What Problem?

[kiaer.ts]

No, where one stops, in the sense meant, isn't where one feels satisfied, it's where one can demonstrate a guaranteed-true conclusion..

Ellen

It seems to me that demonstration of a guaranteed-true conclusion is impossible using induction. Is that, then, the problem?

Well, that's a position you have come to by induction, isn't it? Some inductions fail, so all inductions are suspect?

The difference between deduction and induction is that with deduction you have a closed set of premises, while with induction, there is the possibility that you have left out some relevant evidence. Yet being aware of that you can control for factors just as one does in a well designed scientific experiment. If you pay attention to what you are doing, at some point it becomes absurd to deny the induction that DNA is the genetic medium of the cell or that O J Simpson murdered Nicole Simpson and Ron Goldman.

And deduction is radically parasitic on induction. There is no premise whose truth does not rely on prior induction.

[BaalChatzaf]

Well, that's a position you have come to by induction, isn't it? Some inductions fail, so all inductions are suspect?

All it takes is just ONE failed induction to show that induction does not guarantee a true conclusion from true premises. The demonstration is by counter example, not induction.

The way one show (x)Px is false is to produce one a such that -Pa. Logic 101.

A simple use of De Morgan's theorem applied to infinite conjunctions.

It is absolutely amazing, the degree of ignorance of first order predicate logic exhibited by Objectivists. If I recall correctly, Ayn Rand did not like mathematical logical all that much and the same is true of Pope Leonard. I had a one on one with him about predicate logic, once a long time ago. He is an anti-mathematical logic bigot.

ruveyn

[sjw]

If you take Hume seriously (which I do) causality is hypothetical based on the repeated occurance of event-type pairs. Whenever type A event happens then type B event is observed. When Type A does not happen then Type B does not happen. Conclusion Type A event causes Type B event. It is the elevation of an accidental to a substantial hypothesis. Causality is an itch we cannot scratch. We find it difficult to think of something happening without something before (or at the same time) causing it. Unfortunately, this insistence leads us to infinite regress. It is Turtles all the way down. The good news is that causality is often a good heuristic for making correct predictions. Causality, along with induction is the basis for learning at human scale. We find causes all the time and we seem happy with the results. The bad news is that it does not always work at all scales. What is the cause of spin in some orientation of an electron?

It seems that you are conflating epistemology and metaphysics. Granting Hume's version of how we infer causality does not grant that reality could be different than it is. Our idea of causality works so well because that is actually how reality works, and even on Hume's premises we can come to that causal identification. You can go ahead and say that we can never know that's how reality works, but the fact is we observe a "constant conjunction" in this regard -- we have no justification for making the opposite conclusion, i.e. that reality is not causal.

Shayne

[sjw]

Well, that's a position you have come to by induction, isn't it? Some inductions fail, so all inductions are suspect?

All it takes is just ONE failed induction to show that induction does not guarantee a true conclusion from true premises. The demonstration is by counter example, not induction.

Ted didn't say induction as such guarantees anything, and he's right that you can't point to the failure of a given induction to impugn all others, that's a logical fallacy.

Shayne

[BaalChatzaf]

Granting Hume's version of how we infer causality does not grant that reality could be different than it is. Our idea of causality works so well because that is actually how reality works, and even on Hume's premises we can come to that causal identification.

That is how we think reality works. To find out how reality REALLY works we have to go to a much smaller scale of measuring -- basically Planck Length which is about 15 degrees of magnitude smaller than we have been able to get to in spite of spending zillions of dollars. Write us when we get to Planck Length and let us know the results. In the mean time we do the best we can on the budget we can afford.

Ba'al Chatzaf

[sjw]

Granting Hume's version of how we infer causality does not grant that reality could be different than it is. Our idea of causality works so well because that is actually how reality works, and even on Hume's premises we can come to that causal identification.

That is how we think reality works. To find out how reality REALLY works we have to go to a much smaller scale of measuring -- basically Planck Length which is about 15 degrees of magnitude smaller than we have been able to get to in spite of spending zillions of dollars. Write us when we get to Planck Length and let us know the results. In the mean time we do the best we can on the budget we can afford.

