Newman: What Russell’s Structural Argument Needs

[UPDATE: 15 May 2013; edited for clarity]
As mentioned earlier here, Bertrand Russell’s work in his book The Analysis of Matter was dealt a blow by mathematician M.H.A."Max"Newman. Russell had built an argument supporting partial realism about the physical world. He said that while we are only acquainted with our percepts, there are causal connections between these and unperceived events external to the perceiver. He gave reasons to think that as a result, a system of relations among percepts can share the same structure as that of causally connected but unperceived events. We can therefore infer a great deal about the structure of the physical world. Newman pointed out that using conventional set-theoretic definitions of these terms, a shared structure in fact would not offer much information at all about the external world; formally any collection of things (of a sufficient cardinality) can be organized in relations so as to have a given structure.

Newman’s clearly argued and thoughtful paper, “Mr. Russell’s Causal Theory of Perception,” (also posted here) while delivering a negative result on this crucial point, was nonetheless sympathetic toward Russell’s project. Newman offered a suggestion as to what would be required in order to have a more meaningful result. He said we need to have, in addition to our individual percepts and the notion of a shared structure, some direct acquaintance with relations (and he points out that in some passages this sort of “modified theory” is what Russell seems to have in mind):

The conclusion that has been reached is that to maintain the view that something besides their existence can be known about the unperceived parts of the world it is necessary to admit direct apprehension of what is meant by the statement that two unperceived events are causally adjoined, i.e., happen near each other, temporally and spatially, or overlap, or do something of the sort. The central doctrine is then that while of percepts we have a qualitative knowledge, of other events all that can legitimately be inferred is their structure with regard to a certain directly known relation which may be called “causal proximity”(p.148 emphasis original)

In addition to the abstract structure, knowledge of the relation of causal proximity would give us leverage to extend our knowledge to the specific system of causal relations among the unperceived events (though still not their intrinsic qualities, in line with the “clear-cut” unmodified theory). Newman also points out potential disadvantages of introducing this modification: it adds an additional primitive notion of acquaintance or “direct apprehension” which needs to be better defined; it also might open the door to questioning why we can’t invoke even more sorts of direct knowledge of non-structural aspects of the world. He concluded the paper in this way:

It appears, then, that although a modified form of Mr. Russell’s theory makes an important assertion about our knowledge of the external world, a good deal of further argument will be necessary to show that this assertion is true. (p.148)

Russell wrote a letter to Newman following the publication of this paper (it is included in the second volume of Russell’s autobiography). In the letter, Russell conceded the argument and went on to say:

It was quite clear to me, as I read your article, that 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 another. And co-punctuality I regarded as a relation which might exist among percepts and is itself perceptible. (p. 259, emphasis original).

Newman’s commentary above sketches a notion of perceiving “causal proximity” or the idea of events being spatio-temporally near each other or perhaps overlapping. Russell singles out the notion of perceiving co-punctuality. If events overlap or are simultaneous, perhaps the notion of directly perceiving a relation between them is explicable.

 As I discussed before, Russell’s later book, Human Knowledge, did conclude that we must have some primitive (“animal” or “biological”) grasp of causation in order to have scientific knowledge. He also reiterated key themes from The Analysis of Matter (including, for example, the role of simultaneity in his theory of compresence). I didn’t see in my reading, though, that he specifically built on the notion of perceiving causal relations via co-punctuality as discussed in his letter to Newman.

Reduction as Idealization

I cannot remember who tipped me to this 1972 article in Science by physicist Philip W. Anderson called "More is Different".  It is an exploration of the notions of reduction and emergence.  The main thrust of Anderson's argument is familiar:

The ability to reduce everything to simple fundamental laws does not imply the ability to start from those laws and construct the universe.  In fact, the more the elementary particle physicists tell us about the nature of the fundamental physical laws, the less relevance they seem to have to the very real problems in the rest of science, much less to those of society
The constructionist hypothesis breaks down when confronted with the twin difficulties of scale and complexity.  The behavior of large and complex aggregates of elementary particles, it turns out, is not to be understood in terms of a simple extrapolation of the properties of a few particles.  Instead, at each level of complexity entirely new properties appear...(p.393)

The article is worthwhile for a number of very nice briefly described examples of symmetry breaking and properties which emerge with scale.

There is a absurdly simple insight lurking in these sorts of discussions which I now belated appreciate.  We all realize that coarse-grained descriptions of phenomena which neglect fine details will be limited in their accuracy by definition.  But while reductive analysis of natural systems is extremely fruitful, it is also always an idealization.  Experimenters work hard to break down and isolate some phenomenon, and models and theories are constructed to best capture it.  The environment needs to be screened out  -- it is "noise" which we abstract from.  But what is lost in this idealization is not trivial.  In nature, there are no isolated systems, no ceteris paribus conditions (in fact, there is absolutely no reason to think the universe as a whole is some sharply bounded closed system).

