870 research outputs found
On the Infinite in Mereology with Plural Quantification
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
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
Between Atomism and Superatomism
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 oneâs mereology than either of the other two principles, and it should be regarded as the best formulation of the atomistic thesis
Is mereology empirical? Composition for fermions
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
Formal Theories of Parthood
A compact overview of the main formal theories of parthood and of their mutual relationships, up to Classical Extensional Mereology. Written as an Appendix to the other essays included in the volume
The Semantic Foundations of Philosophical Analysis
I provide an analysis of sentences of the form âTo be F is to be Gâ in terms of exact truth-maker semanticsâan approach that identifies the meanings of sentences with the states of the world directly responsible for their truth-values. Roughly, I argue that these sentences hold just in case that which makes something F is that which makes it G. This approach is hyperintensional, and possesses desirable logical and modal features. These sentences are reflexive, transitive and symmetric, and, if they are true, then they are necessarily true, and it is necessary that all and only Fs are Gs. I close by defining an asymmetric and irreflexive notion of analysis in terms of the reflexive and symmetric one
Parts of Falling Objects: Galileoâs Thought Experiment in Mereological Setting
This paper aims to formalize Galileoâs argument (and its variations) against the Aristotelian
view that the weight of free-falling bodies influences their speed. I obtain this
via the application of concepts of parthood and of mereological sum, and via recognition
of a principle which is not explicitly formulated by the Italian thinker but seems
to be natural and helpful in understanding the logical mechanism behind Galileoâs
train of thought. I also compare my reconstruction to one of those put forward by
Atkinson and Peijnenburg (Stud Hist Philos Sci 35(1):115â136, 2004), and propose
a formalization which is based on a principle introduced by them, which I shall call
the speed is mediative principle
âThe whole is greater than the part.â Mereology in Euclid's Elements
The present article provides a mereological analysis of Euclidâs planar geometry as presented in the first two books of his Elements. As a standard of comparison, a brief survey of the basic concepts of planar geometry formulated in a set-theoretic framework is given in Section 2. Section 3.2, then, develops the theories of incidence and order (of points on a line) using a blend of mereology and convex geometry. Section 3.3 explains Euclidâs âmegethologyâ, i.e., his theory of magnitudes. In Euclidâs system of geometry, megethology takes over the role played by the theory of congruence in modern accounts of geometry. Mereology and megethology are connected by Euclidâs Axiom 5: âThe whole is greater than the part.â Section 4 compares Euclidâs theory of polygonal area, based on his âWhole-Greater-Than-Partâ principle, to the account provided by Hilbert in his Grundlagen der Geometrie. An hypothesis is set forth why modern treatments of geometry abandon Euclidâs Axiom 5. Finally, in Section 5, the adequacy of atomistic mereology as a framework for a formal reconstruction of Euclidâs system of geometry is discussed
The Category of Mereotopology and Its Ontological Consequences
We introduce the category of mereotopology Mtop as an alternative category to that of topology Top, stating ontological consequences throughout. We consider entities such as boundaries utilizing Brentanoâs thesis and holes utilizing homotopy theory with a rigorous proof of Hausdorff Spaces satisfying [GEM]TC axioms. Lastly, we mention further areas of study in this category
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