Tom Rexton

problem of induction

23 posts in this topic

In my human event class we are reading and discussing (for the whole semester) over the works of modern philosophers and writers--that is from the beginning of the Scientific Revolution to the end of the 19th century. Today we discussed in class the writings and ideas of Galileo and Bacon, and next week, Descarte and Pascal, and so fort. Inevitably the problem of induction came up, and nearly everyone, even my professor, accepted the common view that an inductive generalization can only be "not false"--it cannot be "true"--and it does so by passing tests that subject it to potential falsification (experimentation). My professor said to the effect that we can never be absolutely certain of an inductive generalization--only that it has not yet been falsified, but it is always potentially false. I of course did not believe this, but I couldn't figure out a way to introduce my ideas without seeming like I'm directly arguing against the professor, or arguing for a valid method of induction without directing the class discussion away from the particular writings of Galileo and Bacon.

The problem of induction is one I've been thinking deeply about recently, especially since encountering this misconception of induction from two of my professors (the other was my economics professor, who discussed theory-formation via induction). Can any of you direct me to good works (not necessarily Objectivist) concerning the philosophy of science and the problem of induction in particular? (BTW, I am aware of Dr. Peikoff's lecture Induction in Physics and Philosophy, but given its $210 price and my financial situation, it will have to way a while. )

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----------------

Inevitably the problem of induction came up, and nearly everyone, even my professor, accepted the common view that an inductive generalization can only be "not false"--it cannot be "true"--and it does so by passing tests that subject it to potential falsification (experimentation).  My professor said to the effect that we can never be absolutely certain of an inductive generalization--only that it has not yet been falsified, but it is always potentially false.  I of course did not believe this, but I couldn't figure out a way to introduce my ideas without seeming like I'm directly arguing against the professor, or arguing for a valid method of induction without directing the class discussion away from the particular writings of Galileo and Bacon.

-----------

I believe the origin of this theory can be traced to Science as Falsification. Free dinner if you can figure out his mistake.

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My professor said to the effect that we can never be absolutely certain of an inductive generalization--only that it has not yet been falsified, but it is always potentially false.... Can any of you direct me to good works (not necessarily Objectivist) concerning the philosophy of science and the problem of induction in particular?

Since there does not exist a formally correct theory of induction, I assume by "good works" you mean those that highlight the problem and give insight into how it arose in philosophy of science, from an historical perspective. There is nothing like reading the original works on your own, but this can be very time consuming. I briefly discussed Popper and falsification in this post . Read Popper's Conjectures and Knowledge: The Growth of Scientific Knowledge, Routledge, 1963/2002, and The Logic of Scientific Discovery, Routledge, 1959/1992 if you want to see firsthand a major philosophic corruption of the philosophy of physics in general, and induction in particular. However, these books together represent about 1100 pages, much fairly dense, so here are a couple of alternatives.

In the post referenced above I singled out David Stove for his analysis of the four famous irrationalists -- Popper, Lakatos, Kuhn, and Feyerabend. Stove is always much more insightful in identifying what is wrong than in offerring what is right, but with that understanding his analyses are always of value. Stove authored a small but very interesting book that you will find quite helpful: The Rationality of Induction, Clarendon Press - Oxford, 1986. It is short, only some 200 pages, and it has some very nice references.

Another book you will enjoy (not completely directly related to your inquiry here, but somewhat related, and based on your interests expressed in prior posts) is G. Polya's Patterns of Plausible Inference: Vol. II of Mathematics and Plausible Reasoning, Princeton University Press, 1954. Though the context here is mathematics instead of science in general, I think you will find this of value.

And, if you want to see the earlier seeds of corruption, it was in the early 20th century that Hans Reichenbach, in his Experience and Prediction and The Rise of Scientific Philosophy, made the case that all knowledge, by its nature, was probabilistic:

"The causal structure of the physical world is replaced by a probability structure, and the understanding of the physical world presupposes the elaboration of a theory of probability." (The Rise of Scientific Philosophy, University of California Press, p. 164, 1951.

