all the five elements are, you *know* the entire universe. This universe may be such that it consists of ``2 rocks, 1 human, 2 black ravens,'' or ``3 rocks, 2 empty spaces,'' etc.
Now, you observe one element, and it turns out to be a rock. You have 4 elements to go now. For the hypothesis that all ravens are black to be true, one or more of the remaining elements must be black raven, and none of the elements be white raven.
You failed the first try to confirm that at leaset there exists one black raven. But you also avoided the falsifying instance, viz. white raven. As far as the hypothesis is concerned, its likelihood of being true isn't very much affected by this first single observation in either way. It just means that you got one less element to examine, one less task to rach the final verdict. It doesn't matter if you observe 1 or 2 or 3 or 4 black ravens in the process until you finish all the five elements, or encounter a white raven, a single counter instance.
"What´s your solution? I know you have one, so spit it out. ;-)"
I think that you can´t say how much a theory is supported, but I think you can make rules for wether one theory is better supportet than another theory by given data or not. There is no problem if you tret it this way.
In statistics you just need to examine some size of random samples according to the normal curve or what not irrespective of how big the parent population is. Increasing sample size beyond a certain point won't improve the accuracy much relative to the labor it takes to gather samples.
You don´t know the sample size and it´s pretty much impossible to define a probability distribution over all scientific laws. If you will succeed in this, all laws will have probability measure 0, i.e. that doesn´t work.
__) You don't know the sample size
What do you mean by that? You could calculate the apropriate size of sample for a desired level of accuracy.
Perhaps "Science" is being confused with "Taxonomy".
If "Raven" is defined physiologically, it is perfectly reasonable to find a "blue raven". e.g. It's physiology is identical to that of a raven, with the exception of the color. Variations of species are common.
Science does not make statements like "all ravens are black". Science would state "all observed ravens are black", with a more specific definition of what it means to be called a Raven. Also, scientists don't confuse "laws" with absolute reality. Laws represent as close to absolute statements about reality as are possible to make. Big difference.
Soryy, hermeneus. Of course you know the sample size, but you don´t know where the sample comes from.
"Science does not make statements like "all ravens are black". Science would state "all observed ravens are black", with a more specific definition of what it means to be called a Raven."
Well, scientific laws are not only laws about past observations. That´s why they are used to predict the future.
__) but you don't know where the sample comes from.
You just need to select samples randomly.
Anyway, one problem with Hempel was that he construed scientific laws as mere statistical correlations. That ravens are black is not confirmed by just observing a bunch of ravens that are black. Instead you usually seek a deeper cause that exists below the physical appearances (being black-colored and having a raven-like form) that substantially connect the two, some gene responsible for the color of feather in this case.
Well, that would simply mean you look for a common causation. There is no problem with doing that statistically. Patrick Suppes did some work on that.