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I've been a bit perplexed about the "problem" of induction.

Hume challenges other philosophers to come up with a deductive reason for the inductive connection. If the justification of induction cannot be deductive, then it would beg the question. To Hume, induction itself, cannot explain the inductive connection. (Wikipedia)

But I ask, why do we need to show that induction is a necessary truth? We can not demonstrate a necessary truth but we can demonstrate that we have a valid reason to believe.

The principle of uniformity refers to the assumption that the same natural laws and processes that operate in the universe now have always operated in the universe in the past and apply everywhere in the universe.

If nature is uniform, crystal gazing may or may not work, but induction works. If nature is not uniform, then induction will fail, but so will any alternative method. Because if the alternative method did not fail, if it consistently yielded true predictions, and the success of that alternative would constitute a uniformity that could be exploited by the inductive method. Because we could inductively infer the future success of the crystal gazer from her past success. Hence, the inductive method will succeed if any alternative method could.

Why do we need to know whether the inductive method is necessarily true if the inductive method will succeed if any alternative method could? We can’t have a reason for believing that induction is necessarily true because we can’t know in advance whether nature is uniform. We can’t have a reason necessarily true, but we can justify the inductive method by saying that it's the best method for making predictions about the future/unobserved, because if nature is uniform, crystal gazing may or may not work, but induction works. If nature is not uniform all methods will fail.


ADDENDUM

Why we don't need a reason for believing that inductive method is necessarily true.

The problem of induction is a problem of which action to take, or which wager to accept. The injunction is to act so as to maximize expected utility of generate knowledge about the world. A deductive argument can only bring out what is already implicit in its premises, and hence all new knowledge about the world must come from some form of induction.The induction will succeed if any alternative succeed, and if the principle of uniformity doesn't hold, any alternative will not succeed. If an alternative method did not fail, if it consistently yielded true predictions, the success of that alternative would constitute a uniformity that could be exploited we could inductively infer the future success of the alternative method from her past success.

If any rule will lead to positing the correct knowledge, the inductive rule will do this, and it is simplest rule that is successful. The justification of application of Occam's razor is a direct result of generate knowledge about the world. By definition, all assumptions introduce possibilities for error; if an assumption does not improve the accuracy of a knowledge, its only effect is to increase the possibility that the knowledge is wrong.

It is difficult to formulate principle of the uniformity of nature in a coherent and useful manner. For nature is not uniform in all respects and it is uninformative to say simply that nature is uniform in some respects. Inductive inferences are not conclusively verifiable in physics, no crucial experiment is possible. For experiments in physics are observations of phenomena accompanied by interpretations and, therefore, physicists submit whole groups of hypotheses, not a single hypothesis, to experimental tests, and experimental evidence alone cannot conclusively falsify hypotheses. This is known as the Duhem thesis.That all inductive inferences will be justified is false, in any case an inductive inference doesn't need to be necessarily true.

Induction is a matter of following a tentative and self-correcting rule. A key thought is that agents start with their subjective prior hypotheses and then update them by conditionalisation, set within the subjective Bayesian framework. Induction, then, is the process of updating a hypotheses. The problem of justifying conditionalisation on the evidence is again which action to take, or which wager to accept. Again the injunction is to act so as to maximize expected utility of generate knowledge about the world.

Popper wants to say that induction is not justifiable. That a theory has been corroborated in the past "says nothing whatever about future performance." Popper wants to say that it is possible to avoid assuming that the future will, or probably will, be like the past, and this is why he has claimed to have solved the problem of induction. We do not have to make the assumption, he tells us, if we proceed by formulating conjectures and attempting to falsify them. He says that, as a basis for action, we should prefer "the best-tested theory." This can only mean the theory that has survived refutation in the past; but why, since Popper says that past corroboration has nothing to do with future performance, is it rational to prefer this?

Without the inductive assumption, the fact that a theory was refuted yesterday is quite irrelevant to its truth-status today. So demising the inductive assumption makes nonsense of Popper's own theory of the growth of scientific knowledge. The more often a conjecture passes efforts to falsify it, Popper maintained, the greater becomes its "corroboration", although corroboration is also uncertain and can never be quantified by degree of probability. "Corroboration" is a form of induction, and Popper has simply sneaked induction in through a back door by giving it a new name.

