The term quantifier variance refers to claims that there is no uniquely best ontological language with which to describe the world. The term "quantifier variance" rests upon the philosophical term 'quantifier', more precisely existential quantifier. A 'quantifier' is an expression like "there exists at least one 'such-and-such'". ''Quantifier variance'' then is the thesis that the meaning of quantifiers is ambiguous. This thesis can be used to explain how some disputes in

ontology Ontology is the philosophical study of existence, being. It is traditionally understood as the subdiscipline of metaphysics focused on the most general features of reality. As one of the most fundamental concepts, being encompasses all of realit ...

are only due to a failure of the disagreeing parties to agree on the meaning of the quantifiers used. According to

Eli Hirsch Eli Hirsch (born 1938) is an American philosopher and the Charles Goldman Professor of Philosophy at Brandeis University.Urmson's dictum'':

Quantifiers

The word ''quantifier'' in the introduction refers to a variable used in a domain of discourse, a collection of objects under discussion. In daily life, the domain of discourse could be 'apples', or 'persons', or even everything. In a more technical arena, the domain of discourse could be 'integers', say. The quantifier variable ''x'', say, in the given domain of discourse can take on the 'value' or designate any object in the domain. The presence of a particular object, say a 'unicorn' is expressed in the manner of

symbolic logic Logic is the study of correct reasoning. It includes both formal and informal logic. Formal logic is the study of deductively valid inferences or logical truths. It examines how conclusions follow from premises based on the structure o ...

as: ::∃ ''x''; ''x'' is a unicorn. Here the 'turned ''E'' ' or ∃ is read as "there exists..." and is called the symbol for existential quantification. Relations between objects also can be expressed using quantifiers. For example, in the domain of integers (denoting the quantifier by ''n'', a customary choice for an integer) we can indirectly identify '5' by its relation with the number '25': ::∃ ''n''; ''n'' × ''n'' = 25. If we want to point out specifically that the domain of integers is meant, we could write: ::∃ ''n'' ∈

\mathbb

; ''n'' × ''n'' = 25. Here, ∈ = ''is a member of...'' and ∈ is called the symbol for set membership; and

\mathbb

denotes the set of integers. There are a variety of expressions that serve the same purpose in various ontologies, and they are accordingly all quantifier expressions. Quantifier ''variance'' is then one argument concerning exactly what expressions can be construed as quantifiers, and just which arguments of a quantifier, that is, which substitutions for "such-and-such", are permissible.

Usage, not 'existence'?

Hirsch says the notion of quantifier variance is a concept concerning how languages work, and is not connected to the ontological question of what 'really' exists. That view is not universal. The thesis underlying quantifier variance was stated by Putnam: Citing this quotation from Putnam, Wasserman states: "This thesis – the thesis that there are many meanings for the existential quantifier that are equally neutral and equally adequate for describing all the facts – is often referred to as 'the doctrine of quantifier variance'". Hirsch's quantifier variance has been connected to Carnap's idea of a linguistic framework as a 'neo'-Carnapian view, namely, "the view that there are a number of equally good meanings of the logical quantifiers; choosing one of these frameworks is to be understood analogously to choosing a Carnapian framework." Of course, not all philosophers (notably Quine and the 'neo'-Quineans) subscribe to the notion of multiple linguistic frameworks. See meta-ontology. Hirsch himself suggests some care in connecting ''his version'' of quantifier variance with Carnap: "Let's not call any philosophers quantifier variantists unless they are clearly committed to the idea that (most of) the things that exist are completely independent of language." In this connection Hirsch says "I have a problem, however, in calling Carnap a quantifier variantist, insofar as he is often viewed as a verificationist anti-realist." Although Thomasson does not think Carnap is properly considered to be an antirealist, she still disassociates Carnap from Hirsch's version of quantifier variance: "I'll argue, however, that Carnap in fact is not committed to quantifier variance in anything like Hirsch's sense, and that he arnapdoes not rely on it in his ways of deflating metaphysical debates."

