Two Kinds of "Induction": Important similarities and trivial differences

[Daniel Barnes]

Daniel,

How about that idea of falsification being induction sneaking in through the back door? I do not have an opinion yet, but it does seem intriguing since I like to look behind the words.

Michael

Falsification makes use of Modus Tolens which involves an empirical falsification of a consequence, but that is not induction. Induction is deriving a universally quantified proposition from a finite set of particular propositions.

Ba'al Chatzaf

What Ba'al said, which is what we've been saying all along! You're right: It's about the ideas. So take the time to get your head around them so you can usefully contribute. Then you won't keep bringing up obvious non-starters like the above in the first place.

[Daniel Barnes]

GS:

I'm sorry Daniel but I don't see what you mean "that 2) says 1) is invalid.", perhaps you can explain that.

It seems that when it comes to the problem of induction, every day is Groundhog Day

GS, I can't possibly start this thread back at the "what is the problem of induction anyway?" stage and explain it all over again. I've already done so multiple times on this and other threads. If you're truly interested have a look here.

[Michael Stuart Kelly]

Then you won't keep bringing up obvious non-starters like the above in the first place.

Daniel,

Hey... I didn't really bring it up. It was published in a science vehicle with broad circulation by a respected writer. I merely reported it since I found it suddenly pertinent to something I have noticed in what little I have read of Popper's works. Gardner is some non-starter, huh?

Have you noticed something in your own writing? I have. Whenever a writer writes anything at all about Popper, no matter how small the detail, if he is a Popper adherent, you use him for quotes, etc. If he is not a Popper adherent, even if he is friendly to Popper, you mock him.

I find this behavior curious.

Michael

[tjohnson]

GS, I can't possibly start this thread back at the "what is the problem of induction anyway?" stage and explain it all over again. I've already done so multiple times on this and other threads. If you're truly interested have a look here.

From the link;

In other words, the logical problem of induction arises from (1) Hume's discovery (so well expressed by Born) that it is impossible to justify a law by observation or experiment, since it 'transcends experience'; (2) the fact that science proposes and uses laws 'everywhere and all the time'. (Like Hume, Born is struck by the 'scanty material', i.e. the few observed instances upon which the law may be based.) To this we have to add (3) the principle of empiricism which asserts that in science only observation and experiment may decide upon the acceptance or rejection of scientific statements, including laws and theories.

Sorry, I don't see a problem here either. And besides this author says a little further down that;

Hume showed that it is not possible to infer a theory from observation statements; but this does not affect the possibility of refuting a theory by observation statements. The full appreciation of this possibility makes the relation between theories and observations perfectly clear.

This solves the problem of the alleged clash between the principles (1), (2), and (3), and with it Hume's problem of induction

So apparently there is no problem after all? Much ado about nothing.

[Daniel Barnes]

Hey... I didn't really bring it up... I merely reported it..

:lol:

Gardner is some non-starter, huh?

On this issue, yep. Hey, MSK, Gardner believes in God. Do you believe in God because "respectable people" like Martin Gardner do? Guess what: He's a non-starter on that one too.

But you're all about the ideas, not arguments from "respectability", right?

Have you noticed something in your own writing? I have. Whenever a writer writes anything at all about Popper, no matter how small the detail, if he is a Popper adherent, you use him for quotes, etc. If he is not a Popper adherent, even if he is friendly to Popper, you mock him.

This isn't even faintly true. But anyway, you're all about the ideas!

I find this behavior curious.

That MSK: he's all about the ideas!

Edited October 14, 2007 by Daniel Barnes

[Ellen Stuttle]

The problem of induction is, When do you know your empirical generalizations are correct? (That's how AR states the problem as well, btw.) The answer is, You don't, ever. That's actually the same answer Leonard Peikoff gives; only he calls never being sure "contextual certainty."

Then what are the objectivists and Popperians spending so much time debating about on these threads?

Which Objectivists, Martin? Except for some occasional posts by John Dailey, I think Michael is the only one who thinks of himself as an Objectivist who's holding forth. He doesn't see the logical problem with universally quantified statements. In the wider O'ist world, Popper is often classified as a hiss-boo bad guy, as being among those out to destroy the mind, etc. There isn't the recognition that Popper's approach saves empiricism's day from Hume.

