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Your thoughts on Hume's case against induction?

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Inductive generalization is valid only if the conclusion can be said to be certain
But this is the essence of Hume's induction argument - certainty here is claimed to be impossible. The only 'certainty' is psychological - after seeing a certain number of instances all confirming the hypothesis, we feel convinced that it has to be true. A true solution to the problem of induction would need to show that certainty about the whole is logically justified when all you have is observations of a subset.
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"White" is not part of the definition of "swan", so that's where the context dropping comes from.  It would be a better example to say that you see 25 birds that are similiar and call them swans, and then see one that's different.
Well I've no idea what 'the' definition of swan was (or indeed is), so I'm not prepared to say whether whiteness was considered to be defining. There was obviously a strong feeling that all swans were white though otherwise the black ones wouldnt have caused widescale surprise.

A simpler example Peikoff gave in the lectures:  A child doesn't need to see 25 balls rolling -- he only needs to see ONE ball rolling (and one non-ball object not rolling)-- to reach the induction "All balls roll".  He does so by grasping the essential property difference between balls and non-balls which enables them to roll, and mentally connecting that property to the rolling.  It is an implicit recognition of the the law of causality.

The ball example is very different from the swan one, although from a Humean standpoint it is not really capable of justification either.
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But this is the essence of Hume's induction argument - certainty here is claimed to be impossible. The only 'certainty' is psychological - after seeing a certain number of instances all confirming the hypothesis, we feel convinced that it has to be true.

....

The ball example is very different from the swan one, although from a Humean standpoint it is not really capable of justification either.

The key here is that Hume did not understand what induction is. Of course you cannot solve a "problem" if you are wrong about what the problem is. In other words, Hume was an idiot in the realm of epistemology. *shrug*

Induction is a method of generalizing by grasping essential similarities and differences and connecting them to causation. Note that there is no mention of quantity in what induction actually is. Induction is not piling up examples and then jumping from "many" to "all" with no connection to causation. Never has been, never will be -- no matter how times Hume wrote that it was so.

Edited by TomL
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There was obviously a strong feeling that all swans were white though otherwise the black ones wouldnt have caused widescale surprise.
Do you have any concrete evidence that bears on this widespread "surprise"? Was there massive rioting in the streets and pronouncements of the end of the world? I mean, South America was discovered 500 years ago when people hardly knew anything, when concepts of species were very primitive, and people were "surprised" to learn that monkeys in sailor suits are not French spies. Anyhow, I don't see how this would be relevant to contemporary definitions of "swan". You could make it relevant, if you want, but the burden is on you to decide how it is relevant.
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If inducing from one instance that "all balls roll" is false, then the following statement is necessarily true:

There is some ball somewhere in existence that will not roll.

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my impression of Hume was that he says that we can never truly be sure of the future, and that all knowledge is merely statistical probabilities. For example, the sun rises every morning. We know it does, because it has happened every day of our lives. Hume says that this is merely the statistical likeliness; and that the sun may not rise tommorow morning. A supervolcano, for example, might erupt, and cause a nuclear winter, thus preventing us from seeing the sun rise. He says that everything we know of the physical sciences is built this way, and as history points out, new theories and ideas can render old scientific theories obsolete in a heartbeat. Therefor we can not even be sure that physical science is correct.

If I recall correctly, Hume says the only thing we can truly be sure of is logic: 2+2 will always equal 4. Conceptual logic and mathematics, Hume says, is the only constant knowledge, for one must believe that 2+2=4, regardless on wether or not one feels that the universe revolves around Earth, or that the Earth revolves around the sun.

Hume's style of philosophy is very similar to Descarte

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If I recall correctly, Hume says the only thing we can truly be sure of is logic: 2+2 will always equal 4.

This is a good example of context dropping. This is not my example, I just can't recall where I first read it, but it helped me understand why context is important. 2+2=4 only when one is thinking in base 10. If one is using base 3, for example, 2+2=11. Context is everything.

