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Post 20

Wednesday, February 16, 2011 - 8:44amSanction this postReply
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Mike,

I agree with you that asynchronous online discourse is almost by nature adversarial (for the very reasons you give).

we must avoid presentism, expecting people of 2300 years ago to think like us.
Great point. Genius is as genius does ... in a context. Smart people have always existed. I can admit that much.

Without googling the answer, do you know when it was proved that the Earth goes around the Sun and when it was proved that the Earth rotates about an axis?
No.

I say that rather than attempting to capture a new meaning for "inductive" Harriman should just call his program the "objective" or "Objectivist."
Well, okay, but I say that induction should now be officially differentiated into 2 species: one historical, one new. There is now a concept deficiency with regard to induction and it prevents adequate dialogue and understanding. A quick & dirty dichotomy would be this:

1) enumerative, relative frequency induction [ERFI] -- based on the notion of random processes and the play of chance

2) induction by mechanical limitation [IBML]-- based on determinate processes and universal principles
I wrote about this philosophical and scientific need 5 years ago -- almost to the day.

Ed


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Post 21

Wednesday, February 16, 2011 - 3:25pmSanction this postReply
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I recently finished this book. It's very good overall. I found it interesting that he discussed induction in terms of causation, bypassing entirely any discussion of black swans or other cases of false generalization. He got to talk about a interesting topic, but it seems like there's plenty more to work out.

The book is also fun just in terms of his descriptions of the science. Whether it was all historically accurate may be debated, but he did an excellent job showing how critical concepts were necessary to allow much deeper understanding and progress.

I recently saw this video of PZ Myers:


Around 2 minutes into it, he says that nothing can disprove the theory of evolution. He explains why, but I think he's describing how the theory is really an inductive conclusion. Those who have read this book might want to check out his argument.




Post 22

Wednesday, February 16, 2011 - 3:34pmSanction this postReply
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I found it interesting that he discussed induction in terms of causation, bypassing entirely any discussion of black swans or other cases of false generalization.
Not quite on the latter. See pages 8-9 (indexed as "enumeration").


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Post 23

Wednesday, February 16, 2011 - 4:36pmSanction this postReply
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I agree that he mentioned it and dismissed it.  But what he replaces it with is specific to cause and effect relationships. On page 28 he defines generalizations in this way:  "A generalization is the conceptualization of cause and effect...".  I think he does an excellent job of providing an argument for induction in that case.  But is that all there is?  Are there no other generalizations except for cause and effect? 

The black swan is a generalization about the identity of swans, not about a cause and effect.  I don't see how he deals with the difficulty of making that kind of generalization.  His focus on cause and effect relationships almost seems like a change in subject.


Post 24

Thursday, February 17, 2011 - 5:44amSanction this postReply
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GF: Mike,
I don't understand your point about the sled.  It's the same as Newton's magnet and iron on the wood experiment.  In neither case can the system move with respect to the surface it's on and in both cases the forces internal to the system (pushing and pulling of the children on each other, or the force between the magnet and the iron) obey Newton's third law (action-reaction pairs).  Harriman's explanation is correct.
Thanks,
Glenn


Professor, if we already agree with Harriman, and if we already share a lot of physical mechanics developed after Newtwon, then as we read Harriman, we nod in agreement with what he means by what he says.

In the summer of 2007, I had a class in research methods for social science taught by Young S. Kim.  (See "CSI Effect all over, but of course Wikipedia here.)  The bulk of our work was to read and criticise academic journal articles.  After the first class, I went to his office and asked if it was reasonable to expect undergraduates to do that level of work.  He replied that it was not that hard.  Indeed, it was not.  I even found arithmetic errors.  Since then, I have been a much more careful reader, especially when I already agree with the thesis. 

So, with Harriman, I did not read it like re-reading Anthem

As for the sled. If the larger stronger child pushes the smaller childer harder, the little one falls over.  We in our century can write equations of momentum for that and we can point to Newton.  That does not validate Harriman's presentation.  He was attempting to explain how Newton's experiment showed that forces are equal and opposite.  I am not convinced that it demonstrated that, certainly not as Harriman explains it, and absent the 250 years of physics and algebra since Newton, by which we understand it all now.

Suppose the two magnets are unequal in flux density, one a natural lodestone, large, heavy, and weak; the other a rare earth alloy button.  When they leap to each other on the stick in a tub of water, are they going to meet in the middle?  The floating platform - like the sled - will remain stationary, even though it is not intuitvely obvious that the actions we view are the result of equal and opposite forces. That was what Harriman claimed Newton's demonstration proved.  Harriman was in a hurry.  He says up front that he spent all the money they gave him and had to write the book real fast. 

