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BaalChatzaf

Blame David Hume

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Ah, Michael, you had me fooled. I thought you were interested in trying to understand what I was saying. And you yourself provided some statements, in your post#196, quoted in my post #197, which I thought indicated that you were recognizing the difference between the process of concept formation Rand describes and "induction."

Of course a person can define a term however a person wants to define it (albeit at risk of not being understood by others who define the term differently), but Rand doesn't indicate in that passage -- which, I repeat, is the only place in the text of ITOE where either the term "induction" or "deduction" is used (and which is the only entry listed in the Lexicon for either term) -- that she means a stipulated definition.

Also, I'll remind you, in the Workshop she certainly appears to be using "induction" with a standard meaning when she replies to "Prof. M" (a/k/a Larry) that she:

"couldn't begin to discuss [the big question of induction]" because she "[hadn't] worked on that subject enough to even begin to formulate it."

(Appendix, p. 303-04; see my post #168 for the full quote and further comment.)

I think it might at least have behooved her to be informative enough to tell her audience if she meant "induction" and "deduction" on pg. 28, ITOE, in an AR-special-definition way.

In sum, I guess this is the same situation as with the famous "is/ought" passage: What she wrote, as she wrote it, has to be right, never mind how muddled and muddling what she wrote is.

Ellen

___

Edited by Ellen Stuttle

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Ah, Michael, you had me fooled. I thought you were interested in trying to understand what I was saying.

Ellen,

Actually I am interested.

What she wrote, as she wrote it, has to be right, never mind how muddled and muddling what she wrote is.

It might surprise you, but I actually understood your meaning here. This is one instance where I not only disagree with you (for the reasons I have given multiple times), but I think you are mistaken in your approach and especially your evaluation of clarity. Not only that, your presumption about what I (and others) think about Rand being right is about as wrong as wrong can be.

Maybe you consider "understand what you were saying" with "agree with what you were saying"?

On this point it ain't gonna happen. The problem is I understood what you were saying.

:)

Michael

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I've read and re-read this thread three times, in an effort to salve my ignorance and understand the positions at issue.

I must commend Ba'al for several statements that I both understand and accept as reasonable:

Induction is a practical way of producing general statements from a finite set of instances. The generalization might be true or it might be false.

We learn through induction. We formulate rules that guide our future behavior. When the rule does not always work we modify. So induction plus learning through failure is how we progress.

Induction is a heuristic for making generalizations from specific instances. It is NOT a generally valid mode of inference. There is no guarantee that generalizations that flow from instances by induction will be true for all times, places and conditions.

What I see as the lesson of the so-called problem of induction is beware! Beware fallacies of faulty and sloppy inductive reasoning. Beware arguments that seem to use logical induction to reach reasonable conclusions, but are actually hasty generalizations, arguments by analogy, or other deformities of reason. Beware accepting a conclusion about an entire class or type of thing/events -- when the basis for the conclusion is small or unrepresentative in relation to the entire class.

In any case, what the hell do I know?

Here's a funny thing -- David Harriman, accepted as genius by Leonard Peikoff, has an article at the Objective Standard (subscribers only for full text). It's called Induction and Experimental Method. On the OS page he writes that it is "adapted from a chapter of my book in progress, 'Induction in Physics and Philosophy.'" He also notes that the book in progress is "based on Leonard Peikoff’s lecture course of the same title."

Now, what I want to know is if this book will ever make it to print.

A corollary question: if Peikoff 'solved' the so-called problem of induction, what the hell is the issue with putting his solution in print? At least a thread like this one (and the earlier OL threads touching on induction) could reference some text-based information. Otherwise the whole Objectivist solution seems to be something reserved only for acolytes and true believers in the oral tradition. How can the rest of the world seriously engage an argument that is available only on CD-ROM or cassette tapes?

I just cannot get my head around the persistence of the oral/aural tradition. It hobbles Objectivism and leaves the Objectivist rack in the library a fairly scanty stretch of material.

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I've read and re-read this thread three times, in an effort to salve my ignorance and understand the positions at issue.

I must commend Ba'al for several statements that I both understand and accept as reasonable:

Induction is a practical way of producing general statements from a finite set of instances. The generalization might be true or it might be false.

