Blame David Hume


BaalChatzaf

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Hume's argument is nothing more than a straw man. His argument may be logically sound, but since it doesn't pertain to the way people actually think(DB emphasis), it is irrelevant.

Note my emphasis. I didn't know it was the Objectivist position that people don't actually think logically! In which case, you and Hume are in full agreement. For this is the consequential problem that follows the logical problem of induction ie the psychological problem of induction.

Clearly, you did not understand what I plainly stated. People do not generally think in terms of induction. They do not think, "hmmm, I've seen one hundred swans and all of them were white, therefore all swans must be white." It is true that the conclusion does not follow from the evidence, so, in that sense, Hume was right. But most people would never jump to the inductive conclusion anyway, so Hume has discovered a fallacy that does not apply to the manner in which people typically think. People may be somewhat more logical than Hume's straw man.

(In passing, I note that, to use Objectivist parlance, most Objectivist discussion of the problem of induction relies on stolen concepts such as “validity.” They are stolen, of course, from deductive logic).

A fairly presumptuous assertion. But, let us agree to use the concept only in the manner in which it was intended.

Darrell

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People do not generally think in terms of induction. They do not think, "hmmm, I've seen one hundred swans and all of them were white, therefore all swans must be white."

Actually, this was in fact widely believed prior to the discovery of the black swan in Australia. Hence the origin of the example.

It is true that the conclusion does not follow from the evidence, so, in that sense, Hume was right.

Well, we agree on the main point then, which is highly promising.

But most people would never jump to the inductive conclusion anyway, so Hume has discovered a fallacy that does not apply to the manner in which people typically think. People may be somewhat more logical than Hume's straw man.

Hume's point re human psychology is not a "straw man", but a consequence of the main point. Hopefully Popper's use of the modus tollens in conjunction with imaginative hypothesis has defused the psychological version of the problem, even if the logical problem itself is as we agree.

(In passing, I note that, to use Objectivist parlance, most Objectivist discussion of the problem of induction relies on stolen concepts such as “validity.” They are stolen, of course, from deductive logic).
A fairly presumptuous assertion. But, let us agree to use the concept only in the manner in which it was intended.

Fine by me.

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  • 2 weeks later...
People do not generally think in terms of induction. They do not think, "hmmm, I've seen one hundred swans and all of them were white, therefore all swans must be white."

Actually, this was in fact widely believed prior to the discovery of the black swan in Australia. Hence the origin of the example.

I would put this in the category of unusual cases that are often repeated because they are unusual. If you were to ask a random person, unbiased by previous familiarity with the question, whether he thought all swans were white, what kind of response do you think you would get?

Hume's point re human psychology is not a "straw man", but a consequence of the main point. Hopefully Popper's use of the modus tollens in conjunction with imaginative hypothesis has defused the psychological version of the problem, even if the logical problem itself is as we agree.

It seems to me that the so called Problem of Induction is far more often a problem of approximation. It is not that the conclusion is wrong or invalid, but rather that it is only approximate. The classical example of Newtonian physics and, in particular, the Galilean transformation equations (x = x0 + vt) comes to mind. The equations represent a valid approximation of reality, a fact that can be deduced from other (observational) facts. It is not believed because it has been right 100 time before, but because it is experimentally observed to be valid.

Even one observation of the proper kind is often sufficient to establish the validity of a given approximation. I don't need to observe 100 rocks to understand that rock is a solid and not a liquid. An approximation is valid if it gives accurate results within the precision of the measuring instruments available under the conditions of measurement. The problem is extrapolating those results to very different conditions. A rock will become liquid at a sufficiently high temperature. The Galilean approximation breaks down at high speeds. Thus, the process of science is, at least partially, a process of extending approximations to new conditions. It may be difficult to know whether all possible conditions have ever been considered, but that does not invalidate the approximations that we know under the conditions that we know them.

In The Problem of Induction (1953, 1974) (http://dieoff.org/page126.htm) Karl Popper states:

Take as an example classical Newtonian mechanics. There never was a more successful theory. If repeated observational success could establish a theory, it would have established Newton's theory. Yet Newton's theory was superseded in the field of astronomy by Einstein's theory, and in the atomic field by quantum theory. And almost all physicists think now that Newtonian classical mechanics is no more than a marvellous conjecture, a strangely successful hypothesis, and a staggeringly good approximation to the truth.

