I have just proved that observational support for for a universal statement is impossible. — tom

Hypothesis: All unenlightened's pockets are empty.

*checks all pockets, finds each and every one to be empty.*

"Hey Tom, all my pockets are empty. I just looked."

Sure, all ravens in Vienna in 1938 were also black. Perhaps you should consult an elementary text on universal statements?

I don't think so, Tom. I'll let you quote one that rules that not to be a universal. I'll even modify it a bit for you: All unenlightened's pockets everywhere in the universe are empty.

The trouble with ravens is that there are lots of them and it's hard to know if you've seen them all, but if you did see them all, and they were all black, you'd have all the evidence you need.

The difference is that you actually observed all of your pockets. The OP is claiming that a single observation provides evidential support for a universal proposition. @Tom's proof shows that this is not the case - but it no longer applies once you have observed all members of the class, at which point you know whether the universal proposition is true (p=1) or false (p=0).

All unenlightened's pockets everywhere in the universe are empty. — unenlightened

One more point - you also have to stipulate that this was true when the observations occurred. Even then, it is only strictly true if those observations were simultaneous; otherwise, something could have appeared in the first pocket that you checked by the time that you got to the last one. Furthermore, the fact that your pockets were empty then does not warrant the claim that they are still empty now and will remain empty in the future. This gets at my earlier comment about a universal proposition having to include all potential members in the class, not just its actual members.

But Tom's proof shows no such thing. If I have looked at 16 of my 17 pockets and found them empty, I have probable grounds for thinking that the last one will be also empty.

If I have looked at 16 of my 17 pockets and found them empty, I have probable grounds for thinking that the last one will be also empty. — unenlightened

Not really. Why would you think that? The contents (or lack thereof) of the first 16 pockets have no bearing whatsoever on the contents (or lack thereof) of the 17th pocket.

One more point - you also have to stipulate that this was true when the observations occurred. Even then, it is only strictly true if those observations were simultaneous; otherwise, something could have appeared in the first pocket that you checked by the time that you got to the last one. Furthermore, the fact that your pockets were empty then does not warrant the claim that they are still empty now and will remain empty in the future. This gets at my earlier comment about a universal proposition having to include all potential members in the class, not just its actual members. — aletheist

I'm afraid this is just bluster to save the point. A universal does not have to be eternal in scope, and if one cannot rule out pockets that fill themselves or ravens that turn black when looked at, then nothing can be said about anything. curb your skepticism a little.

To the extent that one has explored the logical space and found it empty of non.black ravens or pocketed stuff or whatever, to that extent it is probable that the space is empty. Bring in all the caveats you like to invalidate the observations, the principle holds if statistics and language mean anything at all.

Not really. Why would you think that? The contents (or lack thereof) of the first 16 pockets have no bearing whatsoever on the contents (or lack thereof) of the 17th pocket. — aletheist

Check out the marbles in a bag scene. If there is one white one and sixteen black ones, would you bet on the white one being the last one out of the bag, or some other place?

To the extent that one has explored the logical space and found it empty of non.black ravens or pocketed stuff or whatever, to that extent it is probable that the space is empty. — unenlightened

I am fine with this common-sense approach for everyday living, especially if we substitute "one is confident" for "it is probable." What bothers me is the claim that we can meaningfully calculate a mathematical value for this "probability," as well as the claim that the observation of a non-black non-raven or a non-empty non-unenlightened's-pocket somehow affects the assessment.

If there is one white one and sixteen black ones, would you bet on the white one being the last one out of the bag, or some other place? — unenlightened

That is a different scenario. If I knew nothing about the contents of the bag, and had already drawn 16 black ones, I might very well be tempted to bet that the last one would also be black - and I would be dead wrong.

The difference is that you actually observed all of your pockets. The OP is claiming that a single observation provides evidential support for a universal proposition. Tom's proof shows that this is not the case - but it no longer applies once you have observed all members of the class, at which point you know whether the universal proposition is true (p=1) or false (p=0). — aletheist

In the proof I gave, observation of your own pockets would constitute background knowledge. The hypothesis would be the universal statement "all pockets are empty". I guess you could then set about gathering evidence.

I don't think so, Tom. I'll let you quote one that rules that not to be a universal. I'll even modify it a bit for you: All unenlightened's pockets everywhere in the universe are empty. — unenlightened

Since you won't consult an elementary text, let me help you:

A universal statement is one in which no individual names occur.