(Edited by Michael E. Marotta on 2/17, 6:04am)


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Post 25

Thursday, February 17, 2011 - 6:06amSanction this postReply
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PZ Myers agrees with Paul Krugman that Republican willingness to gut science spending while refusing "to touch anything that might cause immediate pain to the electorate" amounts to cooking our seed corn and eating the future.  http://scienceblogs.com/ For February 17, 2011: "Uniting Against the Axe." 
MEM:  Without googling the answer, do you know when it was proved that the Earth goes around the Sun and when it was proved that the Earth rotates about an axis?
ET: No.


If you did not get around to it, the answers are 1838 and 1851. 

(Google "Bessell parallax" and "Foucault pendulum" to find the Wikipedia articles and other presentations.)

So, Newton and the others were right for the wrong reasons, just as were Democritus and Empedocles.

Or so it would seem.  In fact, Harriman's objectivist theory of induction only works in hindsight ... and after a long catalog of empirical experiences provides validity.  

Harriman commits the fallacy of the stolen concept.  How did Galileo, Newton, Dalton, et al, make those logical leaps?  It was not from single and singular observations integrated with everything else they knew.  As he admits and blanks out on, they performed repeated experiments, carefully.  They controlled for variables.  They did all the work of the scientific method, which in retrospect can be called a "flash of insight" just as a millionaire's success seems "lucky" to those who did not live her daily life before she achieved that. 

As for the problem of the black swan, when they were discovered, they were instantly integrated into the class of "swan" -- not called "snaws" or whatever -- and the generalization that all swans are white was abandoned.  This does not invalidate inductive reasoning.  Rather, it shows the power of it.  For a recent example of that, I point to topological conductors, the tellurides (See here.) Every new fact does not invalidate all previous facts.  That is why they are facts.

Also, Ed, I read that essay of yours from five years ago.  Nice work.  I would have made different points differently, but I did not, and you did.  Good job. 

(Edited by Michael E. Marotta on 2/17, 6:38am)


Post 26

Thursday, February 17, 2011 - 7:13amSanction this postReply
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Joe,
On page 21, Harriman (echoing Peikoff) is even more explicit.  He states that "all generalizations ... are statements of causal connection".  This is also Kelley's position, as presented in his lecture on induction in the "Epistemology" series of lectures on tape.

The generalization "all swans are white" is an example of induction by enumeration.  It's based on generalizing from "all observed swans are white" to "all swans are white" and, according to Harriman, it is invalid.  As he states on page 9: "Enumeration is not the method of induction."  Also, "A generalization reached merely from enumeration is necessarily arbitrary."

In order to induce that "all swans are white", it must be known what the underlying mechanism is that explains (a causal explanation) why swans are white.  Dragsdahl, in his lectures on Popper (an excellent set of lectures on the philosophy of science, BTW), gives the example that there may be an evolutionary explanation for why swans are white; perhaps it has to do with reflecting the sunlight and helping to maintain their body temperature.  This would suggest that in other parts of the world, swans evolved with different coloring for different reasons.  This isn't necessarily a correct explanation, just an example of what is needed before a generalization like "all swans are white" can be made.

Mike said:
... the generalization that all swans are white was abandoned.  This does not invalidate inductive reasoning.  Rather, it shows the power of it. ... Every new fact does not invalidate all previous facts.
But "all swans are white" was not a fact, that's why it was abandoned.  You can't just state "all S are P" because all of the Ss you've observed so far are Ps.  Without knowing an underlying cause that explains why "all S are P", it's always logically possible for the next observation to invalidate the generalization, as the critics of induction point out.  Induction is not simple enumeration.

Thanks,
Glenn



Post 27

Thursday, February 17, 2011 - 8:04amSanction this postReply
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Glenn wrote:
The generalization "all swans are white" is an example of induction by enumeration.  It's based on generalizing from "all observed swans are white" to "all swans are white" and, according to Harriman, it is invalid.  As he states on page 9: "Enumeration is not the method of induction."  Also, "A generalization reached merely from enumeration is necessarily arbitrary."
I would not call it invalid, but rather the weakest form of induction and it is not "scientific induction." As a practical matter, we often use it to correctly predict. For example, suppose you travel to a foreign country where you can't read the language and find that every pharmacy you see has the same icon, e.g. a mortar and pestle. Later you want to go to a pharmacy to buy something. So you look for one of those icons and it works. It was not invalid in that case.

In order to induce that "all swans are white", it must be known what the underlying mechanism is that explains (a causal explanation) why swans are white.
Inserting "scientifically" before "induce", yes. This is one of the main points of my article The Problem of Induction.

Marotta wrote:

... the generalization that all swans are white was abandoned.  This does not invalidate inductive reasoning.  Rather, it shows the power of it. ... Every new fact does not invalidate all previous facts.
Maybe what Michael was trying to say is that other features of a black swan could have been correctly predicted from features of white swans.


