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

[BaalChatzaf]

Another view of this is that Newton unconsciously assumed that the speed of light was infinite, indeed, in the transformation equations when you let the term for the speed of light go to infinity the equation reverts to Newtonian form. Now, does this mean he made an error of induction?

Unlikely. Ole Roemer discovered that light has a finite speed in 1675, which is ten years before Newton published Principia Mathematica. I do not see how Newton would have failed to know this. Can you?

Ba'al Chatzaf

[Michael Stuart Kelly]

Huh? What is the difference? All the dictionaries that I've checked confirm that "deduce" and "derive" are synonyms.

But, my dear Dragonfly, conceptually and philosophically speaking, there is a world of difference between deduce and derive. For to "deduce" is a mere triviality, the sort of careless mistake the likes of David Hume might make, unequipped as he was with a full theory of concept formation. However, to "derive" is something else altogether; an act of powerful integration reuniting logic and reality, fact and value, that unites the endlessly warring dualisms at last in a kind of Simon-and-Garfunkel Reunion Tour kind of way.

Or perhaps, you simply have the wrong concept for "synonym"...

Now you two could not possibly be insinuating that the word is not only as precise as an electron measurement, but that the two words "deduce" and "derive" mean the same thing? You couldn't mean that, could you? Ellen is correct. Rand said "determine." So that makes three words and they all apparently mean to you that Rand was an idiot, er... that Rand was talking about formal deductive logic.

Whatever happened to your sacred vagueness? It suddenly does not apply WHEN THREE WORDS ARE INVOLVED with Rand? The requirement that all three have to mean the same thing to prove Rand wrong is a little bit overkill according to Popper's standards of vagueness, imho.

Michael

[tjohnson]

Unlikely. Ole Roemer discovered that light has a finite speed in 1675, which is ten years before Newton published Principia Mathematica. I do not see how Newton would have failed to know this. Can you?

Ba'al Chatzaf

I have no idea if he did or not, did he know that Leibnitz was formalizing differential calculus at the same time as him? I don't suppose communication was so good in the 1600's. Let me put it this way. He was unconscious that the finite speed of light had anything to do with 'addition of velocities', for example. Knowing a fact and failing to see the significance of the fact are two different things.

[Ellen Stuttle]

Whatever happened to your sacred vagueness? It suddenly does not apply WHEN THREE WORDS ARE INVOLVED with Rand? The requirement that all three have to mean the same thing to prove Rand wrong is a little bit overkill according to Popper's standards of vagueness, imho.

You still haven't connected with what Popper is talking about. He isn't recommending using terminology any old whichway. You won't get far communicating if you do that. The words "deduce" and "derive" in formal-proof contexts have understood meanings. "Deduce" tends to be used more in contexts of propositional logic; "derive" in mathematical contexts. The argument she was addressing ("In answer to those philosophers [....]") is that you can't, by deductive logic, get a "should" in the conclusion when it isn't there in the premises. Now either she understood this context or she didn't. Either way, she didn't actually answer it, though her sweeping of the problem aside looks as if she thought she did. Either that, or as if she was deliberately using words with a nebulous meaning in the context -- "validated," "determines," also "no relation," and in the later sentence "implies," usages the intended meaning of which she doesn't explain -- and thus as if she was pulling the verbal sleight-of-hand of changing the problem while giving the appearance of addressing it. Impossible to be sure from what she wrote whether: (a) she didn't understand the historic problem; (b ) she understood it and thought she'd addressed it; (c ) she understood it and was doing a verbal switch without stating that this was what she was doing.

Whatever she was doing, she did not deduce or derive by logical entailment an "ought" from an "is." It remains, as I was interested to hear Tibor acknowledged (according to your report) that this can't be done.

Ellen

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[Ellen Stuttle]

Knowing a fact and failing to see the significance of the fact are two different things.

Either way -- whether he didn't know it or knew it and failed to see the significance -- he was wrong in the results.

Ellen

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Edited October 8, 2007 by Ellen Stuttle

[Michael Stuart Kelly]

You still haven't connected with what Popper is talking about. He isn't recommending using terminology any old whichway. You won't get far communicating if you do that.

