Induction and Inertia

[Darrell Hougen]

Darrell:

My argument is that even though we may not have the exact formulation of the correct law, we know that we are close.

Any exceptions must be small or must occur infrequently.

Otherwise, we would have seen evidence of them earlier.

The obvious reply to all of the above is: why? These are merely a series of bald assertions, with nothing whatsoever necessary about them.Where's the argument?

I'm still trying to formulate the exact nature of my argument. But, as I alluded to earlier, it has to do with the notion that entities are not infinitely complex.

I may also appeal to the notion that an entity exhibits a limited amount of variability within a finite span of time. Then, if we wish to ascribe an unlimited number of attributes to a single entity, we must at least have a result stating that the sum of all the variances is bounded. These things are reasonable corollaries of the Law of Identity. To be is to be something. Unlimited variability implies no particular identity.

But, if the variability of an entity is bounded and 90% of the observed variability is explained by a particular law, then whatever we don't understand must comprise only 10% of the variability.

Something very much like this occurred with Newtonian Mechanics. Within the realm of ordinary velocities and ordinary gravitational fields, his equations could be tested to within a certain precision using instruments available at the time. Within that realm, his equations may have predicted 99.99% of the variability --- and they still do. It was not until the conditions were changed radically or much more accurate measuring techniques were devised that departures from his predictions could be measured. So, the amount of unexplained variability was limited.

I'm applying a little slight of hand here. For how are we to know that our experience is somehow representative of things we have not seen? But, I believe there are ways for humans to handle this problem. When we are first born, everything we see is a surprise because we have never seen anything before. But, as we get older, the number of surprises we are confronted with gradually decreases, especially with respect the natural world. We may see more and more cows, for example, but each cow is similar to the ones we have seen before. So, we get a sense of how justifiable our conclusions are. If we are usually right, we are, in some sense, justified in assuming we will probably be right about similar things in the future.

Moreover, it should be pointed out that our exploration of the natural world is under our control. From the point of view of the world, it is a kind of random sampling that the world cannot control. Therefore, the probability of missing things is a function of the actual complexity of the world and the amount of exploration that has occurred. If a person has randomly sampled a 100 square mile area on 1000 separate occasions, it is unlikely that he will have missed something that occupies 90% of the area. Similarly, if everything a scientist has ever observed (other than light) has been composed of matter possessing mass, it is unlikely that 90% of the known universe is composed of something entirely different.

The combination of the metaphysical principle of limited complexity --- a consequence of the Law of Identity --- and the roll of free will in the exploration of the world leads to an efficacious method of acquiring knowledge.

But, that amounts to a statement that we actually know something and that our knowledge is a result of our observations. Moreover, our knowledge is not conjectural.

This merely is a confusion over shades of meaning of "knowledge". Plato thought there were two types of knowledge: "episteme" and "doxa", or knowledge in the ultimate, transcendent sense, and mere mortal opinion.

Popper says the only thing humans have to work with is opinion., although we can aim at getting more and more accurate opinions. He says we have no way of attaining "episteme", except perhaps by incredible luck, where our opinions happen to coincide with the absolutely true state of affairs. And even then, we'd never be quite sure we'd hit on it. Hence:

How does Popper know that Newtonian mechanics is, "a staggeringly good approximation to the truth?"

So you see it is, in his opinion (and that of many others), staggeringly close to the truth. He may even experience the passionate sense of conviction that it is close to the truth. But of course, neither his sense of conviction nor his opinion nor that of others justifies it.

So he does not have it both ways, but is in fact perfectly consistent.

Your whole argument amounts to an elaborate dodge of the issue. What makes one opinion better than another? If N scientists agree with your opinion, does that imply that the N + 1st will?

If I produce a sequence of integers, there is an infinite number of extensions of that sequence. It makes no difference whether I give you N examples or N + 1 examples. The number of extensions remains the same. That is the crux of Hume's argument. So, there is no sense in which it is possible to, "aim at getting more and more accurate opinions," in Hume's scenario. No amount of evidence or scientific review or criticism can give any more weight to a statement of opinion than the statement had when uttered by a single individual. Popper states exactly that:

(1) The logical problem: Are we rationally justified in reasoning from repeated instances of which we have had experience to instances of which we have had no experience?

