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Your thoughts on Hume's case against induction?

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What is the solution? Is it simply that A is A and will always be A is axiomatic?
There's an implication in the expression "the problem of induction", that there is, somehow, something wrong. You don't see people complaining about "the problem of life" or "the problem of existence". Now if the question were about how induction should work, that would be an interesting question, but to say "error is possible in knowledge" is a fairly useless statement (especially if you neglect to complain about "the problem of deduction"). I don't object to people talking about "facts about knowledge" (though there is a noun designed for that purpose). I object to people presupposing that the nature of knowledge is a "problem".
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She did not address it. The solution, however, is that it isn't a problem.

I would have thought that she did address it but obliquely. It was addressed in the sense that she combined (i) a proper conception of the law of causality (which Hume, by means of a long series of historical errors, arrived at an opposite conception) with (ii) a correct theory of concept formation and (iii) a contextual theory of knowledge acquisition. These elements (and other crucial insights) provide the basis for a valid theory of induction. Such a theory gets around the Humean criticism because it doesn't accept his underlying suppositions (such as his sensationalism) and general framework.

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Hi

Can anyone tell me what Ayn Rand's solution to Hume's problem of induction was?

thanks

BJ

She didnt have one. Ayn Rand discusses several specific cases of scientific induction in the Appendix to IOE, but makes the following statement about the Humean 'problem' of induction.

Prof M: The question is: when does one stop? When does one decide that enough confirming evidence exists? Is that in the province of the issue of induction?

Ayn Rand: Yes. That's the big question of induction. Which I couldnt begin to discuss - because a) I havent worked on that subject enough to even begin to formulate it, and :thumbsup: it would an accomplished scientist in a given field to illustrate the whole process in that field

But where I disagree is that he claims that you can know nothing because all knowledge is inductive and induction always has the possibility to be wrong. This in essense is claiming that you need to know that you know, in order to possess knowledge. If this is true, then you would need to know that you know that you know, in order to possess knowledge and so on, ad infinitum. That means that in order to hold any one belief you would need to have an infinite amount of beliefs about that belief, and that is just silly. What he describes as knowledge is not what any person would consider as knowledge.

Where does Hume say that we cant know anything? His claim is that there is no 'ultimate justification' for induction - if someone were to propose an alternative method for forming hypothesis', there would be no neutral vantage point outside logic from which we could compare the two.

How would you come to this conclusion, except by induction?

By analysing the concepts of inductive and deductive arguments, like Hume did.

Edited by Hal
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Where does Hume say that we cant know anything?

He says it a million times in his works (Which is why he is considered a skeptic), but here is a taste:

Our reason must be consider’d as a kind of cause, of which truth is the natural effect; but such-a-one as by the irruption of other causes, and by the inconstancy of our mental powers, may frequently be prevented. By this means all knowledge degenerates into probability; and this probability is greater or less, according to our experience.

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He says it a million times in his works (Which is why he is considered a skeptic), but here is a taste:

Our reason must be consider’d as a kind of cause, of which truth is the natural effect; but such-a-one as by the irruption of other causes, and by the inconstancy of our mental powers, may frequently be prevented. By this means all knowledge degenerates into probability; and this probability is greater or less, according to our experience.

Fair enough. I havent read Hume for several years and might have been confusing him with some modern philosophers who agree with his scepticism but dont believe it results in a denial of knowledge. But even in that quote you gave, I'm not if Hume is denying knowledge. Saying that knowledge is probabilistic isnt the same as saying that it is unattainable - if you are 99% sure about something then you are entitled to say that you know it, in most contexts (a jury would probably convict a criminal if they believed there was only a 1 in a 100 chance he was innocent, and might even class it as 'beyond reasonable doubt').

On a sidenote, I dont think Hume's statement there is consistent with his general position. If induction is in question, then you cant really have probabilistic knowledge either - applications of probability generally require some form of induction (you have to have reason to believe the relative frequencies in your finite subset of observations will remain constant when applied to the whole set, which is just the problem of induction all over again).

Edited by Hal
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Hume went on to say that all knowledge is inductive, and I would agree, except for axioms which have no deductive or inductive reasoning behind them.

