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Review: "The Logical Leap: Induction in Physics"

Review: "The Logical Leap: Induction in Physics"

8 Mins
April 19, 2011

BOOK REVIEW: David Harriman, The Logical Leap: Induction in Physics . (NAL Trade, 2010), 272 pages, $16.00.

Spring 2011 -- Induction is the formation of general knowledge from particular evidence. It is induction if you burn your hand once and thereafter always know better than to put your hand in fire again. Induction is the basis of all science and technology. In fact, every piece of factual knowledge you have about types of things or how things act ultimately derives from induction.

Philosophers have argued that there is a “problem of induction.” David Harriman tips his hat to the problem with his title: The Logical Leap. Induction, it is said, “leaps” from a few examples to universal truths that apply to all things of a type. How can you be certain, if you’ve only burned your hand once, that at least some other fires might not be very hot?

In her writings on Objectivism, Ayn Rand never addressed induction in detail. Yet it was plain that a philosophy that claims to be objective must be able to explain how one gets from concrete facts to abstract truths. With this compactly argued volume, David Harriman steps into the breach. He gives a muscular, confident defense and explication of induction, one that is tightly integrated with Ayn Rand’s theory of concepts.

He begins with a discussion of philosophical fundamentals. In the middle chapters Harriman moves into showing how founders of physics such as Galileo, Kepler, and Newton used induction to develop and prove their theories. Galileo and Newton are famous for their controlled experiments. But even Kepler, Harriman shows, looked for natural tests in the astronomical data to reveal the general principles of orbital mechanics. It wasn’t just airy theory, in other words, but rigorous reasoning from the facts.

Harriman uses the development of the atomic theory of matter in the mid-19th century to show how a full scientific theory can be proven through induction. It is a fascinating story as he tells it, as research on chemistry, the properties of gases, and the study of heat all pointed to the truth and utility of the atomic theory, despite the fact that no one at the time could directly observe an atom or molecule. Over the course of 100 years or so, the idea of an atom transformed from an arbitrary and useless metaphysical speculation, mooted since ancient Greece, to a rock-solid scientific truth. Harriman argues that the theory was proven and incontrovertible by the time Mendeleyev drew up the now-immortal Periodic Table of the Elements in 1869.

Examples of induction going right are contrasted throughout with examples of its not going right. And Harriman devotes a chapter to “Causes of Error,” in which he surveys five examples of scientific blunders, such as the recent “cold fusion” fiasco. Some of the cases of error derive from sloppy method. Most of them appear driven by bad philosophical commitments, too.

The book winds down with thoughts on why mathematical reasoning is essential to induction in the physical sciences and how philosophy can be inductive. The final section is a jeremiad against three monuments of 20th-century physics: quantum mechanics (“a mathematical formalism coupled with skepticism,” 250); Big Bang Theory (“the claim that fourteen billion years ago the entire universe inexplicably popped out of a point with infinite mass density,” 251); and string theory (“a magic trick,” 254). We now live in an era where physics, the model of sound inductive reasoning, has many practitioners who exist to create airy castles of mathematical wonder and who avoid seeking experimental proof. Solve real problems? Who, them?


The basic argument of The Logical Leap is sound and much-needed. Harriman’s message is that induction works and it has a specific method. Today, empiricists focus on data, but are skeptical about the truth of abstract ideas. Meanwhile, rationalists, such as many logicians, physicists, and economists, cling to deductive proof as the standard of knowledge, ignoring the fact that no syllogism is worth more than the premises that go into it.

Against these attitudes, Harriman argues that rigorous induction carries all the logical power typically associated with deduction: “If one grasps the observations . . . and knows the conceptual framework is valid, then the generalization follows necessarily. Its denial under these conditions would involve a contradiction” (32). Take that, rationalists!

Harriman's message is that induction works and it has a specific method.

Similarly, he shows through example after example the huge context on which scientific truths depend. These days, philosophers like to call factual knowledge “contingent,” as if diamonds could just turn into tapioca tomorrow. Harriman shows that vast amounts of facts would have to change for such an alteration in reality to exist. It would contradict almost everything one knows. And there is no reason at all to think that could happen. Take that, skeptics!

Harriman is at pains to show how scientific truths grow one from the next. New truths suggest new questions. Vital new concepts open the door to new approaches to issues. Tracing the rise of modern physics from Copernicus, to Kepler and Galileo, and on to Newton, Harriman shows how well-posed experiments and tests have put inductive claims into focus and proved new laws, which each succeeding generation has then refined and improved. He emphasizes that “a rational process is self-correcting” (54) because the inductive method calls the knower to go back to the facts to check what is really true, rather than relying, say, on the authority of predecessors’ claims.

