Editing Proposition

{{Short description|Bearer of truth or falsity}}
{{About|the term in philosophy and logic|the use in mathematics|Proposition (mathematics)|other uses}}
{{Distinguish|Preposition}}
{{merge from|Statement (logic)|discuss=Talk:Proposition#Merger_proposal|date=December 2024}}
{{More citations needed|date=February 2023}}
A '''proposition''' is a central concept in the [[philosophy of language]], [[semantics]], [[logic]], and related fields, often characterized as the primary [[Truth-bearer|bearer]] of [[truth]] or [[False (logic)|falsity]]. Propositions are also often characterized as the type of [[abstract object|object]] that [[Sentence (linguistics)#By purpose|declarative sentences]] [[Denotation|denote]]. For instance, the sentence "The sky is blue" denotes the proposition that the sky is blue. However, crucially, propositions are not themselves [[Phrase|linguistic expressions]]. For instance, the [[English language|English]] sentence "Snow is white" denotes the same proposition as the [[German language|German]] sentence "Schnee ist weiß" even though the two sentences are not the same. Similarly, propositions can also be characterized as the objects of [[belief]] and other [[propositional attitude]]s. For instance if someone believes that the sky is blue, the object of their belief is the proposition that the sky is blue.

Formally, propositions are often modeled as [[Function (mathematics)|functions]] which map a [[possible world]] to a [[truth value]]. For instance, the proposition that the sky is blue can be modeled as a function which would return the truth value <math>T </math> if given the actual world as input, but would return <math>F </math> if given some alternate world where the sky is green. However, a number of alternative formalizations have been proposed, notably the '''structured propositions''' view.

Propositions have played a large role throughout the history of [[logic]], [[linguistics]], [[philosophy of language]], and related disciplines. Some researchers have doubted whether a consistent definition of propositionhood is possible, [[David Lewis (philosopher)|David Lewis]] even remarking that "the conception we associate with the word ‘proposition’ may be something of a jumble of conflicting desiderata". The term is often used broadly and has been used to refer to various related concepts.

==Relation to the mind==
In relation to the mind, propositions are discussed primarily as they fit into [[propositional attitudes]]. Propositional attitudes are simply attitudes characteristic of [[folk psychology]] (belief, desire, etc.) that one can take toward a proposition (e.g. 'it is raining,' 'snow is white,' etc.). In English, propositions usually follow folk psychological attitudes by a "that clause" (e.g. "Jane believes ''that'' it is raining"). In [[philosophy of mind]] and [[psychology]], mental states are often taken to primarily consist in propositional attitudes. The propositions are usually said to be the "mental content" of the attitude. For example, if Jane has a mental state of believing that it is raining, her mental content is the proposition 'it is raining.' Furthermore, since such mental states are ''about'' something (namely, propositions), they are said to be [[intentionality|intentional]] mental states.

Explaining the relation of propositions to the mind is especially difficult for non-mentalist views of propositions, such as those of the logical positivists and Russell described above, and [[Gottlob Frege]]'s view that propositions are [[Platonist]] entities, that is, existing in an abstract, non-physical realm.<ref>{{cite web |url=https://plato.stanford.edu/entries/platonism/#4.2 |title=Platonism in metaphysics: Propositions |last=Balaguer |first=Mark |date=2016 |website=Stanford Encyclopedia of Philosophy |publisher= |access-date=30 June 2021}}</ref> So some recent views of propositions have taken them to be mental. Although propositions cannot be particular thoughts since those are not shareable, they could be types of cognitive events<ref>{{cite book |last=Soames |first=Scott |author-link= |date=2014 |title=New Thinking about Propositions |url=https://global.oup.com/academic/product/new-thinking-about-propositions-9780199693764 |location=New York |publisher=Oxford University Press |editor-last1=King |editor-first1=Jeffrey C. |editor-last2=Soames |editor-first2=Scott |editor-last3=Speaks |editor-first3=Jeff |chapter=Propositions as cognitive event types |chapter-url=https://dornsife.usc.edu/assets/sites/678/docs/BookChapters/New_Thinking_About_Propositions/NTP_Chapter_6.pdf  |isbn=9780199693764}}</ref> or properties of thoughts (which could be the same across different thinkers).<ref>{{cite journal |last1=Joaquin |first1=Jeremiah Joven B. |last2=Franklin |first2=James |date=2021 |title=A causal-mentalist view of propositions |url=https://www.organonf.com/journal/jeremiahjovenjoaquinjamesfranklin/ |journal=Organon F |volume=28 |issue= |pages= |doi= |access-date=30 June 2021}}</ref>