Post 28

Thursday, February 17, 2011 - 8:16amSanction this postReply
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Mike,

The bulk of our work was to read and criticise academic journal articles.  After the first class, I went to his office and asked if it was reasonable to expect undergraduates to do that level of work.  He replied that it was not that hard.  Indeed, it was not.

Well ... now you have a reason to give me some more grace regarding my criticism of world-changing scientists.

:-)

Since then, I have been a much more careful reader, especially when I already agree with the thesis. 

So, with Harriman, I did not read it like re-reading Anthem

Well ... okay, you say you are on the lookout for confirmation bias. That's a very good thing. I would like to say the same thing about myself, but I wouldn't want to create any unneccessary cognitive dissonance.

:-)

I agree with you that it is very important to claim that you are watching out for this, and it is as or more important to actually be doing it. I'm not saying you're not, I'm just saying we're each saying we are engaged in this personal task of watch-doggery.

As for the sled. If the larger stronger child pushes the smaller childer harder, the little one falls over.  We in our century can write equations of momentum for that and we can point to Newton.  That does not validate Harriman's presentation.  He was attempting to explain how Newton's experiment showed that forces are equal and opposite.  I am not convinced that it demonstrated that ...

In presenting this one experiment (iron and magnet attached to wood, floating in calm water), Harriman wasn't attempting to show or to demonstrate that (all) forces are (always) equal and opposite.

All he was doing was attempting to show how it was that Newton discovered that non-contact forces such as magnetism are equal and opposite. Harriman doesn't claim that this isolated experiment was some kind of 'crucial experiment' -- single-handedly proving Newton's 3rd Law. This was one experiment out of many experiments summarily doing that very thing. Harriman makes this clear on p. 128:

At this point, Newton had shown that his law applies to gravitational forces, magnetic forces, elastic collisions, and inelastic collisions--i.e., he gathered evidence over the range of forces and found no exceptions.

And as to what was needed in order to demonstrate a law of motion by an experiment, Harriman wrote:

p. 126
But once the idea of grouping together all pushes and pulls under the concept "force," and of grouping together all changes in velocity under the concept "acceleration," and of ascribing to all bodies a property called "mass," and of searching for a mathematical relationship among these measured quantities--then a few well-designed experiments can give rise to a law.

p. 129
In their final statement, the laws appear deceptively simple. But we can now appreciate that they are very far from self-evident. In order to reach them, Newton needed complex, high-level concepts that did not exist prior to the seventeenth century, concepts such as "acceleration," "limit," "gravity," "mass," and "momentum." He needed a variety of experiments ...

You continue:
Suppose the two magnets are unequal in flux density, one a natural lodestone, large, heavy, and weak; the other a rare earth alloy button.  When they leap to each other on the stick in a tub of water, are they going to meet in the middle? 

But they don't have to -- indeed, shouldn't -- meet in the middle (if they are of differing masses).

Ed

(Edited by Ed Thompson on 2/17, 9:18am)


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Post 29

Thursday, February 17, 2011 - 9:08amSanction this postReply
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Merlin,
Just a quick point.  The example you gave is a valid induction because the causal explanation is that it was manmade and not metaphysical.  BTW, that was a nice article you wrote. 

A second BTW: Hume also argued that the basis for all induction was causation.  He didn't really argue much against induction (even though he's credited with "The Problem of Induction").  He argued against validation of the law of causality, upon which induction, he claimed, rests.

Thanks,
Glenn

(Edited by Glenn Fletcher on 2/17, 10:18am)


Post 30

Thursday, February 17, 2011 - 10:26amSanction this postReply
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Thanks, Glenn. I assume you gave your position, not Harriman's.

Post 31

Thursday, February 17, 2011 - 11:10amSanction this postReply
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Mike,

If you did not get around to it, the answers are 1838 and 1851. 

(Google "Bessell parallax" and "Foucault pendulum" to find the Wikipedia articles and other presentations.)

So, Newton and the others were right for the wrong reasons, just as were Democritus and Empedocles.

Or so it would seem.  In fact, Harriman's objectivist theory of induction only works in hindsight ... and after a long catalog of empirical experiences provides validity.  
But you miss Harriman's point (p. 143) that discovery is proof.

The 2 cases of proof which you mention (Bessell and Foucault) are better characterized as proof-for-skepticists or proof-for-hard-empiricists -- folks who need to see a direct and immediate connection between one variable and another, with little or no regard for background data accrual or background integration and conceptualization processes. Here is a string of quotes (p. 132-141) illustrating that, rather than explaining how, Newton was right for the right reasons:

p. 132
The sun exerts an attractive force on the planets that varies as the inverse square of the distance.

