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Plural Quantification Exposed
English contains two sorts of object quantifiers. In addition to ordinary singular quantifiers, as in the sentence 'There is a Cheerio in the bowl', there are plural quantifiers, as in 'There areExpand
Sets, Properties, and Unrestricted Quantification
Call a quantifier unrestricted if it ranges over absolutely all things: not just over all physical things or all things relevant to some particular utterance or discourse but over absolutelyExpand
Structuralism and the notion of dependence
The notion of dependence figures prominently in recent discussions of non-eliminative mathematical structuralism. Structuralists often argue that mathematical objects from one and the same structureExpand
Hierarchies ontological and ideological
Godel claimed that Zermelo-Fraenkel set theory is ‘what becomes of the theory of types if certain superfluous restrictions are removed’. The aim of this paper is to develop a clearer understanding ofExpand
Superplurals in English
It is now widely believed among philosophers and logicians that ordinary English contains plural terms that may refer to several things at once. But are there terms that stand to ordinary pluralExpand
Category theory as an autonomous foundation
Does category theory provide a foundation for mathematics that is autonomous with respect to the orthodox foundation in a set theory such as ZFC? We distinguish three types of autonomy : logical,Expand
THE POTENTIAL HIERARCHY OF SETS
  • Øystein Linnebo
  • Computer Science, Mathematics
  • The Review of Symbolic Logic
  • 14 March 2013
TLDR
A modal set theory is developed which encapsulates this potentialist conception and is equi-interpretable with Zermelo Fraenkel set theory but sheds new light on the set-theoretic paradoxes and the foundations of set theory. Expand
Predicative fragments of Frege Arithmetic
TLDR
This paper distinguishes two dimensions of impredicativity involved in FA—one having to do with Hume’s Principle, the other, with the underlying second-order logic—and investigates how much of Frege's Theorem goes through in various partially predicative fragments of FA. Expand
Pluralities and sets
Say that some things form a set just in case there is a set whose members are precisely the things in question. For instance, all the inhabitants of New York form a set. So do all the stars in theExpand
Frege's Proof of Referentiality
  • Øystein Linnebo
  • Computer Science, Mathematics
  • Notre Dame J. Formal Log.
  • 20 April 2004
I present a novel interpretation of Frege’s attempt at Grundgesetze I §§29-31 to prove that every expression of his language has a unique reference. I argue that Frege’s proof is based on aExpand
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