What Problem?

[BaalChatzaf]

The "Problem" of Induction? What problem? Any valid inference scheme has the following characteristic: the truth value of the conclusion must be greater than or equal to the truth value of the premises. Assumption: true greater than false.

Induction is clearly not valid. Why? Because it is possible to start with true premises and end up with a false conclusion. The classical example as that of the white swans. A gazillion white swans seen and at some point non non-white swans seen. Inductive conclusion: all swans are white. But one fine day a dark swan is observed showing that the conclusion is false. Induction does not always produce true conclusion from true premises or more precisely, induction does not always produce true general statements from a true conjunction of particular statements.

As I asked: What problem?

Ba'al Chatzaf

[Brant Gaede]

The problem of induction is "the problem of induction." Or: break it and fix it. But nothing gets broken and nothing gets fixed. Just DIM blather.

--Brant

Edited November 16, 2010 by Brant Gaede

[anthony]

Don't knock it 'til you've tried it, oh ye empiricists of little faith.

Just consider induction as short-hand concept building, and don't forget to triple-check those premises. No problemo.

Tony

[kiaer.ts]

The "Problem" of Induction? What problem? Any valid inference scheme has the following characteristic: the truth value of the conclusion must be greater than or equal to the truth value of the premises. Assumption: true greater than false.

Induction is clearly not valid. Why? Because it is possible to start with true premises and end up with a false conclusion. The classical example as that of the white swans. A gazillion white swans seen and at some point non non-white swans seen. Inductive conclusion: all swans are white. But one fine day a dark swan is observed showing that the conclusion is false. Induction does not always produce true conclusion from true premises or more precisely, induction does not always produce true general statements from a true conjunction of particular statements.

As I asked: What problem?

Ba'al Chatzaf

Given that you induced this argument, it defeats itself. Duh.

[BaalChatzaf]

X

Given that you induced this argument, it defeats itself. Duh.

No. I produced a counter example.

Induction looks like this. Conjunction of particulars -> universal proposition.

What I did was universal proposition & counter example -> universal proposition false.

The way to refute any universally quantified proposition is to produce a counter example

(x)P(x) [for all x Px ] is falsified by -Pa for some particular individual Pa.

Ba'al Chatzafr

[sjw]

Induction looks like this.

No, induction looks more like this:

Conjunction of particulars -> universal proposition.

universal proposition & counter example -> universal proposition false.

Though that is not exactly it, it is at least a tiny step closer than your original presumption about what induction is.

Shayne

[kiaer.ts]

X

Given that you induced this argument, it defeats itself. Duh.

No. I produced a counter example.

Induction looks like this. Conjunction of particulars -> universal proposition.

What I did was universal proposition & counter example -> universal proposition false.

The way to refute any universally quantified proposition is to produce a counter example

(x)P(x) [for all x Px ] is falsified by -Pa for some particular individual Pa.

Ba'al Chatzafr

You have claimed that induction is invalid, not to have disproved the claim that no one has made, that all supposed instances of induction are valid.

What premises do you have that weren't first at some point induced, Bob?

God, Bob, do you profit nothing from Rand? The stolen concept is 101 level.

Edited November 17, 2010 by Ted Keer

[Jonathan David Leavitt]

X

Given that you induced this argument, it defeats itself. Duh.

No. I produced a counter example.

Induction looks like this. Conjunction of particulars -> universal proposition.

What I did was universal proposition & counter example -> universal proposition false.

The way to refute any universally quantified proposition is to produce a counter example

(x)P(x) [for all x Px ] is falsified by -Pa for some particular individual Pa.

Ba'al Chatzafr

You have claimed that induction is invalid, not to have disproved the claim that no one has made, that all supposed instances of induction are valid.

What premises do you have that weren't first at some point induced, Bob?

God, Bob, do you profit nothing from Rand? The stolen concept is 101 level.