We learn through induction. We formulate rules that guide our future behavior. When the rule does not always work we modify. So induction plus learning through failure is how we progress.

Induction is a heuristic for making generalizations from specific instances. It is NOT a generally valid mode of inference. There is no guarantee that generalizations that flow from instances by induction will be true for all times, places and conditions.

What I see as the lesson of the so-called problem of induction is beware! Beware fallacies of faulty and sloppy inductive reasoning. Beware arguments that seem to use logical induction to reach reasonable conclusions, but are actually hasty generalizations, arguments by analogy, or other deformities of reason. Beware accepting a conclusion about an entire class or type of thing/events -- when the basis for the conclusion is small or unrepresentative in relation to the entire class.

In any case, what the hell do I know?

Here's a funny thing -- David Harriman, accepted as genius by Leonard Peikoff, has an article at the Objective Standard (subscribers only for full text). It's called Induction and Experimental Method. On the OS page he writes that it is "adapted from a chapter of my book in progress, 'Induction in Physics and Philosophy.'" He also notes that the book in progress is "based on Leonard Peikoff's lecture course of the same title."

Now, what I want to know is if this book will ever make it to print.

A corollary question: if Peikoff 'solved' the so-called problem of induction, what the hell is the issue with putting his solution in print? At least a thread like this one (and the earlier OL threads touching on induction) could reference some text-based information. Otherwise the whole Objectivist solution seems to be something reserved only for acolytes and true believers in the oral tradition. How can the rest of the world seriously engage an argument that is available only on CD-ROM or cassette tapes?

I just cannot get my head around the persistence of the oral/aural tradition. It hobbles Objectivism and leaves the Objectivist rack in the library a fairly scanty stretch of material.

Induction or deduction. WTF!? If you can't relate this palaver to scientific methodology you're just spinning your philosophical wheels. Please understand the essential irrelevance of Leonard Peikoff. As an OBJECTIVIST philosopher he therefore isn't A philosopher much less have anything to do with science. He is absolutely stuck in the Ayn Rand matrix as imagined by him. Ironically, that would be assuredly rejected by Rand for she had her own imagining albeit also stuck in her matrix.

--Brant

Edited by Brant Gaede

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The problem is I understood what you were saying.

:)

Michael

I'm not seeing evidence supporting the statement.

Meanwhile, you've succeeded at arousing my curiosity as to just what you think Rand DID mean by "induction" in the short passage from pg. 28 of ITOE which is the only passage of hers in print on the subject included in the Lexicon.

Can you give a proper O'ist-style genus-differentia (one sentence should suffice) definition of your understanding of her meaning? If so, this might help with mutual comprehension.

Ellen

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Can you give a proper O'ist-style genus-differentia (one sentence should suffice) definition of your understanding of her meaning? If so, this might help with mutual comprehension.

Ellen,

Sure. That's easy.

There are different words that can be used and I am not comfortable with some Objectivist jargon, so I will use several options, but they all mean the same thing.

Induction is a mental process [genus] of integrating and differentiating observations into a single mental unit [differentia].

Here is the same idea in different words.

Induction is a mental process [genus] of recognizing a pattern and creating a single idea for it [differentia].

Here is even another way to say it in different words.

Induction is a mental process [genus] establishing a category based on observation [differentia].

We can call that single mental unit a concept, a principle, a conclusion, an idea or any name we can think of just so long as it is a single name or description.

This definition is not at odds with popular definitions either. You don't have to go far. Look at the The Free Dictionary's definition of induction ("logic" meaning):

a. The process of deriving general principles from particular facts or instances.

b. A conclusion reached by this process.

Notice that my definition above is covered in definition "a." In establishing a category, you automatically create some kind of general principle, such as "XXXX exists as a group" or "XXXXX has members because of some observable similarities between them." One shouldn't be confused by the plural given in the definition. If it had said, "the process of deriving a general principle from particular facts or instances," it would have been just as valid as "deriving general principles."

And your meaning is covered in definition "b." To use "this process" (induction as given in definition "a") to arrive at a conclusion, you need a proposition.

There you have it.

Two definitions for the same word in a mainstream source. And lo and behold, neither proves that Rand was muddled in her thinking about induction or that Objectivists constantly make errors in judging historical figures because they don't understand the words they use. On the contrary, the Objectivist understanding of induction fits into the first definition, not even the second.