References

{{Reflist, refs= {{cite book , url=https://books.google.com/books?id=FTmog32Oz8oC&pg=PA125 , page=125 , title=Metaphysics: The Key Concepts , author1=Helen Beebee , author2=Nikk Effingham , author3=Philip Goff , isbn=978-0203835258 , year=2012 , publisher=Taylor & Francis {{cite book , chapter=Domain of discourse , page=194 , title=Logic and Philosophy: A Modern Introduction , author1=Alan Hausman , author2=Howard. Kahane , author3=Paul. Tidman , publisher=Cengage Learning , year=2012 , edition =12th , isbn=978-1133050001 , chapter-url=https://books.google.com/books?id=i9hf-gJg27EC&pg=PA194 {{cite book , title=Quantifier Variance and Realism: Essays in Metaontology , author=Eli Hirsch , chapter-url=https://books.google.com/books?id=iPRqtcjeHPsC&pg=PR12 , chapter=Introduction , page=xii , publisher=Oxford University Press , year=2011 , isbn=978-0199732111 {{cite book , title=Quantifier Variance and Realism: Essays in Metaontology , author=Eli Hirsch , chapter-url=https://books.google.com/books?id=iPRqtcjeHPsC&pg=PA220 , pages=220–250 , publisher=Oxford University Press , year=2011 , quote=I take it for granted that the world and the things in it exist for the most part in complete independence of our knowledge or language. Our linguistic choices do not determine what exists, but determine what we are to mean by the words "what exists" and related words. , isbn=978-0199780716 , chapter=Chapter 12: Ontology and alternative languages {{cite journal, author=Hilary Putnam, author-link=Hilary Putnam, title=Truth and convention: On Davidson's refutation of conceptual relativism , journal=Dialectica , volume=41 , issue=1–2 , pages=69–77 , year=1987 , doi=10.1111/j.1746-8361.1987.tb00880.x A 'quantifier' in

originally was the part of statements involving the logic symbols ∀ (''for all'') and ∃ (''there exists'') as in an expression like "for all 'such-and-such' ''P'' is true" (∀ x: P(x)) or "there exists at least one 'such-and-such' such that ''P'' is true" (∃ x: P(x)) where 'such-and-such', or ''x'', is an element of a set and ''P'' is a proposition or assertion. However, the idea of a quantifier has since been generalized. See {{cite encyclopedia , author= Dag Westerståhl , title=Generalized Quantifiers , encyclopedia=The Stanford Encyclopedia of Philosophy (Summer 2011 Edition) , editor=Edward N. Zalta , url=http://plato.stanford.edu/archives/sum2011/entries/generalized-quantifiers/ , date=April 19, 2011 {{cite book , title=Writing the book of the world , url=https://books.google.com/books?id=0z_dm_IDpPYC&pg=PA175 , page=175, author= Theodore Sider , quote=Quantifier variance, on my formulation, says that "there are" many candidates for ''being'' meant by quantifiers; but the quantifier variantist needn't take this quantification hat is, this variety of quantifier-meaningsseriously...we could choose to use the sentence "There exists something that is composed of uch-and-such composite object so it comes out true, or we could choose to use it so it comes out false; and under neither choice would our words et closer to realitythan under the other. talics added, 'cute' in-group phrases replaced, as indicated by brackets, isbn=978-0199697908 , year=2011 , publisher=Oxford University Press {{cite web , author=Amie L. Thomasson , author-link=Amie Thomasson , title=Carnap and the Prospects for Easy Ontology , url=http://www.amiethomasson.org/papers%20to%20link/Carnap%20and%20prospects%20for%20easy%20ontology%20revised.docx , access-date=2013-06-20 , url-status=dead , archive-url=https://web.archive.org/web/20131220135908/http://www.amiethomasson.org/papers%20to%20link/Carnap%20and%20prospects%20for%20easy%20ontology%20revised.docx , archive-date=2013-12-20 To be published in ''Ontology after Carnap'', Stephan Blatti and Sandra LaPointe, eds., Oxford University Press. {{cite book , author=J.O. Urmson , author-link=J.O. Urmson , year=1967 , title=Philosophical analysis: its development between the two world wars , url=https://books.google.com/books?id=o8PXAAAAMAAJ&q=%22it+is+not+the+case+that+one+will+be+nearer%22 , publisher=Oxford University Press , page=186 Quoted b
Eli Hirsch
{{cite journal , author=Wasserman, Ryan , title=Material Constitution , journal=The Stanford Encyclopedia of Philosophy (Summer 2013 Edition) , editor=Edward N. Zalta , url= http://plato.stanford.edu/archives/sum2013/entries/material-constitution/ , date=April 5, 2013 Concepts in the philosophy of language Concepts in metaphysics Ontology Quantifier (logic)

Quantifiers

Usage, not 'existence'?

See also

References