Reichenbach thought of induction as the process of finding a series of events with frequency converging to a limit, but for which any sense of surety may be surpassed by a process; for instance, clairvoyance, which might better suit future predictions. So the usual inductive process is, for now, the best we have considering that knowledge has a probabilistic base, which is why induction will never lead to truth (according to Reichenbach).

But Karl Popper still remains the most devasting influence.

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I couldn't figure out a way to introduce my ideas without seeming like I'm directly arguing against the professor, or arguing for a valid method of induction without directing the class discussion away from the particular writings of Galileo and Bacon.

Last summer John McCaskey gave lectures on Bacon and they are available as cassettes or CDs from the Ayn Rand Book Store.

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I of course did not believe this, but I couldn't figure out a way to introduce my ideas without seeming like I'm directly arguing against the professor, or arguing for a valid method of induction without directing the class discussion away from the particular writings of Galileo and Bacon.

It seems from your description that it is your professor who is directing the class away from the writings of Galileo and Bacon. Bacon, at least, explicitly argues against the notion of induction that you describe. The old induction, he says, leaps to generalizations based on the mere absence of a contradictory instance. He offers a new sort of induction, and I suggest that Galileo illustrates the success of the new induction in practice. I suggest a closer consideration of the work of Bacon and Galileo.

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This following lecture course was given at a conference a few summers ago. At $76.95 for the CDs or $63.95 for the cassettes, it may be nearly as inaccessible as Dr. Peikoff's Induction lectures, but it's something to know about. The following is the description offered by the Ayn Rand Bookstore.

Karl Popper's Assault on Science by Bo Dragsdahl

Karl Popper was a minor philosopher, but a major transmitter of Kantian skepticism into the culture. Posing as an exponent of scientific method, he promoted a philosophy whose key tenets are that induction is a myth, that scientific theories are at root arbitrary constructs and that the absence of falsification—rather than positive evidence—is the standard for adopting scientific conclusions. These ideas have inspired an onslaught on science in today's academia, with philosophers claiming that scientific facts are products of the social interaction among scientists and that scientific knowledge represents a Western prejudice. In this course Bo Dragsdahl covers Popper's basic ideas and identifies their roots in Kant.

It lasts five hours and 36 minutes including Q&A.

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Since there does not exist a formally correct theory of induction, I assume by "good works" you mean those that highlight the problem and give insight into how it arose in philosophy of science, from an historical perspective.  There is nothing like reading the original works on your own, but this can be very time consuming. I briefly discussed Popper and falsification in this post . Read Popper's Conjectures and Knowledge: The Growth of Scientific Knowledge, Routledge, 1963/2002, and The Logic of Scientific Discovery, Routledge, 1959/1992 if you want to see firsthand a major philosophic corruption of the philosophy of physics in general, and induction in particular. However, these books together represent about 1100 pages, much fairly dense, so here are a couple of alternatives.

In the post referenced above I singled out David Stove for his analysis of the four famous irrationalists -- Popper, Lakatos, Kuhn, and Feyerabend. Stove is always much more insightful in identifying what is wrong than in offerring what is right, but with that understanding his analyses are always of value. Stove authored a small but very interesting book that you will find quite helpful: The Rationality of Induction, Clarendon Press - Oxford, 1986. It is short, only some 200 pages, and it has some very nice references.

Another book you will enjoy ... is G. Polya's Patterns of Plausible Inference: Vol. II of Mathematics and Plausible Reasoning, Princeton University Press, 1954. ...

And, if you want to see the earlier seeds of corruption, it was in the early 20th century that Hans Reichenbach, in his Experience and Prediction and The Rise of Scientific Philosophy, made the case that all knowledge, by its nature, was probabilistic:

[...]

But Karl Popper still remains the most devasting influence.

Thank you for the suggestions, I appreciate it. :o I've read the first four pages of G. Polya's book from the excerpts available at amazon.com and I'm already "hooked", so to speak. As for Karl Popper and Reichenbach's books, I might find time this summer to read them both, but I'll definitely get G. Polya and David Stove's books from the university libraries this weekend.

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Thank you for the suggestions, I appreciate it.  :o

You're welcome. Two other choices (among thousands) come to mind.