Ellen,

All right. Since you are stepping up to the plate, how far can I get and how do I go about understanding "what Popper is talking about"? I have asked many times what his standard of determining a classification is and, so far, there has been complete silence. Maybe you can help out. What is his standard? If you can't or won't say, I am sure I will find it as I read more of his works.

Impossible to be sure from what she wrote whether: (a) she didn't understand the historic problem; (b ) she understood it and thought she'd addressed it; (c ) she understood it and was doing a verbal switch without stating that this was what she was doing.

This is a false trichotomy . There is a fourth alternative, which I believe might be more correct than your three: Rand understood the issue and thought it was a stupid one in terms of discussing human knowledge. An apples and oranges kind of thing.

"Derive," if MSK is quoting Tibor correctly, is Tibor's interpretation, and was also the interpretation of some in the dicussions here.

It remains, as I was interested to hear Tibor acknowledged (according to your report) that this can't be done.

I did not reproduce Tibor's account word for word since my own memory is not a photographic (or phonographic) kind. But his terminology and conclusions are as I stated: One cannot deduce a conclusion about a fact that is not included in the premises; if an ought is not included in the premises, it cannot be deduced using formal logic; and you can derive ought from is since life is conditional. That's what the man said. I suggest you confirm my version with someone you trust to get the facts right (or ask Tibor himself). In fact, I prefer that if you have time since it eliminates doubt.

Michael

[BaalChatzaf]

I have no idea if he did or not, did he know that Leibnitz was formalizing differential calculus at the same time as him? I don't suppose communication was so good in the 1600's. Let me put it this way. He was unconscious that the finite speed of light had anything to do with 'addition of velocities', for example. Knowing a fact and failing to see the significance of the fact are two different things.

Newtonian Mechanics is Galilean Invariant. The speed of light has no particular significance. Newton probably knew the speed of light is finite, but it made no difference in his theory. Time was absolute and the same everywhere, according to his thinking. Length and time were preserved under a change of co-ordinate axes. Classical momentum was conserved in all collisions. Mass is invariant.

From the standpoint of a Lorentz Transformation that would be true only if the speed of light were infinite, but Newton did not operate from that basis. In Newtonian mechanics the speed of light is irrelevant. In Newton's day there was no Lorentz-Fitzgerald transformation.

This caused a great deal of problems when Maxwell produced his theory. Maxwell's theory is Lorentz Invariant right out of the box. There was no way of reconciling Newton's (Classical) dynamics with Maxwellian Electrodynamics as things stood. Einstein solved the problem. He made mechanics Lorentz Invariant. This required a number of things: a redefinition of momentum so it would be conserved, the inconstancy of mass, time dilation and length shortening. Almost anyone else would have tried to make Electrodynamics Galilean Invariant.

Ba'al Chatzaf

[tjohnson]

From the standpoint of a Lorentz Transformation that would be true only if the speed of light were infinite, but Newton did not operate from that basis. In Newtonian mechanics the speed of light is irrelevant. In Newton's day there was no Lorentz-Fitzgerald transformation.

I think you misunderstood me. I meant from an historical perspective it appears as if he unconsciously assumed. This assumption is present because he failed to take into account that a small amount of time elapses from when light leaves the object until it hits the observer. Of course it was Einstein that realized the importance of this.

[tjohnson]

Either way -- whether he didn't know it or knew it and failed to see the significance -- he was wrong in the results.

Ellen

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Wrong? Why is it so important for you to classify things as right or wrong? This represents outdated 2-valued thinking. His theory was simply not as general as relativity, that doesn't make it "wrong". So our current theories are 'right' now. What about tomorrow, will they be wrong then? Is this the contextual 'true' and 'false' I see here all the time?

[BaalChatzaf]

Either way -- whether he didn't know it or knew it and failed to see the significance -- he was wrong in the results.