I'm somewhat new to the study of Objectivism, so if I have misinterpreted this approach, I would appreciate correction.

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That was a great series of posts, TomL.  Is the Peikoff lecture available in writing or on tape?

Actually, it is.

The first half is the first half of lectures from OCON 2002 in Palo Alto. The second half of the CD is from OCON 2003, at which point Peikoff backed out about half of what he said in '02 and replaced it, thanks to a question posed from the audience by Greg Salmieri, a graduate student in philosophy at the University of Pittsburgh, who has taken courses at OAC and specializes in epistemology. They put him on the staff for OCON 2004, I'm not sure what he's doing now. (I was present for the lectures in both '02 and '03 in person. I've been meaning to buy the CD but I've not gotten around to it yet).

Edited by TomL
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  • 4 weeks later...

I would say that the most direct way of dealing with Hume on an Objectivist foundation would be do argue against his claim that there are no necessary factual truths, and the best way to do this would be to consider Peikoff's article, "The Analytic-Synthetic Dichotomy".

But first a brief summary of Hume reasoning and conclusion:

He thinks that all necessary truths are mere relations of ideas. For example, "All triangle are 3-sided" is true because the idea of triangles contains the idea of 3-sidedness.

As a consequence he concludes that necessary truths cannot be "factual"---that is, about the world (presumably because he thinks that ideas are in the mind, or created by the mind, and that if that is true the same must be true about relations of ideas, and so necessary truths are in the mind or created by the mind, and in that case they wouldn't tell us anything about reality outside the mind).

So necessary truths are not factual, and so any truth that is factual is not necessary but rather is contingent.

Well from this he draws various skeptical conclusions. (1) Since metaphysics is supposed to be about necessary factual truths he concludes that it is nonsense.

(2) Since truths about science are obviously factual they must be contingent. (3) Since truths about causal connections (which are scientific truths) are obviously factual they must be contingent (and so the opposite is possible). (3) Since induction from the present to the future, or from the past to the present or the future, depends on causal connections between these times, and since nothing less than a necessary connection could warrant induction from one to the other, induction cannot be done.

However, Peikoff knocks the foundation out from under this argument. He says that only facts about human free will choices are contingent (though he prefers to call them "man-made"); all others are necessary (though he prefers to call them "metaphysical"). Definitional truths are not the only necessary truths, since, as Peikoff says,a concept does not mean just its definition. Further, Peikoff says that definitions are not arbitrary products of convention anyway. This rebuts those who would say that causal truths are not necessary because they are not analytic and are not analytic because the concept of the effect is not contained in the concept of the cause (on the ground that a concept means only its definition and the effect cannot follow from the effect by definition, because definitional truths are arbitrary since definitions are arbitrary).

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You can kill hume's problem by refering to its self reference.

What hume said is you can't know anything. How did he know that?

That's the problem with all theories trying to attack reason or logic or knowledge. Trying to prove it doesn't exist.

How do you prove it? Without reason or logic.

You can't destroy a hammer with that very same hammer. And you can't destroy reason by using reason. There is no way for your reasoning faculty ever to be impaired as long as you keep your integrity.

Edited by Felix
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You can kill hume's problem by refering to its self reference.

What hume said is you can't know anything. How did he know that?

Hume didnt say you cant know anything - he says that all human knowledge involves either the relations of ideas (mathematics/logic), or empirical experience. He then claims that casuality not given in experience, since all we actually perceive is event A followed by event B, rather than any necessary connection between them. He hence concludes that induction (our belief that the future will resemble the past) cannot be given an ultimate foundation, and that our postulation of casual relations is just a curiosity of human psychology rather than someone we are capable of justifying.

Edited by Hal
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  • 2 months later...

According to Hume, is there any reason to trust science since science he said is based on illogical premise and that a finite number of experiments cannot determine the future consequences of a conclusion? What are your thoughts on this and on Hume's problem with induction?

