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The Logical Leap: Induction in Physics

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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. I should point out that while I do consider myself an Objectivist, I do not consider myself an orthodox one. (This book has nothing to do with politics or ethics in any case.) Having listened to Dr. Harriman's lectures (some such as "The Crisis in Physics--and Its Cause" and "Harriman's Top 10 Scientific Discoveries in Physics" are available free on line) I find fault with his criticism of the Big Bang theory, which he bases on a mistaken idea that the Big Bang necessarily means a creation of the universe, in time, from nothing. (That is not, for example, the finite-yet-unbounded view of Stephen Hawking.) Harriman criticizes Relativity for describing space as curved, saying that space is a relationship, and that relationships cannot be curved. I find that to be a gross and misleading oversimplification of a theory which in no way deviates from explaining observational phenomena. Harriman has criticized Quantum Theory, but his criticisms apply more to a popular if specious interpretation of the theory, rather than to the evidence upon which the theory itself is based. Harriman leaves any detailed discussion of this out of the book, however, and I bring it up only to explain my differences with him and my independence as a reviewer. In fact, there were only absolute objections I had with the work. First was his repetition of an idea from Ayn Rand that animals cannot plan and conceptualize, which is based more on a priori assumptions than on induction from the evidence. The second was Harriman's unfortunate failure to tie his theory to prior work by David Kelley on what Kelley, in his book Evidence of the Senses, calls the "perceptual judgment." That can be remedied by a full treatment by future scholars.

Reason is self-correcting, and Harriman's book is a tribute to reason. At every point Harriman returns to his main theses, which give the book an integrated structure. Students of Rand's philosophy will be fascinated to see how her philosophy relates to science. Scientists who find philosophy at best irrelevant and at worst hostile to their work will find this book enjoyable and eye-opening.

If I might indulge myself, let me tell you to take the logical leap -- and buy this book!

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.

This much-anticipated book, based on the lecture course "Induction in Physics and Philosophy" given some 7-8 years ago now by Dr. Leonard Peikoff, purports to present a "groundbreaking solution to the problem of induction, based on Ayn Rand's theory of concepts." (Back cover) The theory that is developed in the book rests on the following points: (1) inductive generalizations, like concepts, form (part of) a hierarchical structure, with a "first-level" that can be formed (relatively) directly from perception; (2) causal connections can, in certain cases, be perceived directly; and (3) generalizations are produced by applying already-formed concepts to (often single) instances of grasped causal connections.

The book's first chapter presents and develops these ideas as they apply to first-level inductions, largely by sketching an account of how a child forms generalizations like "pushing balls makes them roll" - or, more tersely, "balls roll." The idea is that the child actually perceives the causality involved in the combination of the pushing and the ball's shape and solidity *making* the ball act the way it does in response. And, lacking the conceptual sophistication that would be required to make some highly-specific or highly-qualified description of the perceived causal connection, the child instead describes the events in terms of exclusively first-level concepts: "balls roll." So the idea is that it is the open-endedness of concepts which renders *general* the child's description of perceived causal connection.

The book's middle chapters (2-5) are intended to show that this account of first-level generalization-formation illuminates and clarifies (and supports normative standards for) the formation of higher-level generalizations such as those prevalent in science and physics in particular. Some important issues that arise in the context of such scientific generalizations include (a) that causal connections are established by more sophisticated methods involving especially experimentation and mathematics, and (b) that the higher-level concepts which higher-level inductions utilize are themselves open to normative standards, so it is only and specifically *valid* concepts which are "green lights" to induction. (The red-light / green-light metaphor runs throughout the book.) These issues are developed in the middle chapters through essentialized re-tellings of important episodes from the history of physics (such as the Copernican revolution, the discoveries of Galileo, Kepler, and Newton, and the development of the atomic theory in the 19th century), as well as philosophical commentary on the episodes.

Chapter six presents some very interesting case studies -- most of which, curiously given the book's sub-title, aren't from physics -- in which scientists have made various sorts of inductive *errors*. These are intended to further support, by contrast, the account of proper induction that has been developed previously in the book. So, for example, we have cases in which scientists tried to induce based on mere correlations rather than a genuine grasp of causal connections, cases in which invalid concepts led to wrong generalizations, etc.

The final chapter raises -- and attempts to answer -- some questions about the role of mathematics in physics and philosophy and specifically why (given that physics and philosophy are both fundamentally inductive sciences) math is essential in physics but plays no role in philosophy. The chapter includes also some criticisms of current ideas in physics (for example, string theory and the big bang theory) as being based on a flawed approach to induction, and closes with the hope that physics -- with the help of a proper philosophical foundation -- can get back on track.

The above is intended as a neutral summary of the book's goals and content. Let me now turn to assessing it.

To begin with, I think the three key ideas presented in chapter 1 are important and correct. There *are* first-level generalizations which support and make possible the higher-level sorts of generalizations that scientists are (and unfortunately most philosophers concerned with induction have been) primarily concerned with. And as a matter of epistemological methodology, it is right to focus on these simplest, foundational cases to construct a theory to guide us in the more complex cases. I also think it is profoundly true that causal connections are sometimes perceivable, and Harriman is absolutely right to stress this as the fundamental answer to the skeptical views that emerge ultimately from a Humean, sensationalist account of perception. I would even go so far as to say that this idea (which, however, is not novel -- see for example the important book "Causal Powers" by Madden and Harre) is the key to solving the problem of induction. And second, the idea that generalizations are formed -- i.e., propositions are rendered general -- via the application of (open-ended) concepts to particular causal instances, strikes me as very interesting and pregnant.

However, even at the level of dealing with examples like "balls roll," I find that the book does not go far enough in clarifying and developing these ideas. I see rather large gaps in the account of first-level inductions presented in chapter 1, and these gaps seriously undermine the project of showing, through the subsequent history-of-science case studies, how induction works in physics. Let me explain by discussing three such gaps and some associated problems from the middle chapters.