When this is considered, emergent properties at higher levels of scale lose the sense of being especially surprising or mysterious.

Causal Knowledge is Primitive for Russell

I was rereading portions of Russell’s Human Knowledge (and making comparisons to The Analysis of Matter) with the goal of understanding his arguments regarding the role of structure in linking experience to the physical world. But I was struck by something else.  At the end of the book, his conclusions regarding how scientific inferences are justified trace this question back to the prior question of how we gain knowledge of causation. Causation is presumed in science, but causation is itself not explicated or justified within science: it is a pre-scientific concept.

A main project in Human Knowledge is to identify those unacknowledged postulates which undergird our scientific pursuit of knowledge: “what must we be supposed to know, in addition to particular observed facts, if scientific inferences are to be valid?” (p.513). He ends up with five postulates in total, but notably it turns out all of them “involve the concept of ‘cause’” (p.508).

 How do we know these postulates, then, if indeed we do know them, given their reliance on our knowledge of causation? Russell can only point to our gaining a primitive grasp on cause via our pre-linguistic biological know-how: “Knowledge of general connections between facts has its biological origins in animal expectations “(p.514). It was advantageous in evolutionary terms for our animal expectations to roughly conform to processes in the physical world. The physical world apparently has causal laws, and animal inferences are adapted to these.

 When evaluating the thesis of empiricism, Russell understands that strictly speaking this kind of knowledge is something beyond experience (at least as these terms are usually employed in the debate): “Either, therefore, we know something independently of experience, or science is moonshine” (p.524).

Russell and Structural Realism

My interest in Russell’s The Analysis of Matter came originally from the perspective it offers in sorting through the problem of mind. Recently, thanks to a couple of papers linked to on twitter by @LogicalAnalysis, I learned about its connection with recent work on Structural Realism in the context of philosophy of science. (This continues a long-standing tradition for me where philosophy of mind serves as a “gateway drug” leading to the exploration of a wide range of philosophical concerns - btw this analogy was inspired by this parody poster).

 Very roughly, Russell said that while we only have access to percepts (units of phenomenal perception), and lack access to external objects, these percepts do lie at the end of causal chains which link them to counterparts in the world. He argued that because of this linkage, the structure of our percepts is shared with that of the counterparts, allowing us to draw inferences about this structure.

 In the 2001 “Is Structural Realism Possible” Stathis Psillos discusses the Russellian view as one of several paths toward Structural Realism (SR). Its construction from a starting point of bottom-up empiricism marks it in Psillos’ language as an “upward path” toward SR. The “downward path” characterizes approaches which look to save a broader scientific realism from objections by limiting the realism to certain of the mathematically described structural portions of the theories.

  James Ladyman has a very nice SEP entry on SR, which lays out the contemporary research. In his taxonomy, he distinguishes “epistemic” SR (which includes Russell’s given its basis in concerns about knowledge of the external world) from “ontic” SR. Some versions of the latter (including Ladyman's own work) look to make the case that structure is all there is; that is, they take an anti-realist approach to non-structural elements of physical world (e.g. objects), rather than just taking an agnostic approach based on the epistemic difficulties of knowing about them.

 While I have a lot more to read on this topic, I have an initial suspicion that both approaches to SR have a shortcoming which has to do with causation. Russell invokes causal relations as giving rise to structure, but doesn’t provide details regarding how causation works. Without more to the story, he is apparently left with the claim that we can make the appropriate inferences based on logico-mathematical structure. And this left him open to a logically based criticism due to M.H.A. "Max" Newman (1928 – see discussion in this article by Demopoulos and Friedman). This criticism argues that the inference based only on structure fails because a set of relations among any set of units with sufficient cardinality can be shown to be consistent with it (for a paper which concludes this argument lacks force, see a 2003 article by Ionnis Votsis).

 When it comes to ontic SR, I think it is pretty clear that the formal mathematical structures in physical theories don’t provide a theory of causation, and such a theory will need to invoke additional ontology (e.g. properties, objects) to serve as part of its explanatory apparatus. Therefore, we can’t conclude structure is “all there is.” Psillos has another paper which, in part, argues against ontic SR from this basis.

Upcoming GPPC events

Philosophy on Film Series - Estrangements

The Greater Philadelphia Philosophy Consortium is sponsoring a film series at the Bryn Mawr FilmInstitute again this year featuring commentaries by GPPC philosophers.  There are 3 films on consecutive Thursday evenings beginning March 29^th.

Causal Constraint

The notion of dispositional modality, discussed by Stephen Mumford and Rani Lill Anjum in Getting Causes from Powers, put me in mind of another analysis of the interplay between causation and modality: that of Gregg Rosenberg in A Place For Consciousness (2004).