But, according to Hume's Problem of Induction, since it impossible to ever establish the truth of anything, it is also impossible to know whether anything is, "a staggeringly good approximation to the truth." Thus, Popper contradicts himself.

The key is that most facts are established approximately --- accurately under known, specific conditions --- by a process that has nothing to do with induction.

Darrell

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It seems to me that the so called Problem of Induction is far more often a problem of approximation. It is not that the conclusion is wrong or invalid, but rather that it is only approximate. The classical example of Newtonian physics and, in particular, the Galilean transformation equations (x = x0 + vt) comes to mind. The equations represent a valid approximation of reality, a fact that can be deduced from other (observational) facts. It is not believed because it has been right 100 time before, but because it is experimentally observed to be valid.

Experimentally observed -a finite number of times-. No finite set of observations can establish a general principle, unless the set of observations exhausts the domain of application of the principle, which almost never happens.

There is no difference in principle between 100 experiments and a 100 instances of black crows. Neither logically implies the generality.

Ba'al Chatzaf

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Experimentally observed -a finite number of times-. No finite set of observations can establish a general principle, unless the set of observations exhausts the domain of application of the principle, which almost never happens.

It may or may not be possible to exhaust the domain of application. If not, then we have a series of better and better approximations as we explore more and more of the domain. But, each approximation is valid. It holds under the range of conditions that have been explored. The Induction Problem is different. It says that we can never know anything, even approximately. For example, it states that we can never be sure that the Sun will come up tomorrow because we have only seen it rise a finite number of times in the past. It ignores the fact that we can understand the nature of things that exist. If we understand the nature of the Earth and Sun and the forces governing their movement, then we can know that the Sun will come up --- that the Earth will continue to orbit the Sun and continue to rotate on its axis so that the Earth and Sun will be in the expected relationship with respect to each other tomorrow to the accuracy that we can measure such relationships. (Clouds, an eclipse, or other phenomena may obscure a person's view of the Sun, but, as long as the geometric relationships are generally correct, then the Sun has come up.)

I thought it would be interesting to offer a bet to anyone willing to take it. I will give whoever wants it 10,000 to one odds on the Sun coming up. I'll bet $200,000 and you bet $20. If the Earth stops rotating between now and tomorrow or stops orbiting the Sun or if the rate of rotation or orbital velocity varies by even 10%, you win. Otherwise, I win. We'd have to agree on how such things would be measured, but I doubt that anyone would take me up on the bet, for, despite the interesting nature of this conversation, everyone knows, without a doubt, that the Sun will come up tomorrow.

The number of times that something is observed is irrelevant. The question is whether the observer understands what he is observing. If he does, it may only require one observation to deduce a valid approximation. If this were not true, it would not be possible to recognize two crows as being animals of the same kind. What good would it do to observe a hundred crows if you could never be sure any two of them were of the same kind and hence whether either or both were even crows, irrespective of their color? Before a negative example can be identified, it must be possible to identify it as an example and that means knowing its properties. It means understanding what it is.

Darrell

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The situation is that, in all likelihood, the sun will rise tomorrow and we all know that, BUT, that's not the same as saying it is a certainty. We would have to be able to see into the future for that. But is this really a big problem? It seems rather trivial to me, like the difference between 99.999% and 100%. :D

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Experimentally observed -a finite number of times-. No finite set of observations can establish a general principle, unless the set of observations exhausts the domain of application of the principle, which almost never happens.

It may or may not be possible to exhaust the domain of application. If not, then we have a series of better and better approximations as we explore more and more of the domain. But, each approximation is valid. It holds under the range of conditions that have been explored. The Induction Problem is different. It says that we can never know anything, even approximately.

Nonsense! The induction problem (so-called) is that induction is not a logically valid mode of inference. Induction is a practical way of producing general statements from a finite set of instances. The generalization might be true or it might be false.

We always -know- (or could know) the particulars. It is the generalization that is not guaranteed to be true.

I think you have been reading too much Peikov. Don't. He is more often wrong than right and he is a mathematical and scientific ignoramus.

Ba'al Chatzaf

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I think you have been reading too much Peikov. Don't. He is more often wrong than right and he is a mathematical and scientific ignoramus.