(Many Objectivists do make errors in judging historical figures, but as I said earlier, not because of not understanding induction.)

Michael

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Induction is a mental process [genus] of recognizing a pattern and creating a single idea for it [differentia].

Here is even another way to say it in different words.

Induction is a mental process [genus] establishing a category based on observation [differentia].

Not so. Induction is a (mental) process [genus] by which a universally quantified proposition is derived from a finite set of instances [species].

Your definition overlooks that fact that induction derives a proposition from several propositions. Induction is all about propositions and is not a mode of concept formation. To use induction one must already have the concepts in hand. In the well known "all swans are white" example one -already- has the concept of swan and white prior to the induction.

Schematically induction can be stated thus.

{set of particular propositions} -> general (universally quantified) proposition.

Concept formation has to do with extracting common features or properties from several particular things.

In Objectivist Land a concept is open ended so it isn't a proposition at all. One needs concepts to express propositions, but propositions are not concepts, as such.

Ba'al Chatzaf

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Bob,

I get the idea that you did not even read my post.

What's hard to understand about "two definitions"?

Michael

I quoted what you wrote. What you wrote is incorrect.

If one does not grasp that induction is about -propositions- then one has not grasped induction at all.

Ba'al Chatzaf

Edited by BaalChatzaf
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Here is the Subject Index entry for induction in Objectivity.

Induction V1N2 33–44, V1N3 1–51

Abstractive V1N2 36–37, 44, V2N4 14, 31, 106–7

Ampliative V1N2 36–37, 41, 44, V1N3 15, 17, 21–32, 35–43, V1N4 15, V1N5 138–39, 143, V1N6 63, V2N4 14, 26–27, 48, V2N6 116–17, 124

and Composition Fallacy V1N5 72–73

and Concepts V1N1 29, 35–38, V1N2 36, 42–44, V2N6 81, 115, 117–18, 124

Consilience of V1N3 14, 38, 49

and Deduction V1N2 14, 29, 33–36, 40, V1N3 15, 31–32, 36–37, 40–41, 47–48, V1N4 33–34, 50, V1N5 143, V2N2 13, V2N4 14, 31, 42, 52, 107

and Identity V1N2 33–35, 36–44, V1N3 5–16, 21–32, 35–43, 46–49, V1N4 27–28, V1N5 143, V2N4 31, V2N6 45

Mathematical V1N2 41–42, V1N3 46–48, V1N5 72–73

and Object Perception V1N3 7–8, 61, V2N6 26

Reflective V1N4 50–52

The kind of induction known as abstractive is also known as intuitive. This is the type of induction on stage in Leonard Peikoff’s 1982 paper “Aristotle’s Intuitive Induction” in The New Scholasticism 59(2):185–99.

Here is the Abstract for my Objectivity essay on induction (1991).

“Induction on Identity” by Stephen Boydstun

Part 1 Volume 1, Number 2, Pages 33–46

http://objectivity-archive.com/volume1_number2.html#33

The Aristotelian and Leibnizian roles of non-contradiction and identity in metaphysics and in deductive logic are reviewed. Beyond those roles, Boydstun proposes that Rand’s existential law of identity can fully justify inductive inference.

The two types of induction articulated by Aristotle are rehearsed. These are the abstractive induction and the ampliative induction. Rand had noted that the integration of facts into concepts is a type of induction. This is abstractive induction à la Rand, and Boydstun resolves this type into two components: the bare recursive induction we use in mathematical induction and the ampliative induction needed for the construction of concepts adequate to the concrete existents in the world.

Part 2 Volume 1, Number 3, Pages 1–56

http://objectivity-archive.com/volume1_number3.html#1

Boydstun examines the critiques of the rationality of induction put forth in the fourteenth century by Nicolaus of Autrecourt and in the eighteenth century by David Hume. The stage for Nicolaus was set by Ockham. On this stage were the metaphysical and logical platforms for arguing that there can be no logically necessary connection between distinct existents. Nicolaus’ hour on the stage articulates how to hold fast to identity, non-contradiction, and the existential presentations of immediate perception, while barring any logically justifiable inference to the existence of material substance. Boydstun disputes Nicolaus’ account of our experience of substance and of our rational inferences to the existence and character of substance not directly experienced. The defense of our knowledge of substance here marshals logical considerations, findings of modern developmental psychology, and the history of modern science.

