Necessitism, Contingentism, and Plural Quantification

Mind ◽  
2010 ◽  
Vol 119 (475) ◽  
pp. 657-748 ◽  
Author(s):  
T. Williamson
Keyword(s):  
Plural Quantification

scholarly journals On the Innocence and Determinacy of Plural Quantification

2021 ◽  
pp. 150-173
Author(s):  
Salvatore Florio ◽  
Øystein Linnebo
Keyword(s):  
Ontological Commitment ◽  
Plural Logic ◽  
Plural Quantification ◽  
Plural Reference

Plural logic is widely assumed to have two important virtues: ontological innocence and determinacy. Both assumptions are problematic, as is shown by providing a Henkin-style semantics for plural logic that does not resort to sets but takes a plural term to have plural reference. This semantics gives rise to a generalized notion of ontological commitment, which is used to develop some ideas of earlier critics of the alleged ontological innocence of plural logic.

Plural Quantification and the Iterative Concept of Set

1985 ◽  
Vol 11 ◽  
pp. 579-587 ◽  
Author(s):  
Stephen Pollard ◽  
Keyword(s):  
Plural Quantification

scholarly journals Much Ado About the Many

2021 ◽  
Vol 25 (1) ◽  
Author(s):  
Jonathan Mai
Keyword(s):  
Set Theory ◽  
Formal Theory ◽  
Order Logic ◽  
First Order Logic ◽  
Plural Quantification ◽  
First Order ◽  
Order Language ◽  
The Many ◽  
Second Order Logic ◽  
Alternative Theories

English distinguishes between singular quantifiers like "a donkey" and plural quantifiers like "some donkeys". Pluralists hold that plural quantifiers range in an unusual, irreducibly plural, way over common objects, namely individuals from first-order domains and not over set-like objects. The favoured framework of pluralism is plural first-order logic, PFO, an interpreted first-order language that is capable of expressing plural quantification. Pluralists argue for their position by claiming that the standard formal theory based on PFO is both ontologically neutral and really logic. These properties are supposed to yield many important applications concerning second-order logic and set theory that alternative theories supposedly cannot deliver. I will show that there are serious reasons for rejecting at least the claim of ontological innocence. Doubt about innocence arises on account of the fact that, when properly spelled out, the PFO-semantics for plural quantifiers is committed to set-like objects. The correctness of my worries presupposes the principle that for every plurality there is a coextensive set. Pluralists might reply that this principle leads straight to paradox. However, as I will argue, the true culprit of the paradox is the assumption that every definite condition determines a plurality.

Plural Quantification Exposed

Noûs ◽  
2003 ◽  
Vol 37 (1) ◽  
pp. 71-92 ◽  
Author(s):  
Øystein Linnebo
Keyword(s):  
Plural Quantification

ON THE ONTOLOGICAL COMMITMENT OF MEREOLOGY

2009 ◽  
Vol 2 (1) ◽  
pp. 164-174 ◽  
Author(s):  
MASSIMILIANO CARRARA ◽  
ENRICO MARTINO
Keyword(s):  
Ontological Commitment ◽  
David Lewis ◽  
Plural Quantification ◽  
Plural Reference ◽  
Single Entity ◽  
The Many

In Parts of Classes (1991) and Mathematics Is Megethology (1993) David Lewis defends both the innocence of plural quantification and of mereology. However, he himself claims that the innocence of mereology is different from that of plural reference, where reference to some objects does not require the existence of a single entity picking them out as a whole. In the case of plural quantification “we have many things, in no way do we mention one thing that is the many taken together”. Instead, in the mereological case: “we have many things, we do mention one thing that is the many taken together, but this one thing is nothing different from the many” (Lewis, 1991, p. 87). The aim of the paper is to argue that—for a certain use of mereology, weaker than Lewis’ one—an innocence thesis similar to that of plural reference is defensible. To give a precise account of plural reference, we use the idea of plural choice. We then propose a virtual theory of mereology in which the role of individuals is played by plural choices of atoms.

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