The Logical Leap: Induction in Physics

[Selene]

"Therefore, contractions do not exist."

You had me laughing... I just fixed it. Can't proofread your own stuff.

Thanks, Roger. I appreciate your taking the time both to read it and to point out the gaffe. I am still laughing.

Mike M.

Michael:

That is a funny gaffe. You can proofread your own stuff once, but if you miss it the first time, you are likely not to catch it again.

However, as a general rule you are correct.

Adam

[syrakusos]

That was a very good review.

Thanks, Bob. I some other questions, but Merlin Jetton cleared them up for me. One remains, but I do not feel on firm ground.

Explaining Newton’s experiments with pendulums, Harriman writes: “[Newton] deduced from F = ma that the inertial mass of a pendulum bob is proportional to its weight multiplied by the period squared (assuming the length of the pendulum is held constant.)” (126). That sent me back to the textbook. For a pendulum bob, the mass moment of inertia is expressed as

I = (T²mgl)/4π²

(Sears & Zemanski, 2nd ed. 1955, page 204, Equation 11-14)

I is the mass moment of inertia. T is period. Mass times gravity (mg) is weight. The constant of proportionality is 4π² which comes from the length of the arc. Note that the length l is a variable. We could explore the change in mass moment of inertia relative of a pendulum bob with respect to changes in the length of the rope (Δl/ Δt -> dl/dt). Multiply through by dt and then take the integrals of both sides. Whether you care to do that or not, the length of the string, the mass of the bob, the acceleration due to gravity, and the period of oscillation are all variables when considering the mass moment of inertia of a pendulum bob.

The thing is that Newton is held up as the paradigmatic experimentalist. And he was. I only have biographies (Westfall, White, Berlinski) and two different translations of the Principia, so I do not know what experiments Newton carried out with pendulums, but he must have varied the length of the cord and measured the results from that as well.

Also, I did not get into Harriman's vocabulary. When he says "inertial mass" I assume that he means "mass moment of inertia" as all mass is inertial, right? There was a lot like that all through the book. It came from not defining the audience. I like physics -- but liking it is not the same as knowing it. I think it is telling that people can argue Induction all day and night, but no one noticed any of these other problems.

In the Middle Ages some people argued about how many angels could stand on a pin and others built cathedrals.

[kiaer.ts]

Also, I did not get into Harriman's vocabulary. When he says "inertial mass" I assume that he means "mass moment of inertia" as all mass is inertial, right? There was a lot like that all through the book. It came from not defining the audience. I like physics -- but liking it is not the same as knowing it. I think it is telling that people can argue Induction all day and night, but no one noticed any of these other problems.

Well, the question of why inertial mass (which is the mass accelerated by all forces) should be identical to gravitic mass, rather than, say, electric charge, is an open question.

[syrakusos]

I think it is telling that people can argue Induction all day and night, but no one noticed any of these other problems.

Well, the question of why inertial mass (which is the mass accelerated by all forces) should be identical to gravitic mass, rather than, say, electric charge, is an open question.

That is so far from my level of understanding, I cannot tell if it is serious or humorous. Definitely, if it is serious, it is a whole other area of discussion for Harriman and his readers. If it humorous, then I understand the play on "the electro-dynamics of moving bodies." (I think...)

[kiaer.ts]

I think it is telling that people can argue Induction all day and night, but no one noticed any of these other problems.

Well, the question of why inertial mass (which is the mass accelerated by all forces) should be identical to gravitic mass, rather than, say, electric charge, is an open question.

That is so far from my level of understanding, I cannot tell if it is serious or humorous. Definitely, if it is serious, it is a whole other area of discussion for Harriman and his readers. If it humorous, then I understand the play on "the electro-dynamics of moving bodies." (I think...)

Not humorous at all, Michael. I am no physics expert, but I am surprised that you are not aware that this is an open question.

http://en.wikipedia....vitational_mass

Inertial and gravitational mass

Although inertial mass, passive gravitational mass and active gravitational mass are conceptually distinct, no experiment has ever unambiguously demonstrated any difference between them. In classical mechanics, Newton's third law implies that active and passive gravitational mass must always be identical (or at least proportional), but the classical theory offers no compelling reason why the gravitational mass has to equal the inertial mass. That it does is merely an empirical fact.

Albert Einstein developed his general theory of relativity starting from the assumption that this correspondence between inertial and (passive) gravitational mass is not accidental: that no experiment will ever detect a difference between them (the weak version of the equivalence principle). However, in the resulting theory, gravitation is not a force and thus not subject to Newton's third law, so "the equality of inertial and activegravitational mass [...] remains as puzzling as ever".^[17]

Edited January 7, 2011 by Ted Keer

[Guyau]

Gotta get this one.