Every falsification of a conjecture is simultaneously a confirmation of an opposite conjecture, and every conforming instance of a conjecture is a falsification of an opposite conjecture. If Popper bet on a certain horse to win a race, and the horse won, you would not expect him to shout, "Great! My horse failed to lose!" Astronomers look for signs of water on Mars. They do not think they are making efforts to falsify the conjecture that Mars never had water. For Popper, what Carnap called a "degree of confirmation", a logical relation between a conjecture and all relevant evidence, is a useless concept. Instead, the more tests for falsification a theory passes, the more it gains in "corroboration”. It's not so much that Popper disagreed with inductivists as that he restated their views in a bizarre and cumbersome terminology. Why scratch your left ear with your right hand?

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Paragraphs/formatting would be easier on the eyes. :) –  Sniper Clown Dec 3 '12 at 7:09
    
Also, you answered the question yourself, what do you expect? –  iphigenie Dec 3 '12 at 11:24
    
I not answered the question. There are people who do not accept the pragmatic justification of the method of induction and I want to understand why. –  Ricardo Dec 3 '12 at 11:52
    
@RicardoBevilaqua That's not clear from your question. Perhaps you could be more precise on what your question is. –  iphigenie Dec 3 '12 at 12:21
    
@iphigenie I don't understand what is not clear. Can you be more precise in your doubt? We can’t have a reason for believing that induction is true because we can’t know in advance whether nature is uniform. But why we need justify inductive method with a reason for believing that is true? We can’t have a reason, but we can justify that it is the best method for making predictions, see below the question. –  Ricardo Dec 3 '12 at 14:04
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6 Answers 6

The problem of induction:

Induction, would it work, makes it possible to infer from finite "true" observations to a sentence that ranges over infinite cases.

P1: Oh look, a white swan!

P2: Oh, another one!

P3: And even a third white swan!

C1: All swans are white.

Deductive reasoning for the principle of induction

It is not possible to show deductively that the principle of induction is true. While the deductive method is truth-conserving, the inductive is not. The deductive method allows me to draw from P1-P3 the conclusion:

C2: There are at least 3 white swans

But nothing more.

If the nature is uniform, then induction works

I would doubt that. Wether the nature is uniform or not is a case of something we could only show by doing induction (in observations Oa ... On nature was uniform, therefore it will be uniform in the future).

But the more interesting point here is the consequens. What does it mean that induction works? Clearly, induction is not working truth-conserving, because there are in fact black swans (afaik in australia). But my inductive reasoning P1-P3 still tells me that all swans are white.

But if induction is not working truth-conserving, in what sense does it work and why would we want a method that is not truth-conserving?

But we have a valid reason to believe in induction

Again, I would doubt that. What does it mean to have a valid reason? For ages of ages every morning humanity observed that the sun had risen. But somewhen in a future far away, it won´t. Do we have a valid reason to believe that "The sun rises every morning" is true?

Even if the nature would have been uniform until now, how do we know it will be uniform tommorow? (without using induction? ;)) I think you have a valid reason to believe that there are at least 3 white swans, because of the validity of logical conjunction, and in this sense should we use the notion of validity.

If anything, one would have an inductive reason to believe in induction.

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The problem of induction is a problem of which action to take, or which wager to accept. The injunction is to act so as to maximize expected utility of rendering knowledge possible. The induction will succeed if any alternative is true, and not true if any alternative is not. If any rule will lead to positing the correct knowledge, the inductive rule will do this, and it is simplest rule that is successful. The Occam's rule applies to minimize the number of possible correction of hypothesis, given different possible future observations. –  Ricardo Jan 26 '13 at 3:58
    
That all inductive inferences will be justified, or be necessarily true, is false, and in any case a necessary supposition. –  Ricardo Jan 26 '13 at 3:58
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Not all logical consequences are immediately apparent upon setting up some premises. Pointing out consequences can be a "reason". You have just done this for the inductive method ("it's as true as anything can be about the physical world, and here's why").

(One might also want to know whether to apply it in some particular context.)