First: not enough is done to distinguish cases in which one *can* genuinely perceive the causal connection between an entity (including its attributes and its surrounding conditions) and its actions -- and cases in which, despite being able to perceive an entity acting in a certain way, the action remains (insofar as what's actually given in perception is concerned) mysterious. In pushing a ball, for example, one can literally see and feel how the roundness and solidity allow it to roll across the floor. But take another example: say, a ball (containing batteries and appropriate electronic circuitry) that, when squeezed, plays a little song. Now, there is some sense in which a child who squeezes this ball and hears the song is perceiving causation: he is perceiving an entity acting in accordance with its identity, and that, according to Objectivism, is what causality *is*. But here, it seems to me that -- unlike the case of the rolling ball -- the specific features of its identity which underwrite the action in question are not relevantly available in perception. So *presumably* it would be wrong for a child to generalize, in this case, to "balls sing when you squeeze them" or just "balls sing" for short.

It should be clear that there is a whole spectrum of cases like this, from cases where (so to speak) the full causal "mechanism" of a certain action is itself available in perception, to cases where, despite seeing an entity act, the "mechanism" of the action is perceptually unavailable. This issue, however, is nowhere raised in the book, which instead sometimes gives the unfortunate (and certainly wrong) impression that *whenever* one perceives an entity acting, one is thus grasping a causal connection -- in the sense needed to warrant a generalization.

This same issue haunts the middle chapters of the book. For example, Harriman makes a compelling case that Kepler was motivated to find a genuinely causal understanding of the solar system and indeed produced, early in his career, compelling evidence that the planets' orbits are caused by forces exerted by the sun. This, he argues, is the "causal context" (page 71) in which Kepler famously discovered that, in order to account for the precise observational data gathered by Tycho Brahe, Mars must move in an ellipse with the sun at one focus. Harriman then applauds the rapidity and certainty with which Kepler "immediately generalized" (page 101) to the other planets, thus arriving at what we now call Kepler's first law of planetary motion: *all* planets move in ellipses with the sun at one focus. The crucial question, of course, is whether this generalization was warranted and, if so, what warranted it. But here one faces the question of whether this case is analogous to the case of perceiving a single ball rolling (and, I think, being warranted to generalize because one perceived the causal mechanism of the rolling) or whether it is instead analogous to the case of perceiving the squeezed ball singing. Since Kepler certainly was not aware of the cause of the *specifically elliptical* orbit of Mars, I think it is closer to the latter case -- and hence I am very skeptical of the claim that Kepler's immediate generalization was warranted. Here, though, what matters is not so much what Kepler was or wasn't entitled to infer at this particular moment, but rather just the fact that these kinds of questions are not addressed in -- but are instead in my opinion rather clumsily papered over in -- the book.

A second difficulty with the account of first-level inductions is the claim, stressed in chapter 1, that "all generalizations -- first-level and higher -- are statements of causal connection." (page 21) This idea is obviously crucial to the theory -- or, more precisely, crucial to the claim that the account of generalization presented in the book deserves to be called a theory of induction as such (as opposed to an account of one particular type of induction). Is the claim true? Even in the context of first-level generalizations, there would seem to be a whole class of general propositions which are not "statements of causal connection." I am thinking of propositions of the form "All S is P" -- but where P is a concept not of an action, but of an *attribute*. For example: "balls are round." Does such a proposition really state a causal connection, appearances to the contrary notwithstanding? Or is it somehow not a genuine -- or not a proper -- generalization? Or what?

Such questions are nowhere addressed in the book. But the crucial middle chapters of the book really needed them to be addressed. For example, the whole point of Chapter 5 is to present the gradual accumulation of evidence, during the 19th century, for the generalization: "matter is made of atoms." But this is precisely a proposition of the type mentioned in the previous paragraph: being "made of atoms" is not an *action* that pieces of matter take, so it is on its face implausible that this (obviously important) generalization could be understood as stating a causal connection. When one rises above appreciating and/or quibbling with various sub-points made in this chapter, then, one is left wondering what the chapter is doing in the book: its essence seems in fact to function as a counter-example to one of the central points of the theory the book is intending to present. The claim here is not that propositions like "balls are round" and "matter is made of atoms" are somehow fatal to the presented ideas about first-level generalizations; rather the claim is just that the quality of the book -- indeed, the claim that the book is really presenting a *theory* of induction (as opposed to merely some good preliminary ideas about one special type of induction) -- is seriously undermined by the fact that such propositions (and the questions they raise) are nowhere addressed or even acknowledged.

And here is a third problem with the account of first-level inductions. These are defined as generalizations that are "derived directly from perceptual observation, without the need of any antecedent generalizations. As such [they are] composed only of first-level concepts..." (page 19) As stated, though, this cannot be correct: generalizations (at least, those which attribute a characteristic to a subject -- as opposed to subsuming the subject under some wider concept) involve concepts of actions or attributes, which are not literally first-level. (My premise here -- that only concepts of entities such as "cat," "table," and "car" are literally first-level -- is, I take it, a standard and correct point in the Objectivist theory of conceptual hierarchy. It is perhaps debatable, however, to what extent this point was insisted on by Rand herself, as opposed to being clarified later by especially Harry Binswanger.) I gather that what Harriman meant was that the action (or attribute?) concepts with which one forms first-level generalizations should be *relatively* first-level, i.e., first-level within their category. Thus, action concepts like "roll" or "walk" -- the sorts of action concepts which are the first in that category to be formed by children -- would be first-level in the relevant, qualified sense.

But then the reasons that such qualifiedly-first-level concepts aren't first-level in the full, literal sense become quite relevant. The idea is that, in order to form a concept like (say) "walk" one must already possess concepts for some of the kinds of entities which can perform this action (say, "man" and "dog") -- and perhaps also concepts for some of the kinds of entities which perform distinctively *different* actions (say, "snake"). This is required, in effect, so that one can be in a position to conceptually isolate the actions as distinguished from the entities which take those actions. The relevant differentiation is maybe captured in words like this: "by 'walk' I mean the way that men and dogs move around, as opposed for example to the way snakes move around."