Does that mean, then, that induction is a solution (occasionally) in search of a problem?

[Jonathan David Leavitt]

X

Given that you induced this argument, it defeats itself. Duh.

No. I produced a counter example.

Induction looks like this. Conjunction of particulars -> universal proposition.

What I did was universal proposition & counter example -> universal proposition false.

The way to refute any universally quantified proposition is to produce a counter example

(x)P(x) [for all x Px ] is falsified by -Pa for some particular individual Pa.

Ba'al Chatzafr

You have claimed that induction is invalid, not to have disproved the claim that no one has made, that all supposed instances of induction are valid.

What premises do you have that weren't first at some point induced, Bob?

God, Bob, do you profit nothing from Rand? The stolen concept is 101 level.

Does that mean, then, that induction is a solution (occasionally) in search of a problem?

Karl Popper (1963). Conjectures and Refutations. p. 53. ISBN 0061313769. "Induction, i.e. inference based on many observations, is a myth. It is neither a psychological fact, nor a fact of ordinary life, nor one of scientific procedure." [Wikipedia]

Or does it mean that Peikoff is a Popper in search of a Soros?

[Jonathan David Leavitt]

X

Given that you induced this argument, it defeats itself. Duh.

No. I produced a counter example.

Induction looks like this. Conjunction of particulars -> universal proposition.

What I did was universal proposition & counter example -> universal proposition false.

The way to refute any universally quantified proposition is to produce a counter example

(x)P(x) [for all x Px ] is falsified by -Pa for some particular individual Pa.

Ba'al Chatzafr

You have claimed that induction is invalid, not to have disproved the claim that no one has made, that all supposed instances of induction are valid.

What premises do you have that weren't first at some point induced, Bob?

God, Bob, do you profit nothing from Rand? The stolen concept is 101 level.

Thus spake Rand:

Induction and Deduction

The process of forming and applying concepts contains the essential pattern of two fundamental methods of cognition: induction and deduction.

The process of observing the facts of reality and of integrating them into concepts is, in essence, a process of induction. The process of subsuming new instances under a known concept is, in essence, a process of deduction.

Introduction to Objectivist Epistemology, 28.

Source: http://aynrandlexicon.com/lexicon/induction_and_deduction.html

Anyone got a problem with that?

[Kimmler]

X

Given that you induced this argument, it defeats itself. Duh.

No. I produced a counter example.

Induction looks like this. Conjunction of particulars -> universal proposition.

What I did was universal proposition & counter example -> universal proposition false.

The way to refute any universally quantified proposition is to produce a counter example

(x)P(x) [for all x Px ] is falsified by -Pa for some particular individual Pa.

Ba'al Chatzafr

You have claimed that induction is invalid, not to have disproved the claim that no one has made, that all supposed instances of induction are valid.

What premises do you have that weren't first at some point induced, Bob?

God, Bob, do you profit nothing from Rand? The stolen concept is 101 level.

Thus spake Rand:

Induction and Deduction

The process of forming and applying concepts contains the essential pattern of two fundamental methods of cognition: induction and deduction.

The process of observing the facts of reality and of integrating them into concepts is, in essence, a process of induction. The process of subsuming new instances under a known concept is, in essence, a process of deduction.

Introduction to Objectivist Epistemology, 28.

Source: http://aynrandlexicon.com/lexicon/induction_and_deduction.html

Anyone got a problem with that?