The Nature of Scientific Explanation

Jude P. Dougherty (2013)

Nothing today so powerfully shapes the mind of man as the spirit of positive science. Against this backdrop it takes a critic respectful of the achievements of positive science to expose its conceptual foundations in the thought of Aristotle and his commentators. Jude Dougherty is ideally suited to undertake this task. He is a modern philosopher firmly grounded in classical philosophy, respectful and informed in modern science, and its cultural heritage. Dougherty gets to the ancient conceptual foundations of science with learned candor. –Edmund D. Pellegrino

Prof. Dougherty once sent me the nicest note about Objectivity (V1N3). This new book by Dougherty, I expect to connect with Mcmullin's little book, with Kuhn,* and with Harriman.

. . .

I just learned that Ernan McMullin died in February. . . .

. . .

One little book I think highly of concerning scientific inference:

The Inference that Makes Science

Ernan McMullin

. . .

Rand’s theoretical philosophy and my own understanding of the methods of science are consonant with the following superbly informed view of Ernan McMullin 1992. (See also.)

Let us restrict the term abduction to the process whereby initially plausible and testable causal hypotheses are formulated. This is inference only in the loosest sense, but the extensive discussions of the logic of discovery in the 1970’s showed how far, indeed, it differs from mere guessing. The testing of such hypotheses is of the most varied sort. It does, of course, involve deduction in a central way, as consequences are drawn and tried out. Some of these may be singular, others may be lawlike and hence involve induction. But we shall not restrict induction to the testing of causal hypotheses, as Peirce came to do. (89–90)

[Our concern] is with the process of theoretical explanation generally, the process by which our world has been so vastly expanded. This is the kind of inference that makes science into the powerful instrument of discovery it has become. . . . As a process of inference, it is not rule-governed as deduction is, nor regulated by technique as induction is. Its criteria, like coherence, empirical adequacy, fertility, are of a more oblique sort. They leave room for disagreement, sometimes long-lasting disagreement. Yet they also allow controversies to be adjudicated and eventually resolved.

It is a complex, continuing, sort of inference, involving deduction, induction, and abduction. Abduction is generally prompted by an earlier induction (here we disagree with Peirce). The regularity revealed by the induction may or may not be surprising. Deductions are made in order that consequences may be tested, novel results obtained, consistency affirmed. The process as a whole is the inference by means of which we transcend the limits of the observed, even the instrumentally observed.