Ba'al Chatzaf

Why do you presume that the Plank Length is small enough? On your premises we can never justifiably think reality works in this way or that.

Shayne

[Jonathan David Leavitt]

No, where one stops, in the sense meant, isn't where one feels satisfied, it's where one can demonstrate a guaranteed-true conclusion..

Ellen

It seems to me that demonstration of a guaranteed-true conclusion is impossible using induction. Is that, then, the problem?

And deduction is radically parasitic on induction. There is no premise whose truth does not rely on prior induction.

Interesting point. Does that mean, then, that all logical proofs are based on ideas derived from inductive generalizations? I would think so.

[BaalChatzaf]

Why do you presume that the Plank Length is small enough? On your premises we can never justifiably think reality works in this way or that.

Shayne

For all I know, it might not be small enough. But if we cannot get to Planck Length we cannot get to Small Enough.

Be sure to write when we get to Small Enough and let us know the results.

Ba'al Chatzaf

[kiaer.ts]

Well, that's a position you have come to by induction, isn't it? Some inductions fail, so all inductions are suspect?

All it takes is just ONE failed induction to show that induction does not guarantee a true conclusion from true premises. The demonstration is by counter example, not induction.

The way one show (x)Px is false is to produce one a such that -Pa. Logic 101.

A simple use of De Morgan's theorem applied to infinite conjunctions.

It is absolutely amazing, the degree of ignorance of first order predicate logic exhibited by Objectivists. If I recall correctly, Ayn Rand did not like mathematical logical all that much and the same is true of Pope Leonard. I had a one on one with him about predicate logic, once a long time ago. He is an anti-mathematical logic bigot.

ruveyn

Ah, Ruben, not Robert. Interesting.

No, you would not say that one failed deduction shows that all deduction is invalid. I tire of repeating this. Induction fails if you use an invalid method just as deduction fails if you use an invalid method. Induction by enumeration is a fallacious method in just the same way that affirming the consequent is a fallacy. While I am sure you would not fail to distinguish between proper and improper methods in deduction, you are refusing to distinguish between proper and improper methods in induction. You are not too simple to understand this distinction.

[BaalChatzaf]

Zillion white swans to all swans are white is the way enumerative induction is supposed to work. Using it as advertised in this instance leads to a false conclusion. This instance is sufficient to show that induction used as advertised, taught and advocated by its fans is not a valid mode of inference.

A false deduction is no deduction. If the form of the inference is not valid, the argument so defective is NOT a deduction. A sound deduction requires two things:

1. a valid form of inference

2. true premises

Among the categorical syllogisms there are 15 valid forms. The remained of the 256 possible combinations are not valid syllogisms. Using a busted form is not a deduction. It is a mistake.

A related set of rules applies to first order predicate logic. The best known rule set is Natural Deduction. A "proof" that does not follow the rules is not a proof. It has the appearance of a proof, but it is not a proof. A valid proof will always get from true premises to a true conclusion and its guarantee is as good as the principle of non-contradiction.

Ba'al Chatzaf

[sjw]

Why do you presume that the Plank Length is small enough? On your premises we can never justifiably think reality works in this way or that.

Shayne

For all I know, it might not be small enough. But if we cannot get to Planck Length we cannot get to Small Enough.

Be sure to write when we get to Small Enough and let us know the results.

Ba'al Chatzaf

"Small enough" is a fantasy. There is no "small enough." So what we see is that in order to argue with me, you have to create fantasy constructs to do it. Case closed.

Shayne

[kiaer.ts]

Zillion white swans to all swans are white is the way enumerative induction is supposed to work. Using it as advertised in this instance leads to a false conclusion. This instance is sufficient to show that induction used as advertised, taught and advocated by its fans is not a valid mode of inference.

A false deduction is no deduction. If the form of the inference is not valid, the argument so defective is NOT a deduction. A sound deduction requires two things:

1. a valid form of inference

2. true premises

Among the categorical syllogisms there are 15 valid forms. The remained of the 256 possible combinations are not valid syllogisms. Using a busted form is not a deduction. It is a mistake.

