Equivalent and Inequivalent Formulations of Classical Mechanics

Barrett, Thomas William

doi:10.1093/bjps/axy017

Cited by 40 publications

(51 citation statements)

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“…Philosophers of physics have applied this criterion in several case studies (cf. Barrett, 2017;Barrett et al, 2015;Hudetz, 2015;Rosenstock and Weatherall, 2016;Teh and Tsementzis, 2017;Weatherall, 2016a).…”

Section: Categorical Equivalencementioning

confidence: 99%

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Definable Categorical Equivalence

Hudetz¹

2019

Philos. of Sci.

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This paper proposes to explicate theoretical equivalence by supplementing formal equivalence criteria with preservation conditions concerning interpretation. I argue that both the internal structure of models and choices of morphisms are aspects of formalisms that are relevant when it comes to their interpretation. Hence, a formal criterion suitable for being supplemented with preservation conditions concerning interpretation should take these two aspects into account. The two currently most important criteria-generalised definitional equivalence (Morita equivalence) and categorical equivalence-are not optimal in this respect. I put forward a criterion that takes both aspects into account: the criterion of definable categorical equivalence.

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Section: Categorical Equivalencementioning

confidence: 99%

“…See for exampleAndréka and Németi (2014),Barrett (2017),Barrett and Halvorson (2017),Barrett, Rosenstock, and Weatherall (2015),Hudetz (2015),Lefever and Székely (2018),Rosenstock and Weatherall (2016),Teh and Tsementzis (2017) and Weatherall (2016a).2Putnam (1983, p. 40) argues that formal equivalence is even necessary for full equivalence.…”

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confidence: 99%

Definable Categorical Equivalence

Hudetz¹

2019

Philos. of Sci.

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“…Halvorson (2012Halvorson ( , 2016 and Halvorson and Tsementzis (2017) argue that scientific theories can be represented using the tools of category theory rather than mathematical logic or model theory. Barrett (2017a) and Weatherall (2016aWeatherall ( ,b,c, 2017 argue that the tools of category theory can help us determine when two scientific theories are theoretically equivalent. And Barrett (2015aBarrett ( ,b, 2017b argues that the tools of category theory help us compare the amounts of structure in different scientific theories, or different formulations of a scientific theory.…”

Section: Limits and Structurementioning

confidence: 99%

Deduction and definability in infinite statistical systems

Feintzeig

2017

Synthese

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Classical accounts of intertheoretic reduction involve two pieces: first, the new terms of the higher-level theory must be definable from the terms of the lower-level theory, and second, the claims of the higher-level theory must be deducible from the lower-level theory along with these definitions. The status of each of these pieces becomes controversial when the alleged reduction involves an infinite limit, as in statistical mechanics. Can one define features of or deduce the behavior of an infinite idealized system from a theory describing only finite systems? In this paper, I change the subject in order to consider the motivations behind the definability and deducibility requirements. The classical accounts of intertheoretic reduction are appealing because when the definability and deducibility requirements are satisfied there is a sense in which the reduced theory is forced upon us by the reducing theory and the reduced theory contains no more information or structure than the reducing theory. I will show that, likewise, there is a precise sense in which in statistical mechanics the properties of infinite limiting systems are forced upon us by the properties of finite systems, and the properties of infinite systems contain no information beyond the properties of finite systems.

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“…As noted at the end of Part 1, there are reasons to think that definitional equivalence is either inadequate or of limited use in practice (or both). Motivated by these and related concerns, Halvorson () and Weatherall () have proposed a different criterion of equivalence between physical theories, using methods from category theory; this proposal has subsequently been pursued and developed by numerous authors (Barrett, , , ; Dewar & Eva, ; Halvorson, ; Halvorson & Tsementzis, ; Nguyen, Teh, & Wells, ; Rosenstock, Barrett, & Weatherall, ; Weatherall, , )…”

Section: Categorical Equivalencementioning

confidence: 99%

Part 2: Theoretical equivalence in physics

Weatherall

2019

Philosophy Compass

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I review the philosophical literature on the question of when two physical theories are equivalent. This includes a discussion of empirical equivalence, which is often taken to be necessary, and sometimes taken to be sufficient, for theoretical equivalence; and ''interpretational'' equivalence, which is the idea that two theories are equivalent just in case they have the same interpretation. It also includes a discussion of several formal notions of equivalence that have been considered in the recent philosophical literature, including (generalized) definitional equivalence and categorical equivalence. The article concludes with a brief discussion of the relationship between equivalence and duality. The article is in two parts; this is Part 2, which addresses categorical equivalence, interpretational equivalence, and duality. PREFACEFor reasons related to journal policy, this article has been split into two parts. This is Part 2, which addresses categorical equivalence, interpretational equivalence, and duality; Part 1 addressed empirical equivalence and definitional equivalence. Readers are encouraged to read Part 1 before Part 2.

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Equivalent and Inequivalent Formulations of Classical Mechanics

Cited by 40 publications

References 50 publications

Definable Categorical Equivalence

Definable Categorical Equivalence

Deduction and definability in infinite statistical systems

Part 2: Theoretical equivalence in physics

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