The Logical Leap: Induction in Physics [Paperback]

 

 

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Readers of the book should be aware that the historical accounts presented here often differ from those given by academic researchers working on the history of science and often by the scientists themselves.

Harriman, for example, recounts how Galileo determined that "the rate at which a body falls is independent of its weight."

"Galileo demonstrated the answer with his characteristic flair. He climbed to the top of the famous Leaning Tower and, from a height of more than fifty meters, dropped two lead balls that differed greatly in size and weight. The students and professors assembled below saw both objects hit the ground at very nearly the same time. . . . Galileo then asked the next logical question: Does the rate of fall depend upon the material of the body? He repeated the experiment using one ball of lead and another made of oak. Again, when dropped simultaneously from a great height, they both hit the ground at very nearly the same time. Thus Galileo arrived at a very broad generalization: All free bodies, regardless of differences in weight and material, fall to Earth at the same rate." (p. 43)

Harriman rightly observes that this "seems too easy. It appears as though Galileo arrived at this fundamental truth . . . merely by doing a few experiments that any child could perform." But, Harriman explains, Galileo's breakthrough was not the experiments per se but the application of a concept that had eluded his predecessors, the concept of friction. That is, Galileo arrived at his law by carefully accounting for air friction in the Leaning Tower experiment.

This is not, however, the account that Galileo himself gives. Harriman writes, "Imagine that he attempted to drop the lead or oak balls through water instead of air . . . . The result would not have led to any important discovery." But in the Discorsi Galileo presents the difference between dropping balls through air and dropping them through water as the very heart of his discovery. (Day One, 8:110-116). He begins by recounting a report of the tower experiment but does not consider it sufficient to establish the law. He instead explains that we must consider air as a medium and compare what happens in other mediums, such as water and mercury. He notes that heavier things (ones heavy enough not to float) do land at different times and the difference is bigger the higher the resistance of the medium. In water the difference is higher than in air; in mercury, the difference even higher. Galileo extrapolates and concludes that in a medium that offered no resistance, there would be no difference in speed of fall and all objects would hit at the same time. Galileo claimed that comparing the dropping of objects in air, in water, and in mercury is exactly what justifies his discovery, contra Harriman's claim.

Moreover, the air resistance Galileo speaks of is not the same as friction (though Harriman treats it that way). Instead, at least in this point of Galileo's argument, Galilean resistance is Archimedean buoyancy. (For Galileo, something floats if the medium offers too much resistance.) But then, as Galileo goes on to discuss not the speed of fall but the acceleration (8:119, see Drake's comments), he begins thinking of resistance as what we now call friction. In other words, Galileo's concept of resistance is not the same as our concept of friction but an immature concept that one would expect Harriman to call a "red light" to scientific progress. The remarkable thing is how much progress Galileo actually made using a concept that conflated two (or three) very different things.

Another example of Harriman's account differing from the conventional is his story of the concepts of impetus and inertia. He repeatedly refers to the "false idea that motion requires a mover, i.e., a force" (p. 45). The concept of impetus, "an intrinsic attribute of [a] body that supplies the internal force propelling it," he says, is an invalid concept, a "red light" that "stops the discovery process or actively leads to false generalizations." "Since there is no such attribute, all generalizations referring to it are false." (p. 78) Replacement of this false notion with the new notion of inertia, Harriman explains, provided the "green light" that enabled Newton to develop his mechanics.

This is not the story other scholars have found in Newton's writings. They have concluded the following instead: At first, Newton accepted the concept of impetus and rejected the concept of inertia advanced by Descartes and others. Newton's first derivation of the v-squared-over-r law presumed impetus. Newton soon, however, changed his mind and adopted Descartes' proposal. But then just as quickly he swung back again. He remained committed to impetus for the next twenty years. When he then began work on what would become the Principia, he struggled to reconcile the two concepts, recognizing that each (the way then conceived) had problems. He finally settled on a hybrid, what he called the force of inertia. This force was, for him, one kind of force, another being impressed force. The force of inertia was what keeps a moving body moving and a resting body resting. The concept was a not a rejection of impetus but a combination of impetus with resistance.

But, after Newton died, the utter strangeness of this force of inertia became increasingly apparent. It was that by which a moving body kept moving, but a body not moving had the same amount of this force as it had when it was moving. It took a few generations, but eventually Newton's concept of the "force of inertia," this strange combination of impetus and resistance, got replaced by the modern concept of inertia. Though it was not such in Newton's mechanics, the modern concept is a fundamental one in what we now call Newtonian mechanics. Newton scholars have generally concluded that the replacement of the concept of impetus by the modern concept of inertia was not an event that made Newtonian mechanics possible. Instead, the replacement was a slow process whose completion marked the end, not the beginning, of the formation of Newtonian mechanics. (Introductions to the conventional account can be found in Richard Westfall, Never at Rest, and I. B. Cohen's guide to vis insita in his edition of the Principia.)