A related set of rules applies to first order predicate logic. The best known rule set is Natural Deduction. A "proof" that does not follow the rules is not a proof. It has the appearance of a proof, but it is not a proof. A valid proof will always get from true premises to a true conclusion and its guarantee is as good as the principle of non-contradiction.

Ba'al Chatzaf

Okay, so you simply want to define yourself into victory. Invalid deductions are not deductions, but enumerative inductions, which are invalid, since they do not adduce causes, are the perfect example of induction for you, regardless of their explained invalidity. Wow, you certainly are a genius. Let me know when you publish your discovery in book form.

[Ellen Stuttle]

No, where one stops, in the sense meant, isn't where one feels satisfied, it's where one can demonstrate a guaranteed-true conclusion..

Ellen

It seems to me that demonstration of a guaranteed-true conclusion is impossible using induction. Is that, then, the problem?

Yes.

Well, that's a position you have come to by induction, isn't it? Some inductions fail, so all inductions are suspect?

If there's no method which guarantees reaching a true conclusion inductively, then, yes, all inductions are suspect.

The difference between deduction and induction is that with deduction you have a closed set of premises, while with induction, there is the possibility that you have left out some relevant evidence. Yet being aware of that you can control for factors just as one does in a well designed scientific experiment. If you pay attention to what you are doing, at some point it becomes absurd to deny the induction that DNA is the genetic medium of the cell or that O J Simpson murdered Nicole Simpson and Ron Goldman.

You're including two examples which are different in the extent to which definite proof can be obtained. The murder trial is a particular not a universal theory. There can be conclusive evidence with particular truth claims. (I won't debate whether there is or not in the Simpson case, since I never followed that.)

To ask for conclusive proof for universal theories, however, is in effect to ask for guaranteed answers at the back of the book. Claiming you could get such answers while you're living in the book is in effect to say you could take a sneak peak at how it all turns out. It's actually contradictory to the nature of knowledge, which is a fallible and never-ending process of questioning.

And deduction is radically parasitic on induction. There is no premise whose truth does not rely on prior induction.

Right. Which is why with deductive reasoning the truth of the conclusion of a valid argument is guaranteed IF the premises are true. The quest to solve the problem of induction is the quest to guarantee the premises, so that one has certainty from perception through to the ultimate laws of the universe.

Sorry to be brief. I expect to have some time for elaborating next week.

Ellen

Edited November 24, 2010 by Ellen Stuttle

[sjw]

Ellen,

It seems to me that you (and Harriman) are focusing too narrowly on universal physical theories when thinking about induction. Actually I think it is ironic that ARI would think that the most important area to examine to validate induction would be physics, because in my judgement, the most important area given their alleged purposes, and in fact one of the easier areas to come to conclusive conclusions, is in the area of individual rights. Of course, if they were actually to apply induction to that area, they would find, as I have, that Ayn Rand made some serious errors. Which is perhaps why they are focusing on physics -- it's an area they can safely innovate in without revising anything Ayn Rand said.

In the area of physics, we are experimentally limited in the data we can collect. We are therefore limited in the conclusions we can draw. We can never rule out that more detailed experiments might contradict theories based on less detailed measurements. And in principle, there is no limit to the amount of detail that reality is composed of -- in principle we can never know if we've drilled down all the way. So this is the one area of life where induction has the hardest possible time reaching universal conclusions that will never be subject to revision and refinement, and yet it's also the one people like to focus on. (I happen to believe that Newton's inductions are eternal and universal given the right qualifications, and that their qualifications are implicit even if Newton himself didn't explicitly identify them. But all this is beside my point here).

Individual rights on the other hand is an area where we can know, with guaranteed certainty, universal laws that will never be contradicted. For example, it will never be learned in the future that what some call the "non-initiation of force principle" would be overturned. And there are a plethora of other inductive principles in this area that will never be overturned. A better book on induction than Harriman's would study the principle and also study how induction arrives at it and end up with a far more useful result for humanity. Humanity doesn't need better physics right now, it needs better respect for individual rights.

