It’s now time for me to make a small confession, which is that I don’t care very much really about Hilary Putnam’s late-career misadventures with “internalism.” When I first went off to philosophy grad school many long years ago, Reason, Truth, and History was still relatively new and much talked about. I obtained a copy, but I could never get past chapter one. His arguments entailed certain claims that seemed to be just too obviously wrong. They still seem so to me now, and I have emphasized them in previous posts in this series. One is that a brain in a vat would not be able to think about whether it was a brain in a vat, even though the phenomenology of its thoughts would be identical to that of a normal, embodied person thinking (apparently) about being a brain in a vat. That entails that the brain in a vat has no idea what it is thinking about outside its own mind—and by the same token that neither do we. Another is that no natural relation, whether causation or anything else, can determine the referents of our thoughts and percepts, so that—assuming we reject “Platonism”—we have to admit that our thoughts and percepts do not have mind-independent referents. As I say, these claims seemed obviously false, even silly. Neither did it seem like the best use of time to delve deeply into Putnam’s reasoning and try to sort out what was wrong.

On the other hand, I do care about structural realism, which I have come to think is true but which has been bedeviled in recent decades by an argument essentially similar to Putnam’s model-theoretic argument. It has been to better understand and reply to the argument against structural realism that I have at long last performed the examination of Putnam’s model-theoretic argument presented in the previous posts in this series.

In the present post, I explain the argument against structural realism—which by now can be seen in fact to present no great difficulty—and comment briefly on the abysmal state of current discussion of structural realism. (The whole paper on which these posts are based is available here. To return to the third post in the series, click here. To skip to the fifth and final post, click here.)

Structural Realism

In 1927, Bertrand Russell published The Analysis of Matter, in which he gave the first detailed exposition of the philosophical view that came later to be known as structural realism. The centerpiece of the book is a causal theory of perception, in which he attempts to show how our knowledge of the external world, and especially our physical theories, can be grounded in perception. He also attempted to establish some important limits to what we can know about the world outside our own minds.

Writing in 1927, he assumed an internalist epistemological framework and a view of perception according to which our own percepts are the only immediate objects of sensing. In other words, he assumed the same traditional empiricist framework as Putnam. From this starting point, it follows that the only objects of direct knowledge are our own percepts, which are mental phenomena. Any knowledge of the physical world can be had only indirectly, via inference. Furthermore, in making any inference from our percepts to their probable physical causes, the best we can do is to rely on a principle of same cause, same effect: “any difference between two simultaneous percepts implies a correlative difference between in their stimuli” (252; cf. 226–228, 255). But for this reason, we can infer nothing about what he calls the “intrinsic character” of the physical causes of our percepts. For instance, if one percept is larger than another, then we can infer that they have different causes, but not what those causes are. Specifically, there is no basis for inferring that the causes have larger and smaller spatial sizes of the same kind as the percepts have. Since the external causes that produce the percepts are opaque to us, we really have no idea of the intrinsic character of the physical properties in question. For all we can infer, they might be utterly different from anything in our direct experience. However, the silver lining is that the higher-order relational structure of these properties can be inferred. For example, the relation larger than is transitive, so if a system of percepts instantiates the larger than relation between various members, then we can infer that the corresponding physical causes of those percepts instantiate a corresponding physical relation that is transitive, even if we cannot infer its intrinsic character.

It might be helpful to give a concrete example. A certain musical recording can be reproduced on a vinyl record, on an audio tape, on an audio CD, and in an MP3 file. Thus, the very same music is produced from four entirely different physical causes with different intrinsic characters. There is no way to infer the intrinsic character of the recording medium from the music it produces, but we can infer that, whatever the medium, louder notes are produced differently from softer notes. Moreover, however loudness and softness are encoded in each medium, we can also infer that the structure of those encodings is transitive. Higher-order properties and relations, such as transitivity, Russell calls structure. He has a detailed logical conception of structure, derived from his Principia Mathematica, that needn’t concern us here. It is best to think of structure as the purely logical and mathematical properties of a system, including what might be formulated in the equations of scientific laws. Russell’s view of what we can know about the physical environment from perception can now be summarized compactly: “Thus it would seem that, wherever we infer from perceptions, it is only structure that we can validly infer; and structure is what can be expressed by mathematical logic, which includes mathematics” (254).

