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.