Hume's unrelenting answer was: No, we are not justified, however great the number of repetitions may be. And he added that it did not make the slightest difference if, in this problem, we ask for the justification not of certain belief, but of probable belief. Instances of which we have had experience do not allow us to reason or argue about the probability of instances of which we have had no experience, any more than to the certainty of such instances.

And Popper rejects the psychological power of induction:

Hume, at the same time, and in sharp contrast to myself, believed in the psychological power of induction; not as a valid procedure, but as a procedure which animals and men successfully make use of, as a matter of fact and of biological necessity.

So, he should not experience a, "passionate sense of conviction that [Newtonian Mechanics] is close to the truth." Indeed, he is trying to have it both ways and so are you.

Darrell

[Darrell Hougen]

No, not being 100% certain doesn't mean that we have no idea how good our model is. When we use it to make predictions and it turns out that these are many times experimentally verified with a high degree of accuracy, we may assume that it is a pretty good model.

On what basis may we make that assumption?

Because that is in fact the way we define what a good model is. How do we arrive at the notion of an external reality that is independent of our consciousness? It is the result of our observation that there are consistent regularities in the way our environment reacts to our actions, so that we can often predict succesfully what will happen when we perform a certain action.

Yes. And, at some point we must assume that the reality actually does exhibit regularities and that the regularities we observe are probably not observed by accident.

Darrell

[Daniel Barnes]

Darrell:

I'm still trying to formulate the exact nature of my argument.

Great. Why not get back to us when you have?

The combination of the metaphysical principle of limited complexity --- a consequence of the Law of Identity --- and the roll of free will in the exploration of the world leads to an efficacious method of acquiring knowledge.

If you start from the premiss that "my assumption"="metaphysical principle" you at least will find your arguments metaphysically compelling.

Your whole argument amounts to an elaborate dodge of the issue. What makes one opinion better than another?

Not at all. We can exercise a critical preference; we can prefer testable explanations (A predicts B) than untestable (eg: the Law of Identity, Allah's Will etc) ones. We can also decide to accept falsifying evidence or arguments for our cherished beliefs, and not be like the priest who refused to look through Galileo's telescope. Thus, through criticism, we can arrive at stronger theories.

Popper states exactly that:

"(1) The logical problem: Are we rationally justified in reasoning from repeated instances of which we have had experience to instances of which we have had no experience?

Hume's unrelenting answer was: No, we are not justified, however great the number of repetitions may be. And he added that it did not make the slightest difference if, in this problem, we ask for the justification not of certain belief, but of probable belief. Instances of which we have had experience do not allow us to reason or argue about the probability of instances of which we have had no experience, any more than to the certainty of such instances."

Yes. Now you have looked through the telescope, why do you deny what you see?

And Popper rejects the psychological power of induction:"Hume, at the same time, and in sharp contrast to myself, believed in the psychological power of induction; not as a valid procedure, but as a procedure which animals and men successfully make use of, as a matter of fact and of biological necessity."

So, he should not experience a, "passionate sense of conviction that [Newtonian Mechanics] is close to the truth." Indeed, he is trying to have it both ways and so are you.

Now you are telling Popper what emotions he should have (or might have) felt? That these vague speculations about whaty he may or may not have felt are somehow relevant to the logic of his arguments? How Hume felt about his arguments (he was actually emotionally conflicted by them) matters? You're clutching at straws, man.

Rather than me tryiing to have it both ways, I politely suggest it is you doing so.

For you honestly admit that you have not formulated a coherent answer to Hume.

And indeed, from your post above it seems you understand the problem reasonably well.

Yet you refuse to accept your own conclusions; you insist Hume and Popper must be wrong, even though you can summon no argument as to why.

It's not me who is trying to have it both ways, my friend.