Has any reputable philosopher, objectivist or not, argued that induction can absolutely prove any generalization? If not, then pointing out that induction cannot accomplish this seems like attacking a straw man. Who has argued that it can?

Well, "contextual certainty" is called "absolute," in another of those usages which aren't what the rest of the world would mean. The verificationists whom Popper was most of all arguing against did hold to the idea that enough confirmations provide conclusive proof. They thought that one can establish the positive case for a scientific theory.

Ellen

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[Michael Stuart Kelly]

Daniel,

You do manage to make a large number of posts without any intellectual content whatsoever, don't you?

You used to be good. Sumpin musta snapped... WAKE UP, MAN!

Since the issue of God is soooooo important to you as an attempt to discredit a Popper critic, I happened to have written about this uhmmmmm... 2 days ago.

... one of the signs I look for in a person on the few occasions I have invited someone to check out OL is his ability to think for himself. I cherish this, even and especially among people who disagree with me.

You might notice during discussions that there are some types of criticism of Rand I do not mind and other types I argue against passionately (and, I might add, I have learned to be passionate with correct grammar, without foul language and without calling a person stupid names like slime and so forth). Regardless of how you perceive this, you have to perceive that it is different than orthodox defenses of Rand. If you look at my complaints, they will always be at root that Rand's ideas are not being correctly understood and/or represented. It will rarely be against someone who simply disagrees with her, other than to say that we disagree.

A good example is the belief in God. Some people who post here understand Rand's arguments and, even so, still believe in God. They are very intelligent people—ones who I have noted use their own minds—so I think they have their own reasons, regardless of whether their conclusion is final or they are still thinking the thing through. I have to respect them even if I don't agree with their conclusion. They are bringing their very best efforts—the best within themselves—to the issue and that is the spirit I deeply cherish. I feel very comfortable around people like that.

I have to say that from what little I read of Gardner, he brings his best to his writing. I cannot say that about your recent spate of posts. I know for a fact that you are better than unsupported opinions and mockery, but you must make your own value judgments. You obviously do that because you think it is valuable. Whatever rings your ding-a-ling...

Michael

[Michael Stuart Kelly]

He [yours truly] doesn't see the logical problem with universally quantified statements.

Ellen,

Of course I do. The tie-in with science is to be able to predict the future. Where we actually disagree is on the nature of categorization.

Michael

[Ellen Stuttle]

He famously said it ("Hypotheses non fingo"), but he'd have been wise to take his editor Robert Cotes' advice and leave the statement out of the Second Edition (1713) of The Principia. Cotes and others had already noticed by then that Newton did "feign" hypotheses, even in the section wherein he claimed not to do so.

Be that as it may, Newton hypothesized no causes for gravitation. [...]

Rain check on that one; I'll try to get back to it later. Some quotes from Newton are needed.

Ellen

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[Ellen Stuttle]

Mike:

Ellen just did. I'm sorry.

No, that's only because you don't understand the argument she's making!

You aren't showing any signs I can see of understanding the argument, Michael. The example you give of the tiger doesn't address it. Sure, if you were in the jungle and a charging tiger was approaching, you would wisely get out of there if you could. You'd have reason to on the anticipation -- the prediction -- that the tiger is a hazard to your health. But this by no means establishes that all charging tigers would necessarily be such. We act according to our expectations, our theories about the way the world works. This doesn't mean we know those theories are correct universally.

Ellen

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[Ellen Stuttle]

Notice here that both Daniel and Ellen are bashing Kelley's ideas without any real familiarity with them.

On what basis do you presume that I have no familiarity with his ideas? You forget my history. Nor am I bashing Kelley's ideas. There you go again with that charge. I have a great deal of respect for David's intellect; however, I'm aware that he isn't steeped in a scientific background.

Ellen

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[Ellen Stuttle]

I perceive that my stated intent of making a study about where Poppers's ideas align with Rand's is treated as a threat.

