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<span id="openzim-page-title" class="mw-page-title-main"><span class="mw-page-title-main">Definite description</span></span>
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<p>In <a href="Formal_semantics_(natural_language)" title="Formal semantics (natural language)">formal semantics</a> and <a href="Philosophy_of_language" title="Philosophy of language">philosophy of language</a>, a <b>definite description</b> is a <a href="Denotation" title="Denotation">denoting</a> <a href="Phrase" title="Phrase">phrase</a> in the form of "the X" where X is a noun-phrase or a singular common <a href="Noun" title="Noun">noun</a>. The definite description is <i>proper</i> if X applies to a unique individual or object. For example: "<a href="Yuri_Gagarin" title="Yuri Gagarin">the first person in space</a>" and "<a href="Bill_Clinton" title="Bill Clinton">the 42nd President of the United States of America</a>" are proper. The definite descriptions "the person in space" and "the Senator from Ohio" are <i>improper</i> because the noun phrase X applies to more than one thing, and the definite descriptions "the first man on Mars" and "the Senator from Washington D.C." are <i>improper</i> because X applies to nothing. Improper descriptions raise some difficult questions about the <a href="Law_of_excluded_middle" title="Law of excluded middle">law of excluded middle</a>, <a href="Denotation" title="Denotation">denotation</a>, <a href="Linguistic_modality" class="mw-redirect" title="Linguistic modality">modality</a>, and <a href="Mental_content" class="mw-redirect" title="Mental content">mental content</a>.
</p>
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<div class="mw-heading mw-heading2"><h2 id="Russell's_analysis">Russell's analysis</h2></div>
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</style><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="Theory_of_descriptions" title="Theory of descriptions">Theory of descriptions</a></div>
<p>As <a href="France" title="France">France</a> is <a href="French_Fifth_Republic" title="French Fifth Republic">currently a republic</a>, it has no king. <a href="Bertrand_Russell" title="Bertrand Russell">Bertrand Russell</a> pointed out that this raises a puzzle about the truth value of the sentence "The present King of France is bald."<sup id="cite_ref-ondenoting_1-0" class="reference"><a href="#cite_note-ondenoting-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup>
</p><p>The sentence does not seem to be true: if we consider all the bald things, the present King of France is not among them, since there is <a href="List_of_French_monarchs" title="List of French monarchs">no present King of France</a>. But if it is false, then one would expect that the <a href="Negation" title="Negation">negation</a> of this statement, that is, "It is not the case that the present King of France is bald", or its <a href="Logical_equivalence" title="Logical equivalence">logical equivalent</a>, "The present King of France is not bald", is true. But this sentence does not seem to be true either: the present King of France is no more among the things that fail to be bald than among the things that are bald. We therefore seem to have a violation of the <a href="Law_of_excluded_middle" title="Law of excluded middle">law of excluded middle</a>.
</p><p>Is it meaningless, then? One might suppose so (and some philosophers have) since "the present King of France" certainly does <a href="Failure_to_refer" title="Failure to refer">fail to refer</a>. But on the other hand, the sentence "The present King of France is bald" (as well as its negation) seem perfectly intelligible, suggesting that "the present King of France" cannot be meaningless.
</p><p>Russell proposed to resolve this puzzle via his <a href="Theory_of_descriptions" title="Theory of descriptions">theory of descriptions</a>. A definite description like "the present King of France", he suggested, is not a <a href="Reference" title="Reference">referring</a> expression, as we might naively suppose, but rather an "incomplete symbol" that introduces <a href="Quantifier_(logic)" title="Quantifier (logic)">quantificational</a> structure into sentences in which it occurs. The sentence "the present King of France is bald", for example, is analyzed as a conjunction of the following three <a href="Quantifier_(logic)" title="Quantifier (logic)">quantified</a> statements:
</p>
<ol><li>there is an x such that x is currently King of France: <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \exists xKx}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mi mathvariant="normal">∃<!-- ∃ --></mi>
<mi>x</mi>
<mi>K</mi>
<mi>x</mi>
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<annotation encoding="application/x-tex">{\displaystyle \exists xKx}</annotation>
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</math></span><img src="./0cefdddd38e7ba3ddd3421dd031db2188eaa90e5.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:6.018ex; height:2.176ex;" alt="{\displaystyle \exists xKx}" loading="lazy"></span> (using 'Kx' for 'x is currently King of France')</li>
<li>for any x and y, if x is currently King of France and y is currently King of France, then x=y (i.e. there is at most one thing which is currently King of France): <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \forall x\forall y((Kx\land Ky)\rightarrow x=y)}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mi mathvariant="normal">∀<!-- ∀ --></mi>
<mi>x</mi>
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<mo stretchy="false">(</mo>
<mo stretchy="false">(</mo>
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<mi>x</mi>
<mo>∧<!-- ∧ --></mo>
<mi>K</mi>
<mi>y</mi>
<mo stretchy="false">)</mo>
<mo stretchy="false">→<!-- → --></mo>
<mi>x</mi>
<mo>=</mo>
<mi>y</mi>
<mo stretchy="false">)</mo>
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</mrow>
<annotation encoding="application/x-tex">{\displaystyle \forall x\forall y((Kx\land Ky)\rightarrow x=y)}</annotation>
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</math></span><img src="./a28935a751208338e2fdc4d5eb5f7a25958c54e3.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:27.086ex; height:2.843ex;" alt="{\displaystyle \forall x\forall y((Kx\land Ky)\rightarrow x=y)}" loading="lazy"></span></li>
<li>for every x that is currently King of France, x is bald: <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \forall x(Kx\rightarrow Bx)}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mi mathvariant="normal">∀<!-- ∀ --></mi>
<mi>x</mi>
<mo stretchy="false">(</mo>
<mi>K</mi>
<mi>x</mi>
<mo stretchy="false">→<!-- → --></mo>
<mi>B</mi>
<mi>x</mi>
<mo stretchy="false">)</mo>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle \forall x(Kx\rightarrow Bx)}</annotation>
</semantics>
</math></span><img src="./89783657ba5f47524671f2eb924c17a18adc6947.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:14.535ex; height:2.843ex;" alt="{\displaystyle \forall x(Kx\rightarrow Bx)}" loading="lazy"></span> (using 'B' for 'bald')</li></ol>
<p>More briefly put, the claim is that "The present King of France is bald" says that some x is such that x is currently King of France, and that any y is currently King of France only if y = x, and that x is bald:
</p>
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</style><div class="block-indent"><span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \exists x((Kx\land \forall y(Ky\rightarrow y=x))\land Bx)}">
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<annotation encoding="application/x-tex">{\displaystyle \exists x((Kx\land \forall y(Ky\rightarrow y=x))\land Bx)}</annotation>
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<p>This is <i>false</i>, since it is <i>not</i> the case that some <var style="padding-right: 1px;">x</var> is currently King of France.
</p><p>The negation of this sentence, i.e. "The present King of France is not bald", is ambiguous. It could mean one of two things, depending on where we place the negation 'not'. On one reading, it could mean that there is no one who is currently King of France and bald:
</p>
<div class="block-indent"><span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \lnot \exists x((Kx\land \forall y(Ky\rightarrow y=x))\land Bx)}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mi mathvariant="normal">¬<!-- ¬ --></mi>
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<mi>x</mi>
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<mo stretchy="false">→<!-- → --></mo>
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<annotation encoding="application/x-tex">{\displaystyle \lnot \exists x((Kx\land \forall y(Ky\rightarrow y=x))\land Bx)}</annotation>
</semantics>
</math></span><img src="./e7347ec5bfc9a282b39d35838b5a36922011f0a3.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:36.122ex; height:2.843ex;" alt="{\displaystyle \lnot \exists x((Kx\land \forall y(Ky\rightarrow y=x))\land Bx)}" loading="lazy"></span></div>
<p>On this disambiguation, the sentence is <i>true</i> (since there is indeed no x that is currently King of France).
</p><p>On a second reading, the negation could be construed as attaching directly to 'bald', so that the sentence means that there is currently a King of France, but that this King fails to be bald:
</p>
<div class="block-indent"><span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \exists x((Kx\land \forall y(Ky\rightarrow y=x))\land \lnot Bx)}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mi mathvariant="normal">∃<!-- ∃ --></mi>
<mi>x</mi>
<mo stretchy="false">(</mo>
<mo stretchy="false">(</mo>
<mi>K</mi>
<mi>x</mi>
<mo>∧<!-- ∧ --></mo>
<mi mathvariant="normal">∀<!-- ∀ --></mi>
<mi>y</mi>
<mo stretchy="false">(</mo>
<mi>K</mi>
<mi>y</mi>
<mo stretchy="false">→<!-- → --></mo>
<mi>y</mi>
<mo>=</mo>
<mi>x</mi>
<mo stretchy="false">)</mo>
<mo stretchy="false">)</mo>
<mo>∧<!-- ∧ --></mo>
<mi mathvariant="normal">¬<!-- ¬ --></mi>
<mi>B</mi>
<mi>x</mi>
<mo stretchy="false">)</mo>
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</mrow>
<annotation encoding="application/x-tex">{\displaystyle \exists x((Kx\land \forall y(Ky\rightarrow y=x))\land \lnot Bx)}</annotation>
</semantics>
</math></span><img src="./404bfed1e6768958e852be6df1510e77103e75b1.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:36.122ex; height:2.843ex;" alt="{\displaystyle \exists x((Kx\land \forall y(Ky\rightarrow y=x))\land \lnot Bx)}" loading="lazy"></span></div>
<p>On this disambiguation, the sentence is <i>false</i> (since there is no x that is currently King of France).