Edited October 3, 2007 by Daniel Barnes

[Michael Stuart Kelly]

Yes, that's pretty well what I thought your position was. I don't think there is any way to resolve this issue. I can keep saying there is SOMETHING there whether there is an observer or not, but if there is no observer there can be no discussing it either, right? The moment you say 'star', an observer is implied. Isn't that an instance of 'stolen concept'?

GS,

That point is obvious and is why, in Objectivism, fundamental axioms are not standalone. They all depend on the others (like different facets of the same gemstone). But to use your own standard, the moment you say SOMETHING, aren't you presuming an observer, since the word "something" is an idea?

If one concedes that something can exist without an observer, there is no logical reason whatsoever to conclude that it cannot have a specific nature.

Michael

[tjohnson]

GS,

That point is obvious and is why, in Objectivism, fundamental axioms are not standalone. They all depend on the others (like different facets of the same gemstone). But to use your own standard, the moment you say SOMETHING, aren't you presuming an observer, since the word "something" is an idea?

If one concedes that something can exist without an observer, there is no logical reason whatsoever to conclude that it cannot have a specific nature.

Michael

Korzybski calls the "event" or WIGO unspeakable, but that is not to say there is nothing there. Even our 1st order abstractions (perceptions) are non-verbal (see diagram in other thread). We may sense categories on objective levels and then abstract further to verbal levels and finally infer their existence on the event level. it's one of those 'circle of life' things.

OK it can have a specific nature BUT you cannot tell me ANYTHING about it's nature without SPEAKING, correct? So then you have abstracted through at least 2 levels away from the event.

[Michael Stuart Kelly]

GS,

Tell that to a dog that sees a cat.

Michael

[tjohnson]

GS,

Tell that to a dog that sees a cat.

Michael

Does this mean I won the argument?

[Michael Stuart Kelly]

GS,

Win what?

Do you mean do I agree? I have no idea about what to agree with.

We were talking about the presence of an observer. You changed this to levels of abstraction (implying that there is an observer). Which is it? Ontologically, do you believe things exist without a specific nature or do they exist with one? I have not been able to discern from these last few posts.

Michael

[tjohnson]

Micheal, basically I granted you that things exist with some sort of "nature" but this nature needs to be abstracted through our senses and our language and so in the end we can only infer their nature. (I prefer structure) I suppose you brought the cat and dog into it to illustrate that animals can discern structure without language and I agree with that. But my point is that any structure or nature we SPEAK about can only ever be inferred.

[Michael Stuart Kelly]

GS,

What do you mean by "inferred"? That talking about something is not the same thing as that something's existence, so it is codified?

Also, do you believe that cows run in herds without anyone observing, or do they need to be inferred first?

As to speaking, I thought a speaker was needed to even speak about something, anything at all, not just structure or nature.

Michael

[Darrell Hougen]

If you start from the premiss that "my assumption"="metaphysical principle" you at least will find your arguments metaphysically compelling.

I note that you avoided the substance of my argument.

Your whole argument amounts to an elaborate dodge of the issue. What makes one opinion better than another?

Not at all. We can exercise a critical preference; we can prefer testable explanations (A predicts B) than untestable (eg: the Law of Identity, Allah's Will etc) ones. We can also decide to accept falsifying evidence or arguments for our cherished beliefs, and not be like the priest who refused to look through Galileo's telescope. Thus, through criticism, we can arrive at stronger theories.

First, according to Hume's argument, which Popper accepts uncritically and you seem to accept as well, no amount of criticism will ultimately make any theory any stronger than it was in the beginning. Ultimately it remains a conjecture that could be wildly inaccurate.

Second, what makes one method preferable to another? Why is a testable explanation preferable to an untestable one? No matter how many tests are performed, a hypothesis remains a conjecture and the possible or probable error cannot be bounded.

Finally, you lump the Law of Identity in with Allah's Will which you probably don't hold in high regard. So, am I to conclude that you believe that objects in the real world have no identity? That a thing isn't really any particular thing? Doesn't that strike you as an odd position to hold?