Well, there's a theory which is false. It's perceived as amusing.

Ellen

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[Michael Stuart Kelly]

Notice here that both Daniel and Ellen are bashing Kelley's ideas without any real familiarity with them.

On what basis do you presume that I have no familiarity with his ideas? You forget my history. Nor am I bashing Kelley's ideas. There you go again with that charge. I have a great deal of respect for David's intellect; however, I'm aware that he isn't steeped in a scientific background.

Ellen,

You must have forgotten the context. We were discussing formal logic (you know, induction validating deduction and vice-versa). Here, let me give you an intellectual bandaid for easier comprehension:

Notice here that both Daniel and Ellen are bashing Kelley's ideas about formal logic without any real familiarity with them

Better now?

On the basis of that, you yourself mentioned that you had not read the work being discussed (much less the college text I mentioned), but you did respect his intellect. All I can say is, so what? What does respecting his intellect have to do with formal logic? From you remark, you apparently doubt he can get formal logic right for scientific use. And that is without being familiar with his views on formal logic by your own admission.

Michael

[Ellen Stuttle]

He [yours truly] doesn't see the logical problem with universally quantified statements.

Ellen,

Of course I do. The tie-in with science is to be able to predict the future. Where we actually disagree is on the nature of categorization.

Michael

HUH??? I need a Michael decoder ring.

Since you say that you see the logical problem, would you please state it?

Ellen

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[Ellen Stuttle]

Notice here that both Daniel and Ellen are bashing Kelley's ideas without any real familiarity with them.

On what basis do you presume that I have no familiarity with his ideas? You forget my history. Nor am I bashing Kelley's ideas. There you go again with that charge. I have a great deal of respect for David's intellect; however, I'm aware that he isn't steeped in a scientific background.

Ellen,

You must have forgotten the context. We were discussing formal logic (you know, induction validating deduction and vice-versa). Here, let me give you an intellectual bandaid for easier comprehension:

Notice here that both Daniel and Ellen are bashing Kelley's ideas about formal logic without any real familiarity with them

Better now?

On the basis of that, you yourself mentioned that you had not read the work being discussed (much less the college text I mentioned), but you did respect his intellect. All I can say is, so what? What does respecting his intellect have to do with formal logic? From you remark, you apparently doubt he can get formal logic right for scientific use. And that is without being familiar with his views on formal logic by your own admission.

Michael

That is nonsense, Michael. The context of my original remark, which you've now twisted beyond any recognition, was the supposed use of induction in science. Where do you get the idea that I'm not familiar with his work in formal logic? The hell I'm not. We have copies of all of David's books and they have been read more than once. My understanding of the work in progress is that it pertains to science.

Ellen

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[Brant Gaede]

It's queer how some people need each other, but it's not productive.

--Brant

[Daniel Barnes]

You do manage to make a large number of posts without any intellectual content whatsoever, don't you?

I think people can make their own minds up about that. Happy to compare the intellectual content of my posts on this thread any time, which have drawn compliments from people such as Ba'al and John Dailey, neither of whom has any particular reason to offer such but kindly did anyway. Currently yours seem to consist of nothing more than weak insults interspersed with glowing tributes to your own superior tolerance and concern for the importance of "the ideas," regardless of the fact that neither has been in evidence on this thread.

In fact I think your contribution to the "intellectual content" of this thread has been, unfortunately, pretty much zero. As others have regularly remarked, it's not even clear that you have understood, let alone answered, the arguments put forward. This is to be reasonably expected, given that you know so little about the subject. However, this ignorance does not seem to be balanced by any noticeable modesty. Quite the opposite, which is never a pretty sight. As a result despite the hard work I have put into trying to explain the issue, from my point of view I doubt there is much more productive discussion to be had.

As I say, I will await your forthcoming article on the topic with interest, and that probably is all that needs to be said at this point.

[Michael Stuart Kelly]

Ellen,

I am getting tired of "I said you said." I am tired of quoting your posts because you said you didn't say something, just so you can say you don't understand me. I am not going to get into a formal logic debate with you simply because I don't find your explanation of Rand's concept formation in line with what she wrote. The far-too-many posts are already self-explanatory for anyone who is interested and I do not feel like posting merely to satisfy vanity. I'm gonna go play with someone else for a while.