Hume’s accounts of our experience of cause and effect and of our reasonings to cause or to effect are closely examined and roundly criticized. Various statements of the law of causality in the history of philosophy are recounted and assessed, with due consideration of modern physics. A version of the law of causality logically supportable by Rand’s rich principle of identity is formulated. It does not require that in a given circumstance a given kind of thing could do only the same single thing on repeated trials. It is argued also that Rand’s principle of identity is the broad base of Mill’s methods of induction and of the hypothetico-deductive method of science.

Beyond the corrected law of causality, Boydstun formulates a “principle of substantive propagation.” This is an application of Rand’s principle of identity to all alteration and constancy in time. He argues that the principle of substantive propagation is a fundamental justified justification for our inductive causal inferences and indeed all of our modes of scientific explanation. He concludes with a proposal of how predication can be cast as a triple-identity abstract form, a derivative of Rand’s fundamental thesis that existence is identity.

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I quoted what you wrote. What you wrote is incorrect.

If one does not grasp that induction is about -propositions- then one has not grasped induction at all.

Bob,

The premise of this proposition is incorrect. The premise is that there is only one definition for induction and that definition restricts it to propositions.

The dictionary contradicts this premise. I wrote about this, too. You chose to ignore it.

Ignoring is not a premise.

See Sterphen's post above this one for a bit more on types of induction. (Dayaamm! I wish Stephen wasn't so smart. I have things to do and he gets me juiced on a detour...)

Michael

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I quoted what you wrote. What you wrote is incorrect.

If one does not grasp that induction is about -propositions- then one has not grasped induction at all.

Bob,

The premise of this proposition is incorrect. The premise is that there is only one definition for induction and that definition restricts it to propositions.

The dictionary contradicts this premise. I wrote about this, too. You chose to ignore it.

Ignoring is not a premise.

See Sterphen's post above this one for a bit more on types of induction. (Dayaamm! I wish Stephen wasn't so smart. I have things to do and he gets me juiced on a detour...)

Michael

I read Stephen's piece.

I have a question: If Induction is valid why do so many inductive "inferences" lead to incorrect general conclusions?

The existence of incorrect inductions -proves- that induction is not a valid mode of inference. The leap from a finite set of true particular propositions to a general proposition is not guaranteed to be successful, i.e. the generality might be false. All it takes is one false induction to invalidate induction as a generally valid mode of inference.

Whereas when one -deduces- a conclusion from a set of true premises one is guaranteed a true conclusion, assuming that the law of non-contradiction holds.

Ba'al Chatzaf

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Bob,

You are thinking from the bottom up only.

There are some serious presumptions you are making that just are not present in what you are reading and you are blaming what you are reading for not taking into your presumptions account. Then you make an incorrect... er... generalization.

:)

Michael

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Bob,

You are thinking from the bottom up only.

There are some serious presumptions you are making that just are not present in what you are reading and you are blaming what you are reading for not taking into your presumptions account. Then you make an incorrect... er... generalization.

:)

Michael

Further proof of the invalidity of induction.

Ba'al Chatzaf

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I have a question: If Induction is valid why do so many inductive "inferences" lead to incorrect general conclusions?

The existence of incorrect inductions -proves- that induction is not a valid mode of inference. The leap from a finite set of true particular propositions to a general proposition is not guaranteed to be successful, i.e. the generality might be false. All it takes is one false induction to invalidate induction as a generally valid mode of inference.

Whereas when one -deduces- a conclusion from a set of true premises one is guaranteed a true conclusion, assuming that the law of non-contradiction holds.

Ba'al Chatzaf

It's your idiosyncratic use of "valid." Why do so many inductive inferences lead to correct conclusions?