And Harriman understands that knowledge is contextual. We cannot grasp the extent of a claim unless we know what evidence it integrates. Newton’s laws of motion united observations of the planets, of the sun, of planetary moons, of falling apples, of tidal movements, of comets’ fly-bys, of pendulums, and of cannon-shot. Across that context, within the precision of the telescopes and other measuring apparatus, Newton was certain. Later, Einstein would treat issues Newton was unaware of, with a theory that builds on Newton’s. And we see the same pattern in other fields, such as 19th-century chemistry, through which Harriman gives us a tour as he discusses the discovery of atoms.

To his credit, Harriman takes Newton to task for the one major unjustified element in his physical scheme: absolute space and time. It wasn’t needed for Newton’s mechanics, and it wasn’t justified by any observation. Later, Einstein would show that these concepts are necessarily relative to a frame of reference—a context, one might say.

Still, in his basic method, Newton was a paragon of inductive reasoning. “The most radical aspect of Newton’s theory did not consist of what he said,” recounts Harriman, “but of what he refrained from saying. . . . He reasoned as far as the evidence could take him—and no further” (64). Broad strokes like these make the fan of objectivity want to jump up and cheer!


Who really wrote this book? In the preface, philosopher Leonard Peikoff, éminence gris of the Ayn Rand Institute, offers a ringing endorsement: “This book represents the first major application of Ayn Rand’s epistemology to a field other than philosophy” (xi). Meanwhile, in his own introduction, Harriman writes: “This book is the result of a collaboration between myself and Leonard Peikoff” (1). Harriman explains that “the original philosophical ideas belong to Peikoff, while I provided their illustration in the history of science. . . . In addition, every chapter of the book has benefited greatly from his line-by-line scrutiny.” So Harriman may have written the book, but Peikoff whispered in his ear throughout.

Their collaboration resulted in a book with a distinctly conservative cast. It is conservative about science, lionizing the achievements of the 19th century, while casting a doubtful eye on anything recent (no plaudits for nanotech, for example). It is doctrinally conservative as well: it seems to seek, as much as possible, to use the ideas of Ayn Rand’s Introduction to Objectivist Epistemology and Peikoff’s own survey Objectivism: The Philosophy of Ayn Rand, with as little addition as possible (and no hint of revisions, for sure).

Concepts play an outsize role in their theory, perhaps because Rand’s own most developed epistemological work dealt with concepts. This is in keeping with Peikoff’s stated view that Rand’s philosophy is complete and “closed” as she formulated it, an attitude that is in tension with the aspects of The Logical Leap that creatively enrich and extend Objectivist philosophy (see sidebar,  The New Open Objectivism ).

Now, concepts are essential to the human mode of cognition. And concept-formation and induction are essentially similar processes, too. Both involve a recognition of patterns of similarity and difference. To tell dogs from cats, one must realize something, at least implicitly, about how dogs act and what they look like, as opposed to how cats act and what they look like. Those would be generalizations if one rendered them explicit. Furthermore, if one wants to define a concept, then understanding how the referents differ from their contrast objects—in short, gaining inductive knowledge of both groups—is the thing to do.

Harriman wants to make sure that induction can get off the ground. So, in imitation of Ayn Rand’s treatment of how a child might form concepts from sense-perception, Harriman discusses how a child might induce “first-level generalizations” such as “fire burns paper” (26) from his perceptual awareness. From first-level generalizations we can build our knowledge into more abstract claims, such as knowledge about fuels generally, or theories of combustion.

A little conceptual magic creeps in to the account here: “When our first-level inducer identifies a perceived causal connection in words . . . he at once states a universal truth” (26). This cannot be right as stated. The meaning of the concepts “fire” and “paper” extend to all the referents essentially similar to the instances the knower has directly perceived. But it doesn’t necessarily follow that the causality the knower has observed is present in all referents of the concepts. Wet paper won’t burn, for instance. Certain treated papers won’t burn. But someone who has just burned one paper cannot know that. To generalize that “fire burns paper” is a correct inference from the evidence, but more acquaintance with the referents of “paper” and “fire” is needed to be sure that the inference necessarily holds in virtue of the nature of all things of that type. After all, if a kid has been lovingly licked by one friendly dog, he doesn’t know that all dogs are friendly.

The basic point that we do build up a structure of knowledge from a base of straightforward inductive inferences has to be right. But in this account, Harriman and Peikoff have confounded learning with knowing. The two are related, but it is possible to learn without being right from the start. In his discussions of the history of physics, Harriman shows that Galileo made some inaccurate generalizations from his experiments (taken in context). Yet these errors were corrected by later scientists following Galileo’s own experimental methods: induction is self-correcting. If one finds one has over-generalized from an example, the solution isn’t skepticism; it’s more induction.