Shayne

Incidentally, my book was published on Kindle today:

http://www.amazon.com/For-Individual-Rights-ebook/dp/B004DERH6E/ref=sr_1_18?ie=UTF8&qid=1290579659&sr=8-18

Edited November 24, 2010 by sjw

[BaalChatzaf]

And now a word from Isaac Newton on experimental induction. This excerpt is from his experimental work -Optiks-.

As in mathematics, so in natural philosophy, the investigation of difficult things by the method of analysis, ought ever to precede the method of composition. This analysis consists in making experiments and observations, and in drawing general conclusions from them by induction and admitting of no objections against the conclusions, but such as are taken from experiments, or other certain truths. For hypotheses are not to be regarded in experimental philosophy. And although the arguing from experiments and observations by induction be no demonstration of general conclusions; yet it is the best way of arguing which the nature of things admits of, and may be looked upon as so much the stronger, by how much the induction is more general. And if` no exception occur from phenomena, the conclusion may be pronounced generally. But if` at any time afterwards any exception shall occur from experiments, it may then begin to be pronounced with such exceptions as occur. By this way of analysis we may proceed from compounds to ingredients, and from motions to the forces producing them; and in general, from effects to their causes, and from particular causes to more general ones, till the argument ends in the most general. This is the method of analysis: And the synthesis consists in assuming the causes discovered, and established as principles, and by them explaining the phenomena proceeding from them, and proving the explanations.

Isaac Newton, Optics, or, a Treatise of the Reflections, Refractions, IrMlections and Colours of Light, 4th ed. (London, 1730). [Capitalization and spelling modernized.]

I have bolded the portion where Newton indicates that Induction is not a generally valid mode of inference, but it is necessary to find how things work;

If you want to learn about how scientist use induction go to the scientists.

Ba'al Chatzaf

[kiaer.ts]

Well, that's a position you have come to by induction, isn't it? Some inductions fail, so all inductions are suspect?

If there's no method which guarantees reaching a true conclusion inductively, then, yes, all inductions are suspect.

That's either begging the question, or banal, or both. Bob went from saying that there exist specific invalid inductions (ones which I point out have obviously invalid methods) to saying that all induction is invalid. You chose an even easier path, the tautology that if no induction is guaranteed all are suspect. In any case, each of you is relying on the induced premise that there are inductions which fail. But people also make mistakes in their deductions. What of it?

The difference between deduction and induction is that with deduction you have a closed set of premises, while with induction, there is the possibility that you have left out some relevant evidence. Yet being aware of that you can control for factors just as one does in a well designed scientific experiment. If you pay attention to what you are doing, at some point it becomes absurd to deny the induction that DNA is the genetic medium of the cell or that O J Simpson murdered Nicole Simpson and Ron Goldman.

You're including two examples which are different in the extent to which definite proof can be obtained. The murder trial is a particular not a universal theory. There can be conclusive evidence with particular truth claims. (I won't debate whether there is or not in the Simpson case, since I never followed that.)

Are you accusing me of not having specifically chosen two examples with different scopes and contexts? Of course those examples were deliberately chosen for their different natures.

But you are making another mistake. Any universal claim can be expressed as a particular one, and any particular one as a universal. The particular-universal dichotomy is just as invalid as the analytic-synthetic dichotomy. All killers of Ron Goldman and Nichole Simpson are Orenthal James Simpson. All winners of the 1967 and 1968 Walter Camp award are murderers.

Edited November 27, 2010 by Ted Keer

[RightJungle]

This has been an enjoyable thread. I had listened to Professor Grim's philosophical lectures and liked his way of differentiating deduction and induction, namely that Deduction provides certainty but no new information while Induction provides new information, but no certainty.

[BaalChatzaf]

This has been an enjoyable thread. I had listened to Professor Grim's philosophical lectures and liked his way of differentiating deduction and induction, namely that Deduction provides certainty but no new information while Induction provides new information, but no certainty.

Deduction yields nothing new in the sense that the conclusions were living in the premises all the the time. You might equally say that mining gold does not increase the amount of gold in the world. But both deduction and gold mining bring to sight what was not clearly visible to begin with. Deduction does create accessibility to relations and ideas and sometimes facts that were there but hidden from plain sight.