Just as with the area law, Newton recognized that the law of elliptical orbits is a special case of a more general truth. The geometric properties that Newton had used were not unique to ellipses; they are general properties of conic sections, i.e., they also apply to parabolas and hyperbolas. ...

If the initial conditions are such that the body is captured by the sun's gravitational field, then the orbit will be an ellipse (or a circle). However, if the body's velocity is too great, then it will pass through our solar system in a parabolic or hyperbolic path. Newton presented the details, showing how to calculate the path of a body from any set of initial conditions.
p. 133
For an elliptical orbit, he showed that this relationship between the orbital period and the major radius follows from the nature of the solar force. ...

Here we see yet another example of an astounding connection established by means of mathematics. There is no way to guess that the orbital period is proportional to the three-halves power of the major radius and that it is entirely independent of the minor radius. This fact is implicit in the premises of Newton's argument ...

... the planet exerts an equal and opposite force on the sun, causing it to move in a very small orbit of its own around the center of mass of the two bodies. Newton proved that this effect leads to a slight modification of Kepler's third law; the correction, he showed, depends on the ratio of the planet's mass to the sun's mass. In the case of Jupiter, the most massive planet, the magnitude of this correction is about one part in a thousand.
p. 135
Galileo had discovered four moons orbiting Jupiter, and later Christian Huygens and Gian Cassini had discovered five moons orbiting Saturn. ...

[Newton] showed that for both sets of moons the orbital period squared was precisely proportional to the orbital radius cubed. ...

Jupiter is the most massive of the planets, and at its point of closest approach it exerts a significant pull on Saturn. Newton identified a simple way to improve the model of Saturn's orbit: The focus of the ellipse should be placed at the Sun-Jupiter center of mass, rather than at the sun itself. In this way, Newton reduced the maximum errors in Saturn's angular position to only two minutes arc.
p. 136
The period of the moon's orbit was known very precisely. Since the orbit is nearly circular, Newton could use his law of circular acceleration (as he had years before). However, this time he added a small correction for the attraction of the sun, which slightly decreased (by one part in 179) his estimate of the acceleration caused by Earth. He also estimated the minor effect of the moon's reciprocal pull on the Earth. When he at last arrived at his final answer ... his predicted value for the gravitational acceleration on Earth's surface was 32.2 ft/sec[squared].
p. 137
Years earlier, Huygens had used pendulums to measure this acceleration very accurately. The measured value matched Newton's calculated value: It was 32.2 ft/sec[squared].
p. 138
Starting from the fact that the sun's gravitational acceleration varies as the inverse square of the distance, he showed that the perturbing accelerations caused by the sun vary as the inverse cube. We have already seen that such a force causes the major axis of the orbit to rotate; from the magnitude of the term. Newton was able to explain the three-degree per month rotation in the moon's orbit that had been observed by astronomers. He also explained the variations in the eccentricity of the orbit, the movement of the points at which the moon crosses the plane of the ecliptic, and the annual variations in these anomalies. ...

If the moon were stationary, the time between high tides would be twelve hours; the moon's movement increases this time interval to 12.5 hours. Newton pointed out that the sun also causes ocean tides, but he showed that the sun's effect is less than one-third that of the moon.

He was able to explain all the main features of the tides.
p. 139
Furthermore, he analyzed the reverse tidal effect on the moon caused by the attraction of Earth. This attraction gives rise to bulges of almost a hundred feet on the near and far sides of the moon. Newton pointed out that Earth's pull on thes tidal bulges explains why the same side of the moon always faces Earth. ...

Newton could use his laws of motion and gravitation to calculate the size of equatorial bulge.

Of course, there was no data available regarding variation of mass density within Earth. Newton decided to perform the calculation using a constant density, while explicitly noting that ignorance of this factor caused some uncertainty in the result. He estimated that the equatorial radius exceeded the polar radius by seventeen miles, which is reasonably close to the actual difference of thirteen miles. ...

... it was discovered in the 1670s that pendulum clocks swung more slowly near the equator than in Paris or London. Newton explained that the pendulum bobs move slower at the equator for two reasons: The gravitational force is weaker because they are farther from Earth's center, and their acceleration is further reduced by the centrifugal effect of Earth's rotation.
p. 140
He proved that the mathematical expression for the weight of a terrestrial body contains a small variable term that is proportional to the square of the sine of the latitude, and his analysis accounted for the observed changes in clock rates. ...

Astronomers had discovered that Jupiter's equatorial radius is greater than its polar radius by about one part in thirteen. By observing spots on Jupiter, they knew the rate at which the large planet rotated. Newton calculated its equatorial bulge and his result was close to the measured value. ...

... In addition to the apparent daily rotation, the center of this celestial rotation (i.e., the location of the "north star") also moves slowly around in a small circle. ...