Ellen

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Wrong? Why is it so important for you to classify things as right or wrong? This represents outdated 2-valued thinking. His theory was simply not as general as relativity, that doesn't make it "wrong". So our current theories are 'right' now. What about tomorrow, will they be wrong then? Is this the contextual 'true' and 'false' I see here all the time?

Newton's law of gravitation mispredicts the motion of mercury (or more generally it does not predict the precession of the perihelion right for -any- planet). That is wrong. Newton's law of gravitation mispredicts the bending of light around the sun by a factor of two. That is wrong. It is not just a lack of scope or generality.

Newtonian physics is categorically flawed. It has the wrong model of space and time or more exactly spacetime. Furthermore Newtonian physics is Galilean invariant which is also incorrect. In the real world velocities do not add.

In the real world mass in motion is not invariant (but rest mass is).

Ba'al Chatzaf

[tjohnson]

Newton's law of gravitation mispredicts the motion of mercury (or more generally it does not predict the precession of the perihelion right for -any- planet). That is wrong. Newton's law of gravitation mispredicts the bending of light around the sun by a factor of two. That is wrong. It is not just a lack of scope or generality.

Newtonian physics is categorically flawed. It has the wrong model of space and time or more exactly spacetime. Furthermore Newtonian physics is Galilean invariant which is also incorrect. In the real world velocities do not add.

In the real world mass in motion is not invariant (but rest mass is).

Ba'al Chatzaf

More 2-valued thinking. it's not possible to know when we have the 'correct' or 'right' theory and so it makes no sense to speak about the 'wrong' one. It's really just a question of usefulness. If we could find an ultimate 'right' theory then there will be no improvement possible, which is ridiculous.

Edited October 8, 2007 by general semanticist

[BaalChatzaf]

More 2-valued thinking.

No. It is correct physics. But you learned physics from the Count and you would not know any better.

That two valued thinking made the computer on which you spew your Korzybskian nonsense possible.

Ba'al Chatzaf

[tjohnson]

That two valued thinking made the computer on which you spew your Korzybskian nonsense possible.

Ba'al Chatzaf

I guess you are no smarter than my computer then.

[Daniel Barnes]

Ellen:

Whatever she was doing, she did not deduce or derive by logical entailment an "ought" from an "is." It remains, as I was interested to hear Tibor acknowledged (according to your report) that this can't be done.

Yes. Machan's fiddle-faddle over "deduce" and "derive" is droll hairsplittery. Apparently one can get paid to do this.

If there is no logical relation between "ought" and "is", it would be handy for Objectivists to fill us in on exactly what kind of "relation" Rand did establish between the two. (One also notes that, as with the problem of induction, we now hear that she wasn't replying to Hume at all - who most certainly was talking about logical relations- but once again was talking about something else altogether.)

Someone needs to update the wiki entry on Rand in that case:

'Rand is criticized for her outright rejection of David Hume's ideas at the foundations of her philosophy...."

Maybe something like:

"While Rand is thought to have rejected David Hume's logical arguments regarding both induction and ethics, in fact she did not address them and was in both cases talking about something else entirely."

Edited October 9, 2007 by Daniel Barnes

[Michael Stuart Kelly]

Daniel,

Dayaamm! Whazza madder? Irritated?

Is bashing Rand and making it stick a bit harder than you thought?

Yes. Machan's fiddle-faddle over "deduce" and "derive" is droll hairsplittery. Apparently one can get paid to do this.

No it isn't "droll hairsplittery," but your comment is cute. I have even heard similar remarks about your own arguments.

Michael

[Ellen Stuttle]

Either way -- whether he didn't know it or knew it and failed to see the significance -- he was wrong in the results.

Ellen

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Wrong? Why is it so important for you to classify things as right or wrong? This represents outdated 2-valued thinking. His theory was simply not as general as relativity, that doesn't make it "wrong". So our current theories are 'right' now. What about tomorrow, will they be wrong then? Is this the contextual 'true' and 'false' I see here all the time?

