The fundamental: Ungrounded or all-grounding?

Leuenberger, Stephan

doi:10.1007/s11098-019-01332-x

Cited by 34 publications

(30 citation statements)

References 38 publications

(69 reference statements)

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“…It allows one to choose a maximal chain from any partially ordered set, importantly, including any that is such that, for everything x in it, there is something y in it such that y is less than x in the partial order. 10 The proof of Proposition 6 is rather involved. So I will simply provide an outline of it here.…”

Section: Proposition 7 If Everything Has An Atomic Part Then Everythimentioning

confidence: 99%

“…I have given its counterpart in plural first-order logic. 10 See [4, 56-63] for a proof of the equivalence of the Hausdorff maximal principle and the axiom of choice and several variants of it. For an earlier proof of the Hausdorff maximal principle using the well-ordering theorem, see [7,.…”

Section: Definition Of Final Segments Form a Final Segment Ofmentioning

confidence: 99%

“…This definition has its skeptics. Leuenberger[10], for example, argues that something can be partially grounded by something that is not among any full grounds of it. As it happens, however, the foundationalist argument depends only on the less controversial right-to-left direction: that everything among a thing's full grounds is a partial ground of it.…”

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confidence: 99%

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Between Atomism and Superatomism

Dixon

2020

J Philos Logic

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There are at least three vaguely atomistic principles that have come up in the literature, two explicitly and one implicitly. First, standard atomism is the claim that everything is composed of atoms, and is very often how atomism is characterized in the literature. Second, superatomism is the claim that parthood is well-founded, which implies that every proper parthood chain terminates, and has been discussed as a stronger alternative to standard atomism. Third, there is a principle that lies between these two theses in terms of its relative strength: strong atomism, the claim that every maximal proper parthood chain terminates. Although strong atomism is equivalent to superatomism in classical extensional mereology, it is strictly weaker than it in strictly weaker systems in which parthood is a partial order. And it is strictly stronger than standard atomism in classical extensional mereology and, given the axiom of choice, in such strictly weaker systems as well. Though strong atomism has not, to my knowledge, been explicitly identified, Shiver appears to have it in mind, though it is unclear whether he recognizes that it is not equivalent to standard atomism in each of the mereologies he considers. I prove these logical relationships which hold amongst these three atomistic principles, and argue that, whether one adopts classical extensional mereology or a system strictly weaker than it in which parthood is a partial order, standard atomism is a more defensible addition to one's mereology than either of the other two principles, and it should be regarded as the best formulation of the atomistic thesis.

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Section: Proposition 7 If Everything Has An Atomic Part Then Everythimentioning

confidence: 99%

Section: Definition Of Final Segments Form a Final Segment Ofmentioning

confidence: 99%

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Between Atomism and Superatomism

Dixon

2020

J Philos Logic

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“…In the literature, such a definition enjoys a steady popularity. As Leuenberger (2020, p. 2) puts it, thinking of the fundamental as the ungrounded is one out of “two obvious strategies for defining the fundamental in terms of ground”. For example, Schaffer (2009, p. 373) defines a fundamental entity as one which nothing grounds.…”

Section: The Inadequacy Objection Against the Fundamental Qua The Ungroundedmentioning

confidence: 99%

Fundamental Yet Grounded

Giannotti

2020

Theoria

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Grounding is claimed to offer a promising characterization of the fundamental as that which is ungrounded. Detractors of this view argue that there can be fundamental and yet mutually grounded entities. Such a possibility undermines the definition of the fundamental as the ungrounded. I aim to show, however, that the possibility of fundamental mutually grounded entities does not force us to renounce the prospects of characterizing fundamentality in terms of grounding. To accomplish this aim, I defend a grounding‐based view that accommodates fundamental mutually grounded entities straightforwardly. My definition of fundamentality is similar to, but importantly different from, one that Karen Bennett discusses. I conclude by resisting two objections raised by Jessica Wilson against the Bennettian framework that also target the proposed view.

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“…See for instanceAudi (2012: p. 710),Bennett (2011: p. 1), Bennett (2017),Dixon (2016: p. 442),Leuenberger (2020Leuenberger ( : p. 2650),Rosen (2010: p. 112), Schaffer (2009: p. 373), Shumener (2017 2) andWallner (2021Wallner ( : p. 1260).…”

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confidence: 99%