Editing Proposition (section)

==In modern logic<!--'Proposition (logic)', 'Structured proposition', 'Structured propositions', 'Singular proposition', 'Singular propositions', 'Russellian proposition', 'Russellian propositions', 'General proposition', 'General propositions', 'Particularized proposition', 'Particularized propositions', 'Particularised proposition' and 'Particularised propositions' redirect here-->==

In modern logic, propositions are standardly understood semantically as [[indicator function]]s that take a [[possible world]] and return a truth value. For example, the proposition that the sky is blue could be represented as a function <math> f </math> such that <math>f(w)=T</math> for every world <math> w ,</math> if any, where the sky is blue, and <math>f(v)=F</math> for every world <math> v ,</math> if any, where it is not. A proposition can be modeled equivalently with the [[inverse image]] of <math>T</math> under the indicator function, which is sometimes called the ''characteristic set'' of the proposition. For instance, if <math> w </math> and <math> w' </math> are the only worlds in which the sky is blue, the proposition that the sky is blue could be modeled as the set <math> \{w, w'\} </math>.<ref>{{cite book |last=Gamut |first=L.T.F. |author-link=L.T.F. Gamut |date=1991 |title= Logic, Language and Meaning: Intensional Logic and Logical Grammar |publisher= University of Chicago Press |page=122 |isbn=0-226-28088-8}}</ref><ref name=":2">{{Citation|last=King|first=Jeffrey C. |title=Structured Propositions|date=2019|url=http://plato.stanford.edu/entries/propositions-structured/|encyclopedia=The Stanford Encyclopedia of Philosophy|editor-last=Zalta|editor-first=Edward N.|edition=Winter 2016|publisher=Metaphysics Research Lab, Stanford University|access-date=2022-12-30|at=Section 2}}</ref><ref>{{cite book|author1=Irene Heim|author2=Angelika Kratzer|title=Semantics in generative grammar|year=1998|publisher=Wiley-Blackwell|isbn=978-0-631-19713-3|page=304}}</ref><ref>{{cite encyclopedia |title=Pragmatics |encyclopedia=Semantics |year=1972 |last=Stalnaker |first=Robert |editor-last1= Davidson|editor-first1=Donald | editor-last2=Harman | editor-first2=Gilbert|page=381}}</ref>

Numerous refinements and alternative notions of proposition-hood have been proposed including [[inquisitive semantics|inquisitive propositions]] and '''structured propositions'''.<ref>{{cite book |last1=Ciardelli |first1=Ivano |last2=Groenendijk |first2=Jeroen |last3=Roelofsen | first3=Floris |year=2019 |title=Inquisitive Semantics |publisher=Oxford University Press |pages=13,20–22 |isbn=9780198814795}}</ref><ref name =":2" /> Propositions are called '''structured propositions'''<!--boldface per WP:R#PLA--> if they have constituents, in some broad sense.<ref name=":0" /><ref>{{Citation|last1=Fitch|first1=Greg|title=Singular Propositions|date=2018|url=https://plato.stanford.edu/archives/spr2018/entries/propositions-singular/|encyclopedia=The Stanford Encyclopedia of Philosophy|editor-last=Zalta|editor-first=Edward N.|edition=Spring 2018|publisher=Metaphysics Research Lab, Stanford University|access-date=2019-12-11|last2=Nelson|first2=Michael}}</ref> Assuming a structured view of propositions, one can distinguish between '''singular propositions'''<!--boldface per WP:R#PLA--> (also '''Russellian propositions'''<!--boldface per WP:R#PLA-->, named after [[Bertrand Russell]]) which are about a particular individual, '''general propositions'''<!--boldface per WP:R#PLA-->, which are not about any particular individual, and '''particularized propositions'''<!--boldface per WP:R#PLA-->, which are about a particular individual but do not contain that individual as a constituent.<ref name=":2"></ref>