Ba'al Chatzaf

Please get the spelling right. It's Pea-cough.

reb

Actually, if you were Russian, "Peikov," would be pronounced, "Pea-cough." (I took a couple of semesters of Russian in college.)

Darrell

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Experimentally observed -a finite number of times-. No finite set of observations can establish a general principle, unless the set of observations exhausts the domain of application of the principle, which almost never happens.

It may or may not be possible to exhaust the domain of application. If not, then we have a series of better and better approximations as we explore more and more of the domain. But, each approximation is valid. It holds under the range of conditions that have been explored. The Induction Problem is different. It says that we can never know anything, even approximately.

Nonsense! The induction problem (so-called) is that induction is not a logically valid mode of inference. Induction is a practical way of producing general statements from a finite set of instances. The generalization might be true or it might be false.

If this were true, I might be inclined to agree with you. But lets look at what Popper actually said (http://dieoff.org/page126.htm):

Hume's two problems of induction -- the logical problem and the psychological problem -- can best be presented, I think, against the background of the commonsense theory of induction. This theory is very simple. Since all knowledge is supposed to be the result of past observation, so especially is all expectational knowledge such as that the sun will rise tomorrow, or that all men are bound to die, or that bread nourishes. All this has to be the result of past observation.

It is to Hume's undying credit that he dared to challenge the commonsense view of induction, even though he never doubted that it must be largely true. He believed that induction by repetition was logically untenable - that rationally, or logically, no amount of observed instances can have the slightest bearing upon unobserved instances. This is Hume's negative solution of the problem of induction, a solution which I fully endorse.

He said that, "no amount of observed instances can have the slightest bearing on unobserved instances," [Emphasis mine]. He did not merely say that you can't extrapolate to infinity. He said that you can't know anything at all. In particular, he said that you cannot predict that the sun will rise tomorrow. And, clearly, if you cannot know that the sun will rise tomorrow, you cannot know the probability of it rising either. The probability, in this view, is not 99.999%. It is 50%. It is a toss up. It is simply not possible to know that it will come up or even the probability of it coming up. (In the absence of any evidence about the outcome of a binary experiment it is typical to assign a probability of 0.5 to each possible outcome. That is the assignment corresponding the state of complete ignorance.)

This is simply not a tenable position and is clearly the result of ignoring the law of identity and its corollary, the law of causality. It ignores the fact that every entity has a specific nature and acts in accordance with it. To state that past experience has, "no bearing," on our knowledge of the future, is, in effect, to state that arbitrary things can happen. In this respect, it is similar to the agnostics' view that one must entertain the existence of God because God cannot be disproven. But, of course, it is impossible to disprove the non-existence of something because there can never be evidence for the non-existence of something that does not exist. Similarly, there has never been any evidence for the existence of anything that did not have a specific nature, an identity. But, in fact, the burden of proof is on those that claim that the arbitrary is reality to provide evidence that it is.

If things that exist have a specific nature and if it is possible to understand their nature to some degree, then it is possible to make predictions with some degree of accuracy. The predictions thus made may not extend throughout all of space and time, to very high or very low temperatures, to extreme gravitational or electrical fields, but they do extend beyond the immediate moment. They are valid approximations. That is why it is possible to say, with virtual certainty, that the sun will rise tomorrow. If such were not the case, life would be impossible.

Darrell

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He said that, "no amount of observed instances can have the slightest bearing on unobserved instances," [Emphasis mine]. He did not merely say that you can't extrapolate to infinity. He said that you can't know anything at all. In particular, he said that you

He said no such thing. He said past events cannot, with certainty, predict all future events. Even if an induction breaks down we know every one of the particulars (our could know them) that eventually collided with the generality that does not hold. That is hardly knowing nothing.

Why do you keep repeating this canard? We know every particular observation we make. It is the generality that we cannot be certain of. Here is the bottom line: we cannot deduce, with certainty, general statements (universally quantified statements) from particular instances.

Ba'al Chatzaf

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He said that, "no amount of observed instances can have the slightest bearing on unobserved instances," [Emphasis mine]. He did not merely say that you can't extrapolate to infinity. He said that you can't know anything at all. In particular, he said that you cannot predict that the sun will rise tomorrow. And, clearly, if you cannot know that the sun will rise tomorrow, you cannot know the probability of it rising either. The probability, in this view, is not 99.999%. It is 50%. It is a toss up. It is simply not possible to know that it will come up or even the probability of it coming up. (In the absence of any evidence about the outcome of a binary experiment it is typical to assign a probability of 0.5 to each possible outcome. That is the assignment corresponding the state of complete ignorance.)