The point here is that, inherent in forming concepts that are (say) first-level-within-actions, is -- at least in some cases -- the prior awareness (held of course in perceptual, not conceptual, form) of those same actions as distinctive to the class of entities which perform them. To return to the example that is highlighted in the book, there seems to be a sense in which forming the concept "roll" presupposes a prior awareness of the fact that balls and other round things (like wheels) can move in this distinctive way, because of their shape. There is thus a kind of chicken-and-egg problem: is it (as the book's account of induction suggests) that one forms first-level generalizations by applying previously-formed concepts to newly-perceived causal connections? Or is it instead that grasping the relevant causal connections is part of the means by which one forms (e.g.) first-level-action concepts in the first place, with the formulation of general propositions then being coincident with or subsequent to this, but with no further perceptual input required? Or maybe sometimes it works one way, and sometimes the other? Again, the point here is not to try to answer these questions and not to claim that they can't be answered (and so are fatal to the book's program); rather, the point is just to suggest that such issues need to be addressed by anything purporting to present a complete theory of induction along the lines sketched in this book.

That this particular issue needed to be addressed is supported by the fact that this kind of chicken-and-egg problem arises not only with first-level generalizations about rolling balls, but also in the history-of-science case studies of the middle chapters. For example, much of the discussion of Galileo and Newton is intended to highlight the ways in which their possession of key (valid) concepts allowed them to take the "logical leap" to correct inductive generalizations -- and conversely, how in certain cases the fact that they failed to possess certain key concepts (or held certain invalid concepts) prevented them from grasping general truths that would otherwise have been within reach. But in several of these cases, the actual history suggests a rather messier development than Harriman presents -- namely, a development in which some preliminary or partial grasp of a causal connection (like for example those ultimately posited in Newton's laws) provides a "green light" to the final, clear, full conceptualization of the relevant action or property (like for example with "momentum" and "gravity"). Of course, this in turn allows for the final, clear, full statement of the relevant causal law, so there is still some element of the concepts being a pre-existing "green light" to grasping the generalization. But still, the overall developmental pattern in such cases does not seem to be accurately captured by the idea of pre-existing, fully-formed concepts being applied to instances of (now scientifically-, experimentally-established) causal connections.

Again here, my point is not to assert that there is some kind of fatal circularity in the book's account of induction. Rather, it is just to raise certain questions about how, exactly, the ideas presented in Chapter 1 should be understood -- and then related questions about how these ideas should be extended, developed, and clarified in the context of the scientific case-histories. I do, however, regard it as a serious flaw in the book that such questions are not answered (or even raised), but are instead obscured by what, at times, amounts to a biased re-writing of the historical details to make things appear more congenial to the Chapter 1 ideas than, I think, they in fact are.

Let me now, more briefly, indicate some further problems I see with the book. In contrast to the three points raised and discussed in detail above, which I see as fundamental by the standards of the overall structure and purpose of the book itself, the following are in various ways more marginal (though still sufficiently important to warrant mentioning).

First, there is a recurring ambiguity between two very different senses in which a concept or other idea can be said to be "invalid." That is: some concepts (e.g., "angel") are invalid in the sense that their very formation rests on something irrational such that they in fact never should have been formed in the first place. But others (e.g., at least arguably, "impetus" and "phlogiston") are invalid in the sense that they turn out to involve classification by non-essentials or to refer to hypothesized entities or substances which turn out in fact not to exist. Such concepts can be said to be invalid from the point of view of our present, more sophisticated context of knowledge, but were -- despite this -- perfectly rational to form (at least with some hypothetical status) in the earlier, more primitive context. But in claiming that invalid concepts are "red lights" to induction -- a central thesis of the book -- it is clearly important to distinguish these two senses of "invalid." The point of trying to construct a theory of induction, after all, is to help us -- in the present -- become better inducers. And it is obviously vacuous to advise somebody to base inductive generalizations only on those concepts which it is not only rational to have formed, but which -- in addition -- will turn out to remain "valid" in the presently-unknowable context of future centuries.

Speaking more generally, the complaint about the book here is that sometimes the history suffers from an element of Whiggishness -- i.e., using the benefit of hindsight from our contemporary perspective to present a story of good guys doing exclusively rational things and thereby discovering truths which stand the test of time, and bad guys doing exclusively irrational things and thereby arriving only at falsehoods. One example of many that could be given is Harriman's account of the debates over assigning relative atomic weights to the chemical elements. He dismisses Dalton's scheme for assigning atomic weights as based merely on "simplicity" arguments, and praises Avogadro's alternative scheme as leading to "unambiguous" results. (page 162) But in fact both schemes were argued for on the basis of "simplicity" -- just applied to different sets of phenomena -- and both led to atomic weight assignments that were relatively unambiguous. Of course, we know, today, that Avogadro's scheme leads to the *correct* atomic weights. But nobody at the time, Avogadro himself certainly included, was in a position to know this. (That is why these particular debates existed, and why Avogadro's hypothesis was for several decades regarded as hypothetical.) Anyway, this sort of bias sometimes renders Harriman's accounts bad as history -- and bad in a way that matters in the context of the role that the history is supposed to be playing in this book.

A second marginal problem I see with the book is a kind of sustained confusion about the relationship between causality and math in physics. Harriman stresses that "it is by means of relating quantities that scientists grasp and express causal relationships" (page 84), lobbies for the relative importance of the quantitative over the qualitative (page 181), and indeed suggests that physics should be understood as (merely?) the process of re-introducing measurements that were omitted in the process of originally-forming the involved concepts (page 231-2). All of this strikes me as very floaty and rationalistic (and also inconsistent!), and it just profoundly fails to resonate with my own understanding of how physicists unravel causal connections and formulate mathematical laws. Some examples will have to suffice to indicate my discomfort here. Thus: Max Planck famously stumbled on the correct formula for the spectral intensity of blackbody radiation, but (by his own explicit and indeed impassioned admission) did so without knowing what it meant physically or causally; it was only subsequently that Einstein suggested the particulate-character of electromagnetic radiation as the relevant causal/physical meaning of the formula -- a chronology that strikes me as rather typical in the history of physics. And: it seems to me, contrary to Harriman's explicit statement on page 112, that astronomers *did* precisely "begin by grasping the structure of the solar system in some rough, qualitative way [Copernicus!] and then use mathematics merely to fill in the quantitative details [Kepler!]" -- just as Faraday first grasped in a qualitative way that electromagnetic phenomena should be understood in terms of continuous *fields* before Maxwell could discover his eponymous equations, and just as de Broglie's suggestion that electrons were (qualitatively) wave-like preceded Schroedinger's discovery of the appropriate (quantitative) wave equation. Thus, I see important causal relationships being discovered in a purely qualitative form, equations being put forward in the absence of any relevant causal understanding, and (therefore also) equations that do *not* represent the re-introduction of quantitative measurements to already-grasped causal connections. I will also just note here in passing that almost everything in Chapter 7 about the role of math in physics and the reasons for its not playing that same role in philosophy, strike me as incomprehensibly rationalistic and fundamentally misguided.

