The following review was written before news of Robert Nozick’s death in January. He was Arthur Kingsley Porter Professor of Philosophy at Harvard, and was named a University Professor there in 1998, Harvard’s most distinguished professorial position. Anarchy, State, and Utopia, published in 1974, when Nozick was only thirty-five, was his most publicly visible book, but he wrote several others—most notably, I think, Philosophical Explanations (1981). A recent collection, Robert Nozick, edited by David Schmidtz (Cambridge University Press, 2002), contains essays by ten distinguished philosophers on aspects of Nozick’s philosophy. I never met him, but always admired his prodigious energy and undeniable brilliance. My review is, I hope, written in a spirit of open and honest criticism of which I think he would have approved. I had fully expected a strong reply from him in the correspondence columns of this journal, but that is not to be.


p align=”right”>—C. McG.

Robert Nozick’s intellectual energy is a thing of wonder. In Invariances he ranges copiously over relativity theory and quantum theory, cosmology, modal logic, topology, evolutionary biology, neuroscience, cognitive psychology, decision theory, economics, and even Soviet history—not to mention his strictly philosophical forays into the nature of truth, objectivity, necessity, consciousness, and ethics. There are one hundred pages of tightly packed footnotes to three hundred pages of text. The effect (or the method) is to overwhelm the reader with a heavy arsenal of erudition. Duly intimidated, thoroughly outclassed, reduced to silence, the reader may find himself brooding on his shortcomings.

Nozick’s avowed aim in this book is to bring science to bear on philosophy. He writes:

In investigating the functions of truth (true belief), objectivity, ethics, and consciousness, we will have occasion to keep our eyes peeled for relevant scientific theories and scientific data. Philosophy is not (wholly) an a priori discipline, so it must mesh with current knowledge and also pursue promising and puzzling leads stemming from that knowledge. We shall also seek to identify and separate the empirical substrate or aspect of philosophical questions and, to the extent that this is possible, to transform philosophical questions into factual, empirical ones.

In keeping with this policy, Nozick recommends an exploratory style of philosophical research:

My own philosophical bent is to open possibilities for consideration. Not to close them. This book suggests new philosophical views and theses, and the reasons it produces to support these are meant to launch them for exploration, not to demonstrate conclusively that they are correct.

Not surprisingly, Nozick is an ardent fallibilist. There is, in his view, virtually nothing that we could not be wrong about—even logic and the existence of our own minds:

Everything is open to transformation. Nothing stays fixed. Even something as fundamental as the principle of noncontradiction can be open to questioning and to revision.

Cartesian certainty is not to be had. We have had our common-sense views shattered by science in the past, and there is no limit to how much further the shattering might go. Like most radical fallibilists, Nozick is wide open to the possibility of deep error in what we believe to be true, but he doesn’t extend the same modesty to the question of how possible and how widespread the truth of our beliefs might be. Surely a consistent fallibilist should hold that both options are possible: that we might be wrong about a lot and that we might be right about a lot.

Maybe it will turn out that most of our current common-sense and scientific beliefs are true, well grounded, and unrevisable; if we are consistent fallibilists, we certainly cannot be sure that they will be shown wrong. Fallibilism says that we cannot be certain what the truth status of our beliefs is, and this leaves room for the possibility that an enormous amount of what we believe is perfectly sound and will never be revised (in fact, I think this is very likely to be the case). A fallibilist cannot consistently maintain that he is sure that our current beliefs will eventually be shown false, since he does not think we can be sure of anything. Fallibilists tend to stress the pessimistic possibility, but the optimistic possibility cannot be ruled out, by their own lights.