I certainly agree with you that this statement "no amount of observed instances can have the slightest bearing on unobserved instances" does not make sense. The fact that the sun has come up everyday for the conceivable past most definitely makes one expect it to come up again tomorrow. Like I said, even though we can't say it is a mathematical certainty who cares? I'm not a probability expert but a question that given the sun has come up a bazillion times in the past the odds are higher than 50-50 it will come up tomorrow. And I think you agree or else you wouldn't give 10,000:1 odds in a bet. :D

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Darrell,

A slight shift in language makes this all easier.

A pattern can only be observed over time. A pattern sometimes has elements that are exceptions to it, but that does not negate the existence of the pattern.

(It's the form and content thing I have been going on about recently. We can call it category and member here.)

From what I have read of Popper, this appears to be a core belief of his also. But he plays a lot of word games with it, essentially blaming the pattern for not including the exception instead of refining the pattern.

He also seems to like the shock value of going against common sense and the obvious. But if you look behind the rhetoric and the words he chooses for his concepts and just focus on the concepts, you often find he says the same thing Objectivism does. Many Popperians die seven deaths on contemplating that fact (and many Objectivists also), but there it is. One day I intend to research this in depth and write about it.

I have read enough to know there is a discernible pattern, so the idea can be developed.

One thing I find funny is the approach of excluding time in an observation of a thing in order to predict the future of that thing (or category of thing). The future is time, so it makes no sense to me to exclude time to work with time.

Michael

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He said that, "no amount of observed instances can have the slightest bearing on unobserved instances," [Emphasis mine]. He did not merely say that you can't extrapolate to infinity. He said that you can't know anything at all. In particular, he said that you

He said no such thing. He said past events cannot, with certainty, predict all future events. Even if an induction breaks down we know every one of the particulars (our could know them) that eventually collided with the generality that does not hold. That is hardly knowing nothing.

Why do you keep repeating this canard? We know every particular observation we make. It is the generality that we cannot be certain of. Here is the bottom line: we cannot deduce, with certainty, general statements (universally quantified statements) from particular instances.

Ba'al Chatzaf

How do you know this? Did you deduce it? From what premises? Or did you <shudder> induce it? If so, how does it escape your general statement about general statements?

Actually, I'm not aware that anyone, except maybe proto-Humeans, claim that generalizations are deduced (validly or not) from particular instances. I don't think anyone (with the noted exception) claims that induction is just a disguised, bogus form of deduction, either.

Best regards from the cat that ate the canard,

REB

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How do you know this? Did you deduce it? From what premises? Or did you <shudder> induce it? If so, how does it escape your general statement about general statements?

Actually, I'm not aware that anyone, except maybe proto-Humeans, claim that generalizations are deduced (validly or not) from particular instances. I don't think anyone (with the noted exception) claims that induction is just a disguised, bogus form of deduction, either.

Best regards from the cat that ate the canard,

REB

Because there are white (albino) crows and black swans. Heat is not a fluid and there is no aether or phlogiston.

All one needs to make the point is come up with an induction that leads to a factually false conclusion. I have just given five such examples.

Enjoy your meal.

Ba'al Chatzaf

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He also seems to like the shock value of going against common sense and the obvious. But if you look behind the rhetoric and the words he chooses for his concepts and just focus on the concepts, you often find he says the same thing Objectivism does. Many Popperians die seven deaths on contemplating that fact (and many Objectivists also), but there it is. One day I intend to research this in depth and write about it.

Can you communicate with the dead?

You don't know what Popper liked or disliked. You only know what he wrote and of that what you read.

Ba'al Chatzaf

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Can you communicate with the dead?

You don't know what Popper liked or disliked. You only know what he wrote and of that what you read.

Bob,

I have based my speculation on Popper's writing and history, the parts I am familiar with.

No, I do not communicate with the dead. I also try not to read things like that into where they don't belong.

Do you need an attention fix?