Yes. Now you have looked through the telescope, why do you deny what you see?

The telescope was defective. When I looked through it, all I saw was darkness. It was not at all illuminating.

Now you are telling Popper what emotions he should have (or might have) felt?

No. You're the one that did that a couple of posts back.

That these vague speculations about what he may or may not have felt are somehow relevant to the logic of his arguments?

I have no idea how they are relevant. But he did say that Newtonian mechanics is, "a staggeringly good approximation to the truth?" That sounds like a statement of fact, not an emotional reaction.

... you insist Hume and Popper must be wrong, even though you can summon no argument as to why.

Actually, I think I made a pretty good case for my point of view, despite my hesitancy. Unfortunately, you ignored the substance of my argument.

Darrell

[Daniel Barnes]

Darrell:

I note that you avoided the substance of my argument.

You didn't provide an argument. You just said that your assumption of limited complexity was somehow a metaphysical principle. This seems to overrate it somewhat, to say the least.

First, according to Hume's argument, which Popper accepts uncritically and you seem to accept as well, no amount of criticism will ultimately make any theory any stronger than it was in the beginning.

No, this is where you're quite wrong. I'll explain. There is an logical asymmetry between verification and falsification. Hume's problem says that no matter how many observations we make, we can, from the point of view of pure logic, never verify a theory as true.

However, this is not true of falsification. A single refutation is logically enough to falsify a theory, via the modus tollens.

We can call a theory "strong" if it a) is open to falsification in the first place, and b)survives strong attempts to falsify it (via both argument and experience). Just like we'd describe anything as strong, if it withstood strong tests.

Ultimately it remains a conjecture that could be wildly inaccurate.

Of course! The process is like an intellectual version of Darwinism. Just because an organism has survived to date doesn't mean it is guaranteed to live into the future. Theories are just the same.

Second, what makes one method preferable to another? Why is a testable explanation preferable to an untestable one?

Hopefully this is clearer now.

No matter how many tests are performed, a hypothesis remains a conjecture and the possible or probable error cannot be bounded.

Yes. You have your eye firmly to the telescope once again.

Finally, you lump the Law of Identity in with Allah's Will which you probably don't hold in high regard. So, am I to conclude that you believe that objects in the real world have no identity?

Am I to conclude that you don't believe objects in the real world aren't subject to Allah's Will!!!

No, it just means they are equally untestable assertions. Look at the way you can apply them. If a tree produces apples every day, you can just argue that it is inherent in its nature to do so. If it starts to produce pears every second day, you can simply say that it is in its nature to produce both apples and pears. The difference between this and the will of Allah is minimal.

That a thing isn't really any particular thing? Doesn't that strike you as an odd position to hold?

It is just as well that I don't hold it then.

The telescope was defective. When I looked through it, all I saw was darkness. It was not at all illuminating.

You've probably got the lens cap on.

I have no idea how they are relevant. But he did say that Newtonian mechanics is, "a staggeringly good approximation to the truth?" That sounds like a statement of fact, not an emotional reaction.

I'm not sure you've understood my point. But any rate, we might say of Newton's theory that, given its survival for hundreds of years before being felled by Einstein, that it was both "staggeringly good" but still no more than an "approximation to the truth", as it turned out to be false. And the problem with saying this is...what? Do you have any stronger case than working this one innocuous sentence of Popper's to death? Do you think it might be better to get your head around fundamentals, such as the logical assymetry above before getting too bold about how good your case is?

What is the "substance" of your argument that you keep referring to? Is it simply that you call your personal assumptions "metaphysical principles"?

Edited October 4, 2007 by Daniel Barnes

[tjohnson]

What do you mean by "inferred"? That talking about something is not the same thing as that something's existence, so it is codified?

By 'inferred' I mean basically the same thing as 'assumed' or 'attributed'.

Also, do you believe that cows run in herds without anyone observing, or do they need to be inferred first?

