RoR: Forum

Excellent commentary, Merlin.

You gave quite a comprehensive background on the subject, and accomplished the important and useful task of denigrating "enumerative induction" at the outset (so that the actual subject of induction is made unambiguous).

Bravo.

Ed

Post 1

Friday, December 3, 2010 - 1:17pm

Thanks, Ed.

I didn't intend to "denigrate" enumerative induction -- I have used it often successfully. However, I did intend to be critical of anyone who would say all induction is merely enumerative induction.

Post 2

Monday, December 6, 2010 - 5:32pm

Nicely done, Merlin.

Ed, there is nothing wrong with enumerative induction. The error is in extending it beyond reason.

All swans are white was valid until the discovery of black swans -- but black swans were recognized immediately as swans, not some other animal. The number of cases was enlarged.

The sun has always came up in the east. We don't know why. That it will do so tomorrow is an enumerative induction. If it rises in the north, we then have to include that, perhaps make a different generalization. If it starts rising all over the place with no apparent rhythm, then we might wonder what suddenly changed in a reallly big way. (I believe that geological catastrophes are the origin of religion.) But consider that Stonehenge was built on that enumerative induction. The Antikythera Device (specifically) and the astrolabe (generally) worked for an Earth-centered solar system. Enumerative induction has some value.

As noted, deductive logic rests on truths that were inductively discovered. Deductive logic has its limits. All elephants are tie scores. Ed is an elephant. Therefore, Ed is a tie score. But deductive logic has its place, of course.

Objectivism (with or without the capital-O) is rational-empiricism and both sides of that equation are required. Truth is rational and empirical, logical and evidentiary, analytic and synthetic, theoretical and experimental, ideal and practical, deductive and inductive, and even imaginary and experiential. If you have one side without the other � for instance an ideal political system never put into practice � then you do not have truth.

(Edited by Michael E. Marotta on 12/06, 5:58pm)

Post 3

Monday, December 6, 2010 - 7:46pm

Thank you, Michael.

The sun has always came up in the east. We don't know why. That it will do so tomorrow is an enumerative induction.

There is a reason why the sun appears to the east. Earth spins counterclockwise (viewed from above the north pole) around its own axis daily. See here for a visual. Hence, it is something more than enumerative induction.

On the other hand, if you mean we don't know why the earth spins counterclockwise around its own axis, you are probably correct.

(Edited by Merlin Jetton on 12/06, 7:49pm)

Post 4

Tuesday, December 7, 2010 - 5:03am

MEM: The sun has always came up in the east. We don't know why. That it will do so tomorrow is an enumerative induction.
MJ: There is a reason why the sun appears to the east. Earth spins counterclockwise (viewed from above the north pole) around its own axis daily. See here for a visual. Hence, it is something more than enumerative induction.

Well, yes, we know that now. I was referring to the ancients, which is why I mentioned Stonehenge, the Antikythera and astrolabes.

On that point, however, as clever as Newton was, the assumption that the Earth spins as it revolves about the Sun was still only that, a simplifying assumption. Empirical evidence did not come for over 100 years.

The Earth's rotation was not proved until 1851. On the Foucault Pendulum, Wikipedia is an easy citation, but see here, among many similar.

... the Earth rotates on its axis in 23 hours 56 minutes and 4.1 seconds with respect to the rest of the universe. From our perspective here on Earth, it appears that the entire universe circles us in this time. It is possible to do some rather simple experiments that demonstrate that it is really the rotation of the Earth that makes this daily motion occur.
http://www.astro.louisville.edu/foucault/index.html

The operating Foucault pendulum in the foyer of the McNaughton building is both a work of art and an enchanting mechanical device. That it illustrates the rotation
of the earth is described on the dedication plaque on the pillar supporting the pendulum.
http://www.physics.uoguelph.ca/foucault/F1.html

As for orbiting the Sun, Archimedes tried to measure parallax and failing, he said that either the Earth is the center of the universe, or else the universe is unimaginably large. So, he took the simpler answer and put the Earth at the center. It was not ignorance or superstition; it was empirical science. Stellar parallax was not shown until 1838. Read Bessel's original paper here: http://www.ari.uni-heidelberg.de/gaia/documents/bessel-1838/index.html

Be all that as it may, nice bit of work on induction. You ought to publish, certainly in an Objectivist magazine or journal.