</p><p>Thus, whether "the present King of France is not bald" is true or false depends on how it is interpreted at the level of <a href="Logical_form" title="Logical form">logical form</a>: if the <a href="Negation" title="Negation">negation</a> is construed as taking wide scope (as in the first of the above), it is true, whereas if the negation is construed as taking narrow scope (as in the second of the above), it is false. In neither case does it lack a truth value.
</p><p>So we do <i>not</i> have a failure of the <a href="Law_of_Excluded_Middle" class="mw-redirect" title="Law of Excluded Middle">Law of Excluded Middle</a>: "the present King of France is bald" (i.e. <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \exists x((Kx\land \forall y(Ky\rightarrow y=x))\land Bx)}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mi mathvariant="normal">∃<!-- ∃ --></mi>
<mi>x</mi>
<mo stretchy="false">(</mo>
<mo stretchy="false">(</mo>
<mi>K</mi>
<mi>x</mi>
<mo>∧<!-- ∧ --></mo>
<mi mathvariant="normal">∀<!-- ∀ --></mi>
<mi>y</mi>
<mo stretchy="false">(</mo>
<mi>K</mi>
<mi>y</mi>
<mo stretchy="false">→<!-- → --></mo>
<mi>y</mi>
<mo>=</mo>
<mi>x</mi>
<mo stretchy="false">)</mo>
<mo stretchy="false">)</mo>
<mo>∧<!-- ∧ --></mo>
<mi>B</mi>
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<mo stretchy="false">)</mo>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle \exists x((Kx\land \forall y(Ky\rightarrow y=x))\land Bx)}</annotation>
</semantics>
</math></span><img src="./6de5f41973cf3b2401151bf3b69196fb6968190b.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:34.572ex; height:2.843ex;" alt="{\displaystyle \exists x((Kx\land \forall y(Ky\rightarrow y=x))\land Bx)}" loading="lazy"></span>) is false, because there is no present King of France.
</p><p>The negation of this statement is the one in which 'not' takes wide scope: <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \lnot \exists x((Kx\land \forall y(Ky\rightarrow y=x))\land Bx)}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mi mathvariant="normal">¬<!-- ¬ --></mi>
<mi mathvariant="normal">∃<!-- ∃ --></mi>
<mi>x</mi>
<mo stretchy="false">(</mo>
<mo stretchy="false">(</mo>
<mi>K</mi>
<mi>x</mi>
<mo>∧<!-- ∧ --></mo>
<mi mathvariant="normal">∀<!-- ∀ --></mi>
<mi>y</mi>
<mo stretchy="false">(</mo>
<mi>K</mi>
<mi>y</mi>
<mo stretchy="false">→<!-- → --></mo>
<mi>y</mi>
<mo>=</mo>
<mi>x</mi>
<mo stretchy="false">)</mo>
<mo stretchy="false">)</mo>
<mo>∧<!-- ∧ --></mo>
<mi>B</mi>
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<mo stretchy="false">)</mo>
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<annotation encoding="application/x-tex">{\displaystyle \lnot \exists x((Kx\land \forall y(Ky\rightarrow y=x))\land Bx)}</annotation>
</semantics>
</math></span><img src="./e7347ec5bfc9a282b39d35838b5a36922011f0a3.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:36.122ex; height:2.843ex;" alt="{\displaystyle \lnot \exists x((Kx\land \forall y(Ky\rightarrow y=x))\land Bx)}" loading="lazy"></span>. This statement is <i>true</i> because there does not exist anything which is currently King of France.
</p>
<div class="mw-heading mw-heading2"><h2 id="Generalized_quantifier_analysis">Generalized quantifier analysis</h2></div>
<p><a href="Stephen_Neale" title="Stephen Neale">Stephen Neale</a>,<sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> among others, has defended Russell's theory, and incorporated it into the theory of <a href="Generalized_quantifier" title="Generalized quantifier">generalized quantifiers</a>. On this view, 'the' is a quantificational determiner like 'some', 'every', 'most' etc. The determiner 'the' has the following denotation (using <a href="Lambda_calculus" title="Lambda calculus">lambda</a> notation):
</p>
<div class="block-indent"><span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \lambda f.\lambda g.\exists x(f(x)=1\land \forall y(f(y)=1\rightarrow y=x)\land g(x)=1)}">
<semantics>
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<mo>.</mo>
<mi>λ<!-- λ --></mi>
<mi>g</mi>
<mo>.</mo>
<mi mathvariant="normal">∃<!-- ∃ --></mi>
<mi>x</mi>
<mo stretchy="false">(</mo>
<mi>f</mi>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo stretchy="false">)</mo>
<mo>=</mo>
<mn>1</mn>
<mo>∧<!-- ∧ --></mo>
<mi mathvariant="normal">∀<!-- ∀ --></mi>
<mi>y</mi>
<mo stretchy="false">(</mo>
<mi>f</mi>
<mo stretchy="false">(</mo>
<mi>y</mi>
<mo stretchy="false">)</mo>
<mo>=</mo>
<mn>1</mn>
<mo stretchy="false">→<!-- → --></mo>
<mi>y</mi>
<mo>=</mo>
<mi>x</mi>
<mo stretchy="false">)</mo>
<mo>∧<!-- ∧ --></mo>
<mi>g</mi>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo stretchy="false">)</mo>
<mo>=</mo>
<mn>1</mn>
<mo stretchy="false">)</mo>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle \lambda f.\lambda g.\exists x(f(x)=1\land \forall y(f(y)=1\rightarrow y=x)\land g(x)=1)}</annotation>
</semantics>
</math></span><img src="./ab387a31ad044ce505cd0891c9c8d91ddd735eac.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:55.923ex; height:2.843ex;" alt="{\displaystyle \lambda f.\lambda g.\exists x(f(x)=1\land \forall y(f(y)=1\rightarrow y=x)\land g(x)=1)}" loading="lazy"></span></div>
<p>(That is, the definite article 'the' denotes a function which takes a pair of <a href="Property" title="Property">properties</a> <var style="padding-right: 1px;">f</var> and <var style="padding-right: 1px;">g</var> to truth <a href="If_and_only_if" title="If and only if">if, and only if</a>, there exists something that has the property <var style="padding-right: 1px;">f</var>, only one thing has the property <var style="padding-right: 1px;">f</var>, and that thing also has the property <var style="padding-right: 1px;">g</var>.) Given the denotation of the <a href="Predicate_(mathematical_logic)" class="mw-redirect" title="Predicate (mathematical logic)">predicates</a> 'present King of France' (again <var style="padding-right: 1px;">K</var> for short) and 'bald' (<var style="padding-right: 1px;">B</var> for short)
</p>
<div class="block-indent"><span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \lambda x.Kx}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mi>λ<!-- λ --></mi>
<mi>x</mi>
<mo>.</mo>
<mi>K</mi>
<mi>x</mi>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle \lambda x.Kx}</annotation>
</semantics>
</math></span><img src="./9c628db44c4630e0fff7ce1f7be4b2172066b405.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:7.114ex; height:2.176ex;" alt="{\displaystyle \lambda x.Kx}" loading="lazy"></span></div>
<div class="block-indent"><span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \lambda x.Bx}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mi>λ<!-- λ --></mi>
<mi>x</mi>
<mo>.</mo>
<mi>B</mi>
<mi>x</mi>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle \lambda x.Bx}</annotation>
</semantics>
</math></span><img src="./f5c05e2eb229ae7f1290a1a8d73bbd13a69e4bdb.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:6.813ex; height:2.176ex;" alt="{\displaystyle \lambda x.Bx}" loading="lazy"></span></div>
<p>we then get the Russellian truth conditions via two steps of <a href="Function_application" title="Function application">function application</a>: 'The present King of France is bald' is true if, and only if, <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \exists x((Kx\land \forall y(Ky\rightarrow y=x))\land Bx)}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mi mathvariant="normal">∃<!-- ∃ --></mi>
<mi>x</mi>
<mo stretchy="false">(</mo>
<mo stretchy="false">(</mo>
<mi>K</mi>
<mi>x</mi>
<mo>∧<!-- ∧ --></mo>
<mi mathvariant="normal">∀<!-- ∀ --></mi>
<mi>y</mi>
<mo stretchy="false">(</mo>
<mi>K</mi>
<mi>y</mi>
<mo stretchy="false">→<!-- → --></mo>
<mi>y</mi>
<mo>=</mo>
<mi>x</mi>
<mo stretchy="false">)</mo>
<mo stretchy="false">)</mo>
<mo>∧<!-- ∧ --></mo>
<mi>B</mi>
<mi>x</mi>
<mo stretchy="false">)</mo>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle \exists x((Kx\land \forall y(Ky\rightarrow y=x))\land Bx)}</annotation>
</semantics>
</math></span><img src="./6de5f41973cf3b2401151bf3b69196fb6968190b.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:34.572ex; height:2.843ex;" alt="{\displaystyle \exists x((Kx\land \forall y(Ky\rightarrow y=x))\land Bx)}" loading="lazy"></span>. On this view, definite descriptions like 'the present King of France' do have a denotation (specifically, definite descriptions denote a function from properties to truth values—they are in that sense not <a href="Syncategorematic" class="mw-redirect" title="Syncategorematic">syncategorematic</a>, or "incomplete symbols"); but the view retains the essentials of the Russellian analysis, yielding exactly the truth conditions Russell argued for.