I believe "cows run in herds", yes. But the word 'cow', for example, could mean at least 4 different things.

1. the "real" thing we can touch, milk, etc. (outside our skin)

2. our perception of it that we get with all our senses (inside our skin)

3. a mental image of it, a memory, visualization (you might call 'concept')

4. a verbal definition of 'cow'

Your statement that "cows run in herds" belongs on level 4 and as such, yes, it represents an inference in a general way, albeit, as rather simple one. But as our language becomes abstract (like in zoology) it becomes more inferential, further removed from level 1.

[tjohnson]

No, this is where you're quite wrong. I'll explain. There is an logical asymmetry between verification and falsification. Hume's problem says that no matter how many observations we make, we can, from the point of view of pure logic, never verify a theory as true.

However, this is not true of falsification. A single refutation is logically enough to falsify a theory, via the modus tollens.

We can call a theory "strong" if it a) is open to falsification in the first place, and b)survives strong attempts to falsify it (via both argument and experience). Just like we'd describe anything as strong, if it withstood strong tests.

Very well put Daniel, IMO. Another way of putting this, due to Korzybski, is that we can never say for sure what something IS, we can only say for sure what something IS NOT. The field of geodesy concerns itself with the shape of the earth, for example, no matter how many decimal places of accuracy are attained using any particular model it will never be able to answer the question "what IS the shape of the earth?". We can for sure, however, say it IS NOT a sphere.

[Michael Stuart Kelly]

I believe "cows run in herds", yes. But the word 'cow', for example, could mean at least 4 different things.

1. the "real" thing we can touch, milk, etc. (outside our skin)

2. our perception of it that we get with all our senses (inside our skin)

3. a mental image of it, a memory, visualization (you might call 'concept')

4. a verbal definition of 'cow'

Your statement that "cows run in herds" belongs on level 4 and as such, yes, it represents an inference in a general way, albeit, as rather simple one. But as our language becomes abstract (like in zoology) it becomes more inferential, further removed from level 1.

GS,

No it doesn't. Pure Level 1. The real things run in herds whether we want them to or not or whether we perceive this or not. They do it. That is why we can perceive it and categorize it.

Michael

[tjohnson]

GS,

No it doesn't. Pure Level 1. The real things run in herds whether we want them to or not or whether we perceive this or not. They do it. That is why we can perceive it and categorize it.

Michael

OK, it's as I thought, I can't convince you and you can't convince me, discussion over.

[Darrell Hougen]

You didn't provide an argument. You just said that your assumption of limited complexity was somehow a metaphysical principle. This seems to overrate it somewhat, to say the least.

Actually, that's not what I said. The notion of limited complexity is a corollary of the Law of Identity which is a metaphysical principle.

First, according to Hume's argument, which Popper accepts uncritically and you seem to accept as well, no amount of criticism will ultimately make any theory any stronger than it was in the beginning.

No, this is where you're quite wrong. I'll explain. There is an logical asymmetry between verification and falsification. Hume's problem says that no matter how many observations we make, we can, from the point of view of pure logic, never verify a theory as true.

However, this is not true of falsification. A single refutation is logically enough to falsify a theory, via the modus tollens.

So far, so good.

We can call a theory "strong" if it a) is open to falsification in the first place, and b)survives strong attempts to falsify it (via both argument and experience). Just like we'd describe anything as strong, if it withstood strong tests.

This is where you and Popper try to smuggle induction into the solution under a cloak of obfuscating terminology. In the Humean problem, surviving N strong tests doesn't tell you anything about whether a theory will survive the N + 1th strong test, or, indeed, any test at all. Fundamentally, no amount of testing can make a conjecture any stronger than it was in the beginning. And, it makes no difference whether the conjecture is subjected to argument or experience.

An argument can be thought of as a kind of test. Given a theory to test, you may submit it to a panel of experts, each of which is to go off and independently examine it for logical flaws or unforeseen consequences. If one or more of them finds an error, then the theory is falsified. Otherwise, it is "strong."