Got it?

By believing that the actual color of the eggs is somehow indeterminate until one opens the carton. It is not; it is a fact that either they are all white (p=1) or that at least one is non-white (p=0), unless we are going to treat this as a quantum physics scenario like Schroedinger's cat where each egg is neither white nor non-white until one observes it. — aletheist

I don't think any reasonable person will interpret my claim in this way. It certainly isn't implied, as you suggest.

A universal proposition does not assert the actual existence of anything in the subject class, so it must apply to all potential things in the subject class.

This doesn't seem right. If I say that all humans are shorter than 9 feet I'm not saying that all potential humans are shorter than 9 feet.

You used universal propositions, not singular propositions, in the OP. Now you are claiming that the two propositions of interest are both singular - "if a is a raven, then a is black," and its contrapositive, "if a is not black, then a is not a raven." In this example, a is a green apple, so it is trivial to say that a is not black and not a raven; both propositions are true (p=1). A second observation of a green apple, call it b, would go with a different pair of singular propositions - "if b is a raven, then b is black," and its contrapositive, "if b is not black, then b is not a raven"; again, both are true (p=1). By definition, you cannot say anything general in a singular proposition

I switched to "if something is not black then it is not a raven" and "if something is a raven then it is black" pretty early on, and (unless I've been sloppy) stuck with it since.

And the above interpretation is wrong. When I say that the probability that "if something is not black then it is not a raven" is true is 0.5 I mean that that for any randomly selected non-black thing, the probability is 0.5 that it will not be a raven.

If I say that all humans are shorter than 9 feet I'm not saying that all potential humans are shorter than 9 feet. — Michael

I think you are, unless you qualify it somehow. You are saying that anything taller than 9 feet cannot (ever) be human.

When I say that the probability that "if something is not black then it is not a raven" is true is 0.5 I mean that that for any randomly selected non-black thing, the probability is 0.5 that it will not be a raven. — Michael

Then this is a universal proposition after all, rather than a singular proposition; and it is, in fact, logically equivalent to "all non-black things are non-ravens." Your use of probability in this case is unobjectionable to me; you are simply saying that exactly 50% of all non-black things are non-ravens.

And the above interpretation is wrong. When I say that the probability that "if something is not black then it is not a raven" is true is 0.5 I mean that that for any randomly selected non-black thing, the probability is 0.5 that it will not be a raven. — Michael

How many non-black things do you need to select to show that your assertion that the probability of selecting a non-raven is 0.5?

How many non-black things do you need to select to show that your assertion that the probability of selecting a non-raven is 0.5? — tom

Twice as many as there are non-black non-ravens.

I think you are, unless you qualify it somehow. You are saying that anything taller than 9 feet cannot (ever) be human. — aletheist

I don't think I am. If I say that nobody in my house is American I'm not saying that nobody in my house can ever be American.

Then this is a universal proposition after all, rather than a singular proposition; and it is, in fact, logically equivalent to "all non-black things are non-ravens." Your use of probability in this case is unobjectionable to me; you are simply saying that exactly 50% of all non-black things are non-ravens. — aletheist

Wait, so you're saying that it's unobjectionable to claim that a universal proposition has a greater than 0 but less than 1 probability of being true?

That is a different scenario. If I knew nothing about the contents of the bag, and had already drawn 16 black ones, I might very well be tempted to bet that the last one would also be black - and I would be dead wrong. — aletheist

Let's walk through this elementary probability problem.

Scenario 1. There are 17 marbles in a bag, but they could be any colour in any combination. You take out sixteen in turn, and they are all black. You now know that there are either sixteen black ones, and one non-black, or seventeen black marbles.

Now, scenario 2. How did the marbles get into the bag?

(a). Suppose they were picked at random from a container with equal quantities of each of 5 colours.
Then the chances of the last marble being black would be 0.2 But the chances of getting sixteen black marbles under (a) are 0.2^16. So (a) is rather improbable.
(b). Suppose they were picked at random from a container containing equal quantities of just black and white. Then the chances of the last marble being white would be 0.5 And the chances of getting sixteen black marbles would be 0.5^16 (0.000015, approx.). Still rather improbable.
(c). Suppose they were picked at random from a container with 99 black marbles for every 1 white marble. Then the chances of the last marble being black are 0.99 And the chances of getting sixteen black marbles are 0.99^16 (0.851 approx.).