 Recall (see prior post here) that Mumford and Anjum analyze causation in terms of dispositions, or powers. These powers tend toward (dispose toward) their manifestations -- they do not necessitate them. Necessity is not the modality of causation. In addition, it is argued that dispositional modality is distinct from standard philosophical notions of possibility (logical or metaphysical possibility). Dispositional modality (dispositionality for short) does not involve “pure” possibility, since only certain manifestations are possible. In Chapter 8 of their book, the authors say: “Dispositionality…can be understood as a sort of selection function…that picks out a limited number of outcomes from all those that are merely possible.” Also: “The idea of a selection function is simply one that identifies a subset from a realm of possibilities. (p.189)”

In his book, Gregg Rosenberg introduced a model of causation which featured a notion which seems related to the idea of the selection function: this was a constraining function on the space of possibilities. Rosenberg, unhappy with both the Humean perspective on causation, as well as the theories of causal responsibility or causal production on offer, endeavored in chapter 9 of his book to strip down the notion of real causation to a bare minimum. This led him to the following notion of “causal significance”: “The causal significance of a thing is the constraint its existence adds to the space of possible ways the world could be…Causal significance shows causation to be an operator on a space of possibility. (p.150 emphasis original)” And: “It is a theory designed to understand how constraints propagate, so it explains how the actual world comes to be just a sliver of what could have been. (p.152)”

I say they seem like related notions, but constraint could be viewed as the negative image of selection. Selection picks out a few possibilities, while constraint rules out all of the others.

I find causal constraint to be a beguiling idea. Tentatively, it would seem to leave “pure” possibility in place as the fundamental metaphysical notion, in constrast with Mumford and Anjum’s argument for the irreducibility of dispositional modality.

Short Review of Getting Causes from Powers

In this book, Stephen Mumford and Rani Lill Anjum present their theory of causal dispositionalism, that is, causation based on dispositional properties, or powers. I highly recommend it to anyone interested in the philosophy of causation.

Powers do the causal work in our world, according to the authors: effects are brought about by powers manifesting themselves, and the manifestation is itself a further power or set of powers.

A central idea is that powers don't necessitate their manifestations - they dispose toward them. Causality has long been associated with the idea of necessity, and necessity (and the sense of constant conjunction) is too strong to describe causation. The main insight here is that other factors can prevent or interfere with the expected manifestation (and, indeed, they often do).

To help demonstrate how a disposition can be enhanced or, importantly, hindered by other powers, the authors develop a vector addition diagram. Only when the sum of vectors (with various strengths and directions) exceeds some threshold do we get the manifestation. They extend the model to more complex scenarios to argue that the model is robust enough to explain non-linear and even "emergent" behavior.

In addition to arguing strongly against necessity, the authors want to overthrow another usual notion. The authors reject as misguided the typical "two-event" conception of causation, where cause is temporally prior to effect, in part because no one has a compelling account of how you get from one to the other. Instead causes and effects are simultaneous - they are two aspects of a temporally extended process which brings about a change.

An important and creative part of the book explores the distinctive modality of dispositions in more depth. Dispositional modality (weaker than necessity but stronger than "pure" contingency) is the primitive and fundamental modality of nature. We derive necessity and possibility from our prior experience with dispositionality. Mumford and Anjum argue that we do indeed perceive causation, and present what they see as the clearest examples of this in the case of bodily sensation and specifically proprioception.

The book concludes with a compelling application: showing how the theory fits with processes studied in biology and genetics.

More on Causation and Reduction to Physics

I finished reading GettingCauses from Powers by Stephen Mumford and Rani Lill Anjum.  I recommend the book highly to anyone interested in causation, and I’ll be thinking about many of its arguments and themes for a long time to come.

As touched on at the end of my prior post, one possible challenge to models of causation, including the thesis of causal dispositionalism presented in this book, is the fact that causation doesn’t seem to comport well with physics.   The authors acknowledge this in their first chapter, referencing Russell’s discussion in his "On the Notion of Cause” (1913).  The issue is that dynamical equations associate states of a system with points in time, but nowhere do they invoke the idea of causal production.  They are symmetric with regard to time, where causation is not.  Mumford and Anjum respond in a couple of ways.  First, they say, the fact that causation doesn’t appear at the level of physics doesn’t mean it isn’t present at larger scales:  the reducibility of all phenomena to physics is a controversial idea which we are not compelled to accept.  We don’t know that physics represents a special fundamental level of reality in any case.  And given the provisional nature of scientific theories, should we let them trump our metaphysical reasoning?

This issue recurs as the book progresses.  In Chapter 4, the authors show how the composition of powers in causal situations can plausibly model emergent phenomena in the form of novel powers.  So the theory is robust if it does turn out that reduction of the phenomena in the special sciences isn’t possible.  And the final chapter of the book (ch.10) presents an interesting and persuasive application of the theory by showing how causal dispositionalism fits quite well with examples of processes studied in biology (including genetics).

Just like the situation in philosophy of mind, one must be cautious about drawing metaphysical conclusions from the perceived character of formal physical theory.