The centerpiece of Invariances is Chapter 2, “Invariance and Objectivity.” Here Nozick offers us a theory of objectivity—or of the objective/subjective contrast—in terms of the technical notion of “invariance under transformations.” For example, you can assign different numbers to measure temperature, as with the Fahrenheit and centigrade scales, and yet certain relationships between these numbers stay constant from one scale to the other. In putting forward this theory, Nozick makes it clear that he is partly motivated by recent postmodernist skepticism about the notion of objectivity; partly he simply wishes to provide a rigorous elucidation of a philosophically central concept, with appli- cations from physics to ethics. His question is: What makes a fact objective? And his answer is: That it is invariant under certain transformations. For him, this will be a case of subjecting an old philosophical question to rigorous scientific treatment. To start with, we need some initial grasp of the intended notion of objectivity. Nozick suggests three characteristics that mark a fact as objective: First, “an objective fact is accessible from different angles. Access to it can be repeated by the same sense (sight, touch, etc.) at different times; it can be repeated by different senses of the same observer, and also by different observers. Different laboratories can replicate the phenomenon.” Second, “there is or can be intersubjective agreement about it.” Third, objective facts hold “independently of people’s beliefs, desires, hopes, and observations or measurements.”


Now it is not clear that the first two characteristics are really distinct, since intersubjective agreement seems to be just a matter of the multiple accessibility of the fact: if a fact is available from different perspectives, then there can be intersubjective agreement about it. For example, the shape of an object can be perceived from different perspectives and people can come to an agreement about what the shape is. But the basic idea seems clear enough: objective facts are publicly accessible. The third characteristic has the result that mental facts are not objective, since obviously they are not independent of belief, desire, etc. This is certainly a recognizable notion of objectivity, opposing it to privacy and mentality; it is not merely an arbitrary stipulation about how Nozick intends to use the word “objective”—it corresponds to the accepted meaning of the term.

The big question for Nozick is how this notion is related to his favored idea of invariance under transformations, for he claims that “an objective fact is invariant under various transformations” and that “it is this invariance that constitutes something as an objective truth.” Indeed, he claims that invariance is what “underlies and explains” the three features of objectivity he has outlined. So we need to know what this kind of invariance involves. And here is where we get hit with physics:

That invariance is importantly connected to something’s being an objective fact is suggested by the practice of physicists, who treat what is invariant under Lorentz transformations as more objective than what varies under these transformations. P.A.M. Dirac writes, “The important things in the world appear as the invariants…of… transformations.” Einstein taught us that spatial distance and temporal distance are relative to an observer; their magnitudes will be measured differently by different inertial observers, and spatial and temporal intervals are not invariant under Lorentz transformations.

However, inertial observers will agree about another, more complicated interval between events, involving not just spatial separations alone or temporal separations alone but a particular mixture of the two, namely, the square root of the square of the time separation minus the square of the spatial separation. This more complicated interval is invariant under Lorentz transformations. The principle of relativity of Einstein’s Special Theory holds that all laws of physics are the same for all inertial observers; they are the same in every inertial reference frame, and so are invariant under Lorentz transformations.

That an interval involving both temporal and spatial separation is invariant, while no simpler interval involving only temporal or only spatial separation is invariant under Lorentz transformations, is the reason why talk of a unified space-time is significant.

This key passage invites several queries. First, the only physicist cited as supporting the identification of objectivity with invariance is Dirac, so it is hard to see what authority derives from “the practice of physicists” for Nozick’s novel philosophical suggestion. And my own inquiries have not turned up any such identification in the minds of other physicists. Second, the quotation from Dirac does not in fact support Nozick’s proposal, since Dirac speaks of “importance” and not “objectivity” (important for what—calculation? the formulation of laws?). Third, and most substantial, it appears quite wrong to construe relativity theory as asserting that spatial and temporal intervals are not objective or are subjective, while the appropriate spatiotemporal intervals are deemed objective. What is true is that spatial and temporal intervals are “frame-dependent” in that theory, so that there is a relativity in their nature, while suitable spatiotemporal intervals are “frame-independent” and hence absolute.

But why, according to Nozick’s three tests of objectivity, should this relativity imply any lack of objectivity? Obviously, it does not make spatial and temporal intervals mind-dependent in any way, or not public, or not intersubjectively accessible. Does it make spatiotemporal intervals somehow deeper? Perhaps, but why is depth the same as objectivity? Are physical objects subjective compared to the “deeper” particles that make them up? Are atoms more objective than molecules? The simple fact is that the theoretical primacy of certain entities in physical theories has nothing intrinsically to do with how objective those entities are.