Let us agree to call the entire process retroduction. We are “led backwards” from effect to cause, and arrive at an affirmation, not simply a conjecture. Retroduction in this sense is more than abduction. It is not simply the initial plausible guess. It is a continuing process that begins with the first regularity to be explained or anomaly to be explained away. It includes the initial abduction and the implicit estimate of plausibility this requires. It includes the drawing of consequences, and the evaluation of the match between those and the observed data, old or acquired in light of the hypothesis. Tentative in the first abduction, gradually strengthening if consequences are verified, if anomalies are successfully overcome, if hitherto disparate domains are unified, retroduction is the inference that in the strongest sense “makes science.” (92–93)

~~~~~~~~~~~~~~~~~~~~

PS

From his newly published* paper “Aristotle on Norms of Inquiry,” this note from James Lennox:

Ernan McMullin took up a 2-year residence as a visiting fellow at the Center for Philosophy of Science in 1978–79, shortly after I was appointed assistant professor of history and philosophy of science at the University of Pittsburgh. We eventually became friends. I've never forgotten his kindness and encouragement toward me in those years, and his work served us all as a model for our field.

[syrakusos]

That is so far from my level of understanding, I cannot tell if it is serious or humorous. Definitely, if it is serious, it is a whole other area of discussion for Harriman and his readers. If it humorous, then I understand the play on "the electro-dynamics of moving bodies." (I think...)

Not humorous at all, Michael. I am no physics expert, but I am surprised that you are not aware that this is an open question.

I am now reading Genius by James Gleick, the biography of RIchard P. Feynman. I read many Feynman books, the narratives, of course, but also his own Character of Physical Law and both the Easy and Not-So-Easy Pieces, the latter of which I also have on CD. Gleick goes into the development of the forward-backward/retarding-advancing theory that Feynman worked on with his mentor John Wheeler. (I also read The Curve of Binding Energy by John McFee, a biography of Wheeler, long ago.) Anyway, the point here is that this equivalence between charge and inertia is a subject for discussion. It is way over my head, but I now recognize the problem.

Stephen, thanks! Interesting review and comments.

[Guyau]

For reference I thought this discussion from another thread would be good to link in this thread. My few remarks on The Logical Leap are collected here (&).

On clarifying the nature and role of induction in science, I would like to reiterate the merit of Ernan McMullin’s little book The Inference that Makes Science (1992). A work known to Ayn Rand and Nathaniel Branden in their years of association—a work treating differing roles of induction in ancient, medieval, and modern science—is Philipp Frank’s Philosophy of Science – The Link between Science and Philosophy (1957). A contemporary survey of issues surrounding the nature of induction in science is prominent in Theories of Scientific Method (2007) by Robert Nola and Howard Sankey. Galileo’s appeals to induction and their relation to Aristotle’s Posterior Analytics are discussed in William Wallace’s Galileo’s Logic of Discovery and Proof (1992). The collection of papers in Interpreting Newton (2012) include two on the place and meaning of induction in Newton’s method: “Newton’s Scientific Method and the Universal Law of Gravitation” by Ori Belkind and “Newton, Locke, and Hume” by Graciela De Pierris.

[BaalChatzaf]

For reference I thought this discussion from another thread would be good to link in this thread. My few remarks on The Logical Leap are collected here (&).

On clarifying the nature and role of induction in science, I would like to reiterate the merit of Ernan McMullin’s little book The Inference that Makes Science (1992). A work known to Ayn Rand and Nathaniel Branden in their years of association—a work treating differing roles of induction in ancient, medieval, and modern science—is Philipp Frank’s Philosophy of Science – The Link between Science and Philosophy (1957). A contemporary survey of issues surrounding the nature of induction in science is prominent in Theories of Scientific Method (2007) by Robert Nola and Howard Sankey. Galileo’s appeals to induction and their relation to Aristotle’s Posterior Analytics are discussed in William Wallace’s Galileo’s Logic of Discovery and Proof (1992). The collection of papers in Interpreting Newton (2012) include two on the place and meaning of induction in Newton’s method: “Newton’s Scientific Method and the Universal Law of Gravitation” by Ori Belkind and “Newton, Locke, and Hume” by Graciela De Pierris.

Boltzman did somewhat more to promote atomic and molecular theory than Maxwell. In a way, Boltzman was Max Planck's muse.

The man who nailed the case for atoms shut tight was non-other than Albert Einstein in his paper on Brownian Motion. He even had Ernst Mach almost convinced.

See "Boltzmann's Atom" by David Lindley.

Ba'al Chatzaf

[Ellen Stuttle]

[....]

On clarifying the nature and role of induction in science, I would like to reiterate the merit of Ernan McMullin's little book The Inference that Makes Science (1992). [....] The collection of papers in Interpreting Newton (2012) include two on the place and meaning of induction in Newton's method: "Newton's Scientific Method and the Universal Law of Gravitation" by Ori Belkind and "Newton, Locke, and Hume" by Graciela De Pierris.

I ordered those. I was reading another book by Ernan McMullin, Newton on Matter and Activity - Amazon link - before I got sidetracked by the Harriman news. I'm looking forward to getting back to reading about Newton.

Ellen

[Guyau]

A quibble with Mr. Harriman, when he writes:

Aristotle induced his theory of deduction; he examined an enormous range of particular arguments and arrived at generalizations that identified the various types of valid and invalid structures. Then, ascending to an even greater level of abstraction, he asked: What is the common root of all invalid arguments? He found that all such arguments imply a contradiction, i.e., they imply that something is A and non-A at the same time and in the same respect. Thus he grasped (inductively) that the law of noncontradiction is the fundamental principle of valid thought. (236)

Citations from texts of Aristotle should be provided for such controversial claims about Aristotle's views, particularly the claim that Aristotle saw the law of noncontradiction as root of forms of valid inference (part of valid thinking) such as:

All animals are mortal.

Socrates is an animal.

Therefore, Socrates is mortal.

Beyond Aristotle whatever, to the truth of the matter: From the thesis that contradiction is the root of all invalid inferences joined with the thesis that all inferences are either valid or invalid, one could glide with Harriman to his (and Aristotle’s?) conclusion that the law of noncontradiction is the fundamental principle of all valid inference. That is entering by a window, rather than the door. The less encumbered analysis of the root of such inferences as in the argument about Socrates would be direct appeal to the law of identity, as understood by Rand (Baumgarten, Bolzano, . . .): “A thing is what it is” or “A thing is something specifically.”

Aristotle did not connect the identity formula “A thing is itself” with our “A thing is something specifically.” He thought the former formula nearly empty and useless (Metaphysics 1041a10–24). He did realize that any existent not only is but is a what (1030a20–24).

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