It would take some rather complicated calculation to arrive at the most probable distribution of the marbles in the container, and thus the exact probability of the last marble being black, which are beyond this probability 101 course. But it should already be apparent that the the figure will come out to greater than 0.5

Therefore, probably, the last marble is black.

And therefore, probably, all the marbles in the bag are black.

And note, if it makes a halfpence' difference to you, that neither the bag nor the marbles have been named.

If I say that nobody in my house is American I'm not saying that nobody in my house can ever be American. — Michael

Fair enough, but what you are really saying then is that nobody in your house right now is American.

Wait, so you're saying that it's unobjectionable to claim that a universal proposition has a greater than 0 but less than 1 probability of being true? — Michael

No, but I can see why you misunderstood me. The universal proposition is "if something is not black then it is not a raven"; i.e., "all non-black things are non-ravens." The proposition that I find unobjectionable is "for any randomly selected non-black thing, the probability is 0.5 that it will not be a raven." This is not the same (universal) proposition; it is instead a particular proposition, "some non-black things are non-ravens," with the additional information that the proportion of non-black things that are non-ravens is 50%.

You did not stipulate any knowledge of how the marbles got into the bag. All we knew was that the first 16 marbles that we took out were black. This information alone is insufficient to calculate a meaningful probability that the 17th marble will also be black. Most people would indeed be likely to bet on it being black in that scenario, but again, they would be wrong if it turned out to be white.

No, but I can see why you misunderstood me. The universal proposition is "if something is not black then it is not a raven"; i.e., "all non-black things are non-ravens." The proposition that I find unobjectionable is "for any randomly selected non-black thing, the probability is 0.5 that it will not be a raven." This is not the same (universal) proposition; it is instead a particular proposition, "some non-black things are non-ravens," with the additional information that the proportion of non-black things that are non-ravens is 50%. — aletheist

Probability is a complete red herring until someone states the prior and tells us how to update it.

Then they need to explain why we should set our credence to be equal to the probability. (hint look up the Principal Principle)

Then someone needs to explain how we can test a probability statement, what deviations from the expectation value we are willing to accept, and why.

Then someone might deign to explain why a "probable" theory is "probably true"

Then this

No, but I can see why you misunderstood me. The universal proposition is "if something is not black then it is not a raven"; i.e., "all non-black things are non-ravens." The proposition that I find unobjectionable is "for any randomly selected non-black thing, the probability is 0.5 that it will not be a raven." This is not the same (universal) proposition; it is instead a particular proposition, "some non-black things are non-ravens," with the additional information that the proportion of non-black things that are non-ravens is 50%. — aletheist

And, strange as it may seem, such probabilistic statements, which make no prediction about what will happen, are normative.

.

You did not stipulate any knowledge of how the marbles got into the bag. All we knew was that the first 16 marbles that we took out were black. — aletheist

I'm glad you noticed that. This models the situation with ravens.

This information alone is insufficient to calculate a meaningful probability that the 17th marble will also be black. — aletheist

Then you need to show where my admittedly incomplete calculation has gone wrong, because I think I have shown that the probability is greater than 0.5, and somewhere close to 0.9

Most people would indeed be likely to bet on it being black in that scenario, but again, they would be wrong if it turned out to be white. — aletheist

That's the nature of probability, that one can be wrong. The calculation is of the best bet not the certain bet.

Then you need to show where my admittedly incomplete calculation has gone wrong, because I think I have shown that the probability is greater than 0.5, and somewhere close to 0.9 — unenlightened

The calculation is fine as far as it goes; the interpretation is the problem. The last marble in the bag is either black (p=1) or non-black (p=0), we just do not yet know which. You have basically invented a clever mathematical way of measuring your level of confidence in your guess that the 17th marble is black, based solely on the fact that the first 16 were black.

That's the nature of probability, that one can be wrong. — unenlightened

If one can be wrong, then one is really talking about (subjective) confidence or degree of belief, rather than (objective) probability.

You have basically invented a clever mathematical way of measuring your level of confidence in your guess that the 17th marble is black, based solely on the fact that the first 16 were black. — aletheist

I'm a damn smart dude, but I can't take the credit for inventing elementary probability theory. This is high school stuff that I assumed those discussing probable evidence would be familiar with. I'm amazed at the level of bluff and bluster that passes for argument and understanding in such matters.

