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Dean Rickles: Symmetry, Structure and Spacetime.

Dean Rickles Symmetry, Structure and Spacetime. Amsterdam: Elsevier 2007. Pp. 242. US$136.00 (cloth ISBN-13: 978-0-444-53116-2).

Rickles' book has two main aims. The first is negative: it seeks to argue, contra many contemporary philosophers of physics, that certain issues in physics are orthogonal to certain metaphysical issues. The second is positive: it proposes a new version of structuralism ('minimal structuralism'), which Rickles takes to be motivated by the preceding discussion and to be immune to the objections commonly raised against extant forms of structuralism.

This review examines both aspects of the book. I will argue that the orthogonality claim is overstated, and that Rickles' 'minimal structuralism' reduces to a program-sketch with the problems that (i) the prospects for completion of the program seem dim, and (ii) its claims are anyway too weak to fulfill the original aims of structuralism.

Possibility spaces and ontological commitments. Physicists theorize about spaces of physical possibilities, and face some delicate choices: reduced versus unreduced phase spaces, spaces of electromagnetic fields versus spaces of gauge connections, and so forth.

Philosophers often want to know what there is according to some theory --what objects there are, what properties they have and what relations hold among them. Some philosophers of physics often suspect that such questions are pseudo-questions or, at any rate, that they are irrelevant to science. But other philosophers of physics dissent, claiming that the answers are correlated with resolutions of the uncontroversially physical issues concerning choice of possibility space. Rickles' main claim is that this claim of correlation between the physical and metaphysical issues is false.

For example, in general relativity, one may or may not think that diffeomorphically-related models represent one and the same physical possibility (i.e. that 'Leibniz equivalence' holds). On the metaphysical side, one may or may not think that spacetime points are objects (i.e. that substantivalism is true, relationism false). According to the conventional wisdom that Rickles is attacking, metaphysical commitments go hand in hand with choice of possibility space: relationists will affirm, and substantivalists will deny, Leibniz Equivalence. Rickles disagrees: observing that substantivalists may be 'sophisticated', and relationists may be haecceitists with respect to their material particles, he argues that both the substantivalist and relationist have available to them both reduced and unreduced spaces. Rickles concludes that 'possibility counting simply isn't relevant to spacetime ontology' (39).

The truth, it seems, lies somewhere between the two extremes. Though advocates of the alignment have sometimes claimed otherwise, e.g., it has been claimed that substantivalists are committed to haecceitism with respect to spacetime points, i.e., they cannot consistently affirm Leibniz Equivalence, it is true that a specification of the ontology and ideology (objects, properties and relations) does not determine the choice of possibility space: for each type of object that one posits, one may or may not further posit that objects of that type possess haecceities, and hence one may or may not be led to an inflation of the possibility space corresponding to permutations of objects of that type. On the other hand, it is also true (contra Rickles' conclusion) that different choices of ontology and ideology lead to different lists of options regarding the choice of possibility space: one can be a haecceitist about spacetime points, and hence adopt a possibility space that counts as distinct possible worlds that differ only by permutation of spacetime points, if and only if one thinks that spacetime points exist. So physics does not always uniquely determine metaphysics, but it does constrain it.

Minimal structuralism. Let us turn now to Rickles' positive proposal. Structuralism, broadly conceived, has two main motivations: to provide a 'third way' between standard scientific realism and antirealism, and to dissolve overly 'metaphysical' pseudo-disputes. Extant versions of structuralism include ontic structural realism (OSR) and epistemic structural realism (ESR); Rickles proposes a weaker thesis, minimal structuralism (MS).

MS is a demarcation claim. The thesis is that certain ('structural') information about the world can be 'read off' from our best physical theories, while any further beliefs (e.g. that there is [as in ESR], or that there is not [as in OSR], more to the world than this structure), while they may be equally rational, are 'metaphysical' rather than 'scientific'. (The demarcation is not intended to have normative significance.)

What, then, can be 'read off'? According to Rickles, it is what the theory says about the 'qualitative' properties; equivalently, it is what is invariant under the 'symmetries' of the theory. These terms are placeholders, since we have no general account of what it is for a property to be qualitative, or for a given transformation to be a symmetry. We do, however, agree on their extensions: for existing theories, the 'qualitative properties' are those called 'observable' by physicists. (Rickles defines 'qualitative' as 'observable' [8], but this merely shifts the question; in particular, 'observable' does not here mean 'able to be observed'. The latter point distinguishes MS from constructive empiricism [213].)