</p>
<div class="mw-heading mw-heading2"><h2 id="Fregean_analysis">Fregean analysis</h2></div>
<p>The Fregean analysis of definite descriptions, implicit in the work of <a href="Frege" class="mw-redirect" title="Frege">Frege</a> and later defended by <a href="P._F._Strawson" title="P. F. Strawson">Strawson</a><sup id="cite_ref-onreferring_3-0" class="reference"><a href="#cite_note-onreferring-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> among others, represents the primary alternative to the Russellian theory. On the Fregean analysis, definite descriptions are construed as <a href="Referring_expression" title="Referring expression">referring expressions</a> rather than <a href="Quantifier_(logic)" title="Quantifier (logic)">quantificational expressions</a>. Existence and uniqueness are understood as a <a href="Presupposition" title="Presupposition">presupposition</a> of a sentence containing a definite description, rather than part of the content asserted by such a sentence. The sentence 'The present King of France is bald', for example, is not used to claim that there exists a unique present King of France who is bald; instead, that there is a unique present King of France is part of what this sentence <i>presupposes</i>, and what it <i>says</i> is that this individual is bald. If the presupposition fails, the definite description <i>fails to refer</i>, and the sentence as a whole fails to express a <a href="Proposition" title="Proposition">proposition</a>.
</p><p>The Fregean view is thus committed to the kind of <a href="Truth_value" title="Truth value">truth value</a> gaps (and failures of the <a href="Law_of_excluded_middle" title="Law of excluded middle">law of excluded middle</a>) that the Russellian analysis is designed to avoid. Since there is currently no King of France, the sentence 'The present King of France is bald' fails to express a proposition, and therefore fails to have a truth value, as does its <a href="Negation" title="Negation">negation</a>, 'The present King of France is not bald'. The Fregean will account for the fact that these sentences are nevertheless <i>meaningful</i> by relying on speakers' knowledge of the conditions under which either of these sentences <i>could</i> be used to express a true proposition. The Fregean can also hold on to a restricted version of the law of excluded middle: for any sentence whose presuppositions are met (and thus expresses a proposition), either that sentence or its negation is true.
</p><p>On the Fregean view, the definite article 'the' has the following denotation (using <a href="Lambda_calculus" title="Lambda calculus">lambda</a> notation):
</p>
<div class="block-indent"><span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \lambda f:\exists x(f(x)=1\land \forall y(f(y)=1\rightarrow y=x)).}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mi>λ<!-- λ --></mi>
<mi>f</mi>
<mo>:</mo>
<mi mathvariant="normal">∃<!-- ∃ --></mi>
<mi>x</mi>
<mo stretchy="false">(</mo>
<mi>f</mi>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo stretchy="false">)</mo>
<mo>=</mo>
<mn>1</mn>
<mo>∧<!-- ∧ --></mo>
<mi mathvariant="normal">∀<!-- ∀ --></mi>
<mi>y</mi>
<mo stretchy="false">(</mo>
<mi>f</mi>
<mo stretchy="false">(</mo>
<mi>y</mi>
<mo stretchy="false">)</mo>
<mo>=</mo>
<mn>1</mn>
<mo stretchy="false">→<!-- → --></mo>
<mi>y</mi>
<mo>=</mo>
<mi>x</mi>
<mo stretchy="false">)</mo>
<mo stretchy="false">)</mo>
<mo>.</mo>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle \lambda f:\exists x(f(x)=1\land \forall y(f(y)=1\rightarrow y=x)).}</annotation>
</semantics>
</math></span><img src="./713f823c6843dabb3f6787bc7ea96c4ed135c36e.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:42.87ex; height:2.843ex;" alt="{\displaystyle \lambda f:\exists x(f(x)=1\land \forall y(f(y)=1\rightarrow y=x)).}" loading="lazy"></span> [The unique z such that <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle f(z)=1}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mi>f</mi>
<mo stretchy="false">(</mo>
<mi>z</mi>
<mo stretchy="false">)</mo>
<mo>=</mo>
<mn>1</mn>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle f(z)=1}</annotation>
</semantics>
</math></span><img src="./6eb4a3c501d831d4ceabf363b3b07e4ed54f3dc7.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:8.437ex; height:2.843ex;" alt="{\displaystyle f(z)=1}" loading="lazy"></span>]</div>
<p>(That is, 'the' denotes a function which takes a property <var style="padding-right: 1px;">f</var> and yields the unique object <var style="padding-right: 1px;">z</var> that has property <var style="padding-right: 1px;">f</var>, if there is such a <var style="padding-right: 1px;">z</var>, and is undefined otherwise.) The presuppositional character of the existence and uniqueness conditions is here reflected in the fact that the definite article denotes a <a href="Partial_function" title="Partial function">partial function</a> on the set of properties: it is only defined for those properties <var style="padding-right: 1px;">f</var> which are true of exactly one object. It is thus undefined on the denotation of the predicate 'currently King of France', since the property of currently being King of France is true of no object; it is similarly undefined on the denotation of the predicate 'Senator of the US', since the property of being a US Senator is true of more than one object.
</p>
<div class="mw-heading mw-heading2"><h2 id="Mathematical_logic">Mathematical logic</h2></div>
<div role="note" class="hatnote navigation-not-searchable">Main article: <a href="Uniqueness_quantification" title="Uniqueness quantification">Uniqueness quantification</a></div>
<p>Following the example of <i><a href="Principia_Mathematica" title="Principia Mathematica">Principia Mathematica</a></i>, it is customary to use a definite description operator symbolized using the "turned" (rotated) Greek lower case iota character "℩". The notation ℩<span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle x(\phi x)}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mi>x</mi>
<mo stretchy="false">(</mo>
<mi>ϕ<!-- ϕ --></mi>
<mi>x</mi>
<mo stretchy="false">)</mo>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle x(\phi x)}</annotation>
</semantics>
</math></span><img src="./afbbe3d23afcf671445af86ad88fac4fee5d595d.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:5.854ex; height:2.843ex;" alt="{\displaystyle x(\phi x)}" loading="lazy"></span> means "the unique <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle x}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mi>x</mi>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle x}</annotation>
</semantics>
</math></span><img src="./87f9e315fd7e2ba406057a97300593c4802b53e4.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.33ex; height:1.676ex;" alt="{\displaystyle x}" loading="lazy"></span> such that <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \phi x}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mi>ϕ<!-- ϕ --></mi>
<mi>x</mi>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle \phi x}</annotation>
</semantics>
</math></span><img src="./f0151d2e0a73daf7770c721c0b367972d4e08ab3.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.715ex; height:2.509ex;" alt="{\displaystyle \phi x}" loading="lazy"></span>", and
</p>
<div class="block-indent"><span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \psi (}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mi>ψ<!-- ψ --></mi>
<mo stretchy="false">(</mo>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle \psi (}</annotation>
</semantics>
</math></span><img src="./8cf41e205eb33e5ef0dfdead0a4c639a651e05de.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:2.418ex; height:2.843ex;" alt="{\displaystyle \psi (}" loading="lazy"></span>℩<span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle x(\phi x))}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mi>x</mi>
<mo stretchy="false">(</mo>
<mi>ϕ<!-- ϕ --></mi>
<mi>x</mi>
<mo stretchy="false">)</mo>
<mo stretchy="false">)</mo>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle x(\phi x))}</annotation>
</semantics>
</math></span><img src="./57870e0ddb230e4ea2aac285409e6c4d955612d4.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:6.759ex; height:2.843ex;" alt="{\displaystyle x(\phi x))}" loading="lazy"></span></div>
<p>is equivalent to "There is exactly one <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \phi }">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mi>ϕ<!-- ϕ --></mi>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle \phi }</annotation>
</semantics>
</math></span><img src="./72b1f30316670aee6270a28334bdf4f5072cdde4.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.385ex; height:2.509ex;" alt="{\displaystyle \phi }" loading="lazy"></span> and it has the property
<span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \psi }">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mi>ψ<!-- ψ --></mi>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle \psi }</annotation>