I suspect that Nozick may have been misled by another kind of invariance, exemplified by scales for the measurement of temperature. Referring to the Fahrenheit and centigrade scales, he writes: “The two scales are equally good scales for measuring temperature; anything that varies with the scale of measurement is not an objective fact about temperature.” This is surely correct: these scales of measurement assign arbitrary numbers to particu-lar temperatures, so there is no scale-independent sense in which a particular object has (say) the number 60 as its temperature. The scales are conventional in that the numerical assignments conferred by them are a mat-ter of human choice and convenience; nothing in nature says that 32 is the right number to assign to water at the freezing point, as opposed to any other number. In this case it would be perfectly sensible to say that the particular choice of scale had no objective significance; it belongs to our system of description, not to the world beyond.

But Nozick is not making merely this familiar point; he is after something much more ambitious. And clearly the conventionality of measurement systems won’t help in giving us a conception of objectivity that excludes mental states, since we can also measure such states—as psychologists do, for example, in psychophysics or the measurement of intelligence. Facts about mental states will be invariant under different scales of measurement, and yet will be subjective according to Nozick’s own criteria (they will obviously not be independent of mental states). So the kind of invariance he has in mind cannot just consist in the conventionality of measurement systems.

Nozick indeed seeks to generalize his notion of invariance, writing:

The physicist discovers basic invariances in the world, and the ordinary macro-objects and macrofacts that we encounter also show invariances, at a different level from the invariances of the physicist. A bottle’s shape or color does not change as we rotate it or move it from one place to another.

According to Nozick’s analysis of objectivity, then, the shape and color are objective, while the movement is subjective, since it is not invariant under this particular transformation. But there are two obvious problems with this. First, movement is clearly just as objective as shape or color, and Nozick says nothing to contest this. Second, why can’t we consider another type of invariance—that of an object’s position under transformations of its shape or color? If I dent or paint an object, I may leave its position unchanged—so is it that now its position is objective but its shape and color are not? Some things stay the same while others change; but nothing in this elementary fact tells us what is subjective or objective. My thoughts and sensations may remain the same as I move about the room: Does that show that my mind is objective and my body subjective? Hardly. Invariance and change have nothing essentially to do with the distinction between objective and subjective facts.

Nozick’s discussion of conserved quantities such as mass or energy brings out the oddity of his theory. As if it were self-evident he writes:

So it is not surprising that laws that are invariant under various transformations are held to be more objective. Such laws correspond to a quantity that is conserved, and something whose amount in this universe cannot be altered, diminished, or augmented should count as (at least tied for being) the most objective thing there actually is.

By whom is this “held”? And why should what is not conserved be any less objective than what is? Energy is conserved, shape is not: Is shape therefore not an objective property of things? And what sense is there in saying that it is less objective? Surely shape bears all the marks of objectivity that Nozick himself tabulated: access from different angles, intersubjective agreement, mind-independence. Besides, how can one fact be less objective than another. Facts are either objective or not—though our conception of them may vary in objectivity (I will return to this). Some objective entities are conserved and some are not; but these are not ranked on some supposed scale recording degrees of objectivity. To assert otherwise is to lose all contact with the notion of objectivity we started out with, and which Nozick offered to capture and respect.

Conspicuously absent from Nozick’s book is any serious discussion of alternative accounts of the distinction between what is subjective and what is objective. Thomas Nagel, in particular, has famously written on this subject in The View from Nowhere,* but I could find no reference to that book in the voluminous footnotes to Nozick’s chapter, and no discussion of Nagel’s well-known account of the distinction. That account identifies an objective fact with one that can be grasped from many “points of view” and a subjective fact with one that can be grasped only from one “point of view.” Thus the facts of physics are objective because intelligent beings of varying subjective constitutions—different senses and so forth—can grasp their nature, while the facts of subjective phenomenology—how it feels to see something red or smell a rose, say—can only be grasped by sharing that very phenomenology. On this account, mental facts turn out to be subjective and physical facts do not—which is presumably the way we want any account of the objective/subjective distinction to carve up the territory. It is not that some physical facts are objective and some are not, which is what Nozick seems to be envisaging. It would have been helpful if he had tried to set his theory beside such intuitively natural accounts as Nagel’s; as it is, the theory floats stipulatively in a vacuum.