“A concept is a commandment to go from some to all—it is a ‘green light’ to induction,” writes Harriman, following Peikoff. “The rules of the road mandate that we move forward through a green light; the rules of human cognition mandate that we generalize among the referents of our concepts” (77). And, by contrast: “An invalid concept is a red light to induction; it stops the discovery process or actively leads to false generalizations” (78).

Harriman is at pains, then, to show how holding invalid concepts impeded science and holding objective concepts aided it. For Galileo, “friction” was a vital concept. Galileo designed his tests with falling objects and pendulums to take into account the effects of friction, and he hypothesized motion free of friction. An example of a red light would be the idea of circles as natural motions. This idea ruled astronomy from Ptolemy through Copernicus. Galileo was wedded to it, and so he rejected Kepler’s discovery that the planets were actually following elliptical paths. Harriman thinks that today the Big Bang Theory relies on an invalid concept: “reason cannot approve the idea of creation,” he snipes, perhaps confusing creation of the universe with creation of existence itself (251).

Again, this is insisting on too much of a role for concepts. Scientists often wrestle with inconsistencies between facts and theories, and the evidence can drive the creation of new concepts in the face of invalid old ones. Harriman’s account of the discovery of atoms shows this time and again, as wrong measurements and false conceptions bump up against the data. He gives a moving account of the anti-atomic counter-revolution of the 1860s, when Positivist chemists held up atoms to ridicule for being theoretical entities that could not be directly observed. So, many chemists denounced atomic theory and denied it, yet continued to use it and prove it true. Another classic example comes from one of Harriman’s heroes, the father of chemistry, Antoine Lavoisier. Lavoisier discovered oxygen in the context of the false concept “phlogiston,” which he disproved. In fact, Harriman lauds Lavoisier for defining the basic procedure of separating pure substances from mixtures that would lead to the identification of the elements. But that is an example of discovering valid and useful concepts from an existing context of research. Why weren’t bad concepts a red light to Lavoisier?


There is an internalist, coherentist cast to some of Harriman’s arguments. For example, he makes much of Peikoff’s principle that in induction “the bridge from observation to generalization is not one premise, or even a hundred premises, but the total of one’s knowledge properly integrated” (34, emphasis added). Harriman convincingly shows that what gives broad physical laws their necessity is the way they integrate facts from all across experience. And yet, truth is primarily a correspondence to the facts, not a coherence in one’s ideas. Each connection of an idea into the rest of our knowledge binds the idea down only because each other item of knowledge is also tied to reality. In fact, Newton revolutionized physics and proclaimed an objective method while writing extensively on religious subjects that bore no logical relation to his physics and that didn’t employ his observation-based method. It wasn’t integrated, in other words. It would be better to say, then, that inductive claims need to not plainly contradict other relevant knowledge we hold, and that the more we can integrate our fact-based knowledge, the stronger our knowledge becomes. Remember, for diamonds to turn to tapioca, everything about carbon would have to change, too: we simply couldn’t survive that. But do we test the hardness of diamonds via our knowledge of the music of Bach? No, we try to cut glass.

In the introduction, Leonard Peikoff declares: “This book is a model of inductive thinking” (xi). And Harriman does deserve praise for marshaling evidence from history to support his points. For instance, he uses the proof of the existence of atoms to illustrate “three criteria that are essential to the proof of any broad theory:”

First, every concept and every generalization contained within the theory must be derived from observations by a valid method. ?
. . . Every law subsumed by the theory was rigorously induced from the results of experiments.

Second, a proven theory must form an integrated whole. . . . The various parts of the theory are interconnected and mutually reinforcing, so that the denial of any part leads to contradictions throughout the whole. . . .

Third . . . the scope of a proven theory must be determined by the data from which it is induced, i.e., the theory must be no broader than or narrower than required to integrate the data (184-185).

These are wise words. Yet it is less clear that Harriman has convincingly proved his claims in his own terms.

This book opens the door to a very healthy debate on what exactly the evidence is for the inductive method and how exactly it works. Harriman has matched examples to his claims, but one cannot help but conclude that here the facts were often marshaled to support the hypotheses, while disagreeable facts and alternative hypotheses were given short shrift.

This is a vital first step. It shows the need for more positive contributions to Objectivism, and it shows how much work remains to be done to iron out the rough spots and fully integrate this aspect of Objectivist theory with the facts. More induction is the ticket.

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