A third "marginal" issue pertains to a question of the domain of applicability or scope of inductive generalizations -- mathematical laws in physics in particular. Unlike some issues mentioned earlier, this issue does actually get addressed at several places in the book. It comes up, for example, with Galileo's "discovery" that the period of a simple pendulum is independent of amplitude (or more precisely would be in the absence of air resistance -- or so Galileo thought), and also with the question (already mentioned) of whether Kepler was entitled, having shown that Mars moves in an ellipse, to infer that *all* planets move in ellipses. On both of these examples, I see problematic inconsistencies in the text. But let us focus here on a kind of paradigm example for the kind of issue I'm worried about: Newton's inverse square law of universal gravitation. Harriman is adamant that "Newton's laws are not contradicted by Einstein's discovery of relativity theory" (page 20). He repeats again later that "Newton's laws have not been contradicted by any discoveries made since the publication of the Principia" (page 146). Yet it is known that, for example, Newton's inverse square law makes predictions for the orbit of Mercury that are inconsistent with its actual orbit. How does Harriman propose to reconcile the relevant facts here?

This is not too clear. For example, Harriman asserts that "Newton ... *never* said, 'My laws apply without modification not only to all that is currently known in physics and astronomy...'." (page 146) That is certainly true. But the question is: what *should* he have said? That is -- granted Newton was entitled to infer an inverse-square gravitational force that applied not just to the particular objects he had studied, but one that was in some sense *universal* -- what, precisely, is the relevant sense of "universal"? Was there, for example, some range of distances over which he was in a position to assert the universal applicability of the inverse square law? (At least for objects whose masses lie in a certain range, perhaps? And/or to a certain degree of accuracy, perhaps?) Such questions are nowhere answered, which leaves one wondering if the only universality Newton was entitled to assert was the vacuous: this will apply wherever it does, in fact, turn out to apply. Harriman does suggest an alternative -- but very dubious -- answer in Chapter 1, where he asserts that "Newton's science remains absolute within Newton's context." Here Harriman's intended meaning is unclear. If this means that Newton was entitled to believe only that his laws were true in the domain of situations he had studied (an interpretation that is perhaps supported by Harriman's comments on Galileo's theory of projectiles on page 190), then one must address the kinds of questions I was just raising: what *is* this domain, exactly, and why was Newton (in his context of knowledge) entitled to generalize within it (but not outside it)? But if Harriman's remark means instead that Newton's laws were -- and remain -- "true for Newton" in the sense that Newton, due to his relatively limited context of knowledge, didn't know about the kinds of situations where those laws fail to apply, I would regard that as a profoundly wrong and indeed a profoundly misguided defense of the expansive/cumulative/hierarchical character of knowledge.

Again, on this kind of issue, I find that where Harriman should take advantage of the opportunity to shed light on an important and admittedly difficult set of issues, he instead retreats to vague (but also vaguely Objectivist-sounding) slogans, and windy assertions (one might call them arguments from intimidation) like that which concludes Chapter 5: "The nature of the inductive method is now clear." (page 188)

I have tried to indicate some of the important problems I see with the book. Obviously, I think there are several. But I don't want this to give the impression that I think the book is terrible or worthless. So let me also indicate some of its more successful and convincing aspects (beyond those already mentioned such as the truth and importance of the fact that causal connections are sometimes given in perception, and Harriman's expertly essentialized, if sometimes biased, recounting of the scientific case histories). I found myself not only agreeing but cheering when Harriman explained why the problem of induction "is not merely a puzzle for academics -- it is the problem of human survival" (page 8), when he argued against the alleged dichotomy between discovery and proof (pages 143-150), when he indicated the problems that a wrong understanding of scientific method leads to in science education (page 146), when he described the "bizarre reversal" in which (some) scientists became increasingly hostile to the idea of atoms just as conclusive evidence for their existence was appearing (page 151), and when he brilliantly captured and lampooned the profoundly and obviously unscientific character of the consistently rationalist (Cartesian) and consistently empiricist (Humean) approaches to science and induction (pages 212-223).

The only way to summarize all of the above is to say that the book is mixed. It contains some good -- even great -- elements, and some occasionally brilliant polemical rhetoric against the essential forms of irrationality vis a vis induction in science. And while the account of first-level inductions contains some excellent points and seems overall very promising, there are also some serious inadequacies which rear their heads quite problematically in the case studies of the middle chapters. I am personally left thinking that even the account of first-level generalization is far from complete, and that Harriman's project of applying it to (and developing it based on) the history of science has raised far more questions than it has answered. So although I think this is precisely the right project, and think that Harriman has done a great service not only by charting the project but also by presenting brilliantly essentialized case histories of several key episodes from the history of physics, I certainly can't agree at the end of the day that the book has succeeded in presenting "a groundbreaking solution to the problem of induction, based on Ayn Rand's theory of concepts". Indeed, I would question whether what the book does present even rises to the level of presenting a theory of induction at all -- let alone one that is groundbreaking, true, or somehow uniquely Objectivist.

In conclusion, despite its many virtues, the book fundamentally fails to live up to the extra-ordinary claims made on its back cover and also in Dr. Peikoff's introduction. It is, in the end, valuable but disappointing.