Nozick seems rather coy about how mental facts fit his theory; indeed he hardly discusses this crucial question at all. Here is what he says:

Our speaking of objective facts has not been pleonastic. There are also facts that are not objective ones. That I am now thinking of a particular number, and what number that is, is not, according to our criterion, an objective fact. There are not different routes of access to what number I am thinking of. Yet, that I am thinking of that particular number is some kind of fact. Call this a subjective fact.

Presumably, the point has nothing specifically to do with thinking about numbers; it is intended to apply to any kind of thought, and apparently to other states of consciousness. That is all well and good, since we do want the mental to count as subjective if anything does, but again two questions press for a response. First, Nozick here seems to be committing himself to a very strong thesis of privileged access: he is saying that there is no access to a person’s thoughts save what the thinker herself enjoys—and similarly for other types of mental state. But, unless we are to embrace full-blown skepticism about other minds—which Nozick shows no inclination to do—this is just false. After all, I can ask you what you are thinking and you can tell me—and as a result I may gain “access” to your thoughts. Similarly, I can see you looking at a table and may conclude correctly that you are seeing a table. So mental facts are accessible from different “angles” and do allow intersubjective agreement. Is Nozick really trying to deny this? He doesn’t tell us.

Secondly, even allowing that mental facts are accessible to no one but the person who has them, how does this case fit Nozick’s official theory of objectivity as invariance under transformations? Again, he makes no effort to say; and it is hard indeed to see how. What are the transformations under which mental facts fail to be invariant? And can’t they clearly be invariant under some transformations—such as closing one’s eyes or moving one’s head while thinking of a number? At this point the whole idea of invariance as the basis of objectivity looks wildly misguided, and Nozick volunteers nothing to address the reader’s natural incredulity. He just plows blithely on to his next creative aperçu or chunk of reported science.

There is a second notion of objectivity that Nozick sets out to elucidate, namely the notion of objective belief (as opposed to fact), and here I think he is on much firmer ground. His suggestion is this: “A judgement or belief is objective when it is reached by a certain sort of process, one that does not involve biasing or distorting factors that lead belief away from the truth.” That is, I have an objectively formed belief when my belief is not biased by factors that tend to lead to the formation of false beliefs—such as the desire that something should be so.

Now this has the reassuring ring of banality, but I think it omits something crucial to the notion of rational belief formation. It is not merely that the process must reliably lead toward truth; it is rather that it must be based upon, and be responsive to, good reasons. A rational belief is not merely one that is formed by a process that reliably produces true beliefs; it must also be formed because of objective reasons that objectively support the belief in question. If my brain is rigged up by a scientist in such a way that whenever I believe what I wish the belief always turns out true (the scientist only ever produces wishes in me that fit the facts), then I reliably believe what is true—but my belief formation is a matter of irrational wishful thinking nonetheless. The point is that in this case I don’t form my beliefs because of rational sensitivity to what are objectively good reasons, but rather simply believe what I wish to be so, irrespective of reasons and evidence. So I think there is a misplaced emphasis in Nozick’s apparently banal characterization of what makes a belief rational or objective. But this is clearly a minor quibble (and would require a lot more argument than I have given here to establish) compared to the problems I have identified in his theory of objective facts.

There is much else in Invariances that is less open to criticism, and indeed sometimes stimulating; I have focused here on what is intended as the heart of the book and as its chief novelty. I can only briefly discuss three of Nozick’s other main topics: relative truth, consciousness, and ethics. These topics are largely independent of the strange theory of objectivity, though Nozick keeps insisting on bringing that theory into his other discussions, never very illuminatingly I think.