Objectivism's axioms are derived by induction. At least, that is their position.

But where I disagree is that he claims that you can know nothing because all knowledge is inductive and induction always has the possibility to be wrong. This in essense is claiming that you need to know that you know, in order to possess knowledge.
I do not see how the second sentence follows from the first. Please elaborate.

...  she combined (i) a proper conception of the law of causality (which Hume, by means of a long series of historical errors, arrived at an opposite conception) with ...

Since I am not familiar with Hume, would you please explain the difference between his conception of causality and Ayn Rand's.

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Objectivism's axioms are derived by induction.

explain?

Objectivism's axiomatic concepts are perceptually self-evident, i.e. they are concepts formed by direct observation of reality, i.e. by induction.

How would you come to this conclusion, except by induction?

By analysing the concepts of inductive and deductive arguments, like Hume did.

The point is that one cannot reach a conclusion about the validity of induction without making some use of induction. Since concept formation is an inherently inductive process, one must use induction to grasp the concept of induction as part of any process of analyzing its validity.

Thus the attack on the validity of induction fails for the same reason as the attack on the validity of the senses – it makes use of what it purports to refute.

Hume's argument, as I recall, is that since man is not omniscient, he cannot know anything for certain. And Hume is certain of it.

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Since concept formation is an inherently inductive process
No it isnt, at least not in the sense of 'induction' used by anyone when discussing the problem of induction. Concept formation does involves generalisation from a set of instances, but induction involves making claims about whether future instances will continue to fall in line with the observations made so far. There is no analogue to this with concept formation.

Hume's argument, as I recall, is that since man is not omniscient, he cannot know anything for certain.  And Hume is certain of it.

This is incorrect. Hume's argument is that no non-circular arguments can be given to prefer induction over alternative methods of projection/hypothesis formation

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No it isnt, at least not in the sense of 'induction' used by anyone when discussing the problem of induction. Concept formation does involves generalisation from a set of instances, but induction involves making claims about whether future instances will continue to fall in line with the observations made so far. There is no analogue to this with concept formation.
First, induction is classically defined as deriving general principles from particulars (in contrast to deduction, which is deriving particulars from a general principle). Second, I'm stunned that you can't see the relationship. The essence of measurement omission is a claim that future oberved instances of the thing -- say, "dog" -- will continue to have all of those (essential) characteristics shared among the previously observed instances of "dog", save for those omitted (non-essential) characteristics.
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Since I am not familiar with Hume, would you please explain the difference between his conception of causality and Ayn Rand's.

Well, Hume discusses this famously at length in his Enquiry. I'll supply a few telling quotes, which should give you a taste for his approach.

This first is representative of his criticism of the concept of "necessity," which he considers entirely without foundation (and hence causality dissolves into mere association of one event following another with no independent necessary connection conjoining them):

When we look about us towards external objects, and consider the

operation of causes, we are never able, in a single instance, to

discover any power or necessary connexion; any quality, which binds the

effect to the cause, and renders the one an infallible consequence of

the other. We only find, that the one does actually, in fact, follow the

other. The impulse of one billiard-ball is attended with motion in the

second. This is the whole that appears to the _outward_ senses. The mind

feels no sentiment or _inward_ impression from this succession of

objects; Consequently, there is not, in any single, particular instance

of cause and effect, any thing which can suggest the idea of power or

necessary connexion.

Hume couldn't "find" causality in the external world (stemming from a variety of presuppositions, such as his sensationalism), nor could he find it in the internal world. Hence, causality for Hume became mere association of sensations in succession, and facts were no longer necessary but contigent. As an aside, this is what motivated Kant to develop his [in]famous ground for necessity in the Critique.

A few more quotes from Hume...

From the first appearance of an object, we never can conjecture what

effect will result from it.

and finally in his own words:

It appears, then, that this idea of a necessary connexion among events

arises from a number of similar instances which occur of the constant

conjunction of these events; nor can that idea ever be suggested by any

one of these instances, surveyed in all possible lights and positions.

