Quantifier variance: Difference between revisions
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{{quote|“If two sentences are equivalent to each other, then while the use of one rather than the other may be useful for some philosophical purposes, it is not the case that one will be nearer to reality than the other...We can say a thing this way, and we can say it that way, sometimes...But it is no use asking which is the logically or metaphysically right way to say it.”<ref name=Urmson/>|James Opie Urmson|Philosophical Analysis, p. 186}} | {{quote|“If two sentences are equivalent to each other, then while the use of one rather than the other may be useful for some philosophical purposes, it is not the case that one will be nearer to reality than the other...We can say a thing this way, and we can say it that way, sometimes...But it is no use asking which is the logically or metaphysically right way to say it.”<ref name=Urmson/>|James Opie Urmson|Philosophical Analysis, p. 186}} | ||
The rather technical term "quantifier variance" arose from the philosophical term 'quantifier', more particularly [[existential quantifier]]. A 'quantifier' in logic 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.<ref name=Westerstahl/> There are a variety of statements involving quantifiers that serve the same purpose in various ontologies, and they are accordingly all ''quantifier expressions''.<ref name=Hirsch/> Quantifier ''variance'' is then the topic concerning exactly what expressions can be construed as quantifier expressions, and just which arguments in a quantifier expression are acceptable, that is, which substitutions for ‘such-and-such’, are permissible. | The rather technical term "quantifier variance" arose from the philosophical term 'quantifier', more particularly [[existential quantifier]]. A 'quantifier' in logic 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.<ref name=Westerstahl/> There are a variety of statements involving quantifiers that serve the same purpose in various ontologies, and they are accordingly all ''quantifier expressions''.<ref name=Hirsch/> Quantifier ''variance'' is then the topic concerning exactly what expressions can be construed as quantifier expressions, and just which arguments in a quantifier expression are acceptable, that is, which substitutions for ‘such-and-such’, are permissible.<ref name=Sider> | ||
Hirsch's quantifier variance has been connected to [[Rudolf Carnap|Carnap]]'s idea of a linguistic framework as a 'neoCarnapian' 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."<ref name= Beebee/> Of course, not all philosophers (notably [[Willard Quine|Quine]] and the 'neo'-Qunineans) subscribe to the notion of multiple linguistic frameworks.<ref name=Beebee/> See [[meta-ontology]]. | |||
==Mereology== | ==Mereology== | ||
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Without going into these details, it suffices here to note that quantifier variance does allow the flexibility to speak of the "existence" of an object that is an assembly of components in one formulation or 'language' (perhaps limited to some special kinds of assembly), while in another the assembly may be said not to exist, but only the components. | Without going into these details, it suffices here to note that quantifier variance does allow the flexibility to speak of the "existence" of an object that is an assembly of components in one formulation or 'language' (perhaps limited to some special kinds of assembly), while in another the assembly may be said not to exist, but only the components. | ||
{{quote|Putnam, for example, writes that “[T]he logical primitives themselves, and in particular the notions of object and existence, have a multitude of different uses rather than one absolute ‘meaning’.”[Putnam] This thesis — the thesis that there are many meanings for the existential quantifier that are equally natural and equally adequate for describing all the facts — is often referred to as “the doctrine of quantifier variance”[Hirsch], [Sider]<ref name=Wasserman/>|Ryan Wasserman|Material constitution; The author's references are Putnam,<ref name=Putnam/> Hirsch,<ref name=Hirsch/> and Sider.<ref name= | {{quote|Putnam, for example, writes that “[T]he logical primitives themselves, and in particular the notions of object and existence, have a multitude of different uses rather than one absolute ‘meaning’.”[Putnam] This thesis — the thesis that there are many meanings for the existential quantifier that are equally natural and equally adequate for describing all the facts — is often referred to as “the doctrine of quantifier variance”[Hirsch], [Sider]<ref name=Wasserman/>|Ryan Wasserman|Material constitution; The author's references are Putnam,<ref name=Putnam/> Hirsch,<ref name=Hirsch/> and Sider.<ref name=Sider2/>}} | ||