Newton's laws of motion and gravitation explained this effect. The moon and sun attract the mass of Earth's equatorial bulge, causing a torque that moves Earth's spin axis in a cone with an angular radius of twenty-three degrees (equal to the angle between the plane of the equator and that of the ecliptic). The torque is small and therefore the precession is very slow. Newton carefully estimated the gravitational pull on the equatorial bulge and calculated the precession rate. He arrived at a value close to the one measured by astronomers, who had determined that Earth's axis completes one revolution in about twenty-six thousand years.
p. 141
Astronomers had collected accurate data on the movements of a comet that had appeared in 1680 (first observed by Gottfried Kirch). Newton analyzed this data with great care and concluded that the comet moved in an extremely elongated ellipse. Its speed was observed to change rapidly, but always in perfect conformity to Kepler's area law. The orbit is inclined at an angle of sixty-one degrees with the plane of Earth's orbit. The comet approaches the sun very closely every 575 years and its maximum distance from the sun is 138 times greater than the mean Earth-sun distance. One can hardly imagine an orbit that differs more dramatically from planetary orbits, yet Newton proved that the comet is moving in accordance with the same laws.
How you can look at the above and come away from it concluding that Newton was just getting incredibly and repeatedly lucky in accurately "describing appearances" (i.e., being right for wrong reasons) is beyond me. 

Ed


Post 32

Thursday, February 17, 2011 - 3:36pmSanction this postReply
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Glenn, thanks for finding the more explicit quote.  And in general, I take your comments to support my statement that Harriman didn't deal with that particular issue because he defined 'generalization' to avoid those cases.  Maybe he thought it wasn't a real issue and was actually the product of a misunderstanding about the nature of generalizations.  It sounds like you agree with him.  I have a few problems with it, and I don't think he addressed the issue with any kind of strong argument.  He rejected the enumeration method, but didn't show why every generalization must be a causal connection.

Now let me disagree with a few things you said, and maybe you can see why I'm uneasy with such a leap.  First, you suggest that to induce that all swans are white, you need to know what the underlying mechanism is that explains why swans are white.  Maybe genetics.  But doesn't that simply turn it into deduction?  When you understand the underlying mechanism, and apply that information with other specific information like the genetic makeup of the swans, you're deducing the results.  One of the ways in which people try to make induction more "logical" is by converting it into deduction, which seems more inevitable.  It seems like this is an instance of that approach.

Merlin gave an example of induction with the pharmacy.  You said that was okay because it was man-made.  I don't see the distinction, except that you might be able to guess at the underlying mechanism and therefore convert the problem into deduction (premise 1:  symbols can communicate to customers what kind of products are available; premise 2: we want to communicate what kind of products are available; conclusion: we should use a symbol to communicate what kind of products are available).  But what happens when you find out that your generalization was incorrect.  You find out that that particular symbol doesn't mean pharmacy, but means that the store is protected by a particular security firm, and that a lot of pharmacies happen to use it because their product is expensive and desirable.  When you go to a place with that symbol, and find out that it is a jewelry store, your inductive leap will be proven false.  It seems no different from the white swan example.  Until you know what the underlying mechanism is, your generalization is tentative.

I was thinking of a case from the Simpsons.  3-eyed fish outside of the nuclear power plant.  What if we found a bunch of these in real life, right outside of some nuclear or chemical plant.  I think the natural line of thinking would be to ask what caused this kind of mutation.  We wouldn't see it as natural because we have so much experience with fish as having 2 eyes that we would view this as strange.  Now who knows, maybe there are plenty of 3-eyed fish.  I certain have seen no deductive proof based on genetics that fish have to have 2 eyes.  It could be that there are plenty out there...we certainly don't want to enumerate!  So if this kind of generalization is faulty, wouldn't it be faulty to conclude that something is causing this mutation?  Wouldn't it be logical to kick ourselves for accidentally going from some to all?

Causal connections seem like a relatively unique kind of knowledge.  It does seem like you can identify them with just a single instance, although you might need more examples to gain a deeper understanding.  But does it make sense to conclude it is the only form of knowledge?  Sure, it avoids the traditional problem of induction.  But can we fit every square peg into that round hole?  Is this any better than trying to convert induction into deduction?  It's taking a case of logical reasoning that seems relatively strong, and trying to rethink everything else to conform.