As the subtitle says, this book is about induction. When and why is the inference from "some" to "all" legitimate? The narratives about some famous scientists arriving at inductive generalizations are interesting and illuminating. There are ones about Benjamin Franklin, Kepler, Galileo, Newton, atomic theory, and chemistry. Harriman's emphasis on integration, conceptual hierarchy, and the role of mathematics are excellent. Integration in physics and science generally involves coherence testing a hypothesis with controlled experiments. A new and fundamental generalization has consequences extending well beyond what the generalization was specifically made about. Examples are the "inverse square law" and discoveries of atomic structure having important implications for chemistry. He explains how the chemical revolution that began in the late 18th century was to a large extent a quantitative one. "With the foundation provided by a quantitative method and an objective language, the chemists who followed Lavoisier made rapid progress in understanding how elements combine to form compounds" (p. 153). Some reviewers have disagreed with parts of the specific histories. I am not a physicist and don't know the specifics that well, so my review will mainly be on the philosophical part.

His narrative on Galileo includes the following: "Integration is the process of uniting a complexity of elements into a whole. Cognitive integration is the very essence of human thought, from concept-formation ... to induction ... to deduction. An item of knowledge is acquired and validated by means of grasping its relation to the whole of one's knowledge. A thinker always seeks to relate, grasp hidden similarities, discover connections, unify. A conceptual consciousness is an integrating mechanism, and its product--knowledge--is an inter-connected system, not a heap of isolated propositions" (p. 53).

The book starts with an overview of Ayn Rand's theory of concept formation, which I believe is generally sound. Integration is a significant element. I think Harriman, like Rand, over-generalizes on the role of measurement. He gives a very good account of the use of mathematics and measurement in physics, so it seems he should know that physicists use man-made physical instruments to perform or infer those measurements. Similar measurements are not made when forming all kinds of other concepts to the extent Ayn Rand described, at least until she considered some concepts of consciousness. Harriman says the measurement-omission process is subconscious and automatic (p. 67). What is his alleged "preconceptual measurement" (p. 230)? Do we allegedly have something like little man-made, physical, measuring instruments in our heads? Does "preconceptual measurement" translate to "perceptual measurement"? Do other animal species have this capacity, too? If not, why not? Concept-formation involves "omitting" *qualitative* differences, too. Near the end of the book, Harriman sometimes seems to forget what he said earlier. There he says such things as "consciousness is not numerable" and "numbers are applicable only to entities and their attributes, but conscious states are not entities." If consciousness is an attribute, these claims seem to conflict.

Like the reviewer Todd Becker said, I think Harriman tries to carry quantification too far. An example of such over-generalization is "A generalization is the conceptualization of cause and effect; i.e. induction may be described as measurement-omission applied to causal connections" (p.28). It is true for some, but is it true of every generalization and every induction? I think not. Consider the toddler throwing a ball and watching it roll. That a physicist could understand the action in terms of measurable force and measurable velocity does not imply the toddler does. Also, despite claiming that "induction may be described as measurement-omission applied to causal connections" in Chapter 1, there is a dearth of showing that in the scientific narratives. I found one attempt, that of Galileo and pendulums, for which lengths are proportional to the square of the period (p. 229-30). I submit that this is not omitting measurements, but rather summarizing them.

Another feature of Ayn Rand's theory of concepts is that they are hierarchical. Some concepts are more basic than others and higher level concepts rest on lower level ones. Harriman often applies this idea in his analysis, speaking of first-level and higher level concepts. Isn't measurement a higher level concept? It uses real numbers, including ratios and fractions. Counting and integers are lower level.

"The human intellect is a faculty for grasping quantities" (p.228). I agree, but it is also a faculty for grasping qualities (attributes), relations, and causes. They aren't all reducible to quantity. "Human consciousness is inherently a quantitative mechanism. It grasps reality--i.e., the attributes of entities and their causal relationships to one another--only through grasping quantitative data. In this sense, quantity has epistemological primacy over quality" (p. 231). This seems fine for physics and chemistry, but in general? Grasping of quantity surely enhances the efficacy of human consciousness, but it is only part of the whole. Harriman says his quantitative view is not like that of Pythagoras. However, it does lead him to make some conflicting claims, e.g. p. 231. He first says *if* we could know qualities simply by perception, without quantitative processing, then we could know causal relationships by direct perception, without numerical measurements. Yet in the same paragraph, he says to know that fire burns, we simply touch it and yell "Ouch!" -- no numerical measurements are required.

The over-generalization about measurement is not crucial for the book as a whole, however, since measuring and mathematics are a huge part in physics.

I believe a little more comparing his view of induction to Mill's Methods would have been a plus. He says quite a bit about two of Mill's Methods and gave several examples of Galileo and Newton using them. Guessing, he thinks the diversity of contexts and integration by noting the similarity and ignoring the differences adds to the strength of an induction using the method of agreement. That is at least implicit in his narratives of Galileo and Newton. He said he makes no distinction between the method of agreement and method of [concomitant] variations, but what about the other two Mill's Methods? Some comparison of his view of induction to those of Francis Bacon and William Whewell would have been a plus, too. Both wrote extensively about induction. Harriman's idea of integration seems to have a good deal in common with Whewell's ideas of colligation and consilience. Colligation is the mental operation of bringing together a number of empirical facts to form a general law. Consilience occurs when the evidence in favor of an induction is much stronger when it enables us to explain and predict cases of a kind different from those which were contemplated in the formation of our hypothesis.

What is new about this account of induction? The obvious one is the focus on physics. Others are the emphasis on integration, hierarchy, and the role of mathematics. Another is the similarity between induction and concept-formation in general. It's well worth reading.

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. If you want to know what Newton REALLY meant by "Hypotheses non fingo" (I frame no hypotheses) and why it was such a leap forward in scientific reasoning, read this book.

This is a major work in the philosophy of science. I have been a student of the philosophy of science for 45 years, and this I think is one of those "must-read" books.

For those who wish to appreciate this work in its historical and philosophical context, I would suggest reading a few other books first.

Read Bacon's Novum Organon to set this stage - this is arguably the true inception of Science, prior Islamic and Greek efforts notwithstanding. This will give you a picture of early attempts to apply scientific thinking to the natural world, and the great difficulties that early scientists faced. Science seems easy and simple in hindsight, but if you place yourself in Bacon's shoes, you gain a true appreciation for the height and steepness of the cliff he was attempting to scale.
Francis Bacon: The New Organon (Cambridge Texts in the History of Philosophy) (English and English Edition)

CP Snow's "The Two Cultures" provides some of the cultural background that leads to the arguments in the Logical Leap: Scientific vs. literary cultures.
The Two Cultures (Canto)

Kuhn's "Structure of Scientific Revolutions" is directly attacked by Harriman and Peikoff. Read it before you read The Logical Leap. I will say why later.
The Structure of Scientific Revolutions

Although the works of Paul Feyerabend are also attacked in The Logical Leap, do not read them. They will rot your brain.