The chapter on relative truth distinguishes trivial ways in which truth might be relative from momentous ways. Sentences can obviously be true in some contexts but not in others for the boring reason that they refer to those contexts: “I am hot” can be true relative to my context but not to yours—since I might be hot and you might not be. But this is not the kind of relativity that relativists have claimed when they assert that what is true in one culture might be false in another; and Nozick can find no good defense of this nontrivial relativism about truth. I agree, but I think he gives an extremely implausible reason for the anti-relativist conclusion, namely that there is enough “unity of humankind” to underpin a single concept of truth across cultures. It is not that I doubt this idea of unity; rather, it strikes me as quite misguided to make the existence of such unity a requirement of there being absolute truths. Suppose there were no such unity and people differed markedly in their natures from place to place. Does that mean that what they say cannot be true absolutely—for example, that a giant redwood tree is taller than a blade of grass? Surely not: Why should this admitted diversity prevent them from stating what is nonrelatively true of the world around them? Truth depends upon how the world is, not upon how the speaker is; the laws of physics, say, are the same for everyone, even if people differ a lot in their own natures. So absolute truth does not presuppose a common human nature across times and places.

Consciousness can reduce even the most fastidious thinker to blabbering incoherence, so it is perhaps not surprising that Nozick should be capable of uttering the following:

I suggest that thoughts, that is, linguistic or at any rate semantic items, are the representations of… parallel distributed processing neural states. Thoughts in words or wordlike entities are the way in which these PDP neural states present themselves to us. The reason that linguistic thoughts do not have a phenomenology is that linguistic thoughts themselves are a phenomenology, the phenomenology of neural parallel distributed processing states. Semantic content is the way in which (certain) neural states feel to us. (I feel that at best I am groping toward an insight here; I would be far more comfortable if I understood my own proposal more clearly.)

If he is “groping toward an insight” here, I have no idea what it is. Obviously, thoughts don’t represent neural states in the sense of being about them (except when you are thinking explicitly about neural states, of course); and what could it mean to say that a thought about London, say, is just the way your neural states feel to you? How does such an alleged feeling make your thought about London? And isn’t it simply false to say that your neural states feel any way to you—unless you have your fingers in your brain or something?

The main point of this chapter is to suggest that consciousness has the function of enabling a more flexible and fine-grained response to external objects; it allows the organism to transcend simple reflex. This is a familiar thought, but it faces two formidable difficulties. First, why should such flexibility require the kind of consciousness that we have? Couldn’t the world have been designed in such a way that organisms were flexible but had no inner life? Flexibility is a matter of behavioral capacity; consciousness is a matter of inner phenomenology: Where is the logical connection here?

Secondly, how does this type of account deal with simple sensations such as pain? Pain is certainly a conscious state—it has a highly distinctive phenomenology—yet it can arise by reflex and does not exhibit the kind of flexibility Nozick is associating with consciousness. It is notable that Nozick avoids the subject of pain throughout this chapter (a mainstay of discussions of the mind–body problem), and indeed it is hard to see how his theory can accommodate it.

In the final chapter, “The Genealogy of Ethics,” Nozick undertakes to discover what the “function” of ethics is, and he comes up with this answer:

The function of ethics, of ethical norms and ethical beliefs, is to coordinate our actions with those of others to mutual benefit in a way that goes beyond the coordination achieved through evolutionarily instilled desires and patterns of behavior (including self-sacrificing behavior toward biological relatives).

In other words, the function of ethics is to achieve social benefits (not already achieved by biology). This seems a harmless enough thought, but it is never made clear what the point of speaking of the “function” of ethics is. Can we equally ask what the “function” of physics is? What about art or sport? Not everything has a function in any interesting sense—so why insist that ethics does? True, ethics is concerned with altruistic behavior, but what exactly is the point of saying that this is what ethics is for? What notion of function is at work here? This never becomes clear. Once again, there is a great deal of attention to science but not enough attention to fundamental philosophical assumptions.

It is always good to see someone venturing new philosophical ideas, and trying to bring together science and philosophy. Everyone can learn something from Nozick’s clear expositions of such a broad range of scientific matters. But it is remarkably hard to have new ideas in philosophy, and science is not an automatic font of philosophical riches. Fat with science, the book is philosophically thin. But then who would have expected otherwise? If philosophical problems could really be solved by doing science, then philosophers would all be scientists.

This Issue

June 27, 2002