Similarly, though Newtonian mechanics has the concept of acceleration as a vector quantity, it is not such in Newton's mechanics. In the Principia, "acceleration" is not a technical term meaning anything more than "increase in speed" or just "increase" (for Newton, an area can "accelerate.") Newton may have had the idea that motion is directional, that force is directional, that change in speed occurs in the direction of an applied force, and so on, but he did not hold that idea in the form of a unified concept "acceleration."

Generally, scholars who try to recreate the development of scientific concepts in the minds of great scientists are struck by how successful these scientists are in making propositional generalizations while still forming--and often themselves never fully forming--the concepts that constitute the generalizations. The narrative these scholars present (using Harriman's metaphor, not theirs) is not that a fully formed concept comes into the mind of the scientist who then uses it as a green light to an inductive propositional generalization, but that a partly formed concept serves as a flickering greenish light to a partial generalization, which acts as a less flickering, somewhat greener light to a better concept, which in turn improves the generalization, which then improves the concept, and so on, until well-defined concepts and associated propositional generalizations emerge fully formed together (at which point, the subjectivist says, "See, it's all just a matter of definitions.") Most scholars find the process of scientific progress less linear than Harriman indicates and much more iterative and spiral.

I cannot say that the conventional narratives (or my own) are all correct and Harriman's all wrong--certainly they are not--nor do I want to say how any inaccuracies would affect the theory of induction presented in The Logical Leap. I merely want to alert readers unfamiliar with the field that Harriman's narratives are often not the ones accepted by other scholars who research the conceptual development of great scientists and often not the ones that the scientists themselves give.

The theory of induction proposed here is potentially seminal; a theory that grounds inductive inference in concept-formation is welcome indeed. But the theory is still inchoate. If it is to be widely adopted, it will need to be better reconciled with the historical record as the theory gets fleshed out and refined.

In The Logical Leap: Induction in Physics, David Harriman has two target audiences, scientists interested in the philosophy of induction, and students of Objectivism interested in science. This book has much to say that will be of interest to both. I recommend it most highly.

David Harriman is a professional physicist and philosopher with a wide grasp of his subject. Interested in putting forth a theory of induction based upon Ayn Rand's theory of concept formation, he briefly introduces his theses, and then examines two classical histories of induction. First he makes a detailed analysis of the history of thought about motion from the Greeks through Galileo and Kepler, to Newton. Then he examines atomic theory from the Greeks through Lavoisier and Kelvin to Mendeleev.

His basic theses are that induction is based on a hierarchy of generalization, parallel in form to Rand's hierarchical theory of concept formation (a subject too complex to address here, but which is covered in her monograph, Introduction to Objectivist Epistemology); that progress in science relies not only on the experimental method, which he credits Galileo for first practicing, but on developing an increasingly sophisticated language of concepts, which must be induced in a hierarchical order; and that skepticism results from a flawed, context-dropping view of the history of science.

This last thesis is most informative. He speaks of the flawed Platonic and Cartesian idea of deriving and validating knowledge top-downward from first principles. Having arrived at some level of knowledge through a developmental process of building upon prior knowledge, whether in the history of science, or in the individuals' development from childhood, the rationalist drops the more fundamental foundations from focus and treats higher abstractions, such as that force equals the acceleration of a mass, as if they were self-evident primaries from which more concrete ideas are to be deduced. If valid, one's abstract ideas will have been reached by an arduous process of building upon ideas step-by-step. This upward process of induction is paralleled in the history of science and in the education of an individual from infant to adult. Students who are introduced to scientific ideas in the proper order will see the elegant necessity and certainty of their concepts. Students who start halfway through the process by learning Newton's laws without having fully grasped Galileo's experiments on the acceleration of falling objects will have to accept such formulations as F=ma on faith.

Plato and Descartes had taught that one should begin with first principles and from them derive the facts in a top-downward fashion. Harriman calls this a ponzi scheme, with unsupported abstractions looking for ever higher floating ideas on which to hook themselves. Skepticism is the result when one attempts to take abstract notions as givens. If one begins with an arbitrary hypothesis, such as that the planets must move in "perfect" circles, one becomes mired in trying to explain, with more and more arbitrary assumptions, why they seem to move in ellipses. Harriman describes arbitrary preconceptions as "red lights" to induction, and explains how such concepts as the perfection of spherical motion, since they were arbitrary, lead only to endless rationalization and stagnation so long as they were accepted.