Grover Maxwell later advocated a view similar to Russell’s, which indeed was inspired by Russell among other authors (for example, “Scientific Methodology and the Causal Theory of Perception” [1968]). His argument and starting points are essentially similar to Russell’s: we have direct knowledge only of phenomena, which are mental objects of perception; all other knowledge must therefore be indirect and inferential; but what we are capable of inferring is limited to structural properties and relations. Hence, we can have a great deal of important knowledge of the physical world, but we cannot know its intrinsic character; we cannot know “things in themselves.”

There were some differences between Russell’s and Maxwell’s accounts, however. One was Maxwell’s pioneering use of Ramsey sentences to express what is meant by structure. The Ramsey sentence is a technique for expressing the theoretical terms of a scientific theory developed by F.P. Ramsey in 1929. The idea is to treat theoretical predicates as variables to be quantified over in the statement of the theory. Thus, if electric charge is a predicate, C, of the theory, so we can say things like C(a), meaning that a has electric charge, then we can eliminate C from the theory by introducing the predicate variable Γ­₁, replacing every occurrence of C in our statement of the theory with Γ₁, and existentially quantifying over Γ₁. Now, instead of explicitly naming C, which we will interpret by assigning to it a specific set of objects, we define C implicitly, as a variable that is satisfied by whatever objects make the sentences in which it occurs true. We can do this for all the theoretical terms of the theory. If we do so, and state the entire theory in one long sentence, then that is the Ramsey sentence for the theory. For example, suppose we have a theory T(O₁,…,O_n; T₁,…,T_m), whose nonlogical vocabulary consists of observation predicates O_i and theoretical predicates T_j. We replace the T_j with variables Γ_j as follows.

∃Γ₁, …, ∃Γ_m T(O₁,…,O_n; Γ₁,…,Γ_m)

In this way, rather than try to identify explicitly what the theoretical terms of the theory stand for, we allow them to be defined by their role, their consequences in interaction with other theoretical entities and with observable things. Moreover, except for the observation terms, these consequences are spelled out in purely logical and mathematical terms. This is an elegant way of capturing what Russell meant by structure, and it has been widely adopted by present day structural realist philosophers.

Newman’s Objection

However, a serious problem for Russell’s structuralism emerged almost immediately after he published The Analysis of Matter. In 1928, Cambridge mathematician Max Newman published a critical notice of the book, “Mr. Russell’s ‘Causal Theory of Perception’.” The main point of Newman’s article is to present an argument, which turns out to anticipate Putnam’s model-theoretic argument, showing that Russell’s theory of “structural knowledge” prevents us from saying anything substantive about the external world. For, on Russell’s theory of knowledge, a physical theory of the world will consist of a system R of relations—spatial, gravitational, electrical, whatever—that realizes a logical and mathematical structure W, which structure is the whole content of the theory. Now, if we assume that these relations are defined extensionally in the usual way, by assigning objects (or n-tuples of objects) from some domain, then it is easy to show that for any structure W and domain D, it will be possible to define a system R that realizes W, if only there are enough objects in D. In short, Russell’s structuralism has the consequence that, for any empirically adequate theory of the physical world, no matter what it is, the theory is true as a mere matter of logic and set theory, providing there are enough entities in the world. Thus, the only empirical claim of any substance that can be made about the world by a scientific theory is the minimum number of its entities! But that is not how we think about the import of our scientific theories, which are not supposed to be true a priori given that the world contains enough items. This represents a collapse into phenomenalism, which is not what Russell intended.

The parallel with Putnam’s model-theoretic argument is clear. Putnam used model theory and Newman used set theory, but in both cases the argument is to the effect that the observational and structural constraints of a theory are not strong enough to determine an interpretation that might not be satisfied by the real world: so long as the theory is consistent, the domain is sufficiently large, and its observational consequences are true, its theoretical statements are guaranteed to be true. This is effectively phenomenalism.