This is an appealing argument in a sense. If each expert has some probability, say 90%, of finding fault with the theory, then 10 experts would have a probability of only 0.1^10 = 0.0000000001 of not finding fault if one existed. The problem is that in the Humean problem, it is impossible to assign a probability of being correct. And, if it is impossible to assign a probability to the correctness of the conclusions of one expert, then it is equally impossible to assign a probability to 10 experts or N experts. So, at the end of the day, the conjecture is no stronger than if a little child had uttered it at the breakfast table.

If this seems counterintuitive, it should. The point is that there is something wrong with the Humean problem. The world is not infinite, nor is it infinitely complex in the broadest sense, nor does it change at an unbounded rate. Denial of these facts leaves an insurmountable problem.

Lets return to the problem of the white swans. There is only a finite number of swans in the world. So, if I marshaled sufficient resources, I could, in principle track down every swan on earth and verify that it is white or end up finding some black ones. If I found all swans and they were all white, then I would be justified in stating that all swans are white.

As to the question of the color of future swans, I would have to study and understand the swan genome well enough to determine what gene or genes caused the swan to be of one color or another. Then, if I collected DNA samples from all existing swans, I could, in principle, determine whether any had a gene for some color other than white. If none did, then I could predict that, in the absence of a mutation, all future swans would be white. Case closed.

Even if I could not determine a definitive answer, I could give a probabilistic answer to the question. If I had collected specimens from a certain representative sample of swans, I could ascertain the probability that other swans would be the same color. If I was sophisticated, I might use my knowledge of the colors of other animals to modify my probability predictions. I might note, for example, that color is generally a superficial characteristic that is difficult to predict from the kind of animal in question.

Thus, all kinds of things can be done in finite domains. But none of that applies if the domain is assumed infinite. It is impossible to gather a representative sample of an infinite domain.

No, it just means they are equally untestable assertions. Look at the way you can apply them. If a tree produces apples every day, you can just argue that it is inherent in its nature to do so. If it starts to produce pears every second day, you can simply say that it is in its nature to produce both apples and pears. The difference between this and the will of Allah is minimal.

No, that is not how the Law of Identity is used. It, and its corollaries are used to understand the fact that if a tree produces apples, it is very unlikely to start producing pears. It is used to understand the fact that such probability statements are possible, unlike in the Humean universe in which no such statements are possible.

That a thing isn't really any particular thing? Doesn't that strike you as an odd position to hold?

It is just as well that I don't hold it then.

Good. Then we agree on something.

The telescope was defective. When I looked through it, all I saw was darkness. It was not at all illuminating.

You've probably got the lens cap on.

Lol. I was going to say that very thing, e.g., "Someone forgot to take the lens cap off," but that didn't quite work from my side. I should have anticipated your response though. Funny anyway.

I have no idea how they are relevant. But he did say that Newtonian mechanics is, "a staggeringly good approximation to the truth?" That sounds like a statement of fact, not an emotional reaction.

I'm not sure you've understood my point. But any rate, we might say of Newton's theory that, given its survival for hundreds of years before being felled by Einstein, that it was both "staggeringly good" but still no more than an "approximation to the truth", as it turned out to be false. And the problem with saying this is...what? Do you have any stronger case than working this one innocuous sentence of Popper's to death? Do you think it might be better to get your head around fundamentals, such as the logical assymetry above before getting too bold about how good your case is?

If you're willing to concede the point with regard to that particular example, we can move on, but I think it is typical of the kinds of contradictions that run through Popper's work. Popper cannot overcome Hume's problem without additional assumptions (which he is unwilling to make) so he vacillates between extreme skepticism (ala Hume) and smuggled use of induction. The asymmetry I get, but that is not enough.

Darrell

Edited October 4, 2007 by Darrell Hougen

[BaalChatzaf]

This is where you and Popper try to smuggle induction into the solution under a cloak of obfuscating terminology. In the Humean problem, surviving N strong tests doesn't tell you anything about whether a theory will survive the N + 1th strong test, or, indeed, any test at all. Fundamentally, no amount of testing can make a conjecture any stronger than it was in the beginning. And, it makes no difference whether the conjecture is subjected to argument or experience.