If one can be wrong, then one is really talking about (subjective) confidence or degree of belief, rather than (objective) probability. — aletheist

That is a pile of crap of biblical proportions that I am not going to even try and clear up.

A universal statement is one in which no individual names occur. — tom

That is certainly right. But it illustrates the bigger issue of how logic relates to the world - which you, as a student of Popper, would understand.

Popper nicely brought out how the universal and the individual (or singular) are formally reciprocal bounds ... or a dichotomy. So really, when it comes down to it, each "exists" only in distinction to its "other". Thus both universality and individuality remain always relative concepts. They are never standalone absolutes. And from that, we can understand the need for a triadic epistemology where the universal and the individual are the bounds "to either side" of the actual thing in question - the entity we invoke by calling out its proper name.

So here is my raven called Raven. We have the three things of some actual "bird" I own (a substantial instance), the form of that being (the generality that constitutes "a raven"), and the matter of that being (the individual materiality or collection of properties that allow Raven to be classed as an actual instance of a universal idea).

The world is thus hylomorphic. The debate about universals and singulars, generals and particulars, only repeats the metaphysical causal debate over the nature of substance at the level of the logical modelling of real things.

Anyway, getting back to the point about universal statements not naming individuals, this is how generality would be achieved - by managing to put as much distance as possible between the universal and individual sense of a word like "raven". And yet by the same token, the distancing achieved is only ever relative to itself, never actually absolute. But people then treat the logic as if it has achieved this absolute (deductively valid) status. And the same people look back at the world and see that it is still (inductively) relative to a history of observations.

As Popper says, scientific laws take the "negative" form of proscriptions or constraints when they are expressed as universal statements. The law of energy conservation sounds like it asserts an absolute generality of nature, but in practice it has to be cashed out in terms of the actual observation or measurement of its "other" - the particular or existential claim that "there are no perpetual motion machines". So universality - in practice, in the real world - obtains only by a failure to find otherwise. The absence of not-A as a particular, is inductive confirmation of the presence of A as a generality.

This reciprocal deal - the reason why scientific certainty boils down to lack of falsification - is why universals do get pushed in the direction of a-temporal and a-spatial statements. It is not good enough to talk about my empty pockets, or whatever, "right here and now". To be as absolute as possible, a statement would have to show that it has pushed away to the extreme margins of observation absolutely everything that could be considered individual or particular in relation to that statement. So that shifts us decisively out of the realm of the actual and into the realm of the possible.

That again is why we have to end up with a triadic or hylomorphic logical system. We want to speak about, and reason about, substantial or actual being. And to do that, we find ourselves having to strike out in both directions "beyond" the actual. We have to head towards universally constraining necessity by simultaneously manufacturing its complementary "other" of completely individual or particularised material possibility.

Thus the (Peircean) triad of firstness, secondness and thirdness - as possibility, actuality and necessity. Or individuals, proper names and universals.

And as I say, the thread seems to revolve around the fact that people can see that the absolutism implied by the standard syntax of logical form does not match the relativity of the world being described.

But this is not paradoxical. It is simply evidence of what I keep saying - that the work of logicians, if they hope to talk about existence with true metaphysical generality, is not done. And you only have to go back to Aristotle and Peirce to see how it is triadicy, or hierarchical organisation, that must be the next step to breath relativity back into the dyadic syntactical forms that have been frozen into static absolutism by Frege and others.

I hate to say it Tom, but this is why the many worlds interpretation, computationalism, digital physics and a whole bunch of other bandwagons are metaphysically doomed. They are "illogical" in this sense. They are extrapolations of a logical absolutism where the Universe is going to have to be a case of logical relativism - the kind of triadically self-organising "universal reasonableness" that Peirce was on to, and which Popper was following up on.

I don't understand this idea of increasing probability either. The probability of two coins landing on heads is .25 because with two coins four things can happen. It's .5 with one coin because only two things can happen, whereas the probability of having gotten heads twice after the fact is 100%, as only that can happen, because it already happened. Did the probability change because I changed the variables?

If I keep moving things around it certainly is going to seem so, but it really isn't.

That is a pile of crap of biblical proportions that I am not going to even try and clear up. — unenlightened

I would say that aletheist has it bang on so far. So it is a shame to see you capitulate this way given the thread has been pretty instructive.