Michael

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He said that, "no amount of observed instances can have the slightest bearing on unobserved instances," [Emphasis mine]. He did not merely say that you can't extrapolate to infinity. He said that you can't know anything at all. In particular, he said that you

He said no such thing. He said past events cannot, with certainty, predict all future events.

No, he said that past events cannot predict any future events. In fact, past events have "no bearing" on future events.

Darrell

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He said that, "no amount of observed instances can have the slightest bearing on unobserved instances," [Emphasis mine]. He did not merely say that you can't extrapolate to infinity. He said that you can't know anything at all. In particular, he said that you

He said no such thing. He said past events cannot, with certainty, predict all future events.

No, he said that past events cannot predict any future events. In fact, past events have "no bearing" on future events.

Darrell

We have loads of theories that have predicted some future event. No amount of experimentation will show that those very theories will produce only true predictions. Future events are sometimes predicted on the basis of observing past events and sometimes the predictions are wrong.

Which is why the best thing you can say of a scientific theory is that it has not yet been falsified.

Induction and Abduction are techniques for generating educated guesses (which is what a hypothesis is) from a finite set of data. There is no guarantee that the hypotheses will be true in general (i.e. never produce an incorrect prediction).

Now go to Humes example about sun rises. Someday the sun (most likely) will become a red giant and vaporize the earth. Then there will be no more sunrises. Five billion years of sunrises cannot guarantee the sun will always rise. Also, the earth will lose the moon (it is moving further out). When that happens a tidal lock could occur between the earth and the sun wherein the earth's rotation period may equal its revolution period. That means the sun will occupy a fixed point in the sky. In short, no more sunrises (which means earth turns).

Ba'al Chatzaf

Edited by BaalChatzaf
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Now go to Hume's example about sun rises.

Ba'al, perhaps we could try an even simpler example:

It has rained for four Tuesdays in a row. Therefore it will rain next Tuesday.

Now, this sounds absurd, but there is no logical difference between saying this and the sun has risen X times in the past, therefore it will rise tomorrow.

Darrell has already agreed with Hume's logical argument. From there, I think he has then mistakenly ended up in a simple petitio, in that he claims prior "understanding" despite the fact the whole point of debate is how "understanding" came about in the first place.

Edited by Daniel Barnes
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He said that, "no amount of observed instances can have the slightest bearing on unobserved instances," [Emphasis mine]. He did not merely say that you can't extrapolate to infinity. He said that you can't know anything at all. In particular, he said that you

He said no such thing. He said past events cannot, with certainty, predict all future events.

No, he said that past events cannot predict any future events. In fact, past events have "no bearing" on future events.

Darrell

We have loads of theories that have predicted some future event. No amount of experimentation will show that those very theories will produce only true predictions. Future events are sometimes predicted on the basis of observing past events and sometimes the predictions are wrong.

Which is why the best thing you can say of a scientific theory is that it has not yet been falsified.

Induction and Abduction are techniques for generating educated guesses (which is what a hypothesis is) from a finite set of data. There is no guarantee that the hypotheses will be true in general (i.e. never produce an incorrect prediction).

Now go to Humes example about sun rises. Someday the sun (most likely) will become a red giant and vaporize the earth. Then there will be no more sunrises. Five billion years of sunrises cannot guarantee the sun will always rise. Also, the earth will lose the moon (it is moving further out). When that happens a tidal lock could occur between the earth and the sun wherein the earth's rotation period may equal its revolution period. That means the sun will occupy a fixed point in the sky. In short, no more sunrises (which means earth turns).

Ba'al Chatzaf

Is Mercury in a tidal lock? Venus? Mars? Are you saying that the moon is going to fly free of the Earth's gravity at some point? It's been moving away from the Earth since it was created.

If we feed the planet a lot of beans, the resulting flatulence should keep it turning.

--Brant

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He also seems to like the shock value of going against common sense and the obvious. But if you look behind the rhetoric and the words he chooses for his concepts and just focus on the concepts, you often find he says the same thing Objectivism does. Many Popperians die seven deaths on contemplating that fact (and many Objectivists also), but there it is. One day I intend to research this in depth and write about it.

There is a fundamental difference between Popper's view (and Hume's view) and my own (which I don't claim is the Objectivist view). In order for the the Induction Problem, as stated by Popper and Hume, to be a serious problem it is necessary to ignore the Law of Identity and its corollary, the Law of Causality. That, in turn, allows an equivocation which leads to an enormous amount of confusion.