Logically, you are correct. However the longer your theory lasts under fire, the more you love it. That is the way it is. If it ain't broke don't fix it. If it works, keep on using it until it breaks. If it smiles at you, smile right back at it. And if it does break, fix it or replace it.

There is no greater love than a boy has for his dogma.

Ba'al Chatzaf

[Dragonfly]

Logically, you are correct. However the longer your theory lasts under fire, the more you love it.

And not without reason: it works - you can use it for practical purposes (see the scientific and technological advances during the last century), so we assume that it reflects something out there that we call "reality" - the proof of the pudding is in the eating, not in metaphysical gobbledygook.

[BaalChatzaf]

call "reality" - the proof of the pudding is in the eating, not in metaphysical gobbledygook.

Is metaphysicalgobbledygook one word or two?

Ba'al Chatzaf

[Darrell Hougen]

Logically, you are correct. However the longer your theory lasts under fire, the more you love it.

And not without reason: it works - you can use it for practical purposes (see the scientific and technological advances during the last century), so we assume that it reflects something out there that we call "reality" - the proof of the pudding is in the eating, not in metaphysical gobbledygook.

So, we despair of ever understanding why it works and just accept our success? That is one approach, I suppose.

Darrell

[BaalChatzaf]

So, we despair of ever understanding why it works and just accept our success? That is one approach, I suppose.

Darrell

It works. If it ain't broke don't fix it. And it sure beats failure which has been the fate of most metaphysical theories for the last 2500 years. Metaphysics and $1.67 will get you a medium coffee at your local Dunkin'Donuts ™.

Ba'al Chatzaf

[Daniel Barnes]

Darrell:

Actually, that's not what I said. The notion of limited complexity is a corollary of the Law of Identity which is a metaphysical principle.

There is no reason to accept your corollary in the first place. For example, the integer series is infinite. Does that mean it violates the Law of Identity? Of course not.

However, let's bend over backwards and accept it anyway: the universe is not infinitely complex. Let's say it's reducible to a finite, if enormous, set of singular facts.

But we should not confuse a. the universe with b. our theories about the universe.

Because it turns out the number of possible theories that can fit any given set of facts is infinite. So even if the universe is finite and unchanging, this makes no difference to the nature of our knowledge - which is of course, what Hume's problem applies to.

This is where you and Popper try to smuggle induction into the solution under a cloak of obfuscating terminology. In the Humean problem, surviving N strong tests doesn't tell you anything about whether a theory will survive the N + 1th strong test, or, indeed, any test at all. Fundamentally, no amount of testing can make a conjecture any stronger than it was in the beginning.

Exactly. Thus we agree entirely on the substance of the issue, your only objection is terminological. Fine. If you don't like the terminology "strong" and think it is misleading, then suggest something else. I think it's reasonable myself, as a surviving theory may be indeed called "weak" by comparison to the truth (whatever that is); yet it might be called "strong" by comparison to a falsified theory, which can be reasonably descriibed as weaker.

"Weak" and "weaker" would be fine by me.

And, it makes no difference whether the conjecture is subjected to argument or experience.

No one suggested otherwise. Argument and experience are both vitally important tests.

The problem is that in the Humean problem, it is impossible to assign a probability of being correct...So, at the end of the day, the conjecture is no stronger than if a little child had uttered it at the breakfast table.

Just because a child utters something at the breakfast table or anywhere else does not guarantee its falsity, anymore than a panel of experts guarantees truth.

If this seems counterintuitive, it should. The point is that there is something wrong with the Humean problem.

"Counter-intuitivity" does not mean that there is a problem with Hume's argument. It once seemed highly counter-intuitive that the earth went around the sun, or that man descended from apes, or amoeba. Lots of logically true things are counter-intuitive.

The world is not infinite, nor is it infinitely complex in the broadest sense, nor does it change at an unbounded rate. Denial of these facts leaves an insurmountable problem.