GS,

I think you aren't noticing much who says what here, else you might have noticed that I have several times objected to the "contextual certainty" idea. Indeed, it was in the context of objecting to that idea that I posted above about Newton's being "magnificently wrong." (See post #323.) And if you have so much trouble with the words "right" or "wrong" -- are you hearing moral overtones or something? -- substitute "correct" and "incorrect" if that will help.

As to our current theories, who knows what tomorrow will bring? Which question is pertinent to the purported topic of this thread. I think the "contextual certainty" stuff is just another way of saying, "According to the best evidence we have available today, this theory is holding up, but that doesn't mean it will continue to hold up in the light of further evidence." As to Newton's theory being "simply not as general as relativity," no, it was simply in error, as Bob has abundantly detailed.

Look, suppose you predict that your phone will ring in two minutes, and your phone does not ring in two minutes, your prediction was wrong. You were mistaken. A number of the predictions of Newton's theories did not pan out, and there were premises which have been shown incorrect. Einstein's theories might end up being shown wrong, too. There are those indications of difficulties (which I'm not going to attempt to get into the details of, or we might trigger a complicated physics war.) We can't know that any theory we have is right, but we can know, by straightforward non-A contradicts A, when a prediction flat out doesn't come to pass. (There might be complexities and nebulous circumstances. But some circumstances are clear cut.)

Ellen

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[BaalChatzaf]

Look, suppose you predict that your phone will ring in two minutes, and your phone does not ring in two minutes, your prediction was wrong. You were mistaken. A number of the predictions of Newton's theories did not pan out, and there were premises which have been shown incorrect. Einstein's theories might end up being shown wrong, too. There are those indications of difficulties (which I'm not going to attempt to get into the details of, or we might trigger a complicated physics war.) We can't know that any theory we have is right, but we can know, by straightforward non-A contradicts A, when a prediction flat out doesn't come to pass. (There might be complexities and nebulous circumstances. But some circumstances are clear cut.)

Ellen

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Failure to predict may be because a condition assumed by the theory does not hold. That is why the anomalous motion of Uranus did not falsify Newton's Law of Gravitation. It turned out there was a planet beyond Uranus that no one knew about. Once this planet's trajectory was determined, the motion of Uranus was according to Newton's Law of Gravitation to within instrumental error (such as it was at the time). If the cause of the failure can be located in a violation of the boundary values or the conditions required by the theory, then the anomaly is not a falsification of the core theory. In fact the anomaly is a good clue that Something New is out there.

The failure of Newton's law to predict the precession of the perihelion of mercury correctly was a different sort of failure.

Ba'al Chatzaf

[Daniel Barnes]

Ellen:

Sure does look like a weasel word in the context, since, no, Newton wasn't right within certain boundary conditions and only over-generalizing.

Well, "contextual" doesn't have to be called a "weasel" word, I suppose. But what do you call it? What do you call it when you can say something is "absolutely true" one day, then call its exact opposite "absolutely true" the next?

A revolutionary epistemological insight?

Or lowering the bar for truth to ground level?

Or just plain ol' double talk?

[Michael Stuart Kelly]

Vague?

[Ellen Stuttle]

Ellen:

Whatever she was doing, she did not deduce or derive by logical entailment an "ought" from an "is." It remains, as I was interested to hear Tibor acknowledged (according to your report) that this can't be done.

Yes. Machan's fiddle-faddle over "deduce" and "derive" is droll hairsplittery. Apparently one can get paid to do this.

Daniel, we don't actually know what Tibor said, especially about the "derive" part of it. There are other uses of "derive" besides logical entailment.

If there is no logical relation between "ought" and "is", it would be handy for Objectivists to fill us in on exactly what kind of "relation" Rand did establish between the two.

Conditional relationship based on causal reasoning: IF you want X, it's necessary to do Y. (If you want to live, it's necessary to have an oxygen intake, that sort of reasoning.) That's the sort of relationship she attempted to establish between her list of virtues and the life of a rational being.

(One also notes that, as with the problem of induction, we now hear that she wasn't replying to Hume at all - who most certainly was talking about logical relations- but once again was talking about something else altogether.)