It follows that the claims that can be 'read off the physics' are claims that are agreed on by all parties in characteristically 'interpretive' disputes: substantivalists and relationists, E-and-B-field, connection and holonomy realists, and so forth.

The two most troubling aspects of these suggestions are (a) the obscurity of just what it is that the minimal structuralist does commit to, and (b) the lack of any account of what constitutes 'reading off'. The next two sections elaborate on these concerns in turn.

MS and anti-haecceitism contrasted. First, then, what does the minimal structuralist commit to? MS is not the statement that physics does not deal with haecceities (in the usual sense of the term 'haecceity'). This is worth emphasizing, since several of Rickles' informal glosses on his position are potentially misleading. For example: 'The constraint surface itself is partitioned into gauge orbits containing points that differ by a gauge transformation--(with our philosophical hats on) we can view them as representing physically indistinguishable states, worlds differing haecceitistically' (56, emphasis added). And Rickles' point is that haecceities, whether they exist or not, lie outside the remit of physics. MS, then, seems (perhaps?) to be the logical conclusion that one is led to if one learns the lesson of the hole argument in the context of general relativity, and applies it systematically to all of physics. This conclusion appears nontrivial, but eminently reasonable, and eminently comprehensible.

But this appearance is based on an illicit slide from the introduction of a technical term (Rickles' 'qualitative') to the assumption that that term has its usual meaning. In particular, the idea that MS amounts (only) to the assertion that haecceitistic differences between worlds are non-physical is very hard to make sense of in the case of classical electromagnetism. (The lessons of the hole argument in general relativity do not generalize straightforwardly to arbitrary gauge theories.) Worlds that differ merely haecceitistically are related to one another by a permutation of individuals. But, in the case of electromagnetism, not only does minimal structuralism eschew any verdict on which elements of the formalism represent individuals; there (further) seems to be no plausible candidate for the status of 'individual' that would vindicate the structuralist's claims. The things that are permuted by gauge transformations are not, for example, spacetime points, but elements of the fibre over each spacetime point; these elements do not represent 'individuals' according to any extant (or any plausible) metaphysical interpretation.

So minimal structuralism cannot accurately be glossed in terms of antihaecceitism. With her philosophical hat on, the minimal structuralist can view gauge-related states as not differing observably-in-the-physicist's-sense-of-'observable'--but all parties have been doing that for decades.

Whence the demarcation? MS, as we have seen, proposes a demarcation based on methodology. It is odd, then, that Rickles' book contains precisely no discussion of the methodologies by which one might (i) arrive at a scientific theory, (ii) 'read off' propositions from a given scientific theory, or (iii) otherwise rationally arrive at beliefs about the world. This raises the urgent question of why Rickles thinks that there is any such methodology-based demarcation to be made. Absent some argument, the suggestion seems somewhat implausible. It is, for example, widely (if not universally) recognized that--on pain of inability to select reasonable theories from among a morass of empirically equivalent, but arbitrarily gerrymandered, theories--some sort of principle of simplicity must play a key epistemic role. Yet, appeals to simplicity are precisely the sort of considerations that Rickles wants to ban from the 'reading off' process, and it is only by insisting on this ban that one arrives at the judgment that 'interpretive' discussions go beyond 'reading off'.

Conclusion. MS is an extremely weak thesis. It makes no epistemological or ontological claims, seeking only to demarcate the 'scientific' from the 'metaphysical'. Thus, it does not fulfill either of the original motivations for structuralism. It does not supply a general, precise demarcation criterion, or any reasons for thinking that such a criterion must exist in the vicinity of the particular demarcation judgments it makes. We also lack any tolerably clear account of what the minimal structuralist, qua scientist, does commit to: it is not the 'qualitative' or 'non-haecceitistic' in the usual sense; it is supposed to go beyond the observable-in-the-constructive-empiricist's-sense, the physicists' notion of symmetry playing a key role; but where this takes us remains obscure.

Hilary Greaves

University of Oxford
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Author:Greaves, Hilary
Publication:Philosophy in Review
Date:Dec 1, 2008
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