Category-theoretic structure and radical ontic structural realism

Bain, Jonathan

doi:10.1007/s11229-011-9896-6

Cited by 33 publications

(38 citation statements)

References 20 publications

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“…(Bain 2013(Bain , p 1624 At this stage, category theory looks like a promising formal setting for ROSR, since it seems to be capable of providing a notion of structure that is not conceptually tied to individual relata. However, Bain immediately anticipates a possible objection to his proposal, namely the argument that 'category theory eliminates reference to relata only in name'.…”

Section: Category Theory and Rosrmentioning

confidence: 99%

“…The argument against the radical ontic structural realist then gets translated from the slogan "no relations without relata" to the slogan "no objects (of the relevant sort) without morphisms from the terminal object." ' (Bain 2013(Bain , p 1625 Bain replies to this argument by noting that there are many categories whose objects are not structured sets, and so the structures encoded by these objects can not depend completely on their elements. If it were the case that every category was a category of some kind of structured set, together with the structure-preserving morphisms, then Bain would presumably accept the criticism.…”

Section: Category Theory and Rosrmentioning

confidence: 99%

“…The morphisms in HILB in contrast are general bounded linear operators that do not necessarily have to be unitary.' (Bain 2013(Bain , p 1630 The argument here is that since the morphisms of HILB do not preserve all of the relevant physical structure, the structure of HILB as a whole cannot be adequately expressed purely in terms of the elements of its objects. Bain also cites the fact that, unlike SETS, HILB is a monoidal dagger category, and notes that since HILB has a terminal object, it allows us to talk about elements of objects in the category.…”

Section: Category Theory and Rosrmentioning

confidence: 99%

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Category theory and physical structuralism

Eva

2016

Euro Jnl Phil Sci

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As a metaphysical theory, radical ontic structural realism (ROSR) is characterised mainly in terms of the ontological primacy it places on relations and structures, as opposed to the individual relata and objects that inhabit these relations/structures. The most popular criticism of ROSR is that its central thesis (that there can exist 'relations without relata') is incoherent. Bain (Synthese, 190, 1621(Synthese, 190, -1635(Synthese, 190, , 2013 attempts to address this criticism by arguing that the mathematical language of category theory allows for a coherent articulation of ROSR's key thesis. Subsequently, Wüthrich and Lam (2014) and Lal and Teh (2015) have criticised Bain's arguments and claimed that category theory fares no better than set theory in coherently articulating the main ideas of ROSR. In this paper, we defend Bain's main arguments against these critiques, and attempt to elaborate on the sense in which category theory can be seen as providing a coherent articulation of ROSR. We also consider the relationship between ROSR and Categorical Quantum Mechanics.

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Section: Category Theory and Rosrmentioning

confidence: 99%

Section: Category Theory and Rosrmentioning

confidence: 99%

Section: Category Theory and Rosrmentioning

confidence: 99%

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Category theory and physical structuralism

Eva

2016

Euro Jnl Phil Sci

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“… Bain () attempts such a revision in the mathematical realm. And even if Lam and Wüthrich's () claim that Bain is unsuccessful should prove unjustified, the rewriting itself will be a breach of the naturalistic principles set up by Ladyman and Ross.…”

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confidence: 99%

Metaphysics Within Science: Against Radical Naturalism

Andersen

Arenhart

2016

Metaphilosophy

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In Every Thing Must Go James Ladyman and Don Ross argue for a radical version of naturalistic metaphysics and propose that contemporary analytic metaphysics is detached from science and should be discontinued. The present article addresses the issues of whether (i) science and metaphysics are separable, (ii) intuitions and understanding should be excluded from scientific theory, and (iii) Ontic Structural Realism satisfies the criteria of the radical version of naturalism advanced by Ladyman and Ross. The point underlying those topics is that successful scientific research presupposes metaphysics, and that basic epistemic virtues common to metaphysics and science may allow us—as opposed to what Ladyman and Ross suggest—to increase our understanding of the world and to put constraints on allowable metaphysical theories.

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“…For an approach to eliminativism focusing on category theoretic as opposed to group theoretic descriptions, seeBain (2013), and for skepticism regarding this use of category theory, seeLam and Wüthrich (2013) andLal and Teh (2014).…”

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confidence: 99%

Particles, causation, and the metaphysics of structure

Chakravartty

2015

Synthese

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I consider the idea of a structure of fundamental physical particles (as described, for example, in quantum theory) being causal. Causation is traditionally thought of as involving relations between entities-objects or events-that cause and are affected. On structuralist interpretations, however, it is unclear whether or how precisely fundamental particles can be causally efficacious. On some interpretations, only relations (as opposed to entities) exist; on others, particles are ontologically dependent on their relations in ways that problematize the traditional picture. I argue that thinking about causal efficacy in this context generates an inevitable pattern of reasoning. To assess the cogency of a given structuralist proposal one must take a stand with respect to a significant metaphysical challenge. Two options then emerge: skepticism about the form of structuralism at issue; or a dissolution of the challenge by means of a contentious ontological primitive. I contend that the choice between these options cannot be forced on scientific or philosophical grounds alone.

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Category-theoretic structure and radical ontic structural realism

Cited by 33 publications

References 20 publications

Category theory and physical structuralism

Category theory and physical structuralism

Metaphysics Within Science: Against Radical Naturalism

Particles, causation, and the metaphysics of structure

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