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Re: #212

Bob,

Your use of the term valid is in step with the one sense intended in texts for deductive logic: a valid form of argument is one in which the truth of the premises guarantees the truth of the conclusion drawn from them. Other senses of the term valid given in The American Heritage Dictionary are these:

1. Well-grounded; sound; supportable: a valid objection.

2. Producing the desired results; efficacious: valid methods.

3. Legally sound and effective; incontestable; binding: a valid title.

A funny thing happened to me when I was writing “Induction on Identity” back in 1991. Introducing the concept of ampliative induction in Part 1, I had written:

Ampliative inductions are not absolutely conclusive. By this common saying, we mean not that they are always rationally uncertain, but that taking the starting points of these inductions to be true and the inductions false would not itself entangle one in a contradiction. (37)

Writing Part 2, I dug into how (by 1908) the evidence for the existence of atoms had become conclusive (pages 13–15). With this case in the history of science in view, I had to amend what I had said in the quotation just given. From the discussion of this amendment:

We pass too hastily from (1) the thesis that if premises in a valid deduction are true, the conclusion cannot (cannot ever) be false and (2) the thesis that that is not so for inductive inference to (3) the result that inductions cannot be absolutely conclusive, that is, to the result that true premises in an inductive argument can never ensure truth of the conclusion. But as we know, by our knowledge that atoms exist, this last is not strictly true. It is sometimes the case that the truth of the premises in an inductive argument ensure the truth of the conclusion, but unlike any case of valid deduction, we are not informed of this by the principle of noncontradiction. This circumstance is what one might expect if indeed identity is the broader and deeper principle of reality and the mainstay of induction. (15)

This summer an essay on the atomic example appeared in The Objective Standard.

http://www.theobjectivestandard.com/issues...omic-theory.asp

J. S. Mill emphasized that the truth of the premises in a deductive argument ultimately have to be established by induction. Kelley’s book The Art of Reasoning reiterates this point. Peikoff’s essay “Aristotle’s Intuitive Induction” concerns Aristotle’s attempt to establish the correctness of the principle of non-contradiction itself by an abstractive induction.

Concerning validation of philosophic axioms:

http://rebirthofreason.com/Articles/Boydst...-_Paper_1.shtml

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I have a question: If Induction is valid why do so many inductive "inferences" lead to incorrect general conclusions?

The existence of incorrect inductions -proves- that induction is not a valid mode of inference. The leap from a finite set of true particular propositions to a general proposition is not guaranteed to be successful, i.e. the generality might be false. All it takes is one false induction to invalidate induction as a generally valid mode of inference.

Whereas when one -deduces- a conclusion from a set of true premises one is guaranteed a true conclusion, assuming that the law of non-contradiction holds.

Ba'al Chatzaf

It's your idiosyncratic use of "valid." Why do so many inductive inferences lead to correct conclusions?

Two terms are in use in the field of logic.

1. Valid. That means inferences are according to rule

2. Sound, That means the conclusions are validly inferred from true premises.

See

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

Induction is neither valid nor sound.

However, warts and all, the only ways we have of getting a general statement from particulars is induction and abduction. There is no platinum plated guarantee of correctness for either.

Ba'al Chatzaf

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Can you give a proper O'ist-style genus-differentia (one sentence should suffice) definition of your understanding of her meaning? If so, this might help with mutual comprehension.

Ellen,

Sure. That's easy.

There are different words that can be used and I am not comfortable with some Objectivist jargon, so I will use several options, but they all mean the same thing.

Induction is a mental process [genus] of integrating and differentiating observations into a single mental unit [differentia].

Here is the same idea in different words.

Induction is a mental process [genus] of recognizing a pattern and creating a single idea for it [differentia].

Here is even another way to say it in different words.

Induction is a mental process [genus] establishing a category based on observation [differentia].

OK. I figured you'd suggest something along those lines. I see all three of the variants as just alternate ways to define Rand's meaning of "concept-formation." (I like the 3rd best and the 2nd least, as having the most ambiguity.) However, I think that if such a defintion had been all that Rand meant by "induction" in the statement we're talking about (from pg. 28, ITOE), then she'd have been writing a redundancy -- in effect she'd have been saying: "Concept-formation contains the essential pattern of concept-formation." I strongly doubt that she wouldn't have noticed that she was being redundant if all she'd meant by "induction" was along the lines you indicate.

We can call that single mental unit a concept, a principle, a conclusion, an idea or any name we can think of just so long as it is a single name or description.

I don't agree that your proferred definitions would suit for "principle" or "conclusion" or "any name we can think of just so long as it is a single name or description" (or for types of "idea" other than concepts).