The chief difference between Putnam’s and Newman’s arguments is that Putnam’s aims are much more ambitious. Newman aims only to show that Russell’s severe definition of structure as consisting of nothing more than mathematical and logical relations leaves purely structural theories incapable of fixing a determinate intended interpretation. So, Newman’s argument can be purely logical and still hit its target. On the other hand, the target of Putnam’s attack is any form of realism in which terms and sentences refer to, and are true and false of, mind-independent reality. This is why a purely logical argument—Putnam’s Proof—is insufficient for his purposes and must be supplemented by other, inadequate arguments like impotence of natural mechanisms. The purpose of the supplemental arguments is to block escape routes from the model-theoretic argument that appeal to claimed extra-logical facts such as causal relations between mind and world, modal features of reality such as necessity or lawfulness of certain relations, or the relative fundamentality of certain properties and relations (such as those of fundamental physics à la David Lewis). Newman didn’t need to argue against these possibilities because Russell himself eliminated them. Russell set himself up for this fall. It’s not that he didn’t believe in, for example, causation, or that our percepts are the effects of determinate causes. Rather, it was that his definition of structure in terms of purely logical and mathematical relations is very clean and appealing, and he simply failed to notice the consequence that Newman pointed out.

Much of this story, including the parallel between Newman’s argument and Putnam’s, is recounted by William Demopoulos and Michael Friedman in a terrific 1985 article. (They do not spell out the logical issues very clearly, but that lacuna is filled by Ketland (2004), who gives a complete, formal version of Newman’s proof against Russellian structuralism in the Ramsey sentence formulation.) They reproduce Russell’s reply to Newman in a letter that was included in a series of letters reproduced in Russell’s autobiography (volume II). The letter is brief. Russell concedes Newman’s point and then says:

… I had not really intended to say what in fact I did say, that nothing is known about the physical world except its structure. I had always assumed spacio-temporal continuity with the world of percepts, that is to say, I had assumed that there might be co-punctuality between percepts and non-percepts, and even that one could pass by a finite number of steps from one event to another compresent with it, from one end of the universe to the other. And co-punctuality I regarded as a relation which might exist among percepts and is itself perceptible. (Russell 1968, 259–260; Demopoulos and Friedman 1985, 632)

It is interesting that Russell does not appeal to causal relations as a way out of the problem, but spatiotemporal continuity. And this might seem oddly weak: aren’t spatiotemporal relations just the sort of thing we can know only the structure of, according to Russell, and which accordingly cannot be determinately referred to in the external world? However, there is more to the story, which may be worth telling since I have not seen discussion of this point elsewhere in philosophical discussions of structuralism and Russell’s response to Newman.

The account so far might seem to imply that Russell’s theory is that beyond percepts we can only posit a structure to exist between objects and relations of which we know nothing. This is indeed the picture presented by the Ramsey sentence formulation of structuralism, but that is not Russell’s formulation. In The Analysis of Matter, Russell develops an elaborate account of the construction of an “ideal” world from the series of our percepts (chapter XX, “The Causal Theory of Perception”). He first describes how the multiple perceptions that we might regard as being of a particular object, such as a ball, can be grouped together and arranged spatially in relation to other “object” groupings by means of the laws of perspective. Thus, perceived objects in perceived space are constructed, after which we can fill in complete “biographies” of all these objects by hypothesizing groups of “ideal” percepts (i.e., not actually perceived by anybody so far as we know) to occur that give spatiotemporal continuity for all the objects we perceive at some time over the whole course of their existence. We can also hypothesize other ideal objects that we never actually perceive at all, such as parts of the earth where no one has been and distant stars and all the things that existed before we were born. And to all these we can apply the laws of physics to explain the causal evolution of the world and, ultimately, all of our personal perceptions. Thus, we arrive at a Berkeleyan conception of the world. Russell then argues that, although a Berkeleyan conception is logically possible, it “has no positive grounds in its favor” (214–217). The key argument for him seems to be that, since we are constructing the world from percepts, whose esse is percipi, all the “ideal” (i.e., unperceived) parts of the construction are unreal and therefore cannot participate in causal relations. So, if the construction is really to make any sense, we need to posit real but unperceived entities; i.e., physical entities.

All this is the setup for his later (chapter XXIV) argument that we can infer only the structure of physical things. That argument, to repeat, is that since physical things might be entirely different from percepts, we have no ground to infer that they have the same intrinsic character. However, we can use the principle that “differences in percepts imply differences in stimuli” (226), together with spatiotemporal continuity (227), to infer the structure of the stimuli. I want to emphasize the point about spatiotemporal continuity. Russell says that the process of inferring physical structure from perceptual structure begins locally, with inference from percepts to stimuli, which are “the events just outside the sense-organ” (227). Being co-punctual or nearly so, we can assume that the relation between percept and stimulus is roughly one–one. Thus, the structure of our percepts should be roughly mirrored by the structure of their co-punctual physical events. Moreover, so should the structure of the percepts we would have at another place in the Berkeleyan ideal world be mirrored by the structure of the same type of physical events as would be co-punctual with our percepts if we were there. In this way, specific types of physical events can be mapped onto spatiotemporal locations throughout the Berkeleyan ideal world. It is true that these are merely Berkeleyan ideal locations, but they also will correspond to co-punctual physical spatial locations, whatever those are. Physical space may not be known in its intrinsic character, but it should share the structure of Berkeleyan space, including its topology and continuity.

