Humean Supervenience, Vectorial Fields, and the Spinning Sphere

Busse, Ralf

doi:10.1111/j.1746-8361.2009.01218.x

Cited by 12 publications

(5 citation statements)

References 35 publications

(51 reference statements)

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“…If so, it becomes difficult to model how any world could satisfy the constraints. Others have argued that they can be accommodated, thus that Humean Supervenience is tenable in spite of this challenge (Busse 2009). …”

Section: Humean Superveniencementioning

confidence: 96%

Some Consequences (and Enablings) of Process Metaphysics

Bickhard

2010

Axiomathes

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The interactivist model has explored a number of consequences of process metaphysics. These include reversals of some fundamental metaphysical assumptions dominant since the ancient Greeks, and multiple further consequences throughout the metaphysics of the world, minds, and persons. This article surveys some of these consequences, ranging from issues regarding entities and supervenience to the emergence of normative phenomena such as representation, rationality, persons, and ethics. Contemporary thought is dominated by a particle-based metaphysics that can be traced to at least Parmenides and the responses of Democritus and Empedocles (Graham 2006; cf. Palmer 2010). There are, however, multiple reasons for working within a process metaphysics rather than a substance or particle metaphysics, 1 both in terms of consistency with current science and in terms of the further philosophical and theoretical developments that are thereby enabled. 1 Parmenides argued (against Heraclitus) against change, and Democritus and Empedocles proposed models of apparent change with an unchanging substrate-atoms for Democritus and substances for Empedocles (Graham 2006). It is this underlying assumption of the metaphysical necessity of an unchanging substrate that is crucial to the position in the main text, and I refer to such an assumption as that of a substance metaphysics, for both ''stuffs'' as for Empedocles and ''atoms'' as for Democritus.

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Section: Humean Superveniencementioning

confidence: 96%

Some Consequences (and Enablings) of Process Metaphysics

Bickhard

2010

Axiomathes

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“…If a velocity is the limit of distance divided by time as the time approaches zero, then is it a mere logical construction out of occupying various spacetime points (for example, see Tooley 1988, Arntzenius 2000, Butterfield 2006)? The nature of the electromagnetic field is similarly puzzling: are the vectorial field values extrinsic to spacetime points (see Weatherson 2006, Busse 2009)? Things get even messier when it concerns curved spacetime, which involves tangent spaces and their relations.…”

Section: Continua With Infinitesimal Partsmentioning

confidence: 99%

“…Thus, the electric field value at a point has a spatial direction that determines the trajectory of a charged body passing through that point. Like the case of velocity, there is a debate on whether we should consider those vectors as intrinsic to spatial points (see Weatherson 2006, Busse 2009). If those vectors are intrinsic to the electric field within spatial points, then it is strange that they can have spatial directions since a point does not have any spatial direction.…”

Section: Metaphysics Of Vectorsmentioning

confidence: 99%

Smooth Infinitesimals in the Metaphysical Foundation of Spacetime Theories

Chen

2022

J Philos Logic

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I propose a theory of space with infinitesimal regions called smooth infinitesimal geometry (SIG) based on certain algebraic objects (i.e., rings), which regiments a mode of reasoning heuristically used by geometricists and physicists (e.g., circle is composed of infinitely many straight lines). I argue that SIG has the following utilities. (1) It provides a simple metaphysics of vector fields and tangent space that are otherwise perplexing. A tangent space can be considered an infinitesimal region of space. (2) It generalizes a standard implementation of spacetime algebraicism (according to which physical fields exist fundamentally without an underlying manifold) called Einstein algebras. (3) It solves the long-standing problem of interpreting smooth infinitesimal analysis (SIA) realistically, an alternative foundation of spacetime theories to real analysis (Lawvere 1980). SIA is formulated in intuitionistic logic and is thought to have no classical reformulations (Hellman 2006). Against this, I argue that SIG is (part of) such a reformulation. But SIG has an unorthodox mereology, * Acknowledgments. I want to give special thanks to Jeffrey Russell for the essential discussions and guidance early on and to Tobias Fritz for his very generous technical help, without which the current paper would be impossible. I thank Phillip Bricker and Cian Dorr for their helpful feedback on the early drafts of the paper. Many thanks to the anonymous referee of Journal of Philosophical Logic for their very helpful comments, which have substantially improved the exposition of the paper, among other things. Finally, I would like to thank all the participants at my talks based on various versions of the paper for their stimulating questions and comments, whose names are too numerous to list. 1 in which the principle of supplementation fails.

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“…Because vectors have directedness, and especially because they have sense, Massin [2009] and others have argued that they must be understood as relational, since reference to other entities is needed to attribute a directed property to an object (but see Busse [2009] for a defense of vectors as intrinsic). Without deciding the matter in the general case, it seems that in the case of spin, this worry does not arise.…”

Section: Modeling Spin As a Determinablementioning

confidence: 99%

Spin as a Determinable

Wolff

2015

Topoi

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In this paper I aim to answer two questions: 1) Can spin be treated as a determinable? 2) Can a treatment of spin as a determinable be used to understand quantum indeterminacy? In response to the first question I show that the relations among spin number, spin components and spin values cannot be captured by a single determination relation; instead we need to look at spin number and spin value separately. In response to the second question I discuss three ways in which the determinables model might be modified to account for indeterminacy, and argue that none of them is fully successful in helping us to understand quantum indeterminacy.

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Humean Supervenience, Vectorial Fields, and the Spinning Sphere

Cited by 12 publications

References 35 publications

Some Consequences (and Enablings) of Process Metaphysics

Some Consequences (and Enablings) of Process Metaphysics

Smooth Infinitesimals in the Metaphysical Foundation of Spacetime Theories

Spin as a Determinable

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