</semantics>
</math></span><img src="./45e5789e5d9c8f7c79744f43ecaaf8ba42a8553a.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.513ex; height:2.509ex;" alt="{\displaystyle \psi }" loading="lazy"></span>":
</p>
<div class="block-indent"><span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \exists x(\forall y(\phi (y)\iff y=x)\land \psi (x))}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mi mathvariant="normal">∃<!-- ∃ --></mi>
<mi>x</mi>
<mo stretchy="false">(</mo>
<mi mathvariant="normal">∀<!-- ∀ --></mi>
<mi>y</mi>
<mo stretchy="false">(</mo>
<mi>ϕ<!-- ϕ --></mi>
<mo stretchy="false">(</mo>
<mi>y</mi>
<mo stretchy="false">)</mo>
<mspace width="thickmathspace"></mspace>
<mo stretchy="false">⟺<!-- ⟺ --></mo>
<mspace width="thickmathspace"></mspace>
<mi>y</mi>
<mo>=</mo>
<mi>x</mi>
<mo stretchy="false">)</mo>
<mo>∧<!-- ∧ --></mo>
<mi>ψ<!-- ψ --></mi>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo stretchy="false">)</mo>
<mo stretchy="false">)</mo>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle \exists x(\forall y(\phi (y)\iff y=x)\land \psi (x))}</annotation>
</semantics>
</math></span><img src="./7dd95299fca2727697892a363d14198eb2cd5c91.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:32.755ex; height:2.843ex;" alt="{\displaystyle \exists x(\forall y(\phi (y)\iff y=x)\land \psi (x))}" loading="lazy"></span></div>
<div class="mw-heading mw-heading2"><h2 id="See_also">See also</h2></div>
<ul><li><a href="Lambert's_law_(logic)" class="mw-redirect" title="Lambert's law (logic)">Lambert's law (logic)</a></li>
<li><a href="Philosophy_of_language" title="Philosophy of language">Philosophy of language</a></li>
<li><a href="John_Searle" title="John Searle">John Searle</a></li>
<li><a href="Vacuous_truth" title="Vacuous truth">Vacuous truth</a></li></ul>
<div class="mw-heading mw-heading2"><h2 id="References">References</h2></div>
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<li id="cite_note-ondenoting-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-ondenoting_1-0">^</a></b></span> <span class="reference-text"><style data-mw-deduplicate="TemplateStyles:r1238218222">
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</style><cite id="CITEREFRussell1905" class="citation journal cs1">Russell, Bertrand (1905). "On Denoting". <i>Mind</i>. <b>14</b> (4): <span class="nowrap">479–</span>493. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1093%2Fmind%2FXIV.4.479">10.1093/mind/XIV.4.479</a>.</cite></span>
</li>
<li id="cite_note-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-2">^</a></b></span> <span class="reference-text"><cite id="CITEREFStephen_Neale1990" class="citation book cs1">Stephen Neale (1990). <i>Descriptions</i>. The MIT Press. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a>&nbsp;<bdi>0262640317</bdi>.</cite></span>
</li>
<li id="cite_note-onreferring-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-onreferring_3-0">^</a></b></span> <span class="reference-text"><cite id="CITEREFStrawson1950" class="citation journal cs1">Strawson, Peter (1950). "On referring". <i>Mind</i>. <b>59</b> (235): <span class="nowrap">320–</span>344. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1093%2Fmind%2FLIX.235.320">10.1093/mind/LIX.235.320</a>.</cite></span>
</li>
</ol></div></div>
<div class="mw-heading mw-heading2"><h2 id="Bibliography">Bibliography</h2></div>
<ul><li><a href="Keith_Donnellan" title="Keith Donnellan">Donnellan, Keith</a>, "Reference and Definite Descriptions," in <i><a href="The_Philosophical_Review" title="The Philosophical Review">Philosophical Review</a></i> 75 (1966): 281–304.</li>
<li>Neale, Stephen, <i>Descriptions</i>, MIT Press, 1990.</li>
<li>Ostertag, Gary (ed.). (1998) <i>Definite Descriptions: A Reader</i> Bradford, MIT Press. (Includes Donnellan (1966), Chapter 3 of Neale (1990), Russell (1905), and Strawson (1950).)</li>
<li>Reimer, Marga and Bezuidenhout, Anne (eds.) (2004), <i>Descriptions and Beyond</i>, Clarendon Press, Oxford</li>
<li>Russell, Bertrand, "<a href="On_Denoting" title="On Denoting">On Denoting</a>," in <i><a href="Mind_(journal)" title="Mind (journal)">Mind</a></i> 14 (1905): 479–493. <a rel="nofollow" class="external text" href="http://www.fh-augsburg.de/~harsch/anglica/Chronology/20thC/Russell/rus_deno.html">Online text</a>,</li>
<li>Strawson, P. F., "On Referring," in <i>Mind</i> 59 (1950): 320–344.</li></ul>
<div class="mw-heading mw-heading2"><h2 id="External_links">External links</h2></div>
<ul><li><cite id="CITEREFZalta" class="citation encyclopaedia cs1"><a href="Edward_N._Zalta" title="Edward N. Zalta">Zalta, Edward N.</a> (ed.). <a rel="nofollow" class="external text" href="https://plato.stanford.edu/entries/descriptions/">"Descriptions"</a>. <i><a href="Stanford_Encyclopedia_of_Philosophy" title="Stanford Encyclopedia of Philosophy">Stanford Encyclopedia of Philosophy</a></i>.</cite></li></ul>
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</style><div id="Analytic_philosophy173" style="font-size:114%;margin:0 4em"><a href="Analytic_philosophy" title="Analytic philosophy">Analytic philosophy</a></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%">Related articles</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%">Areas of focus</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">
<ul><li><a href="Metaphysics" title="Metaphysics">Metaphysics</a></li>
<li><a href="Epistemology" title="Epistemology">Epistemology</a></li>
<li><a href="Philosophy_of_language" title="Philosophy of language">Language</a></li>
<li><a href="Philosophy_of_mathematics" title="Philosophy of mathematics">Mathematics</a></li>
<li><a href="Philosophy_of_science" title="Philosophy of science">Science</a></li></ul>
</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Turns</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em">
<ul><li><a href="Virtue_ethics" title="Virtue ethics">Aretaic</a></li>
<li>Historical</li>
<li><a href="Linguistic_turn" title="Linguistic turn">Linguistic</a></li>
<li><a href="Performativity" title="Performativity">Performative</a></li></ul>
</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Logic</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">
<ul><li><a href="Classical_logic" title="Classical logic">Classical</a></li>
<li><a href="Deviant_logic" title="Deviant logic">Deviant</a></li>
<li><a href="Mathematical_logic" title="Mathematical logic">Mathematical</a></li>
<li><a href="Non-classical_logic" title="Non-classical logic">Non-classical</a></li>
<li><a href="Paraconsistent_logic" title="Paraconsistent logic">Paraconsistent</a></li>
<li><a href="Philosophical_logic" title="Philosophical logic">Philosophical</a></li>
<li><a href="First-order_logic" title="First-order logic">Predicate</a></li></ul>
</div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Theories</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em">
<ul><li><a href="Anti-realism" title="Anti-realism">Anti-realism</a></li>
<li><a href="Causal_theory_of_reference" title="Causal theory of reference">Causal theory of reference</a></li>
<li><a href="Descriptivist_theory_of_names" title="Descriptivist theory of names">Descriptivism</a></li>
<li><a href="Emotivism" title="Emotivism">Emotivism</a></li>
<li><a href="Analytical_feminism" title="Analytical feminism">Feminism</a></li>
<li><a href="Functionalism_(philosophy_of_mind)" title="Functionalism (philosophy of mind)">Functionalism</a></li>
<li><a href="Logical_atomism" title="Logical atomism">Logical atomism</a></li>
<li><a href="Logical_positivism" title="Logical positivism">Logical positivism</a></li>
<li><a href="Analytical_Marxism" title="Analytical Marxism">Marxism</a></li>
<li><a href="Neurophilosophy" title="Neurophilosophy">Neurophilosophy</a></li>
<li><a href="Ordinary_language_philosophy" title="Ordinary language philosophy">Ordinary language</a></li>
<li><a href="Neopragmatism" title="Neopragmatism">Pragmatism</a></li>
<li><a href="Quietism_(philosophy)" title="Quietism (philosophy)">Quietism</a></li>
<li><a href="Structuralism_(philosophy_of_science)" title="Structuralism (philosophy of science)">Scientific structuralism</a></li>
<li><a href="Sense_data" title="Sense data">Sense data</a></li>
<li><a href="Analytic_theology" title="Analytic theology">Analytic theology</a></li>
<li><a href="Analytical_Thomism" title="Analytical Thomism">Analytical Thomism</a></li></ul>
</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Concepts</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">
<ul><li><a href="Philosophical_analysis" title="Philosophical analysis">Analysis</a> (<a href="Paradox_of_analysis" title="Paradox of analysis">paradox of analysis</a>)</li>
<li><a href="Analytic%E2%80%93synthetic_distinction" title="Analytic–synthetic distinction">Analytic–synthetic distinction</a></li>
<li><a href="Counterfactual_conditional" title="Counterfactual conditional">Counterfactual</a></li>