Thus, Russell does not conceive of our epistemic situation as one in which we have a set of percepts beyond which is a total black box to be filled in with any theory that is empirically adequate in terms of predicting the set of percepts. Rather, in his view, theory construction is guided by the ideal world of perceptual and ideal objects that can be constructed with the aid of the laws of perspective and given a physical interpretation. For example, the physical laws are supposed to apply between entities that exist not just anywhere, but in the physical locations that are co-punctual with the relevant objects in the Berkeleyan ideal world (whatever that may amount to physically). In this way, the spatiotemporal continuity assumption constrains the interpretation of physical theories.

This understanding of Russell can help to explain his otherwise somewhat puzzling reply to Newman. As just explained, on Russell’s theory, physical events cannot happen just anywhere, but must happen co-punctually with the Berkeleyan ideal objects whose actions they are theorized to explain. This imposes a constraint on physical theory that is not purely structural, since we need “spatial intuitions” (in phenomenal space constructed from our percepts) to guide us. That is, I don’t think that a merely mathematical description of Berkeleyan ideal space would be sufficient. Certainly, he intended it to be a material concession to Newman’s objection. To the end of his career, Russell remained a devotee of structuralism, though he abandoned the notion that our knowledge of the external world is purely structural in his narrow, logical sense. Unfortunately, he never returned to Newman’s objection or spelled out what sort of impurity he thought should be admitted.

In the case of Grover Maxwell, his response to the Newman problem was short and unequivocal: “structure should not be identified with form; rather it is form plus causal connections with experience” (1968, 154, note).

Current Discussion of Newman’s Objection

Unfortunately, the same cannot be said of many other successors to the structural realist philosophy. Despite its promotion by Russell and Grover Maxwell, structural realism gained few adherents until, in 1989, John Worrall published a paper, “Structural Realism: The Best of Both Worlds?” that caught people’s attention and began a discussion of structural realism in the philosophy of science community (see Frigg and Votsis 2011 for a review of the current state). In my opinion, that discussion has been depressingly unproductive. Part of the reason is that the field has been stuck to a surprising degree on Newman’s problem and has failed to reach consensus on any resolution or even on the dominant options and their implications. Which is to say, nearly 35 years since the appearance of Worrall’s article, the state of discussion remains immature.

Part of the problem is that many resolutions are possible, but they often require philosophical commitments that are welcome to some but off-putting to others. So, a resolution that appeals to one is rejected by others. Unsurprisingly, the possibilities are essentially the same as those for modifying model theory in response to Putnam’s Proof described above (see Ainsworth 2009 and Frigg and Votsis 2011 for reviews). These include privileging some predicates as more fundamental than others (Lewis 1984, mentioned in the previous post in connection with Putnam; Lewis also references Newman); applying observational predicates to unobservable entities (Cruse 2005); introducing modal requirements for relations between predicates, such as “is necessarily correlated with” and “is lawfully co-extensive with,” whether as second-order predicates or modal operators of the formal language (Melia and Saatsi 2006); and requiring that the physical relations that satisfy a given structure must be the causal antecedents of corresponding percepts (Votsis 2003).

Unfortunately, most of these suggestions have been offered in one or two papers and not pursued much further by their authors. There seems to be very little in the way of detailed, systematic investigation of how structural realism should be developed beyond the state in which Russell and Maxwell left it in light of Newman’s objection. An indication of the current state of things is that John Worrall, probably the most considerable philosopher among present day structural realists, argues that structural realism must be committed to the Ramsey sentence formulation in its unmodified, purely logical form (2007, 148–149). I.e., he would reject all the just mentioned resolutions (except possibly Cruse 2005). The reason he gives is that we have no independent access to external reality by which to interpret the theoretical vocabulary of our theories, so implicit definition of them in Ramsey sentences must capture “the full cognitive content” of any theory. Yes, but constraints such as causation or lawful co-extension are nonlogical—to introduce them would be to modify the standard Ramsey sentence formulation—yet surely they qualify as structural in the relevant sense (just not in Russell’s strict logical sense). For, they have nothing to do with the intrinsic character of external properties or relations. Yet Worrall does not even consider, much less argue against, the possibility of introducing them. His “solution” turns out to be to concede Newman’s objection, in effect, and say that the terms of a theory may have no referents in the external world, but nevertheless we can say that the theory “globally reflects reality.” In other words, he goes full Putnam! Or so it seems; he does not elaborate.

