Lloyd Humberstone
Monash University
The partitions of a given set stand in a well known one-to-onecorrespondence with the equivalence relations on that set. We askwhether anything analogous to partitions can be found which correspondin a like manner to the similarity relations (reflexive, symmetricrelations) on a set, and show that (what we call) decompositions – of acertain kind – play this role. A key ingredient in the discussion is akind of closure relation (analogous to the consequence relationsconsidered in formal logic) having nothing especially to do with thesimilarity issue, and we devote a final section to highlighting some ofits properties.
Keywords closure operators  partitions  proximity relations  similarity  truth functions
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DOI 10.1023/A:1026132413897
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References found in this work BETA

First-Order Logics for Comparative Similarity.Timothy Williamson - 1988 - Notre Dame Journal of Formal Logic 29 (4):457-481.
Flexibly Structured Predication.Barry Taylor & Allen P. Hazen - 1992 - Logique Et Analyse 35:374-393.
Policing the Aufbau.David K. Lewis - 1969 - Philosophical Studies 20 (1-2):13-17.
Four Modal Modelings.John Bacon - 1988 - Journal of Philosophical Logic 17 (2):91 - 114.
New Work For a Theory of Universals.David Lewis - 1983 - In D. H. Mellor & Alex Oliver (eds.), Properties. Oxford University Press.

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Citations of this work BETA

Yablo on Subject-Matter.Kit Fine - 2020 - Philosophical Studies 177 (1):129-171.
Parts as Counterparts.Aaron Cotnoir - 2013 - Thought: A Journal of Philosophy 2 (3):228-241.
A New Analysis of Quasianalysis.Hannes Leitgeb - 2007 - Journal of Philosophical Logic 36 (2):181-226.
New Work for Carnap’s Quasi-Analysis.Thomas Mormann - 2009 - Journal of Philosophical Logic 38 (3):249-282.

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