<li><a href="Natural_kind" title="Natural kind">Natural kind</a></li>
<li><a href="Reflective_equilibrium" title="Reflective equilibrium">Reflective equilibrium</a></li>
<li><a href="Supervenience" title="Supervenience">Supervenience</a></li></ul>
</div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th id="Modality32" scope="row" class="navbox-group" style="width:1%"><a href="Linguistic_modality" class="mw-redirect" title="Linguistic modality">Modality</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em">
<ul><li><a href="Actualism" title="Actualism">Actualism</a></li>
<li><a href="Metaphysical_necessity" title="Metaphysical necessity">Necessity</a></li>
<li><a href="Logical_possibility" title="Logical possibility">Possibility</a></li>
<li><a href="Possible_world" title="Possible world">Possible world</a></li>
<li><a href="Modal_realism" title="Modal realism">Realism</a></li>
<li><a href="Rigid_designator" title="Rigid designator">Rigid designator</a></li></ul>
</div></td></tr></tbody></table><div>
</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Philosophers</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">
<ul><li><a href="Noam_Chomsky" title="Noam Chomsky">Noam Chomsky</a></li>
<li><a href="Keith_Donnellan" title="Keith Donnellan">Keith Donnellan</a></li>
<li><a href="Gottlob_Frege" title="Gottlob Frege">Gottlob Frege</a></li>
<li><a href="Edmund_Gettier" title="Edmund Gettier">Edmund Gettier</a></li>
<li><a href="Jaakko_Hintikka" title="Jaakko Hintikka">Jaakko Hintikka</a></li>
<li><a href="Giuseppe_Peano" title="Giuseppe Peano">Giuseppe Peano</a></li>
<li><a href="Russ_Shafer-Landau" title="Russ Shafer-Landau">Russ Shafer-Landau</a></li>
<li><a href="Ernest_Sosa" title="Ernest Sosa">Ernest Sosa</a></li>
<li><a href="Barry_Stroud" title="Barry Stroud">Barry Stroud</a></li></ul>
</div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Australian_realism" title="Australian realism">Australian realism</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em">
<ul><li><a href="David_Malet_Armstrong" title="David Malet Armstrong">David Malet Armstrong</a></li>
<li><a href="David_Chalmers" title="David Chalmers">David Chalmers</a></li>
<li><a href="J._L._Mackie" title="J. L. Mackie">J. L. Mackie</a></li>
<li><a href="Peter_Singer" title="Peter Singer">Peter Singer</a></li>
<li><a href="J._J._C._Smart" title="J. J. C. Smart">J. J. C. Smart</a></li></ul>
</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Cambridge</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">
<ul><li><a href="Arif_Ahmed_(philosopher)" title="Arif Ahmed (philosopher)">Arif Ahmed</a></li>
<li><a href="C._D._Broad" title="C. D. Broad">Charlie Broad</a></li>
<li><a href="Casimir_Lewy" title="Casimir Lewy">Casimir Lewy</a></li>
<li><a href="Norman_Malcolm" title="Norman Malcolm">Norman Malcolm</a></li>
<li><a href="G._E._Moore" title="G. E. Moore">G. E. Moore</a></li>
<li><a href="Graham_Priest" title="Graham Priest">Graham Priest</a></li>
<li><a href="Bertrand_Russell" title="Bertrand Russell">Bertrand Russell</a></li>
<li><a href="Frank_P._Ramsey" class="mw-redirect" title="Frank P. Ramsey">Frank P. Ramsey</a></li>
<li><a href="Ludwig_Wittgenstein" title="Ludwig Wittgenstein">Ludwig Wittgenstein</a></li></ul>
</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Ordinary_language_philosophy" title="Ordinary language philosophy">Oxford</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em">
<ul><li><a href="G._E._M._Anscombe" title="G. E. M. Anscombe">G. E. M. Anscombe</a></li>
<li><a href="J._L._Austin" title="J. L. Austin">J. L. Austin</a></li>
<li><a href="Michael_Dummett" title="Michael Dummett">Michael Dummett</a></li>
<li><a href="Antony_Flew" title="Antony Flew">Antony Flew</a></li>
<li><a href="Philippa_Foot" title="Philippa Foot">Philippa Foot</a></li>
<li><a href="Peter_Geach" title="Peter Geach">Peter Geach</a></li>
<li><a href="Paul_Grice" title="Paul Grice">Paul Grice</a></li>
<li><a href="R._M._Hare" title="R. M. Hare">R. M. Hare</a></li>
<li><a href="Alasdair_MacIntyre" title="Alasdair MacIntyre">Alasdair MacIntyre</a></li>
<li><a href="Derek_Parfit" title="Derek Parfit">Derek Parfit</a></li>
<li><a href="Gilbert_Ryle" title="Gilbert Ryle">Gilbert Ryle</a></li>
<li><a href="John_Searle" title="John Searle">John Searle</a></li>
<li><a href="P._F._Strawson" title="P. F. Strawson">P. F. Strawson</a></li>
<li><a href="Richard_Swinburne" title="Richard Swinburne">Richard Swinburne</a></li>
<li><a href="Charles_Taylor_(philosopher)" title="Charles Taylor (philosopher)">Charles Taylor</a></li>
<li><a href="Bernard_Williams" title="Bernard Williams">Bernard Williams</a></li>
<li><a href="Timothy_Williamson" title="Timothy Williamson">Timothy Williamson</a></li></ul>
</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Logical_positivism" title="Logical positivism">Logical positivists</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">
<ul><li><a href="A._J._Ayer" title="A. J. Ayer">A. J. Ayer</a></li>
<li><a href="Ernest_Nagel" title="Ernest Nagel">Ernest Nagel</a></li></ul>
</div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Berlin_Circle" title="Berlin Circle">Berlin Circle</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em">
<ul><li><a href="Carl_Gustav_Hempel" title="Carl Gustav Hempel">Carl Gustav Hempel</a></li>
<li><a href="Hans_Reichenbach" title="Hans Reichenbach">Hans Reichenbach</a></li></ul>
</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Vienna_Circle" title="Vienna Circle">Vienna Circle</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">
<ul><li><a href="Rudolf_Carnap" title="Rudolf Carnap">Rudolf Carnap</a></li>
<li><a href="Hans_Hahn_(mathematician)" title="Hans Hahn (mathematician)">Hans Hahn</a></li>
<li><a href="Otto_Neurath" title="Otto Neurath">Otto Neurath</a></li>
<li><a href="Moritz_Schlick" title="Moritz Schlick">Moritz Schlick</a></li>
<li><a href="Friedrich_Waismann" title="Friedrich Waismann">Friedrich Waismann</a></li></ul>
</div></td></tr></tbody></table><div>
</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Harvard</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em">
<ul><li><a href="Roderick_Chisholm" title="Roderick Chisholm">Roderick Chisholm</a></li>
<li><a href="Donald_Davidson_(philosopher)" title="Donald Davidson (philosopher)">Donald Davidson</a></li>
<li><a href="Daniel_Dennett" title="Daniel Dennett">Daniel Dennett</a></li>
<li><a href="Nelson_Goodman" title="Nelson Goodman">Nelson Goodman</a></li>
<li><a href="Christine_Korsgaard" title="Christine Korsgaard">Christine Korsgaard</a></li>
<li><a href="Thomas_Nagel" title="Thomas Nagel">Thomas Nagel</a></li>
<li><a href="Robert_Nozick" title="Robert Nozick">Robert Nozick</a></li>
<li><a href="Hilary_Putnam" title="Hilary Putnam">Hilary Putnam</a></li>
<li><a href="Willard_Van_Orman_Quine" title="Willard Van Orman Quine">W. V. O. Quine</a></li>
<li><a href="John_Rawls" title="John Rawls">John Rawls</a></li></ul>
</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Notre Dame</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">
<ul><li><a href="Robert_Audi" title="Robert Audi">Robert Audi</a></li>
<li><a href="Peter_van_Inwagen" title="Peter van Inwagen">Peter van Inwagen</a></li></ul>
</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Pittsburgh_School" class="mw-redirect" title="Pittsburgh School">Pittsburgh School</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em">
<ul><li><a href="Robert_Brandom" title="Robert Brandom">Robert Brandom</a></li>
<li><a href="Patricia_Churchland" title="Patricia Churchland">Patricia Churchland</a></li>
<li><a href="Paul_Churchland" title="Paul Churchland">Paul Churchland</a></li>
<li><a href="Adolf_Gr%C3%BCnbaum" title="Adolf Grünbaum">Adolf Grünbaum</a></li>
<li><a href="John_McDowell" title="John McDowell">John McDowell</a></li>
<li><a href="Ruth_Millikan" title="Ruth Millikan">Ruth Millikan</a></li>
<li><a href="Alexander_Pruss" title="Alexander Pruss">Alexander Pruss</a></li>
<li><a href="Nicholas_Rescher" title="Nicholas Rescher">Nicholas Rescher</a></li>
<li><a href="Wilfrid_Sellars" title="Wilfrid Sellars">Wilfrid Sellars</a></li>
<li><a href="Bas_van_Fraassen" title="Bas van Fraassen">Bas van Fraassen</a></li></ul>
</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Neopragmatism" title="Neopragmatism">Pragmatism</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">
<ul><li><a href="Susan_Haack" title="Susan Haack">Susan Haack</a></li>
<li><a href="Nicholas_Rescher" title="Nicholas Rescher">Nicholas Rescher</a></li>
<li><a href="Morton_White" title="Morton White">Morton White</a></li></ul>
</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Princeton</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em">
<ul><li><a href="Alonzo_Church" title="Alonzo Church">Alonzo Church</a></li>
<li><a href="Jerry_Fodor" title="Jerry Fodor">Jerry Fodor</a></li>