While Harriman examines only chemistry and physics, the pernicious nature of arbitrary preconceptions is found in many fields. The example of the rise and fall of historical linguistics will illustrate his point. In 1786, Sir William Jones, an observer in India, noted the correspondences between the grammar of Sanskrit, an ancient Indian literary language, and those of Latin and Greek. A century before Darwin, he reasoned the three languages must have descended from some common ancestor, now lost. Over the next decades, scholars made detailed comparisons of dozens of languages and, like solving a massive cryptogram, induced what form the mother language, proto-Indo-European, must have had. For example, the reconstructed root *weid- ('to see') is the ancient form from which the Latin 'video', the Greek 'idea' & the English 'wise' all evolved.

The climax of this comparative method was achieved when traces of sounds which had become silent in all its daughters (like silent 'e' in English) were used to predict the existence of lost sounds in the proto-language. In 1878, Ferdinand Saussure used "irregular" vowel changes to predict that an H- like sound had once existed in the proto-language, but dissapeared, leaving only this otherwise inexplicable irregularity. After his death, ancient Hittite was deciphered and found to be the oldest known Indo-European language. Hittite had the initial H- sounds Saussure had predicted! Saussure's reasoning was strong enough to predict the form of a lost language that no one had heard for millennia. To see the results of the comparative method, see Calvert Watkins' Dictionary of Indo-European Roots, free at Google Books.

But the painstaking inductions of the 19th century have been forgotten. Chomskyan innate ideas are the rage. Modern students learn proto-Indo-European from textbooks, as if it were an almost miraculous given. They are taught preconceived ideas, such as the "impossibility" of linguistic reconstruction beyond 6,000 years, regardless of what evidence must then be explained away. They learn that reconstruction, in truth the end product of the science, is preliminary to classification, as if saying we can't classify humans as mammals until we dig up every missing fossil link. They forget that Jones began by grouping Greek, Latin and Sanskrit (as opposed to Hebrew, Hungarian & Chinese) on the basis of simple inspection. Had classifying languages based on perceived similarities not been the starting point, there would never have been a way to reconstruct the proto-language. Nowadays, "mainstream" linguists deny detailed pronouns and vocabulary correspondences across the Americas indicate a vast Amerind phylum covering all natives except the Eskimos and Athabaskans. They make ad hoc arguments to explain away similarities as the result of "vague psychological processes." They raise the "possibility" of borrowing between cultures thousands of miles apart, for which no evidence of contact is ever shown, yet deny the simple possibility of common descent as a matter of faith. Such skepticism is seen as 'sophisticated.' Refusing to integrate the evidence over the widest possible scope, Americanists pretend that 50-100 unrelated language families exist in the Americas, all presumably having arrived separately, while there are only four native language families in all of Africa. (The late Joseph Greenberg, with his contextual method of 'mass comparison,' is a rare Newton-like exception.)

The difference in classifications of the two continents isn't based on facts, but on the collapse of the inductive method. The Americanist linguists' skeptical axioms are a perfect example of the "red lights" to induction which Harriman describes. Luckily, historical linguistics is rarely a matter of life and death. But you can see the same phenomena in matters as serious as the O.J. trial, where real world evidence is discounted as imperfect, and abstract theories of what might be imagined to have happened are treated as worthy of serious consideration. The irrational conclusions of the Americanists, arrived at for just the sort of causes Harriman describes in the physical sciences, show the validity of his arguments in regard to a science like historical linguistics with which he may not even be familiar.

Harriman's book is divided into three sections. In the introductory section he sets out the problem, explains Rand's theory of concepts upon which he bases his thesis, and presents his theory of hierarchical generalization. This section is introductory, not a full treatise, and it does beg further scholarly exposition. In the main portion of the book he gives detailed analyses of the bases of Newtonian physics and modern chemistry using the ideas he has introduced. This section is delightful, and, as with the entire book, it is clearly written and well illustrated with examples. Those familiar with Carl Sagan's Cosmos will be reminded of his wonderful series. No math will be needed, and only a few simple diagrams suffice to clarify some of the ideas about planetary orbits. In the final section Harriman examines classical philosophical errors and their modern results and ends with a section on the proper role of mathematics and a rational philosophy in science. Since a preview is unavailable, here are the chapter and section heads:

I The Foundation: The Nature of Concepts * Generalizations as Hierarchical * Perceiving First-Level Causal Connections * Conceptualizing First-Level Causal Connections * The Structure of Inductive Reasoning
II Experimental Method: Galileo's Kinematics * Newton's Optics * The Methods of Difference and Agreement * Induction as Inherent in Conceptualization
III The Mathematical Universe: The Birth of Celestial Physics * Mathematics and Causality * The Power of Mathematics * Proof of Kepler's Theory
IV Newton's Integration: The Development of Dynamics * The Discovery of Universal Gravitation * Discovery is Proof
V The Atomic Theory: Chemical Elements and Atoms * The Kinetic Theory of Gasses * The Unification of Chemistry * The Method of Proof
VI Causes of Error: Misapplying the Inductive Method * Abandoning the Inductive Method
VII The Role of Mathematics and Philosophy: Physics as Inherently Mathematical * The Science of Philosophy * An End - And a New Beginning

This is not a perfect book -- just a great one... Read more ›

I would like to bring this book, by historian of science David Harriman, to the attention of readers with a serious interest in the philosophy of induction. It outlines a fundamentally new approach to the nature of inductive reasoning that I think is of the greatest importance, and indicates how significant episodes in the history of physics illustrate, and provide further evidence for, that approach. The inductive theory was developed by Leonard Peikoff, building on Ayn Rand's revolutionary theory of concepts. Rand's theory (presented in her Introduction to Objectivist Epistemology) explains the way concepts are formed on the basis of perceptual awareness, later concepts being built up hierarchically from first-level concepts of entities and their attributes, actions, relationships and so forth. Peikoff has established that there is a class of first-level generalizations expressing or reflecting perceived causal relationships, and a method of building more abstract generalizations hierarchically from them that generates scientific knowledge, and has shown how the validity of these later generalizations rests on the formation, in the course of scientific discovery, of proper concepts (in accordance with Rand's theory). Harriman has written the book in consultation with Peikoff.

Though I can't speak personally for the full accuracy of the historical accounts, they are essentialized with great skill, and lucidly presented. Harriman helpfully indicates how the episodes he discusses illustrate and support aspects of Peikoff's theory. I would like to have seen the connections between the episodes and the theory developed more fully, and the theory itself amplified in places; and the initial account of Rand's theory of concepts is too compressed. However, I give the book a 5 for the significance of Peikoff's theory (as illuminated by the historical accounts): it is a major advance, and I think that all further thinking about the nature of induction must build on his results.

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5.0 out of 5 stars Don't let the agenda of the psuedoscientists and mystics stop you from reading this book!
An insightful and important book that investigates the crisis in the scientific method at this point in time. Read more

Published 1 month ago by Carl Morano

3.0 out of 5 stars This book sucks - but it's near brilliant.
You might ask how I can recommend a book that fails. This is not easy explanation - the book is not an easy book. I wish I knew Mr. Read more

Published 1 month ago by Steve S. Jones

4.0 out of 5 stars Pushing a ball does not make it roll: Comment on the 1 star review
Tom Minchin gives this book a one star review:
I find his entire review totally subjective.
Objectivists have subjective perceptions. Read more

Published 2 months ago by James Smith

5.0 out of 5 stars One of the most important books ever written
While this book uses physics as its source of examples, the book is really focused on induction, and how it can be done rationally as opposed to the more common "leaps of... Read more

Published 4 months ago by Eric Kassan

5.0 out of 5 stars A major addition to the philosophy of science
First: The Logical Leap is written in clear, simple language, and anyone with a solid high-school education will be able to follow the arguments without difficulty. Read more

Published 5 months ago by K. Conover

1.0 out of 5 stars The Death of the Objectivist Movement as We Now Know It?
The Publication of "The Logical Leap" (TLL hereafter) will prove to be the event which triggers the death of the "official" Objectivist movement as it exists today. Read more

Published 5 months ago by Henrik Unnã

4.0 out of 5 stars A Fascinating Read
I thoroughly enjoyed this book, and its presentation of induction as relying on a hierachical and contextual build up from first level concepts. Read more

Published 7 months ago by Joseph McHugh

1.0 out of 5 stars Objectivism is not 'philosophy.' Full stop.
Harriman writes: 'In my physics lab course, I learned how to determine the atomic structure of crystals by means of x-ray diffraction and how to identify subatomic particles by... Read more

Published 8 months ago by Nicolas Mcginnis

1.0 out of 5 stars You can't get there from here
Update December 31, 2010

On December 20, writing on the Harry Binswanger List, Dr. Binswanger confirmed the essence of my review below. Read more

Published 10 months ago by Tom Minchin

5.0 out of 5 stars Enjoyed it
The standard I used in judging this book was pretty simple: would reading it have benefited me in my formative years? The answer is yes. Read more

Published 11 months ago by William J. Decker

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