LOL

From Ayn Rand Contra Human Nature : -

The problem in question is the well-known problem of induction. Perhaps the most important problem in epistemology, it is also one that, in her own words, Rand never even began to think about. Thus for once Rand's legion of Little Sir Echoes have little or nothing to dutifully recite; for once, they have to formulate an original response to an important problem working by implication from Rand's work, rather than resorting to the usual pull quotes from Galt's speech. Even worse, the problem of induction is a clearcut logical one, and is thus subject to a set of objective rules, rather like mathematics. This makes it more difficult for Objectivism's usual verbalist legerdemain to function, though of course true believers would - and do - happily accept 1+1=5 if Rand says so in a suitably inspirational way. Further, it is problem that goes to the heart of epistemological certainty, a much touted brand differentiator for Rand's philosophy. It is after all the problem made famous by Objectivist hate-figure David Hume, and which inspired Rand's arch-enemy, Immanuel Kant. Surely Rand's philosophy must contain some kind of riposte. Finally, it has been a massively debated problem for the last 100 years, with almost every conceivable angle covered ad nauseum. If Objectivism is such a strikingly original philosophy in every respect, as its followers insist, then we could reasonably expect a strikingly original answer here.

Sadly, original thinking is basically antithetical to Objectivist culture. This, along with the poverty of Rand's own style of argument meant that Objectivism's long promised answer to this famous philosophical problem would inevitably be an intellectual embarrassment. The signs were obvious for years, as Objectivists talked up Leonard Peikoff's supposedly revolutionary solution whilst Peikoff himself refused to actually publish it, opting instead to bury it somewhere in vast, outrageously expensive audio tape lectures only available from the Ayn Rand Institute. After a while, there was the threatened book; but that too never emerged. Finally Peikoff's solution - and it almost certainly will be Peikoff's handiwork at root - has timidly appeared under the auspices of Peikoff's colleague, David Harriman, in the new The Logical Leap: Induction in Physics.

Yet clearly even after all this time, and his convoluted path to publishing, the only thing that's clear is that Peikoff has almost no confidence in his own solution; The McCaskey Objectischism is all about his hysterical overreaction to a mild-mannered, basically favourable critique on Amazon by long time ARI board member and fundraiser John McCaskey, with Peikoff simply pulling rank to shut down any and all such criticism. Since then it has spiralled out of control, resulting in defections from previously ARI-loyal publications such as the Objective Standard as well as numerous rank and file supporters. Neil Parille will detail when we post his latest update here at the ARCHNblog in a day or two. We here at the ARCHNblog will also review the book at some point, although at first glance it does look really, really terrible - a compendium of the most tired, old hat, long-debunked pro-inductive fallacies with a central argument that appears to be nothing more than "assume induction!", all varnished in leaden Objectivese just to add to its delights. If there's any idea that can't be found in say, Anthony O'Hear from 30 years ago I will be very surprised. In fact if there's anything even as modern as that I will be even more surprised. But that will have to wait for now.

While there are no doubt underlying personality clashes and long standing enmities behind the scenes which will play out over time, for once the primary driver of the schism is a genuine philosophical problem - one that Objectivism has long been on a collision course with. And far from triumphantly flattening the dreaded Hume, this culmination of decades-long endeavour from Rand's vaunted New Intellectuals has crumpled like a wet paper bag on first contact. To make matters worse, Peikoff's telling sense of intellectual insecurity has driven to him to a desperate authoritarianism, which in turn has only maximised the debacle and created deep rifts within the movement. In short, Objectivism seems to have confronted its first real intellectual challenge, only to be immediately holed below the waterline.

[BaalChatzaf]

What is induction good for? We have show it is not a valid mode of inference. What induction does: it enables one to generate universally quantified assertions from a conjunction of particular assertion. The universally quantified assertion might be true or it might be false. The truth of the particular conjunctions does not guaranteed the truth of the resulting universally quantified assertion. This is how induction differs from deduction. With a valid deductive inference the truth of the premises guarantees the truth of the conclusion. Induction is handy dandy for generating hypotheses. It is what is needed in the discovery phase of a science. It is not effective as a justification. When dealing with a universally quantified assertion or judgement which ranges over an indefinite or infinite domain there is no way of empirically proving it. Why? Because no matter how many instances of the universal are shown to be true, one might eventually run into an instance which is false. The only thing one can do for sure empirically with a universal is disprove it with a counter example.