Say our caveman ancestors discovered fire.  They learn a few things along the way, such as wood burns, that wet wood doesn't burn as well, the fire will go out when all of the wood is converted to ash, small fires can be blown out by a strong wind, and that enough water puts out a fire.  Some of these are causal processes, like water putting out a fire.  Others are making identifications about a substance, like wood is flammable and that wet wood is less flammable.  But is all wood flammable?  How would they know?  Just because all the wood they found so far has been doesn't mean that it all will be.  And what about wet wood?  Turns out when it is wet with water, it's less flammable, but when soaked in gasoline, it burns pretty well!  Is it really intellectually faulty for them to act as if all wood burns, or that wet wood doesn't?  Sure, it'd be better if they understood the underlying mechanisms for why wood burns, but don't they need to identify the fact that it does burn before they can start looking for the reasons?

I could go on and on.  I don't have a great answer to argue towards.  It just seems like there's still a lot to figure out.  I'm not at all convinced that this approach to induction is thorough.


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Post 33

Friday, February 18, 2011 - 5:38amSanction this postReply
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Merlin said: "I assume you gave your position, not Harriman's."
I'm not sure what that refers to, Merlin.

I thought of a counterexample to your foreigner scenario.  Suppose a man from Poland comes to the USA and doesn't speak any English.  He's told that he will find fellow countrymen at any place called "Polish Home".  So, everywhere he sees "Polish Home" he finds Polish-Americans and he induces the generalization that "All places called 'Polish Home' contain Polish people".  Then one day he goes into a building that has a sign saying "Polish Home" and he finds a bunch of people who want to shine his shoes.  (Alright, I didn't say it was a good counterexample.)
Thanks,
Glenn

P.S.: I just reread Joe's post and his counterexample is much better than mine.

(Edited by Glenn Fletcher on 2/18, 6:29am)


Post 34

Friday, February 18, 2011 - 6:40amSanction this postReply
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Mike,

Suppose you want to discover a way to extend your life.

Your first research question may be "what has ever been shown to be successful in that regard for any life form?" If there are no answers, you make some (by doing relevant experimentation). An entirely different way to go about the issue, though, is to first ask "what admixture of chemicals, metabolic processes, and internal and external environments lead to human aging in the first place?" The first method is the hypothetico-deductive method, the second is "Harriman's objectivist theory of induction."

In the 1990s, it was accidentally thought that a few supplemental DHEA pills might extend your life. The reason folks thought that is because they went with the hypothetico-deductive method. DHEA makes rodents live 20% longer and folks thought it might work for humans. But natural DHEA in rodents is terribly low in the first place. For humans, a boost of DHEA to match the boost noted for rodents (the one which resulted in life extension for the rodents) would be well over 1000-mg a day of DHEA!

Even then, because of our "high" background levels as a start point, we might not get the same results (if we are already well into the "therapeutic range").

Scientists following "Harriman's objectivist theory of induction" would have "pre-recognized" this, and that would be an instance of "Harriman's objectivist theory of induction" working prospectively (rather than only in hindsight). It is a prescription for how best to think about science, not just a description of past thought about science.

Ed


Post 35

Friday, February 18, 2011 - 7:36amSanction this postReply
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Glenn wrote:
Merlin said: "I assume you gave your position, not Harriman's."
I'm not sure what that refers to, Merlin.
I referred to the manmade/metaphysical distinction you made in post 29, which Harriman did not make about enumerative induction on pages 8-9.

By the way, I don't see the distinction as very important to the topic at hand. Regarding my pharmacy example, it wasn't necessary that all had the same icon.

I thought of a counterexample to your foreigner scenario.  Suppose a man from Poland comes to the USA ....
I knew counterexamples could be made. Indeed, the person in my example may have overlooked a pharmacy without the icon or with a different icon. My example was against Harriman's too strong criticisms of enumerative induction in the first paragraph of page 9.

(Edited by Merlin Jetton on 2/18, 7:46am)


Post 36

Friday, February 18, 2011 - 8:19amSanction this postReply
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Merlin,
Harriman's criticism of enumerative induction is weak compared to Peikoff's.  In his "Induction" lectures he uses the phrase, which his wife created, "swine with the swans".  That applies to anyone who thinks that enumeration has anything to do with induction as a means of inferring true generalizations.

Joe,
I'll address your questions a little later.  For now, let me quote David Kelley, from his "Induction" lecture, on the relation between induction and causality:
Whenever we draw an inference that "All S are P" based on a sample, we are relying on the assumption that S and P are connected, and that connection, in one way or another, is a causal connection.
Thanks,
Glenn


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Post 37

Sunday, February 20, 2011 - 8:42amSanction this postReply
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Hi, Joe.
Let me address a couple of the questions you raised in Post #32.  You said:

Causal connections seem like a relatively unique kind of knowledge.  It does seem like you can identify them with just a single instance, although you might need more examples to gain a deeper understanding.  But does it make sense to conclude it is the only form of knowledge?