Philosophical debates surrounding propositions as they relate to propositional attitudes have also recently centered on whether they are internal or external to the agent, or whether they are mind-dependent or mind-independent entities. For more, see the entry on [[Internalism#Philosophy of mind|internalism and externalism]] in philosophy of mind.

==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>

==Objections to propositions==
Attempts to provide a workable definition of proposition include the following:
<blockquote>
Two meaningful declarative sentences express the same proposition, if and only if they mean the same thing.{{citation needed|date=June 2016}}
</blockquote>
which defines ''proposition'' in terms of synonymity. For example, "Snow is white" (in English) and "Schnee ist weiß" (in German) are different sentences, but they say the same thing, so they express the same proposition. Another definition of proposition is:

<blockquote>
Two meaningful declarative sentence-tokens express the same proposition, if and only if they mean the same thing.{{citation needed|date=June 2016}}
</blockquote>
The above definitions can result in two identical sentences/sentence-tokens appearing to have the same meaning, and thus expressing the same proposition and yet having different truth-values, as in "I am Spartacus" said by Spartacus and said by John Smith, and "It is Wednesday" said on a Wednesday and on a Thursday. These examples reflect the problem of [[ambiguity]] in common language, resulting in a mistaken equivalence of the statements. “I am Spartacus” spoken by Spartacus is the declaration that the individual speaking is called Spartacus and it is true. When spoken by John Smith, it is a declaration about a different speaker and it is false. The term “I” means different things, so “I am Spartacus” means different things.

A related problem is when identical sentences have the same truth-value, yet express different propositions. The sentence “I am a philosopher” could have been spoken by both Socrates and Plato. In both instances, the statement is true, but means something different.

These problems are addressed in [[predicate logic]] by using a variable for the problematic term, so that “X is a philosopher” can have Socrates or Plato substituted for X, illustrating that “Socrates is a philosopher” and “Plato is a philosopher” are different propositions. Similarly, “I am Spartacus” becomes “X is Spartacus”, where X is replaced with terms representing the individuals Spartacus and John Smith.

In other words, the example problems can be averted if sentences are formulated with precision such that their terms have unambiguous meanings.

A number of philosophers and linguists claim that all definitions of a proposition are too vague to be useful. For them, it is just a misleading concept that should be removed from philosophy and [[semantics]]. [[W. V. Quine]], who granted the existence of [[Set (mathematics)|sets]] in mathematics,<ref>{{Citation|last1=McGrath|first1=Matthew|title=Propositions|date=2018|url=https://plato.stanford.edu/archives/spr2018/entries/propositions/|encyclopedia=The Stanford Encyclopedia of Philosophy|editor-last=Zalta|editor-first=Edward N.|edition=Spring 2018|publisher=Metaphysics Research Lab, Stanford University|access-date=2020-08-20|last2=Frank|first2=Devin}}</ref> maintained that the indeterminacy of translation prevented any meaningful discussion of propositions, and that they should be discarded in favor of sentences.<ref>{{cite book |last=Quine |first=W. V. |title=Philosophy of Logic |publisher=Prentice-Hall |location=NJ USA |year=1970 |pages=[https://archive.org/details/philosophyoflogi0000quin/page/1 1–14] |isbn=0-13-663625-X |url=https://archive.org/details/philosophyoflogi0000quin/page/1 }}</ref> [[P. F. Strawson]], on the other hand, advocated for the use of the term "[[Statement (logic)|statement]]".