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if I did understand, I can not demonstrate the validity of induction but I can demonstrate that I have a valid reason to believe. –  Ricardo Dec 3 '12 at 15:05
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@RicardoBevilaqua - Exactly. That's what a "reason" is, absent omniscience, isn't it? –  Rex Kerr Dec 3 '12 at 15:07
    
Maybe I need to rephrase the question: Why do we need to show that induction is a necessary truth? What do you think? Do you think the issue is clearer? –  Ricardo Dec 3 '12 at 15:56
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@RicardoBevilaqua - Induction is not a necessary truth. (It would be convenient if it was and we could show it.) –  Rex Kerr Dec 3 '12 at 17:24
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Why do we need to know whether the inductive method is true if the inductive method will succeed if any alternative method could?

All arguments which turn on observations of some regularity (i.e. appeals to the outside world) and projects them into the future are going to be inductive in nature. When you say "any alternative method", I still think you're thinking of induction - you're thinking of past observations of the world projected into the future.

If an argument is made using deduction, it is qualitatively different from an inductive argument. Deductive arguments turn on definitions and what is, and as long as you know what the words mean and what is, you can judge the validity of the argument. Induction seems to require one to accept without any other assurance that what happened today will also happen tomorrow.

Induction as a problem I think catches people's attention because it seems to mirror the scientific method (observations of the world), but it seems invalid!

I've been a bit perplexed about the "problem" of induction. To me, when we make a statement saying that all swans are white, we're not so much making a statement about the world, as we are making a statement about our (my personal view, or the collective wisdom on the matter) understanding of the concept "swan". When we actually find a black swan, we update our notes on the concept "swan".

If there actually is a black swan, but nobody has seen it, and therefore the concept "swan" still allows no black members, then the statement "all swans are white" is true, as long as we acknowledge that by "swan" we mean our concept "swan" - which is what I think we are doing when we're speaking: we're weaving together our concepts, not weaving together entities in the world.

So we find a black swan, and we update our concept of swans. Before we found a black swan, all swans were white - I would call that true. After we found a black swan, swans are either black or white - I would call that true too. I don't think there's a contradiction there, nor do I think there's some inductive 'leap' going on.

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I've been a bit perplexed about the "problem" of induction too. Hume challenges other philosophers to come up with a deductive reason for the inductive connection. If the justification of induction cannot be deductive, then it would beg the question. To Hume, induction itself, cannot explain the inductive connection. But I ask, why do we need to show that induction is a necessary truth? We can not demonstrate a necessary truth but we can demonstrate that we have a valid reason to believe. –  Ricardo Dec 3 '12 at 19:02
    
A while ago I would have said that was a really wishy-washy position, but I think I really support that view now. I got really interested in Kierkegaard when studying and since then I've been of the opinion that Kierkegaard -> Wittgenstein -> Stanley Cavell have hit the nail on the head. I like most Kierkegaard's formulation of skepticism: –  Jeong Kim Dec 4 '12 at 14:09
    
I think Aristotle set up for us a standard of truth that was too abstract (analytic). I like Kierkegaard's statement: "If I want to keep on doubting, I shall never in all eternity advance any further, because doubt consists precisely in and by passing off that certainty as something else. If I hold on to the certainty as certainty for one single moment, I must also stop doubting for that moment. But then it is not doubt that cancels itself; it is I who stops doubting." - Adapting to induction, SK might say inductive proof is certain but not analytic, and unsatisfied, we turn it into doubt. –  Jeong Kim Dec 4 '12 at 14:18
    
Quote is from a pseudonymous work: Concluding Unscientific Postscript, extract from Kierkegaard, Søren. The Essential Kierkegaard. Edited by Howard Vincent Hong and Edna Hatlestad Hong. Princeton, N.J.: Princeton University Press, 2000. pp. 221-222 –  Jeong Kim Dec 4 '12 at 14:20
    
Dogmatism and skepticism are both, in a sense, absolute philosophies; one is certain of knowing, the other of not knowing. What philosophy should dissipate is certainty, whether of knowledge or ignorance (Bertrand Russell).Reason has proof without any certainty. Faith have certainty without any proof. –  Ricardo Dec 4 '12 at 17:55
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The example of the turkey in Nassim Nicholas Taleb's The Black Swan: The Impact of the Highly Improbable is relevant here:

Consider a turkey that is fed every day. Every single feeding will firm up the bird's belief that it is the general rule of life to be fed every day by friendly members of the human race "looking for its best interests" ... On the afternoon of the Wednesday before Thanksgiving, something unexpected will happen to the turkey. It will incur a revision of belief.

