Why Not Categorical Equivalence?

Weatherall, James Owen

doi:10.1007/978-3-030-64187-0_18

Cited by 20 publications

(6 citation statements)

References 45 publications

(50 reference statements)

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“…Although this problem is certainly pressing, it is somewhat assuaged by noticing that the choice of which functors to use to compare two theories is often quite easy. In the case of physical theories there are often particularly ‘natural’ candidates of functors to choose from (Weatherall, 2019a, 2019b). For example, the Legendre transformation gives rise to the most natural functor between Hamiltonian and Lagrangian mechanics, the famous ‘function‐space’ duality gives rise to the most natural functor between general relativity and the theory of Einstein algebras, and as we saw in Example 8 ‘flipping the sign’ of the metric gives rise to the most natural functor between the (1,3) and (3,1) formulations of general relativity.…”

Section: Problems With the Category Approachmentioning

confidence: 99%

How to count structure

Barrett

2020

Nous

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There is sometimes a sense in which one theory posits 'less structure' than another. Philosophers of science have recently appealed to this idea both in the debate about equivalence of theories and in discussions about structural parsimony. But there are a number of different proposals currently on the table for how to compare the 'amount of structure' that different theories posit. The aim of this paper is to compare these proposals against one another and evaluate them on their own merits.

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Section: Problems With the Category Approachmentioning

confidence: 99%

How to count structure

Barrett

2020

Nous

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“…As mentioned in footnote 17, we postpone discussion of structural realism to another paper. 25 Recent discussions include Butterfield (2018: Section 5), De Haro (2020), Dewar (2019), Halvorson (2019), Hudetz (2019Hudetz ( , 2019a and Weatherall (2018Weatherall ( , 2018a. For general arguments against formal analyses of theoretical equivalence, cf.…”

Section: Plenitude As a Problem For Nagelian Reductionmentioning

confidence: 99%

Functionalism as a Species of Reduction

Butterfield,

Gomes

2020

Preprint

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This is the first of four papers prompted by a recent literature about a doctrine dubbed spacetime functionalism. This paper gives our general framework for discussing functionalism. Following Lewis, we take it as a species of reduction. We start by expounding reduction in a broadly Nagelian sense. Then we argue that Lewis' functionalism is an improvement on Nagelian reduction.This paper thereby sets the scene for the other papers, which will apply our framework to theories of space and time. (So those papers address the space and time literature: both recent and older, and physical as well as philosophical literature. But the four papers can be read independently.)Overall, we come to praise spacetime functionalism, not to bury it. But we criticize the recent philosophical literature for failing to stress:(i) functionalism's being a species of reduction (in particular: reduction of chronogeometry to the physics of matter and radiation);(ii) functionalism's idea, not just of specifying a concept by its functional role, but of specifying several concepts simultaneously by their roles;(iii) functionalism's providing bridge laws that are mandatory, not optional: they are statements of identity (or co-extension) that are conclusions of a deductive argument, rather than contingent guesses or verbal stipulations; and once we infer them, we have a reduction in a Nagelian sense.On the other hand, some of the older philosophical literature, and the mathematical physics literature, is faithful to these ideas (i) to (iii)-as are Torretti's writings. (But of course, the word 'functionalism' is not used; and themes like simultaneous unique definition are not articulated.) Thus in various papers, falling under various research programmes, the unique definability of a chrono-geometric concept (or concepts) in terms of matter and radiation, and a corresponding bridge law and reduction, is secured by a precise theorem. Hence our desire to celebrate these results as rigorous renditions of spacetime functionalism.

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“…From this perspective, the "structureless points" of the example above are not structureless after all, and the further restriction to reconstruction functors is unnecessary or, in other words, automatic. (For further discussion of worries along these lines, see Weatherall (2018). )…”

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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Why Not Categorical Equivalence?

Cited by 20 publications

References 45 publications

How to count structure

How to count structure

Functionalism as a Species of Reduction

Part 2: Theoretical equivalence in physics

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