Nor do I agree that "[your] definition above is covered in the definition 'a'" you give from Free Dictionary:

QUOTE(Free Dictionary)

a. The process of deriving general principles from particular facts or instances.

b. A conclusion reached by this process.

The difference between "a" and "b" is that "a" is definining the process and "b" the result. "Induction" in the "b" usage would be prefaced by an article: He formed an induction [via the process described in "a"]. The induction "all swans are white" has a famous history in philosophy.

Ellen

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Ellen,

You might be surprised, but I do agree with you that Rand's description of fundamental characteristic was not consistent. I have been mulling over this a bit.

As to the other stuff, we will just have to agree to disagree. I consider (pointing) "that and that and that are similar enough to be grouped" to be close enough to a proposition to apply. It's the implicit proposition in the formation of any concept. You apparently do not agree this is valid for your usage.

I have defined my terms and, although Rand did not define specifically induction, she was clear enough about what she meant. You are free not to accept those meanings.

Michael

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I thought you might object to my probability assignment. However, in some sense, it is unavoidable. A probability assignment may be thought of as representing a person's state of knowledge. If a person doesn't know anything about an experiment, other than that there are two possible outcomes, it is logical to assign a probability of 0.5 to each outcome.

The thing is that this has nothing to do with induction. This is a deductive argument. You've set the terms in advance (two possible outcomes) thus there is a 0.5 probability. This is true no matter how many times you've observed the sun rising. It's true even if you'd never seen the sun rise at all.

That's true. It has nothing to do with induction. Recall that my argument is that induction is not the normal means for humans to acquire knowledge. The normal means is observation and deduction.

However, note that the conclusion above is wrong. The probability of the sun coming up tomorrow is not 0.5. Therefore, if that is the result of deductive reasoning, then there is a problem with deduction.

Of course, the result above is not the proper result deductive reasoning. The result only follows if you assume that you don't know anything other than the fact that there are two possibilities. But, in fact, you do know a lot more. That is why the sun coming up tomorrow is a virtual certainty.

Consider the Monty Hall problem.

There is nothing inductive about the Monty Hall problem either. Once again it is deductive - that is, the probability is not based on X number of past experiences of "Let's Make A Deal"!! In fact it's true even if you've never experienced it.

True enough. But, recall that I am not defending induction. I am saying that induction isn't used, except, perhaps, in a tangential fashion.

Now recall that Popper and Hume state that past experience has, "no bearing," on future outcomes (a clear contradiction of probability theory). That implies a condition of complete ignorance and demands a probability assignment of 0.5 to each possible outcome of a binary experiment.

Yes, Popper and Hume and you and anyone else would all say that the deductive result would be 0.5. It's the inductive result is the unassignable one.

Again, however, the deductive result is wrong, because, in fact, you do know something.

Let's consider another experiment. Assume that you have an empty urn that you have verified to be empty. You place a single, ordinary blue ball in the urn. The urn remains under your control and nothing is added to or removed from the urn until 10 minutes later at which time you reach into the urn and remove a ball. What color will the ball be? How do you know? What is the probability of it being that color?

If it is possible to correctly predict the outcome of the experiment, that clearly violates Hume's assertion that past experience has no bearing on future outcomes. So, Hume and Popper are at least wrong in one instance, proving that their general assertion is false.

The only way to attack the above example is to claim that there may be forces beyond our understanding that could affect the outcome of the experiment in unpredictable ways. But, where is the evidence? There is none. So, the assertion is arbitrary. The assertion that the outcome might not be known amounts to an assertion that the arbitrary is plausible.

In the context of all that is known, of all those things or events for which there is evidence, the result is certain. The same is not true of the examples of white swans or black crows. In those cases, it is known that color is not an essential characteristic and that, therefore, it should not be surprising if an example departing from the examples seen so far is found. In the case of the ball in the urn, it is the essential characteristics of the items that are in question. Although the color of the ball is in question, it is the color of a particular ball, not the color of all balls. The ball can no more change color under the conditions specified than a swan could change color in ten minutes. So, there is no known way for the experimental result to be other than the obvious prediction, that the ball drawn from the urn will be blue.

I think your basic assumption (and Rand's, and many other philosophers) is faulty. Why is "absolutely certain" knowledge necessary to for people to function? Why can't a series of rough, approximate theories, being gradually improved over time work? Who knows, if you are lucky enough you might hit on the truth (even if you could never inductively confirm that it was the truth). So truth is still possible, even if unlikely.

