3,646 research outputs found

    On the Infinite in Mereology with Plural Quantification

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    In Lewis reconstructs set theory using mereology and plural quantification (MPQ). In his recontruction he assumes from the beginning that there is an infinite plurality of atoms, whose size is equivalent to that of the set theoretical universe. Since this assumption is far beyond the basic axioms of mereology, it might seem that MPQ do not play any role in order to guarantee the existence of a large infinity of objects. However, we intend to demonstrate that mereology and plural quantification are, in some ways, particularly relevant to a certain conception of the infinite. More precisely, though the principles of mereology and plural quantification do not guarantee the existence of an infinite number of objects, nevertheless, once the existence of any infinite object is admitted, they are able to assure the existence of an uncountable infinity of objects. So, ifMPQ were parts of logic, the implausible consequence would follow that, given a countable infinity of individuals, logic would be able to guarantee an uncountable infinity of object

    Topological Foundations of Cognitive Science

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    A collection of papers presented at the First International Summer Institute in Cognitive Science, University at Buffalo, July 1994, including the following papers: ** Topological Foundations of Cognitive Science, Barry Smith ** The Bounds of Axiomatisation, Graham White ** Rethinking Boundaries, Wojciech Zelaniec ** Sheaf Mereology and Space Cognition, Jean Petitot ** A Mereotopological Definition of 'Point', Carola Eschenbach ** Discreteness, Finiteness, and the Structure of Topological Spaces, Christopher Habel ** Mass Reference and the Geometry of Solids, Almerindo E. Ojeda ** Defining a 'Doughnut' Made Difficult, N .M. Gotts ** A Theory of Spatial Regions with Indeterminate Boundaries, A.G. Cohn and N.M. Gotts ** Mereotopological Construction of Time from Events, Fabio Pianesi and Achille C. Varzi ** Computational Mereology: A Study of Part-of Relations for Multi-media Indexing, Wlodek Zadrozny and Michelle Ki

    Is mereology empirical? Composition for fermions

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    How best to think about quantum systems under permutation invariance is a question that has received a great deal of attention in the literature. But very little attention has been paid to taking seriously the proposal that permutation invariance reflects a representational redundancy in the formalism. Under such a proposal, it is far from obvious how a constituent quantum system is represented. Consequently, it is also far from obvious how quantum systems compose to form assemblies, i.e. what is the formal structure of their relations of parthood, overlap and fusion. In this paper, I explore one proposal for the case of fermions and their assemblies. According to this proposal, fermionic assemblies which are not entangled -- in some heterodox, but natural sense of 'entangled' -- provide a prima facie counterexample to classical mereology. This result is puzzling; but, I argue, no more intolerable than any other available interpretative option.Comment: 24 pages, 1 figur

    The nonclassical mereology of olfactory experiences

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    While there is a growing philosophical interest in analysing olfactory experiences, the mereological structure of odours considered in respect of how they are perceptually experienced has not yet been extensively investigated. The paper argues that odours are perceptually experienced as having a mereological structure, but this structure is significantly different from the spatial mereological structure of visually experienced objects. Most importantly, in the case of the olfactory part-structure, the classical weak supplementation principle is not satisfied. This thesis is justified by referring to empirical results in olfactory science concerning the human ability to identify components in complex olfactory stimuli. Further, it is shown how differences between olfactory and visual mereologies may arise from the way in which these modalities represent space

    Whitehead's Principle

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    According to Whitehead’s rectified principle, two individuals are connected just in case there is something self-connected which overlaps both of them, and every part of which overlaps one of them. Roberto Casati and Achille Varzi have offered a counterexample to the principle, consisting of an individual which has no self-connected parts. But since atoms are self-connected, Casati and Varzi’s counterexample presupposes the possibility of gunk or, in other words, things which have no atoms as parts. So one may still wonder whether Whitehead’s rectified principle follows from the assumption of atomism. This paper presents an atomic countermodel to show the answer is no

    Between Atomism and Superatomism

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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

    How Philosophy of Mind Needs Philosophy of Chemistry

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    By the 1960s many (perhaps most) philosophers had adopted ‘physicalism’ ─ the view that physical causes fully account for mental activities. However, controversy persists about what count as ‘physical causes’. ‘Reductive’ physicalists recognize only microphysical (elementary-particle-level) causality. Many (perhaps most) physicalists are ‘non-reductive’ ─ they hold that entities considered by other (‘special’) sciences have causal powers. Philosophy of chemistry can help resolve main issues in philosophy of mind in three ways: developing an extended mereology applicable to chemical combination, testing whether ‘singularities’ prevent reduction of chemistry to microphysics, and demonstrating ‘downward causation’ in complex networks of chemical reactions

    How Philosophy of Mind Needs Philosophy of Chemistry

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    By the 1960s many (perhaps most) philosophers had adopted ‘physicalism’ ─ the view that physical causes fully account for mental activities. However, controversy persists about what count as ‘physical causes’. ‘Reductive’ physicalists recognize only microphysical (elementary-particle-level) causality. Many (perhaps most) physicalists are ‘non-reductive’ ─ they hold that entities considered by other (‘special’) sciences have causal powers. Philosophy of chemistry can help resolve main issues in philosophy of mind in three ways: developing an extended mereology applicable to chemical combination, testing whether ‘singularities’ prevent reduction of chemistry to microphysics, and demonstrating ‘downward causation’ in complex networks of chemical reactions
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