As I say, I will await your forthcoming article on the topic with interest, and that probably is all that needs to be said at this point.

Daniel,

Good. We are wasting each other's time.

As I said earlier, don't expect my article tomorrow, although I stand by my thesis so far. Proper research takes time and I have no reason to rearrange my present priorities to satisfy your vanity or mine. It will get done.

Michael

[Ellen Stuttle]

However, Gardner is a lousy philosopher, who has little to nothing to contribute in that field. How he for example can square his skepticism with a belief in God escapes me. And Objectivists had better not rely too much on his authority in these matters, as he has a very low opinion of Ayn Rand.

I meant to say something about Gardner in my last spate of posts.

He's an odd case. As it happens, Larry and I know someone who had quite a bit of correspondence with him while he was still corresponding and who shared some of the correspondence -- as well as verbal reports -- with us. Gardner has pretty much gone into seclusion since his wife's death about eight years ago (it might be longer than that); the two of them were very close, and her death was a terrible blow to him. As of last I heard, the belief in a personal God, not merely in a God (of some form), wasn't (isn't, assuming he hasn't changed in his views) incidental to his antipathy to UFOlogy; his hatred extended (extends?) to the very idea of extra-terrestrial intelligence at all. It wasn't just that he was out to debunk the reports of UFO sightings, etc. Any idea of the possible existence of intelligent extra-terrestrial life contradicted his belief in a God who had created the universe personally as the domicile of humans. I don't know how he "connected the dots," trying to reconcile science and his religious belief. The task seems a non-trivial one to me.

Ellen

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[Ellen Stuttle]

I am tired of quoting your posts because you said you didn't say something, just so you can say you don't understand me.

It would be interesting to see you quote where I said I hadn't read David's book on logic (or any of his other books).

And answer, thus far, came there none explaining your understanding of where you "see the logical problem with universally quantified statements."

Ellen

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[Ellen Stuttle]

It's queer how some people need each other, but it's not productive.

--Brant

Check your premises, Brant, as to whether it's productive. Substance has been produced, despite all (just as used to happen on Atlantis in similar exchanges).

Ellen

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[Michael Stuart Kelly]

It would be interesting to see you quote where I said I hadn't read David's book on logic (or any of his other books).

And answer, thus far, came there none explaining your understanding of where you "see the logical problem with universally quantified statements."

Ellen,

You mentioned you had not seen Kelley's beta manuscript of the Logical Structure of Objectivism, not The Art of Reasoning. The fact is you made no reference at all to the second book until I did. You just now say you read it, so I'll take you at your word, but from what I have seen skimming Kelley's book, it makes hash out of your smarmy comment about science not being his thing (made in agreement with the idea that he did not know what he was talking about as regards induction/deduction validating each other). You can find the quote if you like (like I said, I am tired of doing that to see you ignore it and say you don't understand my post), but induction/deduction was the issue at the time.

As to the logical problem of universally quantified statements, I don't use this language yet, but I do understand it in Objectivist terms. In the formal language of predicate logic, the logical problem is that they do not allow the domain of discourse to be conditioned enough to make absolutely true or false statements.

HOWEVER, the concept of quantification in any degree in Objectivist language is a measurement. (Ta daaa!!! Here we go again!!!) The way Rand would put it, the unit must be present in some quantity, but may be present in any quantity. In a certain manner of speaking, a universally quantified statement is measurement omission incarnate, and very much used (but not acknowledged) in Popper's idea of vagueness, going from his examples.

Chew on that for a while.

And meanwhile, since we are doing Minimum Understanding 101, I would be very interested in your understanding of measurement in Objectivist concept formation. You have shown all the signs of not understanding this correctly. (Here's a small hint. Numbers and integers, among other things, are used as measurements in Objectivist epistemology.) We can deal with the difference between Aristotle's concept of essence as opposed to Rand's later, since you have shown to have a hard time with that one, too.

