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.

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.

... 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.

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.  

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.

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.

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.

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].

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].

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.

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.

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.

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.

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 ....

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 isn’t 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 man’s means of justifying anything.”  Unless he means inducing in the broader sense, this isn’t 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 don’t need to know what the underlying cause is for a first-level generalization; it’s 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 doesn’t burn, that doesn’t invalidate their first-level generalization.  An additional factor has been added that wasn’t included in their original first-level generalization.  This is like Peikoff’s example of the blood types.  The existence of the Rh factor didn’t 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 doesn’t 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

Hi, Joe.

Sorry about the delay, but I’ve been busy, but also I’ve had to think more about this.  I’m 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 won’t 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 doesn’t burn wood when it’s 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 don’t 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 can’t 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 can’t “know” that the sun will rise tomorrow.

Thanks,

Glenn