Arguably the turkey came to suffer from its inductive reasoning and assumptions about uniformity in his natural environment (nature), and clearly Taleb is (also) in Hume's tradition.

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The problem of induction is a problem of which wager to accept. The induction will succeed if any alternative is true, and not true if any alternative is not. The pragmatic principle is the injunction to act so as to maximize expected utility. The most rational and greater expected utility is to accept induction than don't accept. –  Ricardo Jan 25 '13 at 0:43
    
My understanding is that the likes of Hume, Taleb, etc. point out that the "model" that allows one to calculate expected utilities may be flawed for philosophical/theoretical and practical reasons. Some people (e.g. Tabeb) among them can afford to be "philosophical" about the lack of fully reliable models (say, outside Physics), others clearly have agency problems in pushing/"selling" theirs, IMHO the (also pragmatic) "truth" must be somewhere in the middle. I plan to further consult e.g. Hayek on this :) –  Drux Jan 25 '13 at 11:22
    
The injunction is to act so as to maximize expected utility of rendering knowledge possible. If any rule will lead to positing the correct knowledge, the inductive rule will do this, and it is simplest rule that is successful. The Occam's rule applies to minimize the number of possible correction of hypothesis, given different possible future observations. That all inductive inferences will be justified, or be necessarily true, is false, and in any case a necessary supposition. –  Ricardo Jan 26 '13 at 4:05
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Humes critique of induction is a question in epistemology, how do we guarantee & justify true knowledge. I also think, and this is mere speculation as I'm not familiar thoroughly enough with Humes work that it was an critique on the scientific method. I don't think its a critique on everyday 'induction'.

If Hume could be sceptical about the neccesary truths of Christianity, I suppose he felt it incumbent to also critique those of science, and the obvious place to begin is at the beginning: what justification can we have for induction?

That nature is uniform is a justified belief, as you point out, but it's not a necessary truth in the formal sense of the word (but maybe epistemologically neccesary, as you also point out we can only operate in the world with a framework of justified belief, whether or not those justifications are conscious or with significant foundation).

I'm inclined to think that there are links with romanticism, as clearly Hume was a literary man, and he was good friends with Rousseau - he offered him refuge. I suspect he shared his general disillusionment with rationality as the pre-eminent virtue.

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Humes critic has a psychological aspect. The question is: How can we explain that we use induction everyday when it doesnt work? And one answer to that is: well, just because cars normally stop at red light, I´d go sure by looking left and right before crossing a street, because, and here is the upshot, you can´t be sure they´ll stop this time aswell. –  Lukas Jan 25 '13 at 11:23
    
The problem of induction is a problem of which action to take, or which wager to accept. The injunction is to act so as to maximize expected utility of rendering knowledge possible. The induction will succeed if any alternative is true, and not true if any alternative is not. If any rule will lead to positing the correct knowledge, the inductive rule will do this, and it is simplest rule that is successful. The Occam's rule applies to minimize the number of possible correction of hypothesis, given different possible future observations. –  Ricardo Jan 26 '13 at 4:02
    
That all inductive inferences will be justified, or be necessarily true, is false, and in any case a necessary supposition. –  Ricardo Jan 26 '13 at 4:03
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The doubt that forms answer to your title question is:

How exactly do we "know" that universe is uniform without applying induction to universe?

That is, 'uniform universe' solution to the Induction Problem is circular. The Inductive reasoning (and hence the problem associated with it) is much more general principle then the scope addressed above.

The problem with pragmatic approach

The problem here with pragmatic approach is that it is a pragmatic approach being used to solve an epistemological query. Stating in pragmatic terms: too much is on stake for an explanation for assuming inductive reasoning to be correct. One can not just bet on it and say that bet is more likely to pay off than not as it is not a one time problem - we use Inductive reasoning far too liberally for that.

The correct solution to the Problem of Induction should be an epistemological one.

[ Refer: http://www.proginosko.com/docs/induction.html ]

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I'm a bit perplexed about the reference's Anderson “problem”. Why we need an indication of the actual likelihood of its success? Why do we need a reason for believing that inductive method is necessarily true? Why induction is not reliable if the induction will succeed when any alternative is true, and not true any alternative is not? All we need is a valid reason to believe. –  Ricardo Jan 24 '13 at 2:24
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