First, let us consider the problem of the white swans. That is a typical example of where induction fails. In the problem, one supposedly sees a number of white swans (100 say) and from that concludes that all swans are white. To conclude such a thing is clearly a logical fallacy. Color is not an essential characteristic of a swan. If a bird with the essential characteristics of a swan that was not white was discovered, it would still be called a swan. Moreover, there is no causal link between any of the essential characteristics of a swan and its color. Therefore, there is no mechanism for predicting that a bird having the essential characteristics of a swan must have a certain color. There is no logical basis for concluding that all swans are white.

The mere repetition of the color white does not strengthen the basis for concluding that swans are white. Whether one had seen a single white swan or 100 white swans, there is no logical basis for concluding that all swans are white. Whiteness is not essential to swan-ness. It should also be noted that it is well known that many other animals come in a variety of colors. Consequently, it would seem rash to conclude that all swans are white. But, this is not really central to the argument. Until one has established that some characteristic is essential to the nature of a thing, there is no reason to believe that that characteristic is the same for all instances of that thing.

Now, compare the swan example with the case of the Sun rising in the morning. The fact that the Earth will continue to rotate on its axis is essentially connected to its fundamental nature as a planet moving through space. In order to see a prediction that the Sun will rise as a mere case of induction, one must first suspend one's knowledge of the nature of the Sun and Earth. One must pretend that they have no essential nature and that the Earth could stop rotating or fly off into space or disappear just as easily as one could find a black swan. Or, one must pretend that it is impossible to know anything or understand anything about anything.

The equivocation comes in equating an example in which a conclusion is fallaciously reached by looking only at the inessential characteristics of a thing and ignoring identity and causality and an example in which the conclusion is drawn by carefully examining the properties of the objects in question. This is exactly what Popper and Hume do. But, the Law of Identity is a fact of everything that exists. To posit an exception to it is to posit that the arbitrary is reality.

Darrell

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Darrell,

I agree with this for the most. However something fell into place when I started looking at the top-down, bottom-up thing.

It is inaccurate to say that Popper & Co. do not recognize the Law of Identity and Causality. They do, only they do for the small stuff, not the holon or system or entity level. For instance, to say that a black swan exists, they first have to say "black." That has a definite identity to them. I don't imagine they will find an exception, say black being not black tomorrow. And it doesn't matter if black was black last Tuesday, either. It will be black tomorrow. They seem to be pretty solid on that one. :)

The problem I see is that they look from the bottom up only and try to show how this invalidates the identity and causality of the top-down. In essence, they replace the standards of one with those of the other and then claim it doesn't work.

In the swan case, they do not grant full identity and causality to swans. But they do to parts of swans and they use this to claim that it somehow proves that their view of swan is correct and lacking in fundaments.

The irony is in the end result. If you step outside the jargon, you can still have an open-ended category with these dudes that admits new knowledge to be included into it. (And that is one of the fundaments of a concept in Objectivism.) For instance, swan still continues to be a category to them. The only thing is that not all swans are white. I can't think of any Objectivist who would argue with that, either. The emphasis for them is placed on the new knowledge and not the category, but I haven't seen them state that making categories is invalid. In fact, they use categories all the time, especially when playing these word games.

Here is a real difference with the Popper universe (but this is changing the subject). They have a George Soros who goes around the world unapologetically funding Popper's open society concept in countries under dictatorship. Would it be that Objectivism had the same.

Michael

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Now, compare the swan example with the case of the Sun rising in the morning. The fact that the Earth will continue to rotate on its axis is essentially connected to its fundamental nature as a planet moving through space. In order to see a prediction that the Sun will rise as a mere case of induction, one must first suspend one's knowledge of the nature of the Sun and Earth. One must pretend that they have no essential nature and that the Earth could stop rotating or fly off into space or disappear just as easily as one could find a black swan. Or, one must pretend that it is impossible to know anything or understand anything about anything.

When the Sun becomes a red giant and expands out to where the Earth orbits, the Earth will be vaporized and will no longer rotate. So five billion years of rotation will not imply that the Earth will continue to rotate. The rotation of the Earth -now-, has nothing to do with its ultimate fate.

Ba'al Chatzaf

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