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 In predicate logic, an existential quantification is a type of quantifier, a logical constant which is interpreted as "there exists", "there is at least one", or "for some". It is usually denoted by the logical operator symbol ∃, which, w ...

. 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 In metaphysics, ontology is the philosophical study of being, as well as related concepts such as existence, becoming, and reality. Ontology addresses questions like how entities are grouped into categories and which of these entities exis ...

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 In the formal sciences, the domain of discourse, also called the universe of discourse, universal set, or simply universe, is the set of entities over which certain variables of interest in some formal treatment may range. Overview The domain ...

, 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 Mathematical logic is the study of formal logic within mathematics. Major subareas include model theory, proof theory, set theory, and recursion theory. Research in mathematical logic commonly addresses the mathematical properties of formal ...

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 Writing is a medium of human communication which involves the representation of a language through a system of physically inscribed, mechanically transferred, or digitally represented symbols. Writing systems do not themselves constitute h ...

: ::∃ ''n'' ∈ ℤ; ''n'' × ''n'' = 25. Here, ∈ = ''is a member of...'' and ∈ is called the symbol for

set membership In mathematics, an element (or member) of a set is any one of the distinct objects that belong to that set. Sets Writing A = \ means that the elements of the set are the numbers 1, 2, 3 and 4. Sets of elements of , for example \, are subsets o ...

; and ℤ 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 Rudolf Carnap (; ; 18 May 1891 – 14 September 1970) was a German-language philosopher who was active in Europe before 1935 and in the United States thereafter. He was a major member of the Vienna Circle and an advocate of logical positivism. ...

'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 Meta-ontology is the study of the field of inquiry known as Ontology. The goal of meta-ontology is to clarify what ontology is about and how to interpret the meaning of ontological claims. Different meta-ontological theories disagree on what the go ...

. 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 In analytic philosophy, anti-realism is a position which encompasses many varieties such as metaphysical, mathematical, semantic, scientific, moral and epistemic. The term was first articulated by British philosopher Michael Dummett in an argument ...

." 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 In logic, a set of symbols is commonly used to express logical representation. The following table lists many common symbols, together with their name, how they should be read out loud, and the related field of mathematics. Additionally, the subs ...

∀ (''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