<li><a href="Kurt_G%C3%B6del" title="Kurt Gödel">Kurt Gödel</a></li>
<li><a href="David_Lewis_(philosopher)" title="David Lewis (philosopher)">David Lewis</a></li>
<li><a href="Jaegwon_Kim" title="Jaegwon Kim">Jaegwon Kim</a></li>
<li><a href="Saul_Kripke" title="Saul Kripke">Saul Kripke</a></li>
<li><a href="Richard_Rorty" title="Richard Rorty">Richard Rorty</a></li>
<li><a href="Nathan_Salmon" title="Nathan Salmon">Nathan Salmon</a></li>
<li><a href="Michael_Walzer" title="Michael Walzer">Michael Walzer</a></li></ul>
</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Quietism_(philosophy)" title="Quietism (philosophy)">Quietism</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">
<ul><li><a href="James_F._Conant" title="James F. Conant">James F. Conant</a></li>
<li><a href="Alice_Crary" title="Alice Crary">Alice Crary</a></li>
<li><a href="Cora_Diamond" title="Cora Diamond">Cora Diamond</a></li></ul>
</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Reformed</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em">
<ul><li><a href="Alvin_Plantinga" title="Alvin Plantinga">Alvin Plantinga</a></li>
<li><a href="William_Lane_Craig" title="William Lane Craig">William Lane Craig</a></li>
<li><a href="Nicholas_Wolterstorff" title="Nicholas Wolterstorff">Nicholas Wolterstorff</a></li></ul>
</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Science</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">
<ul><li><a href="Paul_Feyerabend" title="Paul Feyerabend">Paul Feyerabend</a></li>
<li><a href="Thomas_Kuhn" title="Thomas Kuhn">Thomas Kuhn</a></li>
<li><a href="Imre_Lakatos" title="Imre Lakatos">Imre Lakatos</a></li>
<li><a href="Karl_Popper" title="Karl Popper">Karl Popper</a></li></ul>
</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Stanford_School" title="Stanford School">Stanford School</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em">
<ul><li><a href="Nancy_Cartwright_(philosopher)" title="Nancy Cartwright (philosopher)">Nancy Cartwright</a></li>
<li><a href="John_Dupr%C3%A9" title="John Dupré">John Dupré</a></li>
<li><a href="Peter_Galison" title="Peter Galison">Peter Galison</a></li>
<li><a href="Ian_Hacking" title="Ian Hacking">Ian Hacking</a></li>
<li><a href="Patrick_Suppes" title="Patrick Suppes">Patrick Suppes</a></li></ul>
</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Lw%C3%B3w%E2%80%93Warsaw_school" title="Lwów–Warsaw school">Lwow–Warsaw</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">
<ul><li><a href="Jan_%C5%81ukasiewicz" title="Jan Łukasiewicz">Jan Łukasiewicz</a></li>
<li><a href="Alfred_Tarski" title="Alfred Tarski">Alfred Tarski</a></li></ul>
</div></td></tr></tbody></table><div>
</div></td></tr><tr><td class="navbox-abovebelow hlist" colspan="2"><div>
<ul><li><span class="noviewer" typeof="mw:File"><span title="Category"></span></span> Category</li></ul>
</div></td></tr></tbody></table></div>
<div class="navbox-styles"></div><div role="navigation" class="navbox" aria-labelledby="Philosophy_of_language308" style="padding:3px"><table class="nowraplinks hlist mw-collapsible mw-collapsed navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><div id="Philosophy_of_language308" style="font-size:114%;margin:0 4em"><a href="Philosophy_of_language" title="Philosophy of language">Philosophy of language</a></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="List_of_philosophers_of_language" title="List of philosophers of language">Philosophers</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">
<ul><li><a href="Confucius" title="Confucius">Confucius</a></li>
<li><a href="Gorgias" title="Gorgias">Gorgias</a></li>
<li><a href="Cratylus" title="Cratylus">Cratylus</a></li>
<li><a href="Plato" title="Plato">Plato</a></li>
<li><a href="Aristotle" title="Aristotle">Aristotle</a></li>
<li><a href="Eubulides" title="Eubulides">Eubulides</a></li>
<li><a href="Diodorus_Cronus" title="Diodorus Cronus">Diodorus</a></li>
<li><a href="Chrysippus" title="Chrysippus">Chrysippus</a></li>
<li><a href="Zhuang_Zhou" title="Zhuang Zhou">Zhuangzi</a></li>
<li><a href="Xunzi_(philosopher)" title="Xunzi (philosopher)">Xunzi</a></li>
<li><a href="Averroes" title="Averroes">Averroes</a></li>
<li><a href="Ibn_Khaldun" title="Ibn Khaldun">Ibn Khaldun</a></li>
<li><a href="Thomas_Hobbes" title="Thomas Hobbes">Hobbes</a></li>
<li><a href="John_Wilkins" title="John Wilkins">Wilkins</a></li>
<li><a href="Antoine_Arnauld" title="Antoine Arnauld">Arnauld</a></li>
<li><a href="Claude_Lancelot" title="Claude Lancelot">Lancelot</a></li>
<li><a href="Gottfried_Wilhelm_Leibniz" title="Gottfried Wilhelm Leibniz">Leibniz</a></li>
<li><a href="George_Berkeley" title="George Berkeley">Berkeley</a></li>
<li><a href="Johann_Gottfried_Herder" title="Johann Gottfried Herder">Herder</a></li>
<li><a href="Wilhelm_von_Humboldt" title="Wilhelm von Humboldt">von Humboldt</a></li>
<li><a href="Fritz_Mauthner" title="Fritz Mauthner">Mauthner</a></li>
<li><a href="Paul_Ric%C5%93ur" title="Paul Ricœur">Ricœur</a></li>
<li><a href="Ferdinand_de_Saussure" title="Ferdinand de Saussure">de Saussure</a></li>
<li><a href="Gottlob_Frege" title="Gottlob Frege">Frege</a></li>
<li><a href="Franz_Boas" title="Franz Boas">Boas</a></li>
<li><a href="Paul_Tillich" title="Paul Tillich">Tillich</a></li>
<li><a href="Edward_Sapir" title="Edward Sapir">Sapir</a></li>
<li><a href="Leonard_Bloomfield" title="Leonard Bloomfield">Bloomfield</a></li>
<li><a href="Henri_Bergson" title="Henri Bergson">Bergson</a></li>
<li><a href="Lev_Vygotsky" title="Lev Vygotsky">Vygotsky</a></li>
<li><a href="Ludwig_Wittgenstein" title="Ludwig Wittgenstein">Wittgenstein</a></li>
<li><a href="Bertrand_Russell" title="Bertrand Russell">Russell</a></li>
<li><a href="Rudolf_Carnap" title="Rudolf Carnap">Carnap</a></li>
<li><a href="Jacques_Derrida" title="Jacques Derrida">Derrida</a></li>
<li><a href="Benjamin_Lee_Whorf" title="Benjamin Lee Whorf">Whorf</a></li>
<li><a href="J._L._Austin" title="J. L. Austin">Austin</a></li>
<li><a href="Noam_Chomsky" title="Noam Chomsky">Chomsky</a></li>
<li><a href="Hans-Georg_Gadamer" title="Hans-Georg Gadamer">Gadamer</a></li>
<li><a href="Saul_Kripke" title="Saul Kripke">Kripke</a></li>
<li><a href="A._J._Ayer" title="A. J. Ayer">Ayer</a></li>
<li><a href="G._E._M._Anscombe" title="G. E. M. Anscombe">Anscombe</a></li>
<li><a href="Jaakko_Hintikka" title="Jaakko Hintikka">Hintikka</a></li>
<li><a href="Michael_Dummett" title="Michael Dummett">Dummett</a></li>
<li><a href="Donald_Davidson_(philosopher)" title="Donald Davidson (philosopher)">Davidson</a></li>
<li><a href="Paul_Grice" title="Paul Grice">Grice</a></li>
<li><a href="Gilbert_Ryle" title="Gilbert Ryle">Ryle</a></li>
<li><a href="P._F._Strawson" title="P. F. Strawson">Strawson</a></li>
<li><a href="Willard_Van_Orman_Quine" title="Willard Van Orman Quine">Quine</a></li>
<li><a href="Hilary_Putnam" title="Hilary Putnam">Putnam</a></li>
<li><a href="David_Lewis_(philosopher)" title="David Lewis (philosopher)">Lewis</a></li>
<li><a href="John_Searle" title="John Searle">Searle</a></li>
<li><a href="Paul_Watzlawick" title="Paul Watzlawick">Watzlawick</a></li></ul>
</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Theories</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em">
<ul><li><a href="Causal_theory_of_reference" title="Causal theory of reference">Causal theory of reference</a></li>
<li><a href="Contrastivism" title="Contrastivism">Contrast theory of meaning</a></li>
<li><a href="Contrastivism" title="Contrastivism">Contrastivism</a></li>
<li><a href="Conventionalism" title="Conventionalism">Conventionalism</a></li>
<li><a href="Cratylism" title="Cratylism">Cratylism</a></li>
<li><a href="Deconstruction" title="Deconstruction">Deconstruction</a></li>
<li><a href="Descriptivist_theory_of_names" title="Descriptivist theory of names">Descriptivism</a></li>
<li><a href="Direct_reference_theory" title="Direct reference theory">Direct reference theory</a></li>
<li><a href="Dramatism" title="Dramatism">Dramatism</a></li>
<li><a href="Dynamic_semantics" title="Dynamic semantics">Dynamic semantics</a></li>
<li><a href="Expressivism" title="Expressivism">Expressivism</a></li>
<li><a href="Inquisitive_semantics" title="Inquisitive semantics">Inquisitive semantics</a></li>
<li><a href="Linguistic_determinism" title="Linguistic determinism">Linguistic determinism</a></li>
<li><a href="Mediated_reference_theory" title="Mediated reference theory">Mediated reference theory</a></li>
<li><a href="Nominalism" title="Nominalism">Nominalism</a></li>
<li><a href="Non-cognitivism" title="Non-cognitivism">Non-cognitivism</a></li>
<li><a href="Phallogocentrism" title="Phallogocentrism">Phallogocentrism</a></li>
<li><a href="Relevance_theory" title="Relevance theory">Relevance theory</a></li>
<li><a href="Semantic_externalism" title="Semantic externalism">Semantic externalism</a></li>
<li><a href="Semantic_holism" title="Semantic holism">Semantic holism</a></li>