In the world of deductive logic on can make valid inferences from a universal by universal instantiation.

See Natural Deduction or any text book on first order deductive logic.

http://en.wikipedia.org/wiki/Natural_deduction

Ba'al Chatzaf

[Jonathan David Leavitt]

for once the primary driver of the schism is a genuine philosophical problem

Hume, as others before and after him, including LP, induced that induction is a philosophical problem.

Popper and Rand seem to disagree, though Rand is not explicit (am I missing something she wrote or said?) Popper asserts that induction doesn't exist, only falsifiability.

Rand asserts that induction exists as a tool of cognition. Does she mean that induction is a corollary to the axiom "existence exists," since one might induce that cognition exists? If that is what she meant, the "problem" goes away. Also, if that is what she meant LP might have to "solve" the "problem" by restating her assertion, annihilating all intellectual enemies in the process.

Meanwhile, we have other problems: Soros, Pelosi, Reid, RINOs, mystics, altruism, and collectivism, just to name a random few.

[Jonathan David Leavitt]

Induction is handy dandy for generating hypotheses. It is what is needed in the discovery phase of a science. It is not effective as a justification. When dealing with a universally quantified assertion or judgement which ranges over an indefinite or infinite domain there is no way of empirically proving it. Why? Because no matter how many instances of the universal are shown to be true, one might eventually run into an instance which is false. The only thing one can do for sure empirically with a universal is disprove it with a counter example.

Ba'al Chatzaf

At this time I agree with Ba'al Chatzaf, inducing my conclusions from all the white swans of what I know about science. If George Soros' favorite philosopher formulated the idea, it's not my problem.

Interestingly, the Global Warming scientists also seem to agree, since they suppress evidence which might falsify their altruistic, collectivist hypothesis.

Question: if falsifiability is removed from science, what do we have left?

[Michael Stuart Kelly]

The main issue is trying to correspond observation to an abstract mental system.

Induction is the only way to do that.

In the things I have read so far, the people who claim induction does not exist take this correspondence for granted.

In other words, for them it's OK to use induction so long as you don't call it that and do not acknowledge that you are using it.

And all the hooting and hollering and semantics game-playing over whether or not Rand solved "the problem of induction" is inflated camouflage to hide the real issue--that being the nature of cognition. Instead there are reams of writing on how to make Popper win in some kind of imaginary competition with Rand and/or vice-versa.

Michael

[Jonathan David Leavitt]

The main issue is trying to correspond observation to an abstract mental system.

Induction is the only way to do that.

In the things I have read so far, the people who claim induction does not exist take this correspondence for granted.

In other words, for them it's OK to use induction so long as you don't call it that and do not acknowledge that you are using it.

And all the hooting and hollering and semantics game-playing over whether or not Rand solved "the problem of induction" is inflated camouflage to hide the real issue--that being the nature of cognition. Instead there are reams of writing on how to make Popper win in some kind of imaginary competition with Rand and/or vice-versa.

Michael

Bingo!

Karl Popper (1963). Conjectures and Refutations. p. 53. ISBN 0061313769. "Induction, i.e. inference based on many observations, is a myth. It is neither a psychological fact, nor a fact of ordinary life, nor one of scientific procedure." [Wikipedia]

The process of forming and applying concepts contains the essential pattern of two fundamental methods of cognition: induction and deduction.

The process of observing the facts of reality and of integrating them into concepts is, in essence, a process of induction. The process of subsuming new instances under a known concept is, in essence, a process of deduction.

Introduction to Objectivist Epistemology, 28.

[Selene]

Precisely Michael.

"Induction," whether Ayn addressed it sufficiently, or, at all, exists, whether we call it that, or, not. It is axiomatic.

Anyone who has had to solve a problem "in the field," without the availability of books or sources and must discover how to solve a problem knows that "X," or inductive reasoning exists.

