Structuralism in Philosophy of Physics: Alternatives to Realism
OCTOBER 6-8, 2011
Stanford Humanities Center
424 Santa Teresa St.
TITLES & ABSTRACTS OF TALKS
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"Kant, reflective structuralism, and quantum mechanics
Instead of either formulating new metaphysical images such as ontic structuralism, or rejecting any metaphysical attempt, the case of quantum mechanics might require a redefinition of metaphysics. The sought redefinition will be performed in the spirit of Kant, according to whom metaphysics is the discipline of the boundaries of human knowledge. This can be called a "reflective" conception of metaphysics.
Along with this perspective, our understanding of theoretical structures works in two steps :
(1) The most basic structures of a theory like quantum mechanics are neither imposed onto us nor arbitrary, but made necessary by the general characteristics of our demand of knowledge.
(2) Yet, there can also be additional features of theoretical structures corresponding to special characteristics of our demand of knowledge, adapted to certain directions of research or to cultural prejudice. The "surplus structure" of some of the most popular interpretations of quantum mechanics will be understood this way.
Finally, it will be shown that some of the major "paradoxes" of quantum mechanics, such as the measurement problem, can easily be dissolved by way of this reflective attitude.
University of Notre Dame
Whatever version of structuralism one adopts, be it inspired by early twentieth century figures such as Weyl or Cassirer, or triggered by contemporary positions such as ontic structural realism, epistemic structural realism, or structural empiricism, a rich mix of epistemology, ontology, and philosophy of language is at work, either explicitly or implicitly. In all cases, a position is taken concerning the relationship between the structures expressed in our theories and what those theories are intended to be about (whether we be contemporary structural realists, early twentieth-century neo-Kantians, or whatever). I will shift attention away from ontological and epistemic commitments associated with different versions of structuralism, and focus on a philosophy of language appropriate to the view that the content of a theory is exhausted by the structure of that theory. I am interested not in what a theory is about (ontology) or what we should believe (epistemology) but what the theory *says*. What would a structuralist account of what a theory says look like? My interest is in contemporary theoretical physics, and this is the source of my examples.
"Carnap's logico-mathematical neutrality between realism and instrumentalism"
I discuss the evolution of Carnap's treatment of theoretical terms from the late 1930s to his mature work on the Ramsey sentence formulation of scientific theories in the late 1950s and 1960s. I concentrate on Carnap's use of this device to remain completely neutral between realism and instrumentalism. A central point of discussion is his commitment to a purely logico-mathematical interpretation of the quantified existential variables in the Ramsey sentence. Far from being a desperate or ad hoc maneuver, I argue that this is essential to Carnap's point of view and, in particular, to the way in which he understands the characteristically abstract representations of modern mathematical physics throughout his intellectual career. In the end, Carnap recommends nothing more nor less than that we eschew fruitless "ontological" disputes in favor of cooperating with contemporary mathematical physicists in attempting (axiomatically) to clarify the mathematical and conceptual foundations of their discipline.
Bas van Fraassen
San Francisco State University
"Absolute generality, structuralism, and perspective"
To begin I will attempt to show that arguments for and against ontic structuralism are irresolvable. On that basis I urge a different form of structuralist position on science, independent of any metaphysical view of nature. But my main concern will be to explore whether a thorough-going structuralist view of the language of science can be carried through coherently, if we require that the accepted account of that language (formulated scientifically, hence in that language) must not only be consistent but coherently believable from a first person perspective.
Commissariat à lEnergie Atomique
"From structuralism to informationalism"
Quantum theory supplied strange phenomena instrumental in breaching the defense lines of realism and seeing to the advent of structuralism in the philosophy of physics. Now quantum theory hints at a new change: physical theory is about information; its mathematical content formally describes operations with information; and its philosophy is informationalism, i.e. a non-realist stance that emphasizes, not just any structure, but the structure of informational exchange. I'll argue that the primitive notions of 'observer' and 'system' already provide an argument for informationalism.
Université Nancy 2
"The French Connection : Poincaré's structural account of geometry, its reception by Carnap and Schlick, and Lautman's structuralism"
Some writers attribute to Poincaré and Hilbert the shift in foundational purposes from what the axioms of geometry say to a syntactic feature of the axiomatic sentence. This is an one-sided interpretation doing not justice to Poincaré. His conventionalism cannot be the result of a model-theoretical or semantic point of view where the physical geometry is just an interpretation of an abstract calculus. On the contrary, Poincaré does not even distinguish between mathematical and physical geometry, a disturbing fact for many interpreters. According to Poincaré there exists only one single type of geometries, which is the result of a psycho-physiological genesis using theoretical and observational language as two different aspects of the constitution of the geometrical objects.