If she was talking about something else altogether, and if she knew what Hume was talking about ("In answer to those philosphers [....]"), then her wording was that of side-stepping the Humean issue while giving an appearance of addressing it. I think it's a shame she included that paragraph. A lot of trouble could have been spared if she'd either clarified what she meant or left it out.

Ellen

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[Michael Stuart Kelly]

Daniel, we don't actually know what Tibor said, especially about the "derive" part of it. There are other uses of "derive" besides logical entailment.

Ellen,

That is convenient for dismissal, isn't it? Why not find out? It's fairly easy since many people were there that I am sure you know.

Michael

[Ellen Stuttle]

Daniel, we don't actually know what Tibor said, especially about the "derive" part of it. There are other uses of "derive" besides logical entailment.

Ellen,

That is convenient for dismissal, isn't it? Why not find out? It's fairly easy since many people were there that I am sure you know.

Michael

There's no "dismissal" involved, Michael. Daniel was assuming Tibor meant "derive" as logical entailment. If he did, then his comments were sophistry, whatever the details. From your description (assuming the accuracy of your description), he must have meant some other meaning of "derive." Far from "dismissal," I was giving you the benefit of the doubt as having accurately reported. I'm not going to the bother of tracking it down. I'm far from being that curious. I was just interested in hearing that he'd acknowledged that one cannot deduce a "should" from premises that don't contain a "should."

Ellen

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[Ellen Stuttle]

Impossible to be sure from what she wrote whether: (a) she didn't understand the historic problem; (b ) she understood it and thought she'd addressed it; (c ) she understood it and was doing a verbal switch without stating that this was what she was doing.

This is a false trichotomy . There is a fourth alternative, which I believe might be more correct than your three: Rand understood the issue and thought it was a stupid one in terms of discussing human knowledge. An apples and oranges kind of thing.

So why didn't she either say the issue is a stupid one instead of looking as if she was addressing it, or alternately say nothing about it? (She might have thought the issue was stupid as characteristically put, but she doesn't explain this, if so. If she felt the explanation was too long in the context of a public talk, why not leave out the paragraph? One way or another, one cannot tell for sure what she thought she was doing from what she said, and she does give the appearance that she's answered the famous is/ought problem. How many of her followers think she did answer it? Even the wiki quote Daniel provided was written by someone who thought Rand had claimed that Hume's reasoning was wrong.)

Ellen

[Ellen Stuttle]

You still haven't connected with what Popper is talking about. He isn't recommending using terminology any old whichway. You won't get far communicating if you do that.

Ellen,

All right. Since you are stepping up to the plate, how far can I get and how do I go about understanding "what Popper is talking about"? I have asked many times what his standard of determining a classification is and, so far, there has been complete silence. Maybe you can help out. What is his standard? If you can't or won't say, I am sure I will find it as I read more of his works.

I don't know how you might go about understanding what Popper is talking about. Maybe re-reading the essay in the light of all the discussion which has occurred would help. I'm not sure what you mean by "standard of determining a classification." Do you mean how ideas of general categories are formed -- what Rand calls "concepts"? If so, I don't know his views on that. There are hints in the essay but only hints.

Ellen

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Edited October 9, 2007 by Ellen Stuttle

[Michael Stuart Kelly]

I'm not sure what you mean by "standard of determing a classification." Do you mean how ideas of general categories are formed -- what Rand calls "concepts"? If so, I don't know his views on that. There are hints in the essay but only hints.

Ellen,

That is exactly what I mean and a lack of addressing it in the famous is/ought problem is probably why Rand was so dismissive of Hume. (I speculate, I admit, but I have good reasons.) Rand was concerned with actual knowledge for human beings, not simple word games.

As I have stated several times, I think both Popper and Rand were on the same page in this respect. Her rejection of Hume and Popper's acceptance of him merely signals to me a difference in approach and suppositions, not a substantial difference in meaning. Rand saw in Hume an attempt to disconnect evaluation from reality and Popper merely saw the deductive logic. I doubt that Rand would have agreed that one can deduce a fact (say in a syllogism) not included in the premises. I have seen nothing in her writing to indicate this.

Michael