Now your "metaphysical principles" have evolved into insurmountable facts! But as I have explained above, even if we grant your principle is true - and there is no necessity to do so - it does not help your argument, as it confuses two different things: the universe and our knowledge of it.

Lets return to the problem of the white swans. There is only a finite number of swans in the world. So, if I marshaled sufficient resources, I could, in principle track down every swan on earth and verify that it is white or end up finding some black ones. If I found all swans and they were all white, then I would be justified in stating that all swans are white.

But this is no longer Hume's problem! This is simply sayiing: "All the swans I have seen are white, therefore all the swans I have seen are white." Who disputes this?

As to the question of the color of future swans, I would have to study and understand the swan genome well enough to determine what gene or genes caused the swan to be of one color or another. Then, if I collected DNA samples from all existing swans, I could, in principle, determine whether any had a gene for some color other than white. If none did, then I could predict that, in the absence of a mutation, all future swans would be white. Case closed.

"...in the absence of mutation..."? What, the whole basis of evolutionary change itself? Haven't you just undercut your own argument with that offhand clause? Plus you argument implicity assumes you have a perfectly true and completely infallible theory of genetics already. How did you come by this miracle, might I ask?

And you say Popper is "smuggling" in hidden premisses..

Even if I could not determine a definitive answer, I could give a probabilistic answer to the question. If I had collected specimens from a certain representative sample of swans, I could ascertain the probability that other swans would be the same color.

No you can't.

All you can do is ascertain the probability in a fixed population via the deductive laws of statistical probability. This has nothing to do with induction.

I might note, for example, that color is generally a superficial characteristic that is difficult to predict from the kind of animal in question.

This is rather like a lightbulb joke: How many ad hoc assumptions does it take to prop up an argument for induction?

Thus, all kinds of things can be done in finite domains. But none of that applies if the domain is assumed infinite. It is impossible to gather a representative sample of an infinite domain.

Absolutely right.

No, that is not how the Law of Identity is used.

Why?

Popper cannot overcome Hume's problem without additional assumptions (which he is unwilling to make) so he vacillates between extreme skepticism (ala Hume) and smuggled use of induction.

I'm sorry, but you have not demonstrated any of the above. You are definitely demonstrating a good grasp of some aspects of the issue, however; much better than many of the debaters here, so I commend you. However:

1) Popper does not "overcome" Hume's logical problem of induction; he accepts it. His solution overcomes Hume's psychological problem of induction.

2) He does not "vacillate"; he has endorsed it from the start

3) You have not shown he "smuggles" induction in.

Edited October 5, 2007 by Daniel Barnes

[BaalChatzaf]

First, according to Hume's argument, which Popper accepts uncritically and you seem to accept as well, no amount of criticism will ultimately make any theory any stronger than it was in the beginning. Ultimately it remains a conjecture that could be wildly inaccurate.

Second, what makes one method preferable to another? Why is a testable explanation preferable to an untestable one? No matter how many tests are performed, a hypothesis remains a conjecture and the possible or probable error cannot be bounded.

The sooner a bad theory is killed off the sooner a less bad theory will be formulated to replace it.

The way you improve the breed is by culling the weak sisters. Survival of the fit and all that.

Think of what would have happened if Newtonian Gravitation had not been falsified. We would not have the Global Positioning System. When you run GPS in Newtonian Mode (without the relativistic corrections) you end up many kilometers off at the end of the clocking period.

Beating up theories is good for science.

Ba'al Chatzaf

[Michael Stuart Kelly]

So, we despair of ever understanding why it works and just accept our success? That is one approach, I suppose.

Darrell,

There is another approach. Simply gloss over the "why" on purpose and denigrate through verbal games and impossible context shifts those who discover it. The "why" doesn't go away just because we are successful and, more, those who are successful do not contradict the "why" by being so.

You are correct that this is an approach (an attitude) and nothing more. It is not knowledge, which includes identity and causality as fundamental components whether denigrated or not.

Michael