Post 5

Tuesday, December 7, 2010 - 5:37am

The Earth's rotation was not proved until 1851.� On the Foucault Pendulum, Wikipedia is an easy citation, but see here, among many similar.

Thank you for the links (and compliment). There is also a Foucault Pendulum at Fermilab, which is only about 20 miles from where I live (video).

(Edited by Merlin Jetton on 12/07, 5:49am)

Post 6

Tuesday, December 7, 2010 - 8:18am

Mike,

Ed, there is nothing wrong with enumerative induction. The error is in extending it beyond reason.

I agree with you that there is nothing wrong with enumerative induction, in-and-of-itself. As you said, the error is in extending it beyond reason. The problem I have with it is that it would seem that most (>50%) people -- certainly everyone I've ever known -- most people use it beyond reason. Recall the line in The Logical Leap which says it can't establish anything.

Admittedly, I just used enumerative induction in order to disqualify it as something that is used reasonably. I simply reduced to counting. Mentally, I divided a piece of paper and on one side, I listed all the reasonable uses from my memory (zero); and on the other side of the ledger, I listed all the unreasonable uses (e.g., instances in college, where instructors told me induction was fallible, etc).

In the same vein, there is nothing, in-and-of-itself, wrong with a screwdriver -- but a whole lot of hell could break loose if most (>50%) all people using a screwdriver were using it as a hammer. That is the situation with enumerative induction. It is not meant to be used in the way that (most?) folks use it.

Ed

Post 7

Tuesday, December 7, 2010 - 1:30pm

Mike said:
"On that point, however, as clever as Newton was, the assumption that the Earth spins as it revolves about the Sun was still only that, a simplifying assumption. Empirical evidence did not come for over 100 years."
In order for the sun to "go around the Earth" every 24 hours when the Earth revolves around the sun every 365 days, wouldn't the Earth have to rotate on its axis?

Post 8

Wednesday, December 8, 2010 - 4:40am

Nice job, there, professor! People here accuse me of reading unintended meanings into plain statements. Let's try this and see if even I can accept it at face value:

Even after Copernicus, Galileo, and Newton, the two clams that (1) the Earth spins on its axis and (2) revolves in orbit about the Sun were only simplyfing assumptions. Empirical evidence for the first came in 1851, 13 years after the second was demonstrated (1838).

General education at the PBS Nova and Discovery Channel level as delivered in high schools and colleges assert that Galileo's discovery of the moons of Jupiter provided a model for the Copernican heliocentric system. However, that is not necessarily true. A modified geocentric model put Mercury and Venus in orbit around the Sun, which in turn orbited the Earth. Tycho Brahe put all of the other planets in orbit around the Sun and that complete set then in orbit around the Earth. Only in 1785 did William Herschel's map of the Galaxy placed the Sun near -- not at -- the center of the known universe. Models are nice, but measurement is better.

Edited after Merlin's post to clarify Herschel's work.

(Edited by Michael E. Marotta on 12/08, 5:00am)

Post 9

Wednesday, December 8, 2010 - 4:50am

It doesn't explain here (5th paragraph) why Aristarchus thought the earth rotated on its axis daily, but maybe he was thinking like Glenn. I bet he had the direction of spin right, too.
(Edited by Merlin Jetton on 12/08, 4:52am)

Post 10

Thursday, December 9, 2010 - 10:55am

Wikipedia formalizes the Method of Agreement as follows:

Symbolically, the method of agreement can be represented as:
A B C D occur together with w x y z
A E F G occur together with w t u v
��
Therefore A is the cause, the effect, or part of the cause of w. (link)

I like John Stuart Mill�s notation better. On page 278 of A System of Logic, Mill writes:

We shall denote antecedents by the large letters of the alphabet, and the consequents corresponding to them by the small. Let A, then, be an agent or cause, and let the object of our inquiry be to ascertain what are the effects of this cause. If we can either find, or produce, the agent A in such varieties of circumstances that the different cases have no circumstance in common except A; then whatever effect we find to be produced in all our trials, is indicated as the effect of A. Suppose, for example, that A is tried along with B and C, and that the effect is a b c; and suppose that A is next tried with D and E, but without B and C, and that the effect is a d e. Then we may reason thus: b and c are not effects of A, for they were not produced by it in the second experiment; nor are d and e, for they were not produced in the first. Whatever is really the effect of A must have been produced in both instances; now this condition is fulfilled by no circumstance expect a. The phenomenon a can not have been the effect of B or C, since it was produced where they were not; nor of D or E, since it was produced where they were not. Therefore it is the effect of A. (link, then click on "pages" or scroll down)

So using Mill�s notation Wikipedia�s representation can be rewritten and extended as:

A B C D occur together with a b c d

A E F G occur together with a e f g

A H J K occur together with a h j k

etc.

��

Therefore A is the cause, the effect, or part of the cause of a.

Thus the Method of Agreement differs from enumerative induction in that the former is concerned with �why� and the variety of instances. Enumerative induction is a very impoverished version of the Method of Agreement.

(Edited by Merlin Jetton on 12/09, 11:14am)

Post 11

Friday, December 10, 2010 - 2:20pm

There is more mathematical detail about Aristarchus's estimates of the sizes of the moon and sun and distances to the moon and sun here than given in The Logical Leap.

(Edited by Merlin Jetton on 12/10, 2:22pm)

Post 12

Saturday, December 11, 2010 - 5:48pm

Thanks, Merlin. My reference has been A History of Astronomy from Thales to Kepler by J. L. E. Dreyer, a Dover reprint (1953) of a 1906 work. However nice the narrative, it lacks the illustrations you provided via Wikipedia. I am not sure if it was John Paleologos, but one of the Eastern Romaion emperors made a gift of Greek manuscripts, either to the officials at Venice or to the Vatican Library. The lapse of Greek learning in the West by 800 AD is a special problem in classical history. It always continued in some way, but as tendrils only. Petrarch and Dante are credited with creating the Renaissance by searching monestaries for ancient manuscripts. It is said that when Petrarch found a copy of the Iliad, he cried because he knew what he had but could not read it.

The manuscript page from WikiCommons is obviously in medieval Greek script.

One of the problems I had with The Logical Leap was Harriman's use of the unnamed collective "the Greeks." Clearly, not all "Greeks" believed the same things at the same time. (I put "Greeks" in quotes as a nod to Isocrates who said about 330 BCE that the name of Hellene no longer belonged to a race but to a state of mind.)

Post 13

Sunday, May 22, 2011 - 8:14am

More on types of induction:

SB�1991

John McCaskey�2006
Francis Bacon and Aristotle

Post 14

Sunday, May 22, 2011 - 9:13am

re - Foucault Pendulum - there is one at the Physics Department at the University of Wisconsin [or was when I last was there 50 years ago]....

Post 15

Sunday, January 20, 2013 - 9:00am

Check out this quote from Stephen's link to John McCaskey's 400-plus page dissertation on induction:

p. 362

Bacon held that a property and its formal causes are one and the same thing. What is caused is not something else, but the very property itself. As Bacon stressed, heat is not produced by a certain kind of motion; heat is that kind of motion and that kind of motion is heat. By the new thinking, on the other hand, a cause and what is caused are two separate things, a cause and its effect. Causes came to be compared to the motions inside a clock. A clock could be made of several different materials (it could have different material causes) and have any of several mechanisms (it could have different efficient causes) yet still display the same time. If all we see is the clock's face, we cannot know the material and efficient causes of the hands' motion.

That sounds a lot like "existence is identity" to me.

Ed

Post 16

Sunday, June 16, 2013 - 7:28am

This is a very good essay and I'd like to share some of my thoughts on this:

"It seems evident that, if all the scenes of nature were continually shifted in such a manner that no two events bore any resemblance to each other, but every object was entirely new, without any similitude to whatever had been seen before, we should never, in that case, have attained the least idea of necessity, or of a connexion among these objects. We might say, upon such a supposition, that one object or event has followed another; not that one was produced by the other. The relation of cause and effect must be utterly unknown to mankind. Inference and reasoning concerning the operations of nature would, from that moment, be at an end; and the memory and senses remain the only canals, by which the knowledge of any real existence could possibly have access to the mind. Our idea, therefore, of necessity and causation arises entirely from the uniformity observable in the operations of nature, where similar objects are constantly conjoined together, and the mind is determined by custom to infer the one from the appearance of the other. These two circumstances form the whole of that necessity, which we ascribe to matter. Beyond the constant conjunction of similar objects, and the consequent inference from one to the other, we have no notion of any necessity or connexion.