But there is nothing in a number of instances, different from every

single instance, which is supposed to be exactly similar; 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. This connexion, therefore, which we

_feel_ in the mind, this customary transition of the imagination from

one object to its usual attendant, is the sentiment or impression from

which we form the idea of power or necessary connexion.

Therefore, we may conclude, for Hume: necessity is a myth; causality is a myth.

I imagine if you are familiar with Ayn Rand's conception of causality, that the above Humean model will stand in stark relief. If you would a more explicit comparison, please let me know.

I hope this helps a bit.

Edited by Gabriel_S
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First, induction is classically defined as deriving general principles from particulars
And then assuming they can be projected onto future cases in a certain way. What are you describing is abstraction., which is different from induction.

Second, I'm stunned that you can't see the relationship. The essence of measurement omission is a claim that future oberved instances of the thing -- say, "dog" -- will continue to have all of those (essential) characteristics shared among the previously observed instances of "dog", save for those omitted (non-essential) characteristics.

No. If something doesnt have the 'essential characteristics' of a dog then it isnt a dog. Saying that '"future observed instances of dogs will continue to have all those essential characteristics shared among previous observed instances" is just a very long way of saying "we will see more dogs". But this isnt at all essential to the formation of valid concepts - if I form the concept of 'elephant' while at the zoo and never see another elephant again for the duration of my life, my concept is still valid.

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No. If something doesnt have the 'essential characteristics' of a dog then it isnt a dog. Saying that '"future observed instances of dogs will continue to have all those essential characteristics shared among previous observed instances" is just a very long way of saying "we will see more dogs".
Perhaps you think that conceptual classification is metaphysically given and involuntary?
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The identification as a dingo is automatic - I perceive it as a dingo without any need for voluntary action. The knowledge that it isnt a dog is implicit in the identification - I doubt that I've ever looked at a tree and consciously thought "oh, that isnt a dog".

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No it isnt, at least not in the sense of 'induction' used by anyone when discussing the problem of induction. Concept formation does involves generalisation from a set of instances, but induction involves making claims about whether future instances will continue to fall in line with the observations made so far. There is no analogue to this with concept formation.

Concepts are open-ended in nature. For instance, the concept "dog" refers to all dogs that presently exist, all dogs that have ever existed and all dogs that will ever exist in the future. Thus, a "claim about future instances" is implicit in every concept.
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Induction has been addressed by Leonard Peikoff recently. It was never addressed by Ayn Rand. Below is excerpts from my notes from Peikoff's lectures on induction. I hope you find them useful.

Definition of induction: the primary process of reaching knowledge that goes beyond perception.

Deduction, another means of reaching knowledge beyond perception, presupposes induction about its component concepts, thus induction has primacy over deduction.

Induction is the jump from many (or one) to all. It is thus a "generalization". Without generalization, there can be no learning.

The "swan" method of debunking induction is false. "If I see 25 swans on a lake and they are all white, then I induct (generalize) that all swans are white. Oh, but there's a black one I didn't see before.. thus induction is false." This method is arbitrary, i.e. disconnected from reality. It also drops the context of the definition of the concept of "swan".

Generalizations (inductions) are not to be multiplied beyond necessity, i.e. without prerequisite knowledge that gives rise to the question.

The problem must exist in reality

It must have a valid context

i.e. -- not arbitrary

Generalizations are not concepts. Concepts are said to be valid or invalid; generalizations are knowledge and thus said to be true or false. Concepts are file folders, generalizations are the files that go into those folders.

5 rules to follow to proper induction:

1. At every stage, valid concept formation is essential, because valid concepts are the only green light to induction.

2. Induction beings with self-evident, first-level generalizations, to which all other generalizations must ultimately be reduced.

3. Induction requires the contextual discovery of causal connections using the methods of Difference and Agreement.

4. Induction at every stage beyond the first level requires integration with other knowledge -- and on the highest levels requires the discovery of principles which integrate fundamentals from a diversity of fields.

5. In the physical sciences, after their early stage, the above steps depend on and are performed through and only through mathematics.