Michael

[BaalChatzaf]

As to the logical problem of universally quantified statements, I don't use this language yet, but I do understand it in Objectivist terms. In the formal language of predicate logic, the logical problem is that they do not allow the domain of discourse to be conditioned enough to make absolutely true or false statements.

Tautologies and negations of tautologies (respectively) are just such statements. The only problem with these absolute statements is that they don't -tell- you anything useful about the world, even when interpreted.

Ba'al Chatzaf

[Michael Stuart Kelly]

Bob,

With all due respect, I am looking at that word "useful" in this context and I just can't get a handle on it. I couldn't the first time I heard this observation a couple of years or more ago (on SoloHQ) and I can't in some technical reading I have been doing. It seems like a terrible fudge.

Michael

[Michael Stuart Kelly]

Here's the Table of Contents to The Art of Reasoning by David Kelley to show just how little he understands deduction and induction and how far removed from science he is.

(Each chapter is further broken down into technical sections, but I did not list those.)

1. Introduction

Part One - Concepts and Propositions

2. Classification

3. Definition

4. Propositions

Part Two - Arguments

5. Basic Argument Analysis

6. Fallacies

7. Advanced Argument Analysis

Part Three - Classical Deductive Logic

8. Categorical Propositions

9. Categorical Syllogisms

10. Disjunctive and Hypothetical Syllogisms

11. Syllogisms in Ordinary Reasoning

Part Four - Modern Deductive Logic

12. Propositional Logic-Symbolic Notation

13. Propositional Logic Arguments

14. Predicate Logic

Part Five - Classical Deductive Logic

15. Inductive Generalizations

16. Argument by Analogy

17. Statistical Reasoning

18. Explanation

On the inside covers, there are the following rules. Each one has one or more equations with standard logic symbols. I will merely give the names to show they were covered, but not the symbols and equations. Later I suppose I could scan those two pages and put them up for the sake of completion.

Inference Rules

Simplification (Simp): (two equations)

Conjunction (Conj):(one equation)

Addition (Add): (two equations)

Disjunctive syllogism (DS): (two equations)

Hypothetical syllogism (HS): (one equation)

Modus ponens (MP): (one equation)

Modus tolens (MT): (one equation)

Constructive dilemma (CD): (one equation)

Destructive dilemma (DD): (one equation)

Equivalence Rules

Tautology (Taut): (two equations)

Double negation (DN): (one equation)

Commutation (Com): (two equations)

Association (Assoc): (two equations)

Distribution (Dist): (two equations)

De Morgan's Law (DM): (two equations)

Contraposition (Contra): (one equation)

Implication (Imp): (two equations)

Biconditional (Bicon): (two equations)

Exportation (Exp): (one equation)

Quantifier-negation (QN): A negation sign may be moved across a quantifier in accordance with the following equivalences: (four equations)

Instantiation and Generalization Rules

General restrictions:

1. The same variable must replace all occurrences of the same name (for universal but not existential generalization), and vice versa (for both types of instantiation).

2. The quantifier that is added (in the case of generalization) or dropped (in the case of instantiation) must include the entire line within its scope.

Universal instantiation (UI): (one equation)

Existential generalization (EG): (one equation)

Existential instantiation (EI): (one equation)

Restriction:

a must not have occurred previously in either the proof of the conclusion.

Universal generalization (UG): (one equation)

Restrictions:

1. a must be introduced by UI or be introduced in the assumption of a conditional or reductio proof (not in a premise or by EI);

2. the inference must not occur within a a conditional or reductio proof whose assumption contains a; and

3. the statement . . . a . . . must not contain any other name introduced by EI on a line containing a.

This text is accompanied by an online supplementary tutorial program (see here) and another book called The Art of Reasoning: Readings for Logical Analysis by Hicks and Kelley (containing 44 essays by Bacon, Mencken, Doyle, Freud, Reagan, Rousseau, Machiavelli, Jefferson, and a host of others from a broad spectrum of authors and fields, from literature to case law to science and other areas, to illustrate the different types of reasoning). An Instructor's Manual and Test Bank with 500 problems are also available as supplements.

Michael