Though some would say that you need to read some of Karl Popper, I think you can get along without him, at least initially.

Next, to address the critics: this is not a narrative work, it is a rhetorical work. Harriman and Peikoff have a particular point to get across, and they do an excellent job of presenting evidence that supports their view. While they address some potential criticisms of their views, they are not trying to be "objectively neutral" whatever that may mean.

The authors' view is that induction is the key to true science, and that "science" without induction is really faith, as in religious faith.

I find their arguments persuasive, and indeed this is one of the first works in the philosophy of science that seems rational and fully satisfying to the end - even their classification of the Big Bang theory as religion and not science.

To add a critique of my own: while they decry "scientism" (the view that science is a religion just like any other), they do not address some issues with how humans tend to view the world. While induction is indeed the key to science, humans do not think scientifically except when we force ourselves to do it. We tend to use heuristics - rules of thumb that have evolved by the survival of the fittest cognitive strategies for dealing with everyday issues. Any attempt to deal with how humans approach science needs to acknowledge how we are both helped and hampered by our mind's predilections. And the field of evolutionary psychology is starting to illuminate these brain-workings of ours. I would love to see a new edition of this work come out with a couple of chapters on human thinking and how our traditional modes of thinking both aid and hamper scientific induction. This is why I suggested you read Kuhn before this book; once you have read Kuhn, and then read Harriman and Peikoff, then you will understand why a study of science cannot be complete without a study of human minds.

If you wish to read more on the evolutionary background of the human mind, I suggest you start with these three books:

A Mind So Rare: The Evolution of Human Consciousness
Origins of the Modern Mind: Three Stages in the Evolution of Culture and Cognition
Mind in Science (Penguin Press Science)

In summary, this is one of the best books I have read in a long time. It is an extreme rarity, in that it is a deeply philosophical work that is a quick and easy read. Required reading for anyone who wishes to be considered an educated adult.

Have you ever though it strange that we can travel to the moon and back and that still, some claim that we cannot be certain of anything and that the great scientists follow no better method than mystical medicine men?

Harriman's book sets the record straight: scientists can be sure of what they do, and they have been so on many occasions in the past. There are good reasons for that the famous scientists were right, and it is not an accident that we can enjoy the many benefits we have today of adapting nature to our best.

It is important to note, however, that this book is about an advanced topic in epistemology. It is a good read if you have the required background knowledge. To get the most out of the book I recommend good knowledge of high-school-level physics and a basic understanding of Ayn Rand's epistemology. Without knowledge of Rand's epistemology, however, it is still valuable to read the book. The story about the great scientists at work is inspiring and fascinating.

Well written, a true page-turner, new and exciting insights in every section, I could not recommend this book more warmly. Happy reading!

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. Harriman because leaving our major differences aside, I believe we would be otherwise brothers at arms. Yet, the book has a suspicious agenda.

David Harriman has done an immense amount of research to find the true basis of modernism. And I think he has found it: radical idealism. He labors to show how radical idealism, the denial of a knowable reality, infiltrated modern philosophy and eventually left its mark on science. This `denial of reality' principle was formalized by physicists into what is now called Quantum Mechanics. It is often taught that objective scientific procedure forced these physicists to come to the conclusion that `reality is unknowable' and `truth is contradictory'. Harriman goes through great lengths to show that these very physicists who arrived at these conclusions were pre-loaded with these philosophies prior to having done any research, and that the results of the scientific procedures were purposely contrived in defiance of these very procedures. The results is (and Harriman produces the quotes) that both science and philosophy have ended by science's own admission. The ripple effect of these `truths' have created a modern society based on nihilism where contradiction is truth, ugliness is beauty, and defiance is the rule. I agree, but true Scholastic philosophy has been preaching this for centuries. What's important here is that Harriman convicts the villains with their own words... fascinating.

However, as a student of pre-Vatican II scholastic philosophy, I also detect a fraud in this book... and an agenda. The book is largely a shill for Ayn Rand's Objectivist philosophy. It is admitted in the book that Rand based her philosophy on Aristotelian logic. But my suspicion is deeper. The key terms defined by Rand in her philosophy (which Harriman presents in the first part of the book) were obviously lifted from Scholasticism and drained of their theological implications. It is a bit of an act of plagiarism. The `Philosophia Perennis' which Rand uses and abuses was once THE philosophy of the Church going back to a time centuries before Galileo. As so much of the book pivots on the Trial, it is important that the record be set straight. One does not understand the trial if one mis-portrays the philosophy.

The result of this is a built-in antagonism towards religion, if not an out right blame of it for the whole mess society currently is in. This is where Harriman has completely bolloxed up his research. He blames Kant as the inventor of this ideology. He wasn't. It is very old (Dualism) and the modern day advocate before Kant was Berkeley. Heisenberg himself admitted basing his theory on Berkeley. Errors such as blaming the Inquisition, portraying Copernicus as himself an antagonist of the Church (he wasn't, he was a Catholic priest), and mis-portraying Cardinal Bellarmine's philosophy, abound. Ultimately, Harriman must simplify the discussion and blames the Church for all that is wrong.

The actual debate is far more subtle and far more interesting. Had Harriman completely done his research (I suspect his admiration for Rand coupled with his disgust of the Church prevented him), he would have had a much better book.