Ba'al Chatzaf

[merjet]

The problem of induction is the philosophical question of whether inductive reasoning leads to knowledge. That is, what is the justification for either:

1. generalizing about the properties of a class of objects based on some number of observations of particular instances of that class (for example, the inference that "all swans we have seen are white, and therefore all swans are white," before the discovery of black swans) or

2. presupposing that a sequence of events in the future will occur as it always has in the past (for example, that the laws of physics will hold as they have always been observed to hold). Hume called this the Principle of Uniformity of Nature. Link.

Induction is an attempt to infer 'All S is P', given 'Some S is P.' How is that ever justified? It seems to me the justification must be at least one additional premise of the form 'Why each S is P'.

Iterative induction -- simply 'One S is P', 'A second S is P', 'A third S is P', and so forth -- amounts to nothing more than a mockery of induction. In effect and by omission, it says 'Why S is P' is irrelevant.

Consider the case 'All swans are white', which apparently many people believed before learning there were black swans. (Incidentally, the black-necked swan is both black and white. Link.) Said belief was merely an iterative induction, based simply on all observed swans being white. There was no additional justification why they must be white, i.e. of the form 'Why each S is P'. Not only that, there was room for doubting that all swans are white. Many species of birds come in different colors. Even the closest relatives of swans, geese, come in different color patterns.

Let's move on to the induction 'All swans have necks'. While somebody might believe it is a mere iterative induction, I think not. By the way, Ba'al has -- not surprisingly -- not given a counterexample since I asked for one here. Can you even imagine a swan without a neck? What would having no neck imply? It would imply a creature with no connection between it head and its body. It would imply no channel between its mouth and lungs for breathing, and no channel between its mouth and stomach for ingesting food.

I could proceed to many more scientific examples, but will give only one. In all instances water boils at 100°C (212 °F) at standard pressure, i.e. at sea level. I'm confident somebody else could give a better explanation than me. Regardless, there is a good reason why having to do with molecular motion and heat that justifies this induction.

To summarize, the problem of induction is when is 'Why every S is P' sufficiently strong? Pretty clearly no uniform strength test can be given for every field of endeavor. Mill's Methods are for arriving at generalizations and are not strength tests.

Edited November 29, 2010 by Merlin Jetton

[BaalChatzaf]

As for Harriman, while he does not claim that induction always leads to true generalizations, he seems to believe that there does exist a method of valid induction that can prove the geralizations to which it leads.

David Harriman, The Logical Leap, p. 7:

"When and why is the inference from "some" to "all" legitimate? What is the method of valid induction that can prove the generalization to which it leads?" (end quote)

But how is Harriman going to prove the truth of a generalization reached by a "method of valid induction"?

I have not yet received TLL so it is difficult for me to parse the above statement. Does Harriman mean to say induction works when it works and fails when it fails?

That is pretty thin gruel.

Ba'al Chatzaf

[Brant Gaede]

As for Harriman, while he does not claim that induction always leads to true generalizations, he seems to believe that there does exist a method of valid induction that can prove the geralizations to which it leads.

David Harriman, The Logical Leap, p. 7:

"When and why is the inference from "some" to "all" legitimate? What is the method of valid induction that can prove the generalization to which it leads?" (end quote)

But how is Harriman going to prove the truth of a generalization reached by a "method of valid induction"?

I have not yet received TLL so it is difficult for me to parse the above statement. Does Harriman mean to say induction works when it works and fails when it fails?

That is pretty thin gruel.

Ba'al Chatzaf

Deductively or inductively, yes or no?--the world wants to know.

--Brant

Edited November 29, 2010 by Brant Gaede

[BaalChatzaf]

Deductively or inductively, yes or no?--the world wants to know.

--Brant

The world will find out in due course.

Ba'al Chatzaf

[BaalChatzaf]

The problem of induction is the philosophical question of whether inductive reasoning leads to knowledge. That is, what is the justification for either:

1. generalizing about the properties of a class of objects based on some number of observations of particular instances of that class (for example, the inference that "all swans we have seen are white, and therefore all swans are white," before the discovery of black swans) or

2. presupposing that a sequence of events in the future will occur as it always has in the past (for example, that the laws of physics will hold as they have always been observed to hold). Hume called this the Principle of Uniformity of Nature. Link.