<li><a href="Situation_semantics" title="Situation semantics">Situation semantics</a></li>
<li><a href="Structuralism" title="Structuralism">Structuralism</a></li>
<li><a href="Supposition_theory" title="Supposition theory">Supposition theory</a></li>
<li><a href="Symbiosism" title="Symbiosism">Symbiosism</a></li>
<li><a href="Theological_noncognitivism" title="Theological noncognitivism">Theological noncognitivism</a></li>
<li><a href="Theory_of_descriptions" title="Theory of descriptions">Theory of descriptions</a> ()</li>
<li><a href="Theory_of_language" title="Theory of language">Theory of language</a></li>
<li><a href="Unilalianism" title="Unilalianism">Unilalianism</a></li>
<li><a href="Verificationism" title="Verificationism">Verification theory</a></li></ul>
</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Concepts</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">
<ul><li><a href="Ambiguity" title="Ambiguity">Ambiguity</a></li>
<li><a href="Cant_(language)" title="Cant (language)">Cant</a></li>
<li><a href="Class_(philosophy)" title="Class (philosophy)">Class</a></li>
<li><a href="Concept" title="Concept">Concept</a></li>
<li><a href="Categorization" class="mw-redirect" title="Categorization">Categories</a></li>
<li><a href="Family_resemblance" title="Family resemblance">Family resemblance</a></li>
<li><a href="Intension" title="Intension">Intension</a></li>
<li><a href="Language" title="Language">Language</a></li>
<li><a href="Linguistic_relativity" title="Linguistic relativity">Linguistic relativity</a></li>
<li><a href="Logical_form" title="Logical form">Logical form</a></li>
<li><a href="Mental_representation" title="Mental representation">Mental representation</a></li>
<li><a href="Metalanguage" title="Metalanguage">Metalanguage</a></li>
<li><a href="Modality_(natural_language)" class="mw-redirect" title="Modality (natural language)">Modality (natural language)</a></li>
<li><a href="Presupposition" title="Presupposition">Presupposition</a></li>
<li><a href="Principle_of_compositionality" title="Principle of compositionality">Principle of compositionality</a></li>
<li><a href="Property_(philosophy)" title="Property (philosophy)">Property</a></li>
<li><a href="Proposition" title="Proposition">Proposition</a></li>
<li><a href="Sense_and_reference" title="Sense and reference">Sense and reference</a></li>
<li><a href="Sentence_(linguistics)" title="Sentence (linguistics)">Sentence</a></li>
<li><a href="Set_(mathematics)" title="Set (mathematics)">Set</a></li>
<li><a href="Sign_(semiotics)" title="Sign (semiotics)">Sign</a></li>
<li><a href="Speech_act" title="Speech act">Speech act</a></li>
<li><a href="Statement_(logic)" class="mw-redirect" title="Statement (logic)">Statement</a></li>
<li><a href="Symbol" title="Symbol">Symbol</a></li>
<li><a href="Truth-bearer" title="Truth-bearer">Truth-bearer</a></li>
<li><a href="Use%E2%80%93mention_distinction" title="Use–mention distinction">Use–mention distinction</a></li>
<li><i><a href="Index_of_philosophy_of_language_articles" class="mw-redirect" title="Index of philosophy of language articles">more...</a></i></li></ul>
</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Works</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em">
<ul><li><i><a href="Cratylus_(dialogue)" title="Cratylus (dialogue)">Cratylus</a></i> <span style="font-size: 85%;">(n.d.)</span></li>
<li><i><a href="Port-Royal_Grammar" title="Port-Royal Grammar">Port-Royal Grammar</a></i> <span style="font-size: 85%;">(1660)</span></li>
<li><i><a href="De_Arte_Combinatoria" title="De Arte Combinatoria">De Arte Combinatoria</a></i> <span style="font-size: 85%;">(1666)</span></li>
<li><i><a href="An_Essay_Towards_a_Real_Character%2C_and_a_Philosophical_Language" title="An Essay Towards a Real Character, and a Philosophical Language">An Essay Towards a Real Character, and a Philosophical Language</a></i> <span style="font-size: 85%;">(1668)</span></li>
<li><i><a href="Alciphron_(book)" title="Alciphron (book)">Alciphron</a></i> <span style="font-size: 85%;">(1732)</span></li>
<li>"<a href="On_Denoting" title="On Denoting">On Denoting</a>" <span style="font-size: 85%;">(1905)</span></li>
<li><i><a href="Tractatus_Logico-Philosophicus" title="Tractatus Logico-Philosophicus">Tractatus Logico-Philosophicus</a></i> <span style="font-size: 85%;">(1921)</span></li>
<li><i><a href="Language%2C_Truth%2C_and_Logic" title="Language, Truth, and Logic">Language, Truth, and Logic</a></i> <span style="font-size: 85%;">(1936)</span></li>
<li><i><a href="Two_Dogmas_of_Empiricism" title="Two Dogmas of Empiricism">Two Dogmas of Empiricism</a></i> <span style="font-size: 85%;">(1951)</span></li>
<li><i><a href="Philosophical_Investigations" title="Philosophical Investigations">Philosophical Investigations</a></i> <span style="font-size: 85%;">(1953)</span></li>
<li><i><a href="Of_Grammatology" title="Of Grammatology">Of Grammatology</a></i> <span style="font-size: 85%;">(1967)</span></li>
<li><i><a href="Naming_and_Necessity" title="Naming and Necessity">Naming and Necessity</a></i> <span style="font-size: 85%;">(1980)</span></li>
<li><i><a href="Wittgenstein_on_Rules_and_Private_Language" title="Wittgenstein on Rules and Private Language">Wittgenstein on Rules and Private Language</a></i> <span style="font-size: 85%;">(1982)</span></li>
<li><i><a href="Limited_Inc" title="Limited Inc">Limited Inc</a></i> <span style="font-size: 85%;">(1988)</span></li></ul>
</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Related articles</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">
<ul><li><a href="Analytic_philosophy" title="Analytic philosophy">Analytic philosophy</a></li>
<li><a href="Philosophy_of_information" title="Philosophy of information">Philosophy of information</a></li>
<li><a href="Philosophical_logic" title="Philosophical logic">Philosophical logic</a></li>
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<li><a href="Semantics_(natural_language)" class="mw-redirect" title="Semantics (natural language)">Semantics</a>
<ul><li><a href="Formal_semantics_(linguistics)" class="mw-redirect" title="Formal semantics (linguistics)">Formal semantics</a></li></ul></li>
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</div></td></tr><tr><td class="navbox-abovebelow" colspan="2"><div>
<ul><li>Category</li>
<li>Task Force</li>
<li>Discussion</li></ul>
</div></td></tr></tbody></table></div>
<div class="navbox-styles"></div><div role="navigation" class="navbox" aria-labelledby="Formal_semantics_(natural_language)78" style="padding:3px"><table class="nowraplinks mw-collapsible autocollapse navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><div id="Formal_semantics_(natural_language)78" style="font-size:114%;margin:0 4em"><a href="Formal_semantics_(natural_language)" title="Formal semantics (natural language)">Formal semantics (natural language)</a></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%">Central concepts</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">
<ul><li><a href="Principle_of_compositionality" title="Principle of compositionality">Compositionality</a></li>
<li><a href="Denotation" title="Denotation">Denotation</a></li>
<li><a href="Linguistic_entailment" title="Linguistic entailment">Entailment</a></li>
<li><a href="Extension_(semantics)" title="Extension (semantics)">Extension</a></li>
<li><a href="Generalized_quantifier" title="Generalized quantifier">Generalized quantifier</a></li>
<li><a href="Intension" title="Intension">Intension</a></li>
<li><a href="Logical_form_(linguistics)" title="Logical form (linguistics)">Logical form</a></li>
<li><a href="Presupposition" title="Presupposition">Presupposition</a></li>
<li><a href="Proposition" title="Proposition">Proposition</a></li>
<li><a href="Reference" title="Reference">Reference</a></li>
<li><a href="Scope_(formal_semantics)" title="Scope (formal semantics)">Scope</a></li>
<li><a href="Speech_act" title="Speech act">Speech act</a></li>
<li><a href="Syntax%E2%80%93semantics_interface" title="Syntax–semantics interface">Syntax–semantics interface</a></li>
<li><a href="Truth-conditional_semantics" title="Truth-conditional semantics">Truth conditions</a></li></ul>
</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Topics</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%">Areas</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em">
<ul><li><a href="Anaphora_(linguistics)" title="Anaphora (linguistics)">Anaphora</a></li>
<li><a href="Ambiguity" title="Ambiguity">Ambiguity</a></li>
<li><a href="Binding_(linguistics)" title="Binding (linguistics)">Binding</a></li>
<li><a href="Conditional_sentence" title="Conditional sentence">Conditionals</a></li>
<li><a href="Definiteness" title="Definiteness">Definiteness</a></li>
<li><a href="Disjunction" class="mw-redirect" title="Disjunction">Disjunction</a></li>
<li><a href="Evidentiality" title="Evidentiality">Evidentiality</a></li>
<li><a href="Focus_(linguistics)" title="Focus (linguistics)">Focus</a></li>