I'm not sure that I'm arguing for "absolutely certain" knowledge. I have used the term "virtually certain" instead. To me, that means something like, "with probability equal to one." There may be exceptions, but they have probability zero. This may not be precisely the right concept either, but it is closer to what I mean.

Virtually certain knowledge is required to understand the world. If a person doesn't know anything with certainty, then he can't know the probability of anything either. Imagine going to buy a new car. You examine a nice, new, shiny car and an old, beat up car. According the theory of Hume/Popper, both have a probability of 0.5 of running. So, your choice is a toss-up. There is no reason to prefer one over the other (ignoring appearance for the time being).

BTW, as stated in earlier posts, I am indeed arguing for a series of "rough, approximate theories, being gradually improved over time." But, to me, approximate is distinct from being tentative. Newtonian Mechanics still works very well within the bounds of low velocities and macroscopic objects. It has never been proven wrong in the sense that it has never been proven not to work under the conditions under which it was derived. Instead, it has been refined to work under a broader range of conditions by relativity theory and quantum theory. Moreover, many of the principles of classical physics have never been questioned, F = dp/dt, energy conservation, conservation of momentum, etc.

A theory that is tentative or hypothetical could turn out to be a lousy approximation. The implication of Hume/Popper is that eggs thrown against concrete floors might never break again -- because past experiences have "no bearing" on future outcomes.

Darrell

P.S. Sorry about the delay in responding, but I have been busy.

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Wow, a lot of interesting info here. Here is a quick summary of the highlights on which I base my conclusion below:

ITOE (2nd), Chapter 3, Abstraction from Abstractions, p. 28:
Thus 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.

Michael

For instance, a baby forms a concept of man after he has encountered a few. The file folder gets opened. He will no longer in his life form a new concept of man. Instead, he will add to the already formed concept. Over time he will form new concepts about different aspects of man and add those to his original concept, but never again will he do the concept of man from scratch. Once done, its done.

That is not the same thing as forming a conclusion, which is more in the universe of propositions, not primary cognitive identification.

This broad meaning of "induction" (and of "inductively") -- I went on to say in the post to which you replied -- is often what Objectivists are talking about when they speak of arriving at conclusions by "induction" (or "inductively").

But they can then be thrown off, with resultant error in interpreting thinkers other than Rand, because they import their usage into what those other thinkers are talking about even when those other thinkers are using the formal meanings. They thus end up believing, for example, that David Hume denied that you can get knowledge from experience ("induction" broadly defined) because he denied the validity of inductive inference as a formal method of reasoning from particulars to certainty about general laws. The error I'm talking about is their not realizing that they aren't meaning the same procedure by the same term.

Ellen

___

Induction -

a. The process of deriving general principles from particular facts or instances.

b. A conclusion reached by this process.

...Induction is a (mental) process [genus] by which a universally quantified proposition is derived from a finite set of instances [species].

... induction derives a proposition from several propositions. Induction is all about propositions and is not a mode of concept formation. To use induction one must already have the concepts in hand. In the well known "all swans are white" example one -already- has the concept of swan and white prior to the induction.

Schematically induction can be stated thus.

{set of particular propositions} -> general (universally quantified) proposition.

Concept formation has to do with extracting common features or properties from several particular things.

In Objectivist Land a concept is open ended so it isn't a proposition at all. One needs concepts to express propositions, but propositions are not concepts, as such.

Ba'al Chatzaf

"A definition is a statement that identifies the nature of a concept's units. A correct definition must specify the distinguishing characteristic(s) of the units (the differentia), and indicate the category of existents from which they were differentiated (the genus). The essential distinguishing characteristic(s) of the units and the proper defining characteristic(s) of the concept must be a fundamental characteristic. ..." (ITOE 84-5).
Ellen,

"Forming conclusions based on experience" would include forming a definition of a group of similar things [i.e, forming concepts].