Edited by Dragonseeker
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Dragonseeker, I am confused about what you are seeking. Your Viewing Profile, unfortunately, provides almost no information about you, that is, no information that would help set a context for these questions you are asking.

So, to set a context and thereby facilitate appropriate answers, could you explain ...

- What is your purpose in asking these questions?

- How did these questions arise in your life, and, when you find answers, how will that affect your life?

For example, are you a scientist? Are you having doubts about the validity of your work?

Since this forum is dedicated primarily to trade among Objectivists, I assume you are an Objectivist. Is that true? If so, how do you see your questions relating to Objectivism?

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According to Hume, is there any reason to trust science since science he said is based on illogical premise and that a finite number of experiments cannot determine the future consequences of a conclusion? What are your thoughts on this and on Hume's problem with induction?

Hume's objection to induction is due to a false idea of induction. If induction were, in fact, merely a numerical catalog of concretes, it wouldn't be valid. Induction's vailidity lies in moving beyond concretes and determining some kind of causal relationship.

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Hume's objection to induction is due to a false idea of induction. If induction were, in fact, merely a numerical catalog of concretes, it wouldn't be valid. Induction's vailidity lies in moving beyond concretes and determining some kind of causal relationship.

Does Hume not object to causality itself, on the grounds that past cause/effect observation is not solid evidence that in the future the cause/consequence chain will remain valid?

mrocktor

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Does Hume not object to causality itself, on the grounds that past cause/effect observation is not solid evidence that in the future the cause/consequence chain will remain valid?

I believe that is his fundamental objection, yes: that in perceiving A do some action B, one only sees what could have been one way--one does not perceive any "necessity" about it anywhere. Thus, since things can be some way without necessarily being that way, one cannot say how they will be in the next instant. Thus he really attacked causality, like you say, and not induction per se.

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I believe that is his fundamental objection, yes: that in perceiving A do some action B, one only sees what could have been one way--one does not perceive any "necessity" about it anywhere. Thus, since things can be some way without necessarily being that way, one cannot say how they will be in the next instant. Thus he really attacked causality, like you say, and not induction per se.

Now I need some clarification. I haven't actually read Hume, just other people's references to him, so I may be misunderstanding things a bit. It is my understanding that he didn't necessarily attack metaphysical causality; rather, he said that we can not make an epistemological inference of causality through observation. I was under the impression that he didn't deny causes exist, just that we can't know them. That's why I say he attacked induction, rather than causality as such. Is my understanding incorrect?

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Now I need some clarification. I haven't actually read Hume, just other people's references to him, so I may be misunderstanding things a bit. It is my understanding that he didn't necessarily attack metaphysical causality; rather, he said that we can not make an epistemological inference of causality through observation. I was under the impression that he didn't deny causes exist, just that we can't know them. That's why I say he attacked induction, rather than causality as such. Is my understanding incorrect?

(Caveat: I am not a professional philosophical historian. I don't even watch them on TV.) Executive summary: he said primarily that we cannot possibly know causation, but it follows pretty quickly for him and his followers that it doesn't exist.

It has been over a decade since I read Hume, so I decided to check my claim. I don't have any primary sources by Hume handy, so I will have to do with a web search. From wikipedia, which I am quoting because 1) it tends to be most accurate when it summarizes a school of thought, rather than asserting whether that school is correct, and 2) the author(s) clearly agree with Hume:

When one event causes another, most people think that we are aware of a connection between the two that makes the second event follow from the first. Hume challenged this belief, noting that whereas we do perceive the two events, we don't perceive any necessary connection between the two. And how else but through perception could we gain knowledge of this mysterious connection? Hume denied that we could have any idea of causation other than the following: when we see that two events always occur together, we tend to form an expectation that when the first occurs, the second will soon follow. This "constant conjunction" and the expectation thereof is all that we can know of causation, and all that to which our idea of causation can amount.