The fact that Ayn's nimrod intellectual heir cannot induce or deduce a solution to a non-existent problem speaks volumes about why the closed system Objectivist "movement" has suffered from intellectual constipation for decades.

Time for a high colonic.

Let us begin.

Adam

[Jonathan David Leavitt]

Precisely Michael.

"Induction," whether Ayn addressed it sufficiently, or, at all, exists, whether we call it that, or, not. It is axiomatic.

Anyone who has had to solve a problem "in the field," without the availability of books or sources and must discover how to solve a problem knows that "X," or inductive reasoning exists.

The fact that Ayn's nimrod intellectual heir cannot induce or deduce a solution to a non-existent problem speaks volumes about why the closed system Objectivist "movement" has suffered from intellectual constipation for decades.

Time for a high colonic.

Let us begin.

Adam

Adam, at this point I cannot resist asserting that LP's prospects for eternal glory from having solved the Problem of Induction are growing DIMmer and DIMmer.

[sjw]

The main issue is trying to correspond observation to an abstract mental system.

Induction is the only way to do that.

In the things I have read so far, the people who claim induction does not exist take this correspondence for granted.

In other words, for them it's OK to use induction so long as you don't call it that and do not acknowledge that you are using it.

And all the hooting and hollering and semantics game-playing over whether or not Rand solved "the problem of induction" is inflated camouflage to hide the real issue--that being the nature of cognition. Instead there are reams of writing on how to make Popper win in some kind of imaginary competition with Rand and/or vice-versa.

Michael

Yes. I think it misses the point to talk about the "problem of induction". Induction isn't merely "generalizing from instances", it is learning from reality as such. One cannot properly "generalize from instances" without employing one's whole repertoire of reasoning to do it. In other words, to validate induction is to validate reason and vice versa; if induction is valid then reason must be, and if reason is valid then induction must be. Deduction is not in the same category, as it truly does isolate one particular aspect of thinking, but it's impossible to do that isolation concerning induction.

Induction isolates the product of thought -- a generalization; it does not isolate any distinct process of thought or even a distinct aspect of that process. So I would say that technically speaking, the problem of induction does not exist. All that exists is the "problem" of reasoning.

Shayne

[BaalChatzaf]

Yes. I think it misses the point to talk about the "problem of induction". Induction isn't merely "generalizing from instances", it is learning from reality as such.

Learning is a special case of learning from instances. The instances are our attempts to accomplish some end. From the attempts we learn ways of accomplishing the end. We learn from our failures. The fact that there can be failures in the learning processes is further proof the induction is not a sure fire way of getting to true generalities from specific true instances.

Induction from instances is our primary way of learning things in an unco-operative and uncertain environment. No guarantees, but stay with the program long enough and success comes often.

Ba'al Chatzaf

[Ellen Stuttle]

Quick omnibus post.

The "problem of induction" is that there's no way to construct an argument form such that the truth of a universal claim of fact is entailed by specific claims of fact. And, no, that isn't itself an inductive argument. It follows directly from the meaning of "some" and "all" and "entails." For the premises of an argument to "entail" the conclusion, the conclusion has to be contained as a subset of the premises, but an "all" statement is not contained as a subset of "some," "all" being bigger than "some."

Furthermore, re the "stolen concept" fallacy, contra Ted, I think the stolen concept is any claim to knowledge of the truth of a universal claim of fact. The knowledge claim steals the meaning of "knowlege," since it requires knowing without any way of knowing. By what means exactly could you know the truth of a universal claim of supposed fact?

Thus spake Rand:

Induction and Deduction

The process of forming and applying concepts contains the essential pattern of two fundamental methods of cognition: induction and deduction.

The process of observing the facts of reality and of integrating them into concepts is, in essence, a process of induction. The process of subsuming new instances under a known concept is, in essence, a process of deduction.

Introduction to Objectivist Epistemology, 28.