A litany of mis-construed facts:
1) Copernicus was a Catholic Priest. He was hired by the Pope to find the reason that the calendars were falling into error. The calendar was fixed decades before the Trial of Galileo.
2) The Church was actually the advocate of Aristotelian philosophy against the rising Platonism instilled and sponsored by the Medici Family. Galileo was part of this new movement.
3) It is now well known the the true heart of the Galileo Trial was not Solar Centricity. It was about the constitution of reality itself. See, The Atom in the History of Human Thought, and Galileo Heretic for the actual trial documents. Galileo was not a martyr. All the primary participants in the trial, not just Galileo, were separated from society. It cost Bellarmine the Papacy (he was actually a friend of Galileo). The reason for this was the feared volatility of the matter, something Harriman's book in spirit agrees with.
4) Most recent science history books now acknowledge that the Church acted relatively reasonably as to Solar Centricity. It was trying to save the appearances and the conclusive proof didn't arrive until after the Trial. My belief is that they already more-or-less knew. The debate itself caused them to change the calendar decades before the trial.
5) Galileo was not as scientific as modern history books often portray him. Even Newton was an alchemist. The dilemma is just not as open-and-shut as Harriman portrays it.
6) Kant was not in league with the Catholic Church as implied. It was the `faith alone' Protestants who were attempting to re-define `faith' itself. This concept was derived from Ockham who believed `reason' was not necessary to salvation (the Razor). This was the very reason the Protestants split.
7) Most importantly. There was a difference between how moderns hear the word `faith' and the way it was understood in Scholastic Philosophy, and in the Bible. Today we hear the term as `willed belief', or `a mental conviction defying reason'. In Aristotle, Greek thought, and Scholastic Philosophy `faith' is merely the senses perceiving. `Belief' is the mind conceiving. The words are different and a distinction is made. The motto of the Scholastic Church was, `there is nothing in the intellect that is not first in the senses'. This was done precisely to make the very point Harriman spends an entire book to make. Understood in this light, Bellarmine's philosophical position in the Trial is completely understandable and actually consistent with Harriman's own philosophical disposition: reality is something you accepted as true `on faith' because your senses do not lie, a position Harriman specifically states as true later in this book (there are subtleties however he misses). This revealed, Rand's Objectivism becomes less unique, and more contrived.

There are several more examples.

The reason I've attempted to challenge Mr. Harriman so extensively is that the problem of the emergence of Modern Science is not as simple as he portrays it. While Copernicus is often shown as a scientist, in fact, the very Solar Centric Theory that emerged during the Renaissance did not arise out of science, but from the very ancient Platonic Mysticism Harriman criticizes. A consultation of Copernicus' test, On the Revolutions, would have revealed this as his famed diagram is itself in homage to the God Hermes. Harriman criticizes modern physicists for throwing away the appearances in favor of pure mathematics, but he fails to consult primary texts in his research which would have revealed this is precisely the dilemma the Church was faced with: an exhaustive mathematical work trying to promote what was then considered a `mysticism' that was not yet quite consistent with the appearances. Because of this mis-step, Harriman is antagonistic to the very people who would otherwise be in league with him (myself for example).

Ultimately, Harriman is right, at least on the pedigree of Quantum Mechanics. However his `new' inductive method of logic isn't appreciably different from what the Scholastics taught: induction was scientific, deduction philosophical, they are supposed to keep each other in check (I have the texts). Harriman tries to create a purely inductive approach to reason, but the book itself is a hypothesis deductively reasoned in an attempt to correct science. That IS philosophy. Harriman throws the baby out with the bath water to make his point. A better researched book could have still gotten him where he wants to be, would've been more open minded, and more interesting. The Church and Galileo were faced with a dilemma. We are still faced with that dilemma. However, his argument and conviction of modern physics is precious. Perhaps it was his allegiance to Rand, or his atheism, that clouded his judgment. None-the-less, the book is provocative, unique and worth the read. I would love to have it out with him.

I thoroughly enjoyed this book, and its presentation of induction as relying on a hierachical and contextual build up from first level concepts.

The section comparing Rationalism and Empiricism (and rejecting both as false alternatives) is a must read for anyone interested in the philosophical issues involved, and by this I most certainly mean that it has practical application across all spheres of human life. This section was incredibly illuminating.

The scientific history has been challenged by some. I'm not in a position to judge that, but I will say that Mr. Harriman and his defenders on this issue have sometimes reponded in a churlish fashion.

My only suggestion for improvement would be the addition of a section, or at least a chapter, to applying the theory outside of science (as it clearly is intended to be.) I think it is much harder to apply induction to such areas as psychology, human relations, and moral judgement.

All in all a fascinating read.

In 'The Logical Leap', David Harriman provides a compelling account of how progress is made in science, by starting with a solid foundation in sensory experience and using stepwise induction to build ever more abstract concepts and laws into a hierarchical framework of increasing explanatory and predictive power. Harriman's detailed account of major advances in several fields of classical physics works to counteract the textbook version of science, the so-called "hypothetico-deductive method" in which hypotheses are proposed out of thin air, and validated or falsified by sheer numerical repetition of experiments. That account of induction always struck me as a false and unconvincing caricature of what scientists actually do. In its stead, Harriman shows how valid scientific laws and concepts do not arise from "intuition" or disembodied reasoning, but rather represent the integration of a large number of specific observations made under a wide range of circumstances. Induction does not require any particular number of repetitions of the same experiment, but rather works by means of applying Mill's principles of agreement and difference to isolate common causal factors while varying other factors in order to show they are not causal. When done correctly in this way, science does not merely report regularities, but actually elucidates real causal connections.

That said, Harriman's book is uneven - very strong and engaging in some places, and weak or unconvincing in other places. The strongest sections are those where he illustrates his thesis about induction by applying it to several detailed historical reconstructions of real scientific advances. This includes Chapter 2 (Experimental Method) and Chapter 4 (Newton's Integration) which recount how Isaac Newton marshalled experimental evidence to prove his theory of color and later his theory of universal gravitation, and Chapter 5 (The Atomic Theory) which shows how Antoine Lavoisier and others provided conclusive experimental proof of the reality and explanatory power of chemical atoms, at the very same time that Berthelot and other nineteenth century positivists were arguing against the possibility of any theory based on unobservables, instead attempting to reduce science to the mere description of regularities.

Harriman also nicely differentiates the Newtonian approach to induction -- building theory step by step by inductive abstraction from experimental evidence -- from the extremes of Platonism (which distrusts sensory experience as deceptive and only crudely reflective of a perfect reality accessible only to pure reason) and empiricism (which aims only to describe empirical regularities and denies the reality of any concepts, causes, or theoretical reality beyond what is given in sensory experience).