Induction is an attempt to infer 'All S is P', given 'Some S is P.' How is that ever justified? It seems to me the justification must be at least one additional premise of the form 'Why each S is P'.

Iterative induction -- simply 'One S is P', 'A second S is P', 'A third S is P', and so forth -- amounts to nothing more than a mockery of induction. In effect and by omission, it says 'Why S is P' is irrelevant.

Consider the case 'All swans are white', which apparently many people believed before learning there were black swans. (Incidentally, the black-necked swan is both black and white. Link.) Said belief was merely an iterative induction, based simply on all observed swans being white. There was no additional justification why they must be white, i.e. of the form 'Why each S is P'. Not only that, there was room for doubting that all swans are white. Many species of birds come in different colors. Even the closest relatives of swans, geese, come in different color patterns.

Let's move on to the induction 'All swans have necks'. While somebody might believe it is a mere iterative induction, I think not. By the way, Ba'al has -- not surprisingly -- not given a counterexample since I asked for one here. Can you even imagine a swan without a neck? What would having no neck imply? It would imply a creature with no connection between it head and its body. It would imply no channel between its mouth and lungs for breathing, and no channel between its mouth and stomach for ingesting food.

I could proceed to many more scientific examples, but will give only one. In all instances water boils at 100°C (212 °F) at standard pressure, i.e. at sea level. I'm confident somebody else could give a better explanation than me. Regardless, there is a good reason why having to do with molecular motion and heat that justifies this induction.

To summarize, the problem of induction is when is 'Why every S is P' sufficiently strong? Pretty clearly no uniform strength test can be given for every field of endeavor. Mill's Methods are for arriving at generalizations and are not strength tests.

Here is the technical definition of the word swan:

swan

1. (Science: zoology) Any one of numerous species of large aquatic birds belonging to Cygnus, Olor, and allied genera of the subfamily Cygninae. They have a large and strong beak and a long neck, and are noted for their graceful movements when swimming. most of the northern species are white. In literature the swan was fabled to sing a melodious song, especially at the time of its death.

The European white, or mute, swan (Cygnus gibbus), which is most commonly domesticated, bends itsneck in an S-shaped curve. The whistling, or trumpeting, swans of the genus Olor do not bend the neck in an S-shaped curve, and are noted for their loud and sonorous cry, due to complex convolutions of thewindpipe. To this genus belong the European whooper, or whistling swan (Olor cygnus), the American whistling swan (O. Columbianus), and the trumpeter swan (O. Buccinator). The Australian black swan (Chenopis atrata) is dull black with white on the wings, and has the bill carmine, crossed with a white band. It is a very graceful species and is often domesticated. The south American black-necked swan (Sthenelides melancorypha) is a very beautiful and graceful species, entirely white, except the head and neck, which are dark velvety seal-brown. Its bill has a double bright rose-coloured knob.

Since by DEFINITION the swan has a long neck, we may DEDUCE that all things that are swans have long necks hence they have necks.

Anymore difficult questions?

Ba'al Chatzaf

Edited November 29, 2010 by BaalChatzaf

[sjw]

Excellent try Merlin, but when you can't imagine something being any other way, it's usually the case that you're dealing with deduction. Another way to say it is: "given my premises, I can't imagine it being any other way." Which is to say that you are deducing something from your premises. Why do all swans need a neck? Because they have a head and body that must be connected. That's a deductive conclusion.

Now, you *can* imagine contrary premises that require rewriting reality. You could imagine a magical head that levitates and transports food to the stomach. That is, the idea that there is no magic is an inductive conclusion.

To come to the conclusion that water *must* boil at 100F at a certain pressure requires deeper premises regarding the nature of various atomic forces. That is, it is a deductive conclusion based on premises arrived at by induction.

Shayne

[BaalChatzaf]

For those of you who have read Harriman's book - The Logical Leap -, please offer an opinion.

First look at this presentation of an essay by Isaac Asimov:

It is about seven and a half minutes long.

Did Harriman say what needed to be said better than Assimov?

Thank you.

Ba'al Chatzaf