David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
Synthese 112 (3):403-430 (1997)
In §54 of the Grundlagen, Frege advances an interesting proposal on how to distinguish among different sorts of concepts, only some of which he thinks can be associated with number. This paper is devoted to an analysis of the two criteria he offers, isolation and non-arbitrary division. Both criteria say something about the way in which a concept divides its extension; but they emphasize different aspects. Isolation ensures that a concept divides its extension into discrete units. I offer two construals of this: isolation as discreteness, i.e. absence of overlap, between the objects to be counted; and isolation as the drawing of conceptual boundaries. Non-arbitrary division concerns the internal structure of the units we count: it makes sure that we cannot go on dividing them arbitrarily and still find more units of the kind. Non-arbitrary division focuses not only on how long something can be divided into parts of the same kind; it also speaks to the way in which these divisions are made, arbitrarily or non-arbitrarily, as well as to the compositional structure of the objects divided
|Keywords||Philosophy Philosophy Epistemology Logic Metaphysics Philosophy of Language|
|Categories||categorize this paper)|
Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
|Through your library|
References found in this work BETA
No references found.
Citations of this work BETA
No citations found.
Similar books and articles
Steven J. Brams, Paul H. Edelman & Peter C. Fishburn (2003). Fair Division of Indivisible Items. Theory and Decision 55 (2):147-180.
Marco Ruffino (2000). Extensions as Representative Objects in Frege's Logic. Erkenntnis 52 (2):239-252.
Markus Schmitz (2001). Erkenntnistheorie der Zahldefinition Und Philosophische Grundlegung der Arithmetik Unter Bezugnahme Auf Einen Vergleich Von Gottlob Freges Logizismus Und Platonischer Philosophie (Syrian, Theon Von Smyrna U.A.). Journal for General Philosophy of Science 32 (2):271-305.
William Demopoulos (1994). Frege, Hilbert, and the Conceptual Structure of Model Theory. History and Philosophy of Logic 15 (2):211-225.
Joan Weiner (2007). What's in a Numeral? Frege's Answer. Mind 116 (463):677 - 716.
Wylie Breckenridge & Ofra Magidor (2012). Arbitrary Reference. Philosophical Studies 158 (3):377-400.
Hans-Rolf Gregorius (2006). The Isolation Principle of Clustering: Structural Characteristics and Implementation. Acta Biotheoretica 54 (3):219-233.
Neil Pickering (2013). Extending Disorder: Essentialism, Family Resemblance and Secondary Sense. [REVIEW] Medicine, Health Care and Philosophy 16 (2):185-195.
David V. Ward (1984). Identity. Philosophy Research Archives 10:353-382.
Kathrin Koslicki (1997). Isolation and Non-Arbitrary Division: Frege's Two Criteria for Counting. Synthese 112 (3):403-430.
Added to index2009-08-17
Total downloads26 ( #77,062 of 1,410,269 )
Recent downloads (6 months)2 ( #107,949 of 1,410,269 )
How can I increase my downloads?