Aletheist is showing how our claims about objective reality always wind up being founded on subjectively reasonable seeming beliefs. People get used to talking about knowing stuff - like what's not in their pockets, or what they know they put in a bag, or included in a pack of cards. But in the end, that confidence is rather manufactured - a play of signs that we ourselves create to replace the world (whatever it is as the thing-in-itself).

My own key point in support of aletheist was to draw out how we do in fact go about manufacturing the "objective" grounds of our own certainty using games of chance. We make a physical determination (in shaping a die or printing a pack of cards) that then underwrites our claims to a concept of "randomness", or "accident", or "probability" based on a principle of indifference.

So we have a model of probability that is derived from subjective actions. We construct a machinery that divides the world sharply, counterfactually, into the bit we care absolutely about (some device like a coin that can only land on one of two sides), and then the bit we claim absolute indifference about (the spin that lands unpredictably). And then we compare this construction against the behaviour of the world to talk about "how the world actually is".

What is going on should be transparent. But people seem to hate their metaphysical realism being undermined even slightly.

So universality - in practice, in the real world - obtains only by a failure to find otherwise. The absence of not-A as a particular, is inductive confirmation of the presence of A as a generality. — apokrisis

Or as Peirce succinctly put it, "A particular proposition asserts the existence of something of a given description. A universal proposition merely asserts the non-existence of anything of a given description." (CP 5.155; 1903)

Firstly, if there are a limited number of ravens, then there are some ravens. So we are not saying merely that there are no non-black ravens, but also that there are some black ravens. Then each black raven found in the absence of any white ones decreases the population of potential non-black ravens, and so increases the probability that they are all black. — unenlightened

Yes, this was pretty much exactly the point of my egg thought experiment. So, if each black raven observed in the absence of white ones decreases the potential population of non-black ravens, thereby increasing the probability that they are all black, can we then not say that successive observations of black ravens confirms the hypothesis "all ravens are black" (contra some claims on this thread that no such confirmation can be had for universally-quantified propositions)?

I beg to differ! If there is such a thing as probabilistic support for a universal statement, then green apples do indeed support "all ravens are black". I have given the solution to this paradox earlier in the thread, so now let me prove it:

A well known result from probability calculus is:

p(he|b) = p(h|eb)p(eb)

Let h = "all ravens are black" i.e. the hypothesis
Let b = background knowledge e.g. all the ravens previously encountered
Let e = new evidence - the sighting of another raven

h logically implies e, so "h and e" is equivalent to h, so

p(h|b) = p(h|eb)p(eb)

Thus

p(h|eb)=p(h|b)/p(eb)

Do this again with an alternative hypothesis:

k = "NOT all ravens are black"

And divide one expression by the other, you get:

p(h|eb)/p(k|eb) = p(h|b)/p(k|b)

Now notice that no matter how h and k generalize under new evidence e, the evidence is incapable of affecting the ratio of their probabilities! What you are left with is the ratio of the prior probabilities, which you can have done nothing except arbitrarily set.

Thus there is no such thing as probabilistic support for a universal statement! — tom

I have some questions about this. I don't see how H (hypothesis) logically implies E (evidence). I understand the hypothetico-deductive mode of reasoning (which, in very general terms, science adheres to), i.e. posit a hypothesis, deduce observational consequences of said hypothesis, and perform a test to look for said consequences. However, in this case, I don't see how "all ravens are black" implies "the sighting of another raven." I'm not sure what the latter statement even means, exactly (H seems to imply only that, if one were to observe a raven, then said raven would be black).

Also, in order for the posterior probabilities not to matter here (because E cancels out), H and K must somehow imply the same "E". But, how can a hypothesis and its negation imply the same observational consequences?

I don't understand thing idea of increasing probability either. The probability of two coins landing on heads is .25 because with two coins four things can happen. It's .5 with one coin because only two things can happen, whereas the probability of having gotten heads twice after the fact is 100%, as only that can happen, because it already happened. Did the probability change because I changed the variables?

If I keep moving things around it certainly is going to seem so, but it really isn't. — Wosret

If you've already flipped a coin (your first of the day) and it's landed heads then what's the probability that the first two coins you flip today will be heads? Given that one of them landing heads is certain (it's already happened) the probability is the probability that the next one will land heads, which is 0.5.

So it would have been correct to say that the probability of "the first two coins I flip today will land heads" being true is 0.25 before your first flip, and correct to say that it's probability is 0.5 after the first flip (but before the second).

Might be related to the Monty Hall problem (or maybe it isn't, I don't know).