==Historical usage==

===By Aristotle===

In [[Aristotelian logic]] a proposition was defined as a particular kind of sentence (a [[declarative sentence]]) that affirms or denies a [[Predicate (grammar)|predicate]] of a [[subject (grammar)|subject]], optionally with the help of a [[Copula (linguistics)|copula]].<ref name=":1" /> Aristotelian propositions take forms like "All men are mortal" and "Socrates is a man."

[[Aristotelian logic]] identifies a [[categorical proposition]] as a sentence which affirms or denies a [[Predicate (grammar)#Traditional grammar|predicate]] of a [[Subject (grammar)|subject]], optionally with the help of a [[Copula (linguistics)|copula]].  An Aristotelian proposition may take the form of "All men are mortal" or "Socrates is a man."  In the first example, the subject is "men", predicate is "mortal" and copula is "are", while in the second example, the subject is "Socrates", the predicate is "a man" and copula is "is".<ref name=":1">{{Cite web|url=https://www.iep.utm.edu/aris-log/#H3|title=Aristotle: Logic — From Words into Propositions|last=Groarke|first=Louis|website=Internet Encyclopedia of Philosophy|access-date=2019-12-10}}</ref>

===By the logical positivists===
Often, propositions are related to [[Sentence (mathematical logic)|closed formulae (or logical sentence)]] to distinguish them from what is expressed by an [[open formula]]. In this sense, propositions are "statements" that are [[truth-bearer]]s. This conception of a proposition was supported by the philosophical school of [[logical positivism]].

Some philosophers argue that some (or all) kinds of speech or actions besides the declarative ones also have propositional content. For example, [[yes–no question]]s present propositions, being inquiries into the [[truth value]] of them. On the other hand, some [[Semiotics|sign]]s can be declarative assertions of propositions, without forming a sentence nor even being linguistic (e.g. traffic signs convey definite meaning which is either true or false).

Propositions are also spoken of as the content of [[belief]]s and similar [[propositional attitude|intentional attitudes]], such as desires, preferences, and hopes. For example,  "I desire ''that I have a new car''", or "I wonder ''whether it will snow''" (or, whether it is the case that "it will snow"). Desire, belief, doubt, and so on, are thus called propositional attitudes when they take this sort of content.<ref name=":0">{{cite web|url=http://plato.stanford.edu/entries/propositions/|title=Propositions (Stanford Encyclopedia of Philosophy)|last1=McGrath|first1=Matthew|last2=Frank|first2=Devin|website=Plato.stanford.edu|access-date=2014-06-23}}</ref>

===By Russell===
[[Bertrand Russell]] held that propositions were structured entities with objects and properties as constituents. One important difference between [[Ludwig Wittgenstein]]'s view (according to which a proposition is the set of [[possible world]]s/states of affairs in which it is true) is that on the Russellian account, two propositions that are true in all the same states of affairs can still be differentiated. For instance, the proposition "two plus two equals four" is distinct on a Russellian account from the proposition "three plus three equals six". If propositions are sets of possible worlds, however, then all mathematical truths (and all other necessary truths) are the same set (the set of all possible worlds).{{citation needed|date=November 2014}}

==See also==
{{Portal|Philosophy}}
*[[Categorical proposition]]
*[[Probabilistic proposition]]

==References==
{{Reflist}}

==External links==
*{{Commons category-inline|Propositions}}

{{philosophy of language}}
{{Formal semantics}}
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[[Category:Propositions| ]]
[[Category:Logical expressions]]
[[Category:Philosophy of language]]
[[Category:Semantic units]]
[[Category:Statements]]
[[Category:Syntax (logic)]]
[[Category:Semantics]]
[[Category:Term logic]]
[[Category:Propositional attitudes]]
[[Category:Mathematical logic]]
[[Category:Propositional calculus]]
[[Category:Ontology]]
[[Category:Formal semantics (natural language)]]