However, Harriman's account is unsatisfying in other places. Perhaps the most serious weakness of the account is its apparent circularity regarding the "contextual validity" of induction. In attempting to fend off skepticism, Harriman argues that valid induction can never lead to a false conclusion, so long as it only claims to apply within the context of its discovery and proof. As Harriman claims on pp. 146-147:

"A theory reached and validated by this method is never overthrown. Thus, for example, Newton's laws have not been contradicted by any discoveries made since the publication of the Principia...he knew that the process of inductive reasoning that led to his laws established the context within which they are proven. Further evidence is required if the laws are to be extended into previously unstudied realms."

In saying this, Harriman is attempting to counter the criticism that Newton's laws were "overthrown" when they were later found not to apply strictly at the very large or very small scales of length, where the laws of relativity and quantum theory govern with greater precision. But this begs the question: how does one know in advance (before finding new "exceptions") how wide a "context" or "realm" of validity one can justifiably claim for a given theory? Newton's laws of motion derived from a very specific set of experiments, including the work of his predecessors such as Gallieo who studied the kinematics of certain terrestial objects and astronomical bodies, to which he added a wider range of examples, including multi-body interactions between the sun and planets, ocean tides, and the orbits of comets. There is no doubt that the range of phenomena used to inductively validate Newton's laws was wide. But how do we generalize from a specific set of examples to the determination of a delimited "context" or "realm" over which derived laws should apply. How broadly are we justified in generalizing from the causes seen to act on the the specific set of terrestial and astronomical bodies studied to causes that act other bodies where the theory has not yet been applied? This is not an easily answered question, since there was no reason to think that Newton's laws would cease to strictly apply at larger or smaller scales than the specific ones tested. In fact, this brings us back to the very problem of induction: how far beyond the range of "context" of specific instances examined are we justified in extending or generalizing the applicability of a theory. Harriman seems to be saying we cannot fail, because a theory applies only within the context in which it is valid. But this is circular and begs the question: how far is it valid beyond the specific examples tested? In fact, relativistic effects are seen even at the scale of the distances of the solar system, a scale which was encompassed within Newton's "context" of study, even though the effects were beyond the precision of measurement techniques he had at his disposal. So Newton would not have been unjustified in generalizing based upon scale. And if we try to draw the line of applicability in terms of the speed of the objects he tested, why can we point to speed but not to scale? If one always has the "excuse" of imperfect measurement techniques or limited experience, this would seem to be a way to wiggle out of virtually any challenge to a theory being overthrown.

The other significant weakness of Harrison's account is his attempt to explain the role of mathematics in physics. "Mathematics is the language of physics--but why?", he asks at the outset of Chapter 7 (The Role of Mathematics and Philosophy). To answer this, he takes off from Rand's theory of concepts, in which a concept is "mental integration" of individual percepts, with the particular quantitative measurements are omitted. Physics, according to Harriman, reverses the process by adding back the quantitative measurements to the concepts, and using experimental evidence to relate concepts causally and quantitatively. While we can experience certain immediate causal relationships directly -- e.g. pushing a ball so that it rolls-- higher order causal relationships cannot be directly perceived. "Mathematics enables us to reduce to the scale of our perception countless instances beyond our perception....We study the fall of the apple, which is easily perceivable--and we can now deal with the force of attraction one galaxy exerts on another." (p. 230). So far so good.

But then Harrison proceeds to go too far with this idea of quantification:

"Human consciousness is inherently a quantitative mechanism. It grasps reality--i.e., the attributes of entitites and their causal relationships to one another--only through grasping quantitative data. In this sense, quantity has epistemological primacy over quality."

Really? Does human consciousness reduce to quantitative relationships? This contention appears to contradict Rand's thesis that conceptualization is the process of omitting measurements. (And it would be absurdly cumbersome to posit that whenever we form a concept we first measure each percept and subsequently omit the measurement). It is certainly not true of most everyday experience regarding our interactions with people, our appreciation of music, art, food, our thinking of past events and future plans; measurement is absent from such thoughts. While quantitative thinking may be part of our consciousness, it is a stretch to assert that consciousness is solely and inherently quantitative. Furthermore, not even all science is purely quantitative; many aspects of science are qualitative, and qualitative science can be as rigorous as quantitative science. For example much of science deals with qualitative classification or identification, and the inductive methods of difference and agreement are often applied to identify causal factors which are categorical or qualitative, rather than of a quantitative nature. This is true, for example, in chemistry and evolutionary biology. Even certain parts of physics deal with qualitative or quantum entities which do not represent continuous functions, but rather discrete values such as charge or spin. None of this is to deny that mathematics play an important role in physics and science, but it is absurd to state that all of physics or science reduces to mathematical relationships.

Beyond the unconvincing claim about the inherent quantitative nature of consciousness, Harriman never really answers the question that interests most people: why is it that fundamental scientific principles so often reduce to very simple, elegant mathematical relationships? For example, why is gravitational force proportional to the square of the distance between two bodies, rather than some non-integer power like 2.135--or perhaps to a relationship that not even reducible to a polynomial or other simple algebraic relationship. This elegance and simplicity is what has attracted some scientists towards the temptation of Platonism. I think that Harrimon provides very strong arguments that Platonic elegance is a false idol which has resulted in many false and experimentally ungrounded theories, from Ptolemy and Descartes to contemporary string theory. His arguments in favor of Newton's method are compelling. But he has failed to provide any insights into why the mathematical laws, that were both induced from and explain the physical world, are as simple and powerful as they are.

There are other minor flaws, including a number of dogmatic assertions which are surprisingly non-empirical for a treatise whose emphasis is the need to ground science in experience. One glaring example of this is Harriman's attitude towards animals: "Animals are perceptual-level organisms. They learn from experience, but only by highly delimited perceptual association. They cannot imagine the unobserved, the future or the world beyond such associations. They know, deal with, and react to concretes, and only concretes." (p. 7). This flies in the face of extensive evidence showing that many animals can in fact generalize beyond highly specific percepts in their learning and problem solving behaviors.

Despite these flaws, I think Harriman's book has broken new ground with an original account of induction that has the possibility of not only describing the successful advances in science and differentiating them from fallacious science...but also of helping working scientists develop greater insight into what they need to do in order to proceed on solid ground to make progress in their own contemporary research.