<li><a href="Indexicality" title="Indexicality">Indexicality</a></li>
<li><a href="Lexical_semantics" title="Lexical semantics">Lexical semantics</a></li>
<li><a href="Linguistic_modality" class="mw-redirect" title="Linguistic modality">Modality</a></li>
<li><a href="Negation" title="Negation">Negation</a></li>
<li><a href="Propositional_attitudes" class="mw-redirect" title="Propositional attitudes">Propositional attitudes</a></li>
<li><a href="Tense%E2%80%93aspect%E2%80%93mood" title="Tense–aspect–mood">Tense–aspect–mood</a></li>
<li><a href="Quantifier_(logic)" title="Quantifier (logic)">Quantification</a></li>
<li><a href="Vagueness" title="Vagueness">Vagueness</a></li></ul>
</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Phenomena</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">
<ul><li><a href="Antecedent-contained_deletion" title="Antecedent-contained deletion">Antecedent-contained deletion</a></li>
<li><a href="Cataphora" title="Cataphora">Cataphora</a></li>
<li><a href="Coercion_(linguistics)" title="Coercion (linguistics)">Coercion</a></li>
<li><a href="Conservativity" title="Conservativity">Conservativity</a></li>
<li><a href="Counterfactuals" class="mw-redirect" title="Counterfactuals">Counterfactuals</a></li>
<li><a href="Crossover_effects" title="Crossover effects">Crossover effects</a></li>
<li><a href="Cumulativity_(linguistics)" title="Cumulativity (linguistics)">Cumulativity</a></li>
<li><a href="De_dicto_and_de_re" title="De dicto and de re">De dicto and de re</a></li>
<li><a href="De_se" title="De se">De se</a></li>
<li><a href="Deontic_modality" title="Deontic modality">Deontic modality</a></li>
<li><a href="Discourse_relation" title="Discourse relation">Discourse relations</a></li>
<li><a href="Donkey_anaphora" class="mw-redirect" title="Donkey anaphora">Donkey anaphora</a></li>
<li><a href="Epistemic_modality" title="Epistemic modality">Epistemic modality</a></li>
<li><a href="Exhaustivity" title="Exhaustivity">Exhaustivity</a></li>
<li><a href="Faultless_disagreement" title="Faultless disagreement">Faultless disagreement</a></li>
<li><a href="Free_choice_inference" title="Free choice inference">Free choice inferences</a></li>
<li><a href="Givenness" title="Givenness">Givenness</a></li>
<li><a href="Homogeneity_(linguistics)" class="mw-redirect" title="Homogeneity (linguistics)">Homogeneity (linguistics)</a></li>
<li><a href="Hurford_disjunction" title="Hurford disjunction">Hurford disjunction</a></li>
<li><a href="Inalienable_possession" title="Inalienable possession">Inalienable possession</a></li>
<li><a href="Intersective_modifier" title="Intersective modifier">Intersective modification</a></li>
<li><a href="Logophoricity" title="Logophoricity">Logophoricity</a></li>
<li><a href="Mirativity" title="Mirativity">Mirativity</a></li>
<li><a href="Modal_subordination" title="Modal subordination">Modal subordination</a></li>
<li><a href="Opaque_context" title="Opaque context">Opaque contexts</a></li>
<li><a href="Performative_utterance" title="Performative utterance">Performatives</a></li>
<li><a href="Polarity_item" title="Polarity item">Polarity items</a></li>
<li><a href="Privative_adjective" title="Privative adjective">Privative adjectives</a></li>
<li><a href="Quantificational_variability_effect" title="Quantificational variability effect">Quantificational variability effect</a></li>
<li><a href="Responsive_predicate" title="Responsive predicate">Responsive predicate</a></li>
<li><a href="Rising_declarative" title="Rising declarative">Rising declaratives</a></li>
<li><a href="Scalar_implicature" title="Scalar implicature">Scalar implicature</a></li>
<li><a href="Sloppy_identity" title="Sloppy identity">Sloppy identity</a></li>
<li><a href="Subsective_modifier" title="Subsective modifier">Subsective modification</a></li>
<li><a href="Subtrigging" title="Subtrigging">Subtrigging</a></li>
<li><a href="Telicity" title="Telicity">Telicity</a></li>
<li><a href="Temperature_paradox" title="Temperature paradox">Temperature paradox</a></li>
<li><a href="Veridicality" title="Veridicality">Veridicality</a></li></ul>
</div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Formalism</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%">Formal systems</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em">
<ul><li><a href="Alternative_semantics" title="Alternative semantics">Alternative semantics</a></li>
<li><a href="Categorial_grammar" title="Categorial grammar">Categorial grammar</a></li>
<li><a href="Combinatory_categorial_grammar" title="Combinatory categorial grammar">Combinatory categorial grammar</a></li>
<li><a href="Discourse_representation_theory" title="Discourse representation theory">Discourse representation theory (DRT)</a></li>
<li><a href="Dynamic_semantics" title="Dynamic semantics">Dynamic semantics</a></li>
<li><a href="Generative_grammar" title="Generative grammar">Generative grammar</a></li>
<li><a href="Glue_semantics" title="Glue semantics">Glue semantics</a></li>
<li><a href="Inquisitive_semantics" title="Inquisitive semantics">Inquisitive semantics</a></li>
<li><a href="Intensional_logic" title="Intensional logic">Intensional logic</a></li>
<li><a href="Lambda_calculus" title="Lambda calculus">Lambda calculus</a></li>
<li><a href="Mereology" title="Mereology">Mereology</a></li>
<li><a href="Montague_grammar" title="Montague grammar">Montague grammar</a></li>
<li><a href="Segmented_discourse_representation_theory" class="mw-redirect" title="Segmented discourse representation theory">Segmented discourse representation theory (SDRT)</a></li>
<li><a href="Situation_semantics" title="Situation semantics">Situation semantics</a></li>
<li><a href="Supervaluationism" title="Supervaluationism">Supervaluationism</a></li>
<li><a href="Type_theory" title="Type theory">Type theory</a></li>
<li><a href="Type_theory_with_records" title="Type theory with records">TTR</a></li></ul>
</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Concepts</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">
<ul><li><a href="Autonomy_of_syntax" title="Autonomy of syntax">Autonomy of syntax</a></li>
<li><a href="Context_set" class="mw-redirect" title="Context set">Context set</a></li>
<li><a href="Continuation" title="Continuation">Continuation</a></li>
<li><a href="Conversational_scoreboard" title="Conversational scoreboard">Conversational scoreboard</a></li>
<li><a href="Downward_entailing" title="Downward entailing">Downward entailing</a></li>
<li><a href="Existential_closure" title="Existential closure">Existential closure</a></li>
<li><a href="Function_application" title="Function application">Function application</a></li>
<li><a href="Meaning_postulate" title="Meaning postulate">Meaning postulate</a></li>
<li><a href="Monad_(functional_programming)" title="Monad (functional programming)">Monads</a></li>
<li><a href="Plural_quantification" title="Plural quantification">Plural quantification</a></li>
<li><a href="Possible_world" title="Possible world">Possible world</a></li>
<li><a href="Quantifier_raising" class="mw-redirect" title="Quantifier raising">Quantifier raising</a></li>
<li><a href="Quantization_(linguistics)" title="Quantization (linguistics)">Quantization</a></li>
<li><a href="Question_under_discussion" title="Question under discussion">Question under discussion</a></li>
<li><a href="Semantic_parsing" title="Semantic parsing">Semantic parsing</a></li>
<li><a href="Squiggle_operator" title="Squiggle operator">Squiggle operator</a></li>
<li><a href="Strawson_entailment" title="Strawson entailment">Strawson entailment</a></li>
<li><a href="Strict_conditional" title="Strict conditional">Strict conditional</a></li>
<li><a href="Type_shifter" title="Type shifter">Type shifter</a></li>
<li><a href="Universal_grinder" title="Universal grinder">Universal grinder</a></li></ul>
</div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">See also</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">
<ul><li><a href="Cognitive_semantics" title="Cognitive semantics">Cognitive semantics</a></li>
<li><a href="Computational_semantics" title="Computational semantics">Computational semantics</a></li>
<li><a href="Distributional_semantics" title="Distributional semantics">Distributional semantics</a></li>
<li><a href="Formal_grammar" title="Formal grammar">Formal grammar</a></li>
<li><a href="Inferentialism" class="mw-redirect" title="Inferentialism">Inferentialism</a></li>
<li><a href="Logic_translation" title="Logic translation">Logic translation</a></li>
<li><a href="Linguistics_wars" title="Linguistics wars">Linguistics wars</a></li>
<li><a href="Philosophy_of_language" title="Philosophy of language">Philosophy of language</a></li>
<li><a href="Pragmatics" title="Pragmatics">Pragmatics</a></li>
<li><a href="Semantics_of_logic" title="Semantics of logic">Semantics of logic</a></li></ul>
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