If it appear, therefore, that all mankind have ever allowed, without any doubt or hesitation, that these two circumstances take place in the voluntary actions of men, and in the operations of mind; it must follow, that all mankind have ever agreed in the doctrine of necessity, and that they have hitherto disputed, merely for not understanding each other."

Enquiry Concerning Human Understanding, Section VIII Of Liberty and Necessity Part I

"When we have lived any time, and have been accustomed to the uniformity of nature, we acquire a general habit, by which we always transfer the known to the unknown, and conceive the latter to resemble the former. By means of this general habitual principle, we regard even one experiment as the foundation of reasoning, and expect a similar event with some degree of certainty, where the experiment has been made accurately, and free from all foreign circumstances."

David Hume, Section IX Of the Reason of Animals

For Hume, "uniformity of nature" is about perceived regularities. We notice a resemblance (pattern recognition) and we arbitrarily imagine the pattern will continue. Now if you notice an effect and a factor go together, that constitutes ground for further investigation. Maybe there's something to it. There is nothing arbitrary with gaining *inspiration* from a regularity

But the fact that one can link an effect with any factor that just happens to coincide is no basis for generalization. If one insisted that it was a generalization, it would be flat-out guessing. It would violate hierarchy; concepts aren't formed that way. It would drop context; we do other things besides recognize patterns. It would fail to provide unity; a single association by itself does not connect anything else besides the factor and the effect. Such a habit would be, in short, non-objective.

The elevation of regularity to a metaphysical law is a demand that every perceived regularity continue for no better reason than past correspondence, regardless of anything else we know, regardless of the rigorous demands of logic. It is a demand that nature fit some random association we made -- as a contextless absolute. That is a demand for omniscience.
(Edited by Michael Philip on 6/16, 7:42am)

Post 17

Sunday, June 16, 2013 - 8:47am

Thank you, Michael Philip.
(Edited by Merlin Jetton on 6/16, 8:47am)

Post 18

Sunday, June 16, 2013 - 10:16am

Good thoughts, Michael.

The only issue I have with what you wrote is with this phrase:

The elevation of regularity to a metaphysical law ...

There are a couple ways to take such a phrase, and you seem to be taking it in the right way -- where perceived regularity is reified into real law, as a na�ve realist would have it. But there is also a wrong way to take it. As Wallace Matson said in his 1984 proof of the validity of induction (in The Philosophic Thought of Ayn Rand; edited by DJ Den Uyl and DB Rasmussen), the former induction problem had stemmed from not taking the proposition:

"The course of nature will continue uniformly the same."

... as a necessary truth, even after the marriage of logic and experience calls on you to take it as a necessary truth (e.g., when the contradiction of a generalization can be shown to be physically impossible).

For instance, if I generalize from logic, applied to the empirical experience of rolling 2 normal dice, that you will not ever roll a "13" with 2 normal dice -- because it is physically impossible to do so -- then I have accepted it as necessarily true that the course of nature will continue uniformly the same. In this context, the nature is the nature of the dice acting in a certain manner whenever rolled -- and always acting in the same manner in the future, come hell or high water.

In performing such a valid generalization (to future dice rolls), it might be said that I elevated regularity up to the status of a metaphysical law.

:-)

Just because you can retroactively deduce a generalization from the previously-discovered nature of something -- does not mean that you didn't arrive at your initial generalization inductively. Induction isn't a process that is completely-free of all deduction, so that the very hint of a deduction tarnishes an induction -- just like deduction isn't a process that is completely-free of all induction. It has to do with a growing sphere of a priori knowledge.

Ed

(Edited by Ed Thompson on 6/16, 10:24am)

Post 19

Sunday, July 14, 2013 - 10:12am