==Realism and antirealism== | ==Realism and antirealism== | ||
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==References== | ==References== | ||
<ref name=Beebee> | |||
{{cite book |url=http://books.google.ca/books?id=FTmog32Oz8oC&pg=PA125 |page=125 |title=Metaphysics: The Key Concepts |author=Helen Beebee, Nikk Effingham, Philip Goff |isbn=0203835255 |year=2012 |publisher=Taylor & Francis}} | |||
</ref> | |||
{{reflist|refs= | {{reflist|refs= | ||
<ref name=Eklund> | <ref name=Eklund> | ||
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{{cite book |author=Jonathan Schaffer |chapter=Chapter 12: On what grounds what |url=http://www.jonathanschaffer.org/grounds.pdf |quote=The dispute is over ''mind-dependence'': are entities, like rocks, grounded in ideas, or independent of them?...[Are numbers] independent of the mind, or based upon our concepts? |title=Metametaphysics: New Essays on the Foundations of Ontology |editor=David Chalmers, David Manley, Ryan Wasserman, eds |publisher=Oxford University Press |year=2009 |isbn=0199546045}} | {{cite book |author=Jonathan Schaffer |chapter=Chapter 12: On what grounds what |url=http://www.jonathanschaffer.org/grounds.pdf |quote=The dispute is over ''mind-dependence'': are entities, like rocks, grounded in ideas, or independent of them?...[Are numbers] independent of the mind, or based upon our concepts? |title=Metametaphysics: New Essays on the Foundations of Ontology |editor=David Chalmers, David Manley, Ryan Wasserman, eds |publisher=Oxford University Press |year=2009 |isbn=0199546045}} | ||
</ref> | </ref> | ||
<ref name=Sider> | <ref name=Sider> | ||
{{cite book |title=Writing the book of the world |url=http://books.google.com/books?id=0z_dm_IDpPYC&pg=PA175 |pages=p. 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 [that is, this variety of quantifier-meanings] seriously...we could choose to use the sentence "There exists something that is composed of [such-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 [get closer to reality] than under the other.  [Italics added, 'cute' in-group phrases replaced, as indicated by brackets] |isbn=0199697906 |year=2011 |publisher=Oxford University Press}} | |||
</ref> | |||
<ref name=Sider2> | |||
{{cite book |author=Theodore Sider |year=2009 |chapter=Chapter 13: Ontological Realism |editor= D. Chalmers, D. Manley, and R. Wasserman, eds |title=Metametaphysics: New Essays on the Foundations of Ontology |publisher=Oxford University Press |pages= pp. 384–423 |url=http://books.google.ca/books?id=6nqzIi16CY0C&pg=PA384}} | {{cite book |author=Theodore Sider |year=2009 |chapter=Chapter 13: Ontological Realism |editor= D. Chalmers, D. Manley, and R. Wasserman, eds |title=Metametaphysics: New Essays on the Foundations of Ontology |publisher=Oxford University Press |pages= pp. 384–423 |url=http://books.google.ca/books?id=6nqzIi16CY0C&pg=PA384}} | ||
</ref> | </ref> | ||
<ref name=Stanley> | <ref name=Stanley> | ||
Revision as of 10:24, 20 June 2013
The term quantifier variance refers to a position in meta-ontology that claims there is no uniquely best ontological language with which to describe the world.[1] According to Hirsch, it is an outgrowth of Urmson's dictum:
| ‘ | “If two sentences are equivalent to each other, then while the use of one rather than the other may be useful for some philosophical purposes, it is not the case that one will be nearer to reality than the other...We can say a thing this way, and we can say it that way, sometimes...But it is no use asking which is the logically or metaphysically right way to say it.”[2] | ’ |
—James Opie Urmson, Philosophical Analysis, p. 186 | ||
The rather technical term "quantifier variance" arose from the philosophical term 'quantifier', more particularly existential quantifier. A 'quantifier' in logic 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.[3] There are a variety of statements involving quantifiers that serve the same purpose in various ontologies, and they are accordingly all quantifier expressions.[1] Quantifier variance is then the topic concerning exactly what expressions can be construed as quantifier expressions, and just which arguments in a quantifier expression are acceptable, that is, which substitutions for ‘such-and-such’, are permissible.Cite error: Closing </ref> missing for <ref> tag
- ↑ 1.0 1.1 Eli Hirsch (2011). “Introduction”, Quantifier Variance and Realism : Essays in Metaontology: Essays in Metaontology. Oxford University Press, p. xii. ISBN 0199732116.
- ↑ J.O. Urmson (1967). Philosophical analysis: its development between the two world wars. Oxford University Press, p. 186. Quoted by Eli Hirsch.
- ↑ Dag Westerståhl (April 19, 2011). Edward N. Zalta, ed:Generalized Quantifiers. The Stanford Encyclopedia of Philosophy (Summer 2011 Edition).
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