In this talk I begin with a discussion in which sense Poincaré's psycho-physiological genesis of geometry where conventions play an essential role, can be read as the expression of a "structural" account of knowledge. I then show that Poincaré's project has a strong affinity with Carnap's Aufbau and Schlick's General Theory of Knowledge. Nevertheless, Poincaré's concept of structure is not the new Hilbertian deriving from his axiomatization of Euclidean geometry, but the traditional algebraic one and concerns continuous groups. Against this background, I finally consider Albert Lautman's approach to conceive mathematical reality as an unification of "theories" and "ideas".
Universidade Federal de Minas Gerais
"A transcendental approach to scientific structuralism"
In the current debate between scientific realism and empiricism, both
sides seem to embrace some sort of structuralism as an important component of their descriptions of science. It has been argued that Structural Realism comes in two versions, one ontic and the other epistemic, and that the Epistemic Structural Realism (ESR) is close, if not identical, to a Kantian approach. We aim to show that this is not the case, since ESR, being fundamentally a realist position, cannot be a fully consistent transcendental development of structuralism. Such a position is what we would like to call Transcendental Structuralism, an alternative that we believe is worth being investigated on its own.
"Bohr's self-dissolving commitment to macrorealism"
The consistency of Bohr's instrumentalist interpretation of the quantum formalism is generally taken to rest on the assumption that certain objects and processes are not describable by quantum mechanics. According to this view, while the instrumentalist formulation seems to imply that the meaning of an empirical claim cannot be fixed, nor its objectivity established, independently of the meaning and objectivity of all other empirical claims, the occurrence of a particular phenomenon can nevertheless be ascertained and reported in so far as one can relate it to a 'classical' framework (with which we are supposedly acquainted). I will suggest, however, that the preceding proviso really instantiates the very principle it prima facie denies, namely that, whatever the domain of experience considered, we are faced with semantic and epistemological holism. Arguably, quantum mechanics is designed to deal with precisely this situation, which alone determines the empirical reach of the theory (when it comes for example to macroscopic objects) as well as its structural features (e.g., the uncertainty relations).
"The structural link between « external » metric and « internal » gauge symmetries in noncommutative geometry"
One of the main problems in reconciling quantum field theory with general relativity is to mix non-abelian gauge theories, which are noncommutative at the level of their internal space of quantum variables, with the geometry of the external space-time expressed by its group of diffeomorphisms. The noncommutative solution is a principled one linking the standard « inner » noncommutativity of quantum internal degrees of freedom with the new « outer » geometrical noncommutativity of the external space-time. In that context, gauge connections can be interpreted as internal perturbations of the spectral metric induced by the degrees of freedom of gauge transformations. This coupling between metric and gauge transformations is one of the theoretical constructs needed for coupling gravity with quantum field theory.
"Is unitary inequivalence a problem for structuralism?"
The (Stone-) von Neumann uniqueness theorem does not hold for a field system with infinitely many degrees of freedom. Such systems do not then meet the criterion of physical equivalence of theories in ordinary quantum mechanics, i.e., equivalence up to unitary transformation of representations of the (Weyl form of the) canonical commutation relations in Hilbert space. Accordingly, structural realists recognize the existence of unitary inequivalent representations in QFT as posing problems of principle for their structuralist program. However, both axiomatic and algebraic QFT have long recognized the limitations of a canonical formalism based on representations of the Weyl relations. In particular, the C* algebraic reformulation of quantum field theory locates the structure of the theory in the algebraic relations of local bounded observables. In Segal's famous phrase, "the important thing here is that the observables form some sort of algebra, and not the representative Hilbert space on which they act". This shift to an algebraic rather than a spatial perspective naturally invokes an epistemic rather than an ontological and referential understanding of structure. In this regard, the local algebraic approach to QFT, despite criticisms that it is excessively operationalist and insufficiently general, serves as a guiding model for a non-realist structuralism.
"Negative probabilities in physics"
University of Puget Sound
"Ontic structural realism as a metaphysics of modality"
In my paper I try to make sense of ontic structural realism as a metaphysical view of modality. I suggest that Humean Supervenience must be regarded as the main metaphysical opponent for structural realism. We should reinterpret the modal and ontological commitments of OSR in light of this opposition. The result, I argue, will not be a radical 'eliminative' structural realism according to which there are no objects at all. Instead the view will be one according to which there are objects, but some of their essential properties are determined by structure. Finally I suggest why this metaphysical component of structural realism might be relevant to non-realists and anti-metaphysicians.
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