From the Catholic Encyclopedia:

Having previously reduced mind to no more than a succession of perceptions, he declares: "To me there appear to be only three principles of connection among ideas, namely, Resemblance, Contiguity in time or place, and Cause or Effect" (Works, IV, 18). Thus, for Hume, causality is no more than a relation between ideas. It is not an a priori relation, "but arises entirely from experience, when we find that any particular objects are constantly conjoined with each other" (ibid., 24). However, we can never comprehend any force or power, by which the cause operates, or any connection between it and its supposed effect. The same difficulty occurs in contemplating the operations of mind on body.... So that, upon the whole, there appears not, throughout all nature, any one instance of connection, which is conceivable by us" (ibid., 61 sqq.). Whence, then, does our conception of cause come? Not from a single observed sequence of one event from another, for that is not a sufficient warranty for us to form any general rule, but from the conjunction of one particular species of event with another, in all observed instances. "But there is nothing", he writes,

in a number of instances, different from every single instance, which is supposed to be exactly; except only, that after a repetition of similar instances, the mind is carried by habit, upon the appearance of one event, to expect its usual attendant, and to believe that it will exist.... When we say, therefore, that one object is connected with another, we mean only, that they have acquired a connection in our thought, and give rise to this inference, by which they become proofs of each other's existence (p. 63)

Hence Hume defines cause as that object, followed by another, "where, if the first object had not been, the second would never have existed", or "an object followed by another, and whose appearance always conveys the thought to that other" (ibid.). In this doctrine Hume advances a psychological explanation of the origin of the idea (habit), but inculcates an utter scepticism as to the reality of causation.

From this and some other reading I did, I would say that he rejects not only our knowledge of necessary causation (epistemologically), but the fact of it as well (metaphysically). Naturally he still speaks of "cause," but to him it means something entirely different than to Aristotelians/Objectivists: he means a mental construct that comes from "constant conjunction" unchanged only for as long as we have observed it, whereas we mean "identity in action" and therefore universal.

Thus the chickens come home to roost when it comes to induction:

Most of us think that the past acts as a reliable guide to the future. For example, physicists' laws of planetary orbits work for describing past planetary behavior, so we presume that they'll work for describing future planetary behavior as well. But how can we justify this presumption – the principle of induction? Hume suggested two possible justifications and rejected them both:

The first justification states that, as a matter of logical necessity, the future must resemble the past. But, Hume pointed out, we can conceive of a chaotic, erratic world where the future has nothing to do with the past – or, more tamely, a world just like ours right up until the present, at which point things change completely. So nothing makes the principle of induction logically necessary.

The second justification, more modestly, appeals only to the past reliability of induction – it's always worked before, so it will probably continue to work. But, Hume pointed out, this justification uses circular reasoning, justifying induction by an appeal that requires induction to gain any force.

So since induction requires determination of the underlying cause, Hume naturally rejects induction as a consequence of his view of causality.

As a bonus, the analytic/synthetic dichotomy rears its ugly head here, in the words "logically necessary." I have to give credit here to Dr. Peikoff's deep but worthwhile essay in ITOE for my understanding of how a denial of identity (and its corollary, causality) is at the heart of the dichotomy.

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  • 11 months later...
Is he correct in doubting the predictablity of future events?

I think Hume makes an interesting argument. Sir Karl Popper believed he had solved the problem of induction as proposed by Hume. Inductive generalization from observations is not possible (this is logical positivism, which Popper helped negate). Popper argued that scientific progress was made through conjectures and refutations and that theories are accepted when all their rivals are falsified, and not by sheer virture of earning a solid track record in correctly predicting future events. Scientific theories are tentatively adopted. It is the nature of scientific progress that new and better-corroborated theories be proposed to supplant their rivals. The experiment which corroborated Special Relativity, did so in part by vanquishing its rival: Newtonian Mechanics. Still, Popper would have argued that we cannot logically justify asserting that Special Relatively is capable of correctly predict all future events. And no doubt, one day S.R. will be vanquished by a rival theory, the corroborating experiments for which will refute S.R.

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