I regard this sort of position as having lost the thread. There are multiple arguments that motivate structural realism—and Worrall must be credited with developing or resurrecting some important innovations in this regard—yet the key consideration unquestionably is that the intrinsic character of external properties and relations is inaccessible to us, simply because they are intrinsic. Intrinsic here means how something is in itself, independent of its causal effects. But we know the external world only through causal interaction with it. Accordingly, we cannot know the intrinsic character of external things, but we might know how they affect us and how they affect each other; i.e., we might know their causal properties. Thus, there is no reason to restrict the “structure” in structural realism to purely logical relations, which exclude causation. Russell thought briefly that he could make a purely logical definition of structure work in a structuralist philosophy of science. He was wrong. Move on.

The insight that the fact that we can know the external world only through causal interaction means that we cannot know what it is like in itself is important. It has the implication that the way we experience the world intrinsically, including not only its colors and temperatures and tastes and sounds, but shapes and sizes and even the character of space and time, is not necessarily how it really is. This strikes me as being a matter, not of philosophical ideology—“the philosophy of structural realism”—but of plain fact, which, unfortunately, has been mostly neglected in the history of philosophy up to and including the present day. Philosophers ought to be working out just what limits this imposes on empirical knowledge of the physical world, how it affects our conception of the physical, what it means for the status of the sensory qualities we encounter in experience, the status and role of consciousness, the content of our percepts, and much else. Newman’s objection has nothing to do with any of this. Once it is recognized that the narrow, merely logical definition of structure proposed by Russell is inadequate, Newman’s objection evaporates. The contemporary concentration on it among structural realist philosophers is a distraction.

References

• Ainsworth, Peter M. 2009. “Newman’s Objection.” British Journal for the Philosophy of Science, 60: 135–171.
• Cruse, Pierre. 2005. “Ramsey Sentences, Structural Realism, and Trivial Realization. Studies in the History and Philosophy of Science Part A, 36: 557–576.
• Demopoulos, William and Michael Friedman. 1985. “Bertrand Russell’s The Analysis of Matter: Its Historical Context and Contemporary Interest.” Philosophy of Science, 52: 621–639.
• Frigg, Roman and Ioannis Votsis. 2011. “Everything Your Always Wanted to Know about Structural Realism but Were Afraid to Ask.” European Journal for the Philosophy of Science, 1: 227–276.
• Ketland, Jeffrey. 2004. “Empirical Adequacy and Ramsification.” British Journal for the Philosophy of Science, 55: 287–300.
• Lewis, David. 1984. “Putnam’s Paradox.” In Papers in Metaphysical and Epistemology, Cambridge U.P., 1999: 56–77.
• Maxwell, Grover. 1968. “Scientific Methodology and the Causal Theory of Perception.” In Imre Lakatos and Alan Musgrave (eds.), Problems in the Philosophy of Science, North-Holland Publishing Co., 1968: 148–160.
• Melia, Joseph and Juha Saatsi. 2006. “Ramseyfication and Theoretical Content.” British Journal for the Philosophy of Science, 57: 561–585.
• Newman, M.H.A. 1928. “Mr. Russell’s ‘Causal Theory of Perception’.” Mind, 37: 137–148.
• Russell, Bertrand. 1927. The Analysis of Matter. Allen and Unwin.
• ———. 1968. The Autobiography of Bertrand Russell: 1914–1944. Allen and Unwin.
• Votsis, Ioannis. 2003. “Is Structure Not Enough?” Philosophy of Science, 70: 879–890.
• Worrall, John. 1989. “Structural Realism: The Best of Both Worlds?” Dialectica, 43: 99–124.
• ———. 2007. “Miracles and Models: Why Reports of the Death of Structural Realism May Be Exaggerated.” Royal Institute of Philosophy Supplements, 61: 125–154.