 

On page 6, Harriman states that Induction is the primary process of gaining knowledge that goes beyond perceptual data.  [Italics added.]  Now, there are two different meanings of the term induction that I think Harriman ignores.  Some use induction to mean any inference that isnt deduction.  That includes inferences other than generalizations from some to all; it includes, for example, inference to the best explanation (abduction).  In this usage, there are only induction and deduction.  Others, including Harriman, use induction only to mean generalizing from some to all.  However, on p. 8, Harriman says: Inducing and deducing are mans means of justifying anything.  Unless he means inducing in the broader sense, this isnt true.

You continued:

Say our caveman ancestors discovered fire.  They learn a few things along the way, such as wood burns, that wet wood doesn't burn as well, the fire will go out when all of the wood is converted to ash, small fires can be blown out by a strong wind, and that enough water puts out a fire. Is it really intellectually faulty for them to act as if all wood burns, or that wet wood doesn't?  Sure, it'd be better if they understood the underlying mechanisms for why wood burns, but don't they need to identify the fact that it does burn before they can start looking for the reasons?


 

This is my understanding of Peikoff/Harriman: When the cavemen identify the fact that wood burns, they are making a first-level generalization.  By using the concepts wood and fire, which are first-level concepts, when they say that fire makes wood burn they are conceptualizing the causal connection they have observed.  And this generalization is self-evident.  They dont need to know what the underlying cause is for a first-level generalization; its perceptual.  In order to validate higher-order generalizations based on this, they have to find causal connections with lower-level generalizations until they reach the first-level generalization fire makes wood burn.  That is, they have to reduce a higher-level generalization down to a first-level generalization, which is self-evident.

If they then find that wet wood doesnt burn, that doesnt invalidate their first-level generalization.  An additional factor has been added that wasnt included in their original first-level generalization.  This is like Peikoffs example of the blood types.  The existence of the Rh factor didnt change the fact that type A blood was compatible with type A blood.  Likewise, the statement that fire makes wood burn is still true, even though wet wood doesnt burn.  The same holds for all of the other facts that they learn about wood burning.  This is an example of the requirement of a preamble that Rand talks about on page 296 of ITOE: Within my present context, omitting elements of which I have no knowledge at present, .

You also asked:

But doesn't that simply turn it into deduction?


 

The first-level generalization is perceived.  Higher-level generalizations are reduced to these by showing causal connections.  It's exactly analogous to reducing higher-level concepts to first-level concepts (of which first-level generalizations must consist).  I'm not sure I would call that deduction.

I'm still trying to understand the Peikoff/Harriman model of induction, so I may have misrepresented their view above.  But, the underlying idea is the fact that all inductive generalizations must be based on causal relations.  Here's a quote from Harriman, p. 21, that sums it up:

The only justification for inferring the future from the actions of the past is the fact that the past actions occurred not arbitrarily or miraculously, but for a reason, a reason inherent in the nature of the acting entities themselves; i.e., the justification is that the past actions were effects of causes -- and thus if the same cause is operative tomorrow, it will result in the same effect.


 

I should add that Rand does talk briefly about induction in the Q&A of ITOE, pages 295-301.  When asked how a person can determine that all water boils at the same temperature, or whether that temperature is specific to the particular sample, she says:

By whether you can or cannot establish a causal connection between what you have determined to be the essential characteristic of water and the fact that it boils at a certain temperature.


Thanks,

Glenn













Post 38

Sunday, February 20, 2011 - 3:49pmSanction this postReply
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Hi Glenn, I appreciate your efforts.  Let me try to comment.

First, I'm okay with using induction in the very broad sense, at long as it's interpreted as gaining knowledge from experience/reality, and isn't used as a way of defining away issues.

Now take the fire and wood case.  You point out that it is a first-level "generalization" (scare quotes because I don't know that I'm willing to accept the terminology) that they are conceptualizing the causal connection, and that it is self-evident.  Let's assume that the causal relationship itself is actually self-evident.  They see the fire burning the wood, and they recognize the cause and effect relationship.  Even if that is self-evident, that doesn't make the conceptualization automatic or self-evident.  I think it's like seeing that a swan is white.  The recognition of that fact may be self-evident (or as close to it as recognizing that the fire is burning the wood), but there's no automatic step to generalize it to say that all swans are white.  We only know that this swan is white.  And with the fire and wood, we only know that this fire burns this wood. 

How do we justify taking the next step and say that fire in general burns wood in general?  We could see many cases of it happening.  But that's enumeration.  We could understand the atomic nature of matter and show how the chemical reaction is necessitated by the elements involved and the kinetic energy, but that's deduction.  We could see how fire interacts with other things, and by comparison determine that it's the material that's flammable or not (we'd also learn other things like wet material doesn't burn).  So I think we could identify the fact that what fire burns is dependent on what something is made of.  But we still have the problem of saying that wood is flammable in general,or that all fire can burn wood.