Source: http://aynrandlexicon.com/lexicon/induction_and_deduction.html

Anyone got a problem with that?

I do, a big problem. I don't know what she means there by "induction" and "deduction." She doesn't explain anywhere in the text -- that quote is the only place "induction" and "deduction" are mentioned in the monograph. In the extended edition which includes the workshops, she says that she "couldn't begin to discuss the problem of induction, [never having] worked on that subject enough to even begin to formulate it [...]." There she seems to mean the standard meaning of "induction." If she meant the standard meaning in the passage you quoted, then I think her statement is just false. If all she meant was learning from and applying experience, then her using "induction" and "deduction" confuses. Plus it gave license to Peikoff's project (in combination with her statement on pp 303-04 of the expanded edition, which I'll reprovide):

ITOE (2nd), Appendix, p. 303-04:

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?

AR: Yes. That's the big question of induction. Which I couldn't begin to discuss--because (a) I haven't worked on that subject enough to even begin to formulate it, and (b ) it would take an accomplished scientist in a given field to illustrate the whole process in that field.

[Prof M was Larry, and the exchange is quoted accurately according to his notes from the live workshop. (JDL, FYI since you're new to the list: "Larry" is Larry Gould, my significant other then, my husband of many years.)]

Yes. I think it misses the point to talk about the "problem of induction". Induction isn't merely "generalizing from instances", it is learning from reality as such. One cannot properly "generalize from instances" without employing one's whole repertoire of reasoning to do it. In other words, to validate induction is to validate reason and vice versa; if induction is valid then reason must be, and if reason is valid then induction must be. Deduction is not in the same category, as it truly does isolate one particular aspect of thinking, but it's impossible to do that isolation concerning induction.

Induction isolates the product of thought -- a generalization; it does not isolate any distinct process of thought or even a distinct aspect of that process. So I would say that technically speaking, the problem of induction does not exist. All that exists is the "problem" of reasoning.

Shayne, are you meaning "learning from reality as such" as your definition of "induction"? If so, you're using the term "induction" differently than is meant by the historic "problem of induction." Possibly "learning from reality as such" is what Rand meant by those two paragraphs in the monograph. But it isn't what Peikoff means in the course used "nearly verbatim" in The Logical Leap.

The Logical Leap

pg. 6

[underscore added]

[...] the failure of philosophers to offer a solution to what has been called 'the problem of induction.' Induction is the process of inferring generalizations from particular instances. [....] The primary process of gaining knowledge that goes beyond perceptual data is induction. Generalization -- the inference from some members of a class to all -- is the essence of human cognition.

Ellen

[Ellen Stuttle]

Kimmler,

Could you please provide a link for the ARCHN post you quoted in your post #11?

Ellen

[kiaer.ts]

Why? Because no matter how many instances of the universal are shown to be true, one might eventually run into an instance which is false.

How do you know this, if not by induction, Bob?

Truly sad.

[BaalChatzaf]

Why? Because no matter how many instances of the universal are shown to be true, one might eventually run into an instance which is false.

How do you know this, if not by induction, Bob?

Truly sad.

Stop the nonsense. I have already provided an example of induction leading to a false generalization. This a a logical falsification of the general proposition that induction always leads to true generalizations. To falsify a universal proposition (x)P(x) one needs only a single instance f, such that -P(f). This is logic 101. A single false induction is sufficient to show induction starting with true premises does not necessarily lead to true conclusions. As a mode of inference, induction is not valid. As a mode of generating general (i.e. universally quantified statements) is a powerful heuristic. Learning by trial and error is a form of induction. But sometimes trials lead to errors so trial and error is not guaranteed to work in every instance.

Pointing to a singular true statement is not induction. Induction is going from the conjunction of singular propositions to a universally quantified proposition.

Ba'al Chatzaf

[Jonathan David Leavitt]

Post removed: redundant.

Edited November 19, 2010 by Jonathan David Leavitt