There is the three-volume set by Jefferson Hane Weaver, The World of Physics: A Small Library of the Literature of Physics from Antiquity to the Present, Simon and Schuster, 1987. These volumes contain excerpts from some of the most important and most interesting writings in physics throughout the ages. A marvelous collection, punctuated by Weaver's sometimes insightful comments. The set is, unfortunately, out of print, but readily available on the used book market.

While Weaver's little library of firsthand writings takes some time to consume, a nice quick overview can be found in John Losee's A Historical Introduction to the Philosophy of Science, Oxford University Press, 1972/1992. Like Stove's book on induction this too is quite short, and it is a nice way to get a quick overview of issues in the philosophy of science from an historical perspective.

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...the common view that an inductive generalization can only be "not false"--it cannot be "true"
The only alternative is true or false; there is no third possibility of "not false" but not true either. They confuse the status of evidence with truth.

Does your professor think that what he says about inductive generalizations is true? All of them? Is that an inductive generalization? Isn't that just a variation on the self-refuting arguments of the chronic skeptic?

Clearly you are up against gibberish, but the more important issue is a positive formulation explaining a proper epistemology.

In the realm of mathematics, Polya's first volume is very good, too, but except for the specialized principle of mathematical induction he won't give you more than how to work with plausible patterns (which is still very useful). Mathematics, however, is a special case because it is restricted to methods (not because of the fallacious view of mathematics as "tautologies" and the analytic-synthetic dichotomy).

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The only alternative is true or false; there is no third possibility of "not false" but not true either. 

This claim is false. Arbitrary generalizations are neither true nor false. And I'm not sure the aforementioned professor would be wrong to call some of the generalizations made by the pre-Baconian inductive method arbitrary.

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This claim is false. Arbitrary generalizations are neither true nor false. And I'm not sure the aforementioned professor would be wrong to call some of the generalizations made by the pre-Baconian inductive method arbitrary.

Falsification does not mean not true or not false. Nor does falsification refute the arbitrary.

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"True or false" is the law of the excluded middle. If you claim to say something, i.e., make a statement, your thoughts either correspond to reality or they don't. If something is so arbitrary that you don't know what it means or how or why it is intended to correspond to reality then it is not a statement.

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"True or false" is the law of the excluded middle.  If you claim to say something, i.e., make a statement, your thoughts either correspond to reality or they don't.  If something is so arbitrary that you don't know what it means or how or why it is intended to correspond to reality then it is not a statement.

Unfortunately, Popper never thought of that one.

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The only alternative is true or false; there is no third possibility of "not false" but not true either.  They confuse the status of evidence with truth.

 

Does your professor think that what he says about inductive generalizations is true?  All of them?  Is that an inductive generalization?  Isn't that just a variation on the self-refuting arguments of the chronic skeptic?   

 

Clearly you are up against gibberish, but the more important issue is a positive formulation explaining a proper epistemology.   

 

...

Apparently my professor is not aware of the contradiction in his position, since he said that a fact is one that has not yet been falsified, but is not true and can never be true because "truth" and "certainty" are concepts from God's point of view, who can see and know reality directly and immediately, unlike man whose perception of reality is "distorted" by his senses.

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Apparently my professor is not aware of the contradiction in his position, since he said that a fact is one that has not yet been falsified, but is not true and can never be true because "truth" and "certainty" are concepts from God's point of view, who can see and know reality directly and immediately, unlike man whose perception of reality is "distorted" by his senses.

In other words, he is certain that one can never be certain.

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Tom Rexton: ..."truth" and "certainty" are concepts from God's point of view, who can see and know reality directly and immediately, unlike man whose perception of reality is "distorted" by his senses.
That is right out of Kant. Here you see how a bad epistemology of perception and concepts leads to skepticism and mysticism, and why you can't start epistemology plunging into the middle with a theory of induction. With no valid means of human knowledge he can't know anything with certainty, which he grasps, but he still realizes that he has to think and talk to function (especially as a professor), and is then so confused that he can't figure out what he knows and what he doesn't, inevitably basing his "certainty" on contradictory subjectivism. Your only hope to learn anything from the course is in the reading and to the extent that he can function rationally in spite of his own professed epistemology. You are lucky that at least the reading is from classical works worth learning instead of contemporary analytic sophistry from second-handers not worth the time to read.