--Mindy

I think Mindy points the way to reconciling all the above information. Rand says about concept formation: "The process of observing the facts of reality and of integrating them into concepts is, in essence, a process of induction." Why? Because the first stage of induction is one of concept formation. Why? Because induction ultimately involves propositions to fulfil its function, and as said above one needs concepts to express these propositions. So first the concepts must be formed, at some point, and then they are used in propositional instances to make the generalizing proposition. Of course these inductive generalizations are not absolute, undeniable certainties as in deduction (given true premises), but this is a separate issue of stage 2 and does not impact on the correctness of the concepts formed and being employed.

So I would propose that the standard definition does not tell the whole story of induction, and would suggest a more precise definition:

induction - The mental process of forming conclusions based on experience via concepts in two stages:

stage 1. observing the facts of reality and of integrating them into concepts (Rand)

stage 2. deriving a universally quantified proposition from a finite set of propositional instances, using these concepts so formed

I think we could all probably agree on this or something like it.

Edited by worldlogicleague

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Worldlogicleague,

I am glad you are distilling the essentials in the discussions. Something really good might come from all this.

One thing is obvious to me, but I have not yet been able to pin it down with some other lines of thought. No one can make a proposition without concepts. In many of the arguments I have read in favor of deductive logic over inductive, concepts are taken for granted. I still find that a bit weird. When I look, there is a hole where something should be and it is ignored. There is a jump straight into propositions without defining the building blocks of propositions.

Bob K (Ba'al) elsewhere stated that deduction only applies to truth in relation to the premises. It does not state whether the premises are true or not. One can examine each premise with deductive logic, but that would not state whether the premises of that check are true or not.

This leads to infinite regress.

Unless, of course, you start somewhere solid like induction, which is a hell of a lot better than an arbitrary supposition (chosen at random so it can be checked with deduction).

Michael

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Worldlogicleague,

I am glad you are distilling the essentials in the discussions. Something really good might come from all this.

One thing is obvious to me, but I have not yet been able to pin it down with some other lines of thought. No one can make a proposition without concepts. In many of the arguments I have read in favor of deductive logic over inductive, concepts are taken for granted. I still find that a bit weird. When I look, there is a hole where something should be and it is ignored. There is a jump straight into propositions without defining the building blocks of propositions.

Bob K (Ba'al) elsewhere stated that deduction only applies to truth in relation to the premises. It does not state whether the premises are true or not. One can examine each premise with deductive logic, but that would not state whether the premises of that check are true or not.

This leads to infinite regress.

Unless, of course, you start somewhere solid like induction, which is a hell of a lot better than an arbitrary supposition (chosen at random so it can be checked with deduction).

Michael

Premises are not checked (individually) by deduction. The can be jointly checked if the conclusion is a contradiction or false. Then jointly (i.e. the conjunction of the )premises cannot be true.

Deduction assures you that IF the premises are true AND the conlusion is inferred from those premises according to deduction rules THEN the conclusion is true. Deduction, as I have said, also assures you that IF the conclusion is false or a contradiction and it followed from the premises, THEN the conjunction of the premises is false which means one of the premises (at least) must be false. But argument by modus tolens will not tell you which of the several premises are false.

Deduction does not really crank out starting points or bases of arguments. It only checks the validity of inferences. To come up with general starting statements you need induction and/or abduction. To come up with particular starting statements, you have to look and/or measure. That is the good news. The bad news is that general statements gotten from true particular statements by induction or abduction are not guaranteed to be true.

One thing for sure, reality can not be -deduced- a priori. To get reality one must look, measure and fiddle around hands on.

Ba'al Chatzaf

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Premises are not checked (individually) by deduction.

Bob,

Of course they are. You simply abandon the problem you are working on for a while and examine them. You use deduction in that examination.

Michael

I think we have a divergence in terminology. Deduction is a mode of inference based on the following principles:

1. Modus Ponens:

a, and a -> b produce b.

2. Universal Instantiation

(x)P(x)(see note 1) yield P(a) where a is some arbitrary constant.

That is the technical definition of deduction.

There are some other rules, but those are the main rules.

See http://en.wikipedia.org/wiki/Deductive_reasoning

and

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

Contrary to literary myth Sherlock Holmes did not deduce. He abduced in the sense of C.S.Peirce's abductive reasoning.

In real life people use a combination of deduction, induction, abduction and educated guessing.

Ba'al Chatzaf

note 1: (x)P(x) means for all x, P(x) where P is some predicate. If a proposition is true for all x it is true for any arbitrarily chosen a.

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