Without a defined method of induction, the inducer uses emotion or authority to perform the generalizing, and thus the "problem of induction". Erroneous methods of induction include:

1. Over-generalization (limitation to context overlooked)

2. Premature integration (not enough analyzed data) (piling up examples without analysis pointless)

3. Occam's Razor -- if its simpler, its truer

Philosophy is the broadest science -- any philosophic principle is wider than any principle in physics. All other sciences are hierarchically layered on philosophy.

Indispensibility of Math to Physics

Why is physics without math possible? What does math do for man in knowing external reality [beyond perception]?

Consciousness on the conceptual level is inherently a quantitative mechanism, it is an apparatus for measuring quantity. Quantity has epistemological primacy over quality. One can identify qualities only by grasping quantity.

Just as in concept formation, so in grasping what the essential causes are of effects being observed -- by quantity. Measurements available to consciousness are in two forms: 1. the approximate, preconceptual, and 2. the numerical, conceptual.

It is impossible to know a quality without measurement. Why? Because that is the nature of consciousness as such.

Physics completes the job of concept formation. For example, in pendulum damping, the length of the pendulum is proportional to the period squared. To begin, one needs the concepts of "length", and the specific type, the length of a pendulum. One also needs the concept of "time", then the actual numbers are dropped and replaced with unspecified quantities to denote the mathematical formula and thus the concept of the relation between pendulum length and period.

There is no way to grasp relationships among objects except to reinsert the measurements dropped to form the concepts in the first place. In thinking about the above example, one's mind begins by imagining 1 for T, then 2, then 3, and calculating the other side...

Relation of Math to Reality

There are two false theories of math, both of which make physics impossible to explain.

Intrinsicist theory: numbers are metaphysical and God thinks in integers. In such a theory, there can be no relation between numbers, cognition, and reality. This theory detaches physics from matter.

Subjectivist theory: numbers are an arbitrary concept of consciousness. Leaves you with the same problem.

Numbers are facts of reality, i.e. objective, and they are constructed as concepts by consciousness. Reality contributes the fact that entities are real (basis for the concept "1"), and that variations in quantity are real. Consciousness establishes the need to establish relationships among quantities, and thus the need to select measurable units to do so.

Consciousness creates the numbers. For example, pi, the ratio of the circumference of a circle to its diameter. Only round things exist in nature -- the relationship between the circumference and the diameter is constructed by man's consciousness, and thus the concept of pi.

Conclusion

Philosophy explains the relation of math to reality, i.e. what numbers are. It cannot use numbers to do so!

Philosophy is the arbiter of measurements. Philosophy subsumes the proper relationship between one object (the universe!) and consciousness. The message of philosophy is "perceive reality", and philosophy doesn't need and can't use numbers to express it.

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The "swan" method of debunking induction is false. "If I see 25 swans on a lake and they are all white, then I induct (generalize) that all swans are white. Oh, but there's a black one I didn't see before.. thus induction is false." This method is arbitrary, i.e. disconnected from reality. It also drops the context of the definition of the concept of "swan".

Does he actually give any arguments to support this, since its the only thing there that seems relevant to the traditional problem of induction?

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Does he actually give any arguments to support this, since its the only thing there that seems relevant to the traditional problem of induction?
I haven't heard the lecture, but based on Tom's notes and things I've heard others say, I will venture a guess. The leap from seeing 25 white swans to the universal statement requires you to posit an unsupported causal claim about color. If you don't know "the basic facts" about color in animals, the conclusion is arbitrary since you don't know what causes color. (Induction is not an unlimited license to impute causation to correlation). OTOH if you do know those facts, then it would be at best arbitrary because you have omitted a number of non-white swan species. Inductive generalization is valid only if the conclusion can be said to be certain; when you know about species / color correlations and of the geographical distribution of various animal species, you have a material unknown that prevents you from saying that all species of swan are white. An analogous induction about polar bears being white would be valid (given the further knowledge that there is just one species of polar bear, living in the Arctic).
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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.

The fact is: you don't need to see 25 swans to induce what a swan is. You only need to see ONE, and grasp the essential differences between "swan" and other foul in its genus.

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.

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