What do we know?  We've identify a particular causal mechanism, that fire burns some stuff.  But that's not much of a generalization at all.  At first, we're really only identifying that this particular log is burned by this particular fire.  Generalizing from there still has all of the typical problems, doesn't it?

It doesn't seem to me that you can escape the need to generalize attributes.  Identifying causal connections is useful, but at the end of the day, when we go to collect firewood, we have to have concluded that wood in general burns.

So my point was that you can identify causal relationships, but you still seem to have the problem of generalizing that the "problem of induction" describes.  Maybe you can generalize the causal relationship by recognizing that it  is a product of identity, and so whenever you get the right kind of fire and the right kind of wood, it will burn.  You've identified a relationship, and you can recognize that the relationship is not unique, but applies whenever the context is right.  But that's not terribly useful unless you can generalize when the context is right.  As I said, it seems like he avoided this typical issue.

You mentioned the Rh factor, and Rand's disclaimer: Within my present context, omitting elements of which I have no knowledge at present, .

Both of those seem to deal with the "problem of induction".  We see that this fire burns this wood, and we generalize to fire in general burns wood in general.  If we find new information or factors, we narrow our statement or add sufficient context.  One could say that there's no necessary problem with going from some to all.

Of course, that doesn't mean enumeration is a proper method of induction.  We don't have to say that we saw fire burn wood 12 times, so we generalize.  We can get a plethora of information and figure out that fire burns lots of things under the right conditions, and stuff we categorize as wood seems to be one of them.  We can recognize that the material of the object seems to determine whether it'll burn (instead of the shape or color or something else).  And we might draw the conclusion that all trees/wood are made of approximately the same material because they look the same, grow the same, and burn the same.  So we have reasons to believe that we can generalize from some to all, while still admitting that there is the possibility of exceptions or mistakes.

Similarly, the pharmacy example is somewhere where we can generalize based on a variety of evidence.  It's a man-made symbol, designed to communicate something.  You see them in pharmacies so far.  You don't see them in other stores so far.  You formulate a hypothesis that explains the evidence, and the hypothesis, if true, suggests you can generalize to all pharmacies in that country.  You might still be wrong, but who says induction guarantees correct results?

Anyway, I agree with much of what you say Glenn.  I just think there is a different kind of generalization than Harriman focuses on, and by talking about generalizations as if they only apply to causal relationships, it seems like he's defined the problem away.


Post 39

Friday, February 25, 2011 - 7:44amSanction this postReply
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Hi, Joe.

Sorry about the delay, but Ive been busy, but also Ive had to think more about this.  Im still trying to understand it and your questions have helped to clarify it for me. 

You said:

Let's assume that the causal relationship itself is actually self-evident.  They see the fire burning the wood, and they recognize the cause and effect relationship.  Even if that is self-evident, that doesn't make the conceptualization automatic or self-evident.  I think it's like seeing that a swan is white. 

If you recognize the cause and effect relationship, and you formulate it in conceptual terms, then, according to Peikoff, you have formed a generalization.  If a primitive person saw fire burning wood, and he had the concepts of fire, burning, and wood, then if he expressed the proposition fire burns wood, based on his observation, he would be stating a true generalization.  He had perceived the causal connection and, as Peikoff puts it in his lectures on Induction, in the act of naming what he perceives, [the inducer] automatically drops the measurements of the perceived cause and effect and gains knowledge transcending the given concrete.  A generalization is the conceptualization of the percept of cause and effect.

Suppose he later learns that fire burns wood only in certain circumstances.  For example, if the wood is wet, it wont burn.  His original generalization is still true.  It has to be because, in order to grasp that fire burns wood in certain circumstances, he had to grasp that fire burns wood.  Knowledge is contextual and hierarchical.  Initially he knew that fire burns wood.  Later he learned that there could be other factors that could affect fire burning wood.  If he integrates this knowledge with what he knows, eventually he may be able to justify the generalization fire doesnt burn wood when its wet (after all, maybe wet wood does burn if the fire is hot enough) by reducing it to first-level generalizations. 

This differs from the all swans are white example because, in that case, we have no causal explanation for the color of the swans.  We dont observe any causal connection between the color white and being a swan, so we have no justification for the generalization.  It isn't a first-level generalization, so to justify it you need to be able to reduce it to first-level generalizations.

Another example that Peikoff gives is: without some kind of causal explanation for the phenomenon of the sun rising in the morning, you cant know that the generalization is true.  So, Hume was right in the sense that just having seen the sun rise every morning for your whole life (simple enumeration) is not evidence for the fact that it will rise tomorrow morning.  Unless you have a causal explanation (from Kepler, Newton, Einstein, whatever), you cant know that the sun will rise tomorrow.

Thanks,

Glenn







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