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That is right out of Kant.  Here you see how a bad epistemology of perception and concepts leads to skepticism and mysticism, and why you can't start epistemology plunging into the middle with a theory of induction.  With no valid means of human knowledge he can't know anything with certainty, which he grasps, but he still realizes that he has to think and talk to function (especially as a professor), and is then so confused that he can't figure out what he knows and what he doesn't, inevitably basing his "certainty" on contradictory subjectivism.  Your only hope to learn anything from the course is in the reading and to the extent that he can function rationally in spite of his own professed epistemology.  You are lucky that at least the reading is from classical works worth learning instead of contemporary analytic sophistry from second-handers not worth the time to read.

Yes, that's the best thing about the course: 90% of the time we (the students mainly) are discussing primary classical sources (which are the only works we read), and all our papers must be based on those texts; thus the class doesn't get too far into nonsense. I wouldn't have taken the course if all I could do was listen to my professor expound his own philosophy! Last semester was pretty good, too. We read the works of the Ancient Greeks and Romans and Renaissance philosophers, with a little bit of Eastern philosophers mixed in (Lao Tsu and Confucius).

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Quoting your professor: "truth" and "certainty" are concepts from God's point of view, who can see and know reality directly and immediately, unlike man whose perception of reality is "distorted" by his senses.

This prevailing attitude among academicians is one reason I started a thread on the Forum regarding Epistemology and Hierarchy. It is a vile and evil attitude that didn't begin with Kant, but he was the first philosopher to take it as far as it could be taken. If one doesn't perceive existence, then all appeals to facts and reason are out -- and you should assume this is the attitude of your professor, since he has come right out and said so himself.

However, don't despair, you have a whole semester to enjoy this class! And I will tell you how you can do this. You are going to have to be subtle, and keep in mind that you are not trying to convert your professor. Put on your best "poker face" and gradually put him on the spot in class.

The next time he points to the chalk board and says "Look at this" ask him how you are supposed to know if he is really pointing to the board or doing flips? After all, you don't perceive existence, correct?

Be careful not to laugh when he hesitates, because though he explicitly rejects the evidence of the senses, he is implicitly expecting you to go by the evidence of your senses when he gives a class assignment and expects you to read the material, correct?

Be sure to keep up with the reading material, however, so that if he asks you a question about what so and so said, you can answer it. And be sure to regurgitate what he thinks is important on the tests.

And if he asks you why you are doing this, just tell him that you are following in the footsteps of philosophy students; for it is said that when Plato defined the concept of "man" as a "featherless biped" some of Aristotles students plucked a chicken, threw it into Plato's class, and said "Here's another student for you!"

Just in case some of you think that I'm not being serious, I am. This is real advise when one is being confronted with brazen irrationality. I've done it myself in many philosophy classes, and it works. After a while, the professor becomes hesitant to point to anything, which is just what he deserves because that's the state of mind he wants you to fall into.

Oh, and if he is honest and is merely presenting material that he disagrees with (which sometimes happens when one has to teach classes even at universities), then he will get the joke and will be appreciative of it.

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Since there does not exist a formally correct theory of induction,

Do you mean a mathematical or logical restatement of the rules of induction in

Peikoff's "Induction in Physics and Philosophy?" Or? How might "generalize from valid concepts

and self-evident generalizations" be formalized?

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What, in Zeus's name, is a "human event" class? Is is like a '60s "happening?"

No. It's a Western literature/philosophy course in seminar form. We read a broad variety of the classics of Western literature, from Classical Antiquity down to the present, discuss our thoughts in class, and write argumentative papers on a particular work of our choice. Because of the time limits, however, we do not read all the works in their entirety. Only a few--most of them fiction--are read in their entirety. The professor selects which works (or passages thereof) we read, so the experience is highly dependent on the professor's selections. Thankfully, my professor selected a lot of works by philosophers of Ancient Greece, the Age of Reason and the Enlightenment, and only a relatively few works by Romantic, postmodern and Eastern philosophers. (He admitted that his favorite philosopher is Nietzsche, and the influence is sometimes palpable. :angry2: )

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Human Events sounds like a synonym for "history".
"When in the course of human events, it becomes necessary..."

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