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In
logic Logic is an interdisciplinary field which studies truth and reasoning Reason is the capacity of consciously making sense of things, applying logic Logic (from Ancient Greek, Greek: grc, wikt:λογική, λογική, label=none, lit ...

logic
and
linguistics Linguistics is the scientific study of language A language is a structured system of communication used by humans, including speech (spoken language), gestures (Signed language, sign language) and writing. Most languages have a writing ...

linguistics
, a proposition is the meaning of a declarative
sentence Sentence(s) or The Sentence may refer to: Common uses * Sentence (law), the punishment a judge gives to a defendant found guilty of a crime * Sentence (linguistics), a grammatical unit of language * Sentence (mathematical logic), a formula not cont ...
. In
philosophy Philosophy (from , ) is the study of general and fundamental questions, such as those about reason, Metaphysics, existence, Epistemology, knowledge, Ethics, values, Philosophy of mind, mind, and Philosophy of language, language. Such ques ...

philosophy
, "
meaning Meaning most commonly refers to: * Meaning (linguistics), meaning which is communicated through the use of language * Meaning (philosophy), definition, elements, and types of meaning discussed in philosophy * Meaning (non-linguistic), a general ter ...
" is understood to be a non-linguistic entity which is shared by all sentences with the same meaning. Equivalently, a proposition is the non-linguistic bearer of
truth Truth is the property of being in accord with fact or reality.Merriam-Webster's Online Dictionarytruth 2005 In everyday language, truth is typically ascribed to things that aim to represent reality or otherwise correspond to it, such as beliefs ...

truth
or
falsity Deception or falsehood is an act or statement which misleads, hides the truth Truth is the property of being in accord with fact or reality.Merriam-Webster's Online Dictionarytruth 2005 In everyday language, truth is typically ascribed to th ...
which makes any sentence that expresses it either true or false. While the term "proposition" may sometimes be used in everyday language to refer to a linguistic statement which can be either true or false, the technical philosophical term, which differs from the mathematical usage, refers exclusively to the non-linguistic meaning behind the statement. The term is often used very broadly and can also refer to various related concepts, both in the history of philosophy and in contemporary
analytic philosophy Analytic philosophy is a branch and tradition of philosophy Philosophy (from , ) is the study of general and fundamental questions, such as those about reason, Metaphysics, existence, Epistemology, knowledge, Ethics, values, Philosophy o ...
. It can generally be used to refer to some or all of the following: The primary bearers of
truth value In logic Logic (from Ancient Greek, Greek: grc, wikt:λογική, λογική, label=none, lit=possessed of reason, intellectual, dialectical, argumentative, translit=logikḗ)Also related to (''logos''), "word, thought, idea, argument, ...
s (such as "true" and "false"); the objects of
belief A belief is an attitude Attitude may refer to: Philosophy and psychology * Attitude (psychology) In psychology Psychology is the science of mind and behavior. Psychology includes the study of consciousness, conscious and Unconsci ...

belief
and other
propositional attitude A propositional attitude is a mental state held by an agent toward a proposition In logic and linguistics, a proposition is the meaning of a declarative sentence (linguistics), sentence. In philosophy, "Meaning (philosophy), meaning" is understood ...
s (i.e. what is believed, doubted, etc.); the
referent A referent () is a person or thing to which a name – a linguistics, linguistic Phrase, expression or other symbol – reference, refers. For example, in the sentence ''Mary saw me'', the referent of the word ''Mary'' is the particular person calle ...
s of "that"-clauses (e.g. "It is true ''that the sky is blue''" and "I believe ''that the sky is blue''" both involve the proposition ''the sky is blue''); and the
meaning Meaning most commonly refers to: * Meaning (linguistics), meaning which is communicated through the use of language * Meaning (philosophy), definition, elements, and types of meaning discussed in philosophy * Meaning (non-linguistic), a general ter ...
s of declarative sentences. Since propositions are defined as the sharable objects of attitudes and the primary bearers of truth and falsity, this means that the term "proposition" does not refer to particular thoughts or particular utterances (which are not sharable across different instances), nor does it refer to concrete events or facts (which cannot be false).
Propositional logic Propositional calculus is a branch of logic Logic is an interdisciplinary field which studies truth and reasoning Reason is the capacity of consciously making sense of things, applying logic Logic (from Ancient Greek, Greek: grc, ...
deals primarily with propositions and logical relations between them.


Historical usage


By Aristotle

Aristotelian logic In philosophy Philosophy (from , ) is the study of general and fundamental questions, such as those about reason, Metaphysics, existence, Epistemology, knowledge, Ethics, values, Philosophy of mind, mind, and Philosophy of language, langu ...
identifies a
categorical proposition In logic Logic is an interdisciplinary field which studies truth and reasoning Reason is the capacity of consciously making sense of things, applying logic Logic (from Ancient Greek, Greek: grc, wikt:λογική, λογική, label= ...
as a sentence which affirms or denies a
predicate Predicate or predication may refer to: Computer science *Syntactic predicate (in parser technology) guidelines the parser process Linguistics *Predicate (grammar), a grammatical component of a sentence Philosophy and logic * Predication (philo ...
of a subject, optionally with the help of a 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".


By the logical positivists

Often, propositions are related to closed formulae (or logical sentence) to distinguish them from what is expressed by an
open formulaAn open formula is a formula In science Science (from the Latin word ''scientia'', meaning "knowledge") is a systematic enterprise that Scientific method, builds and Taxonomy (general), organizes knowledge in the form of Testability, testabl ...
. In this sense, propositions are "statements" that are
truth-bearer A truth-bearer is an entity Entity may refer to: Computing * Character entity reference, replacement text for a character in HTML or XML * Entity class, a thing of interest within an entity–relationship model or diagram * SGML entity, a prim ...
s. This conception of a proposition was supported by the philosophical school of
logical positivism Logical positivism, later called logical empiricism, and both of which together are also known as neopositivism, was a movement in Western philosophy whose central thesis was the verificationism, verification principle (also known as the verifiab ...
. 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 In linguistics Linguistics is the science, scientific study of language. It encompasses the analysis of every aspect of language, as well as the methods for studying and modeling them. The traditional areas of linguistic analysis include p ...
s present propositions, being inquiries into the
truth value In logic Logic (from Ancient Greek, Greek: grc, wikt:λογική, λογική, label=none, lit=possessed of reason, intellectual, dialectical, argumentative, translit=logikḗ)Also related to (''logos''), "word, thought, idea, argument, ...
of them. On the other hand, some
sign A sign is an object Object may refer to: General meanings * Object (philosophy), a thing, being, or concept ** Entity, something that is tangible and within the grasp of the senses ** Object (abstract), an object which does not exist at ...

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 A belief is an attitude Attitude may refer to: Philosophy and psychology * Attitude (psychology) In psychology Psychology is the science of mind and behavior. Psychology includes the study of consciousness, conscious and Unconsci ...

belief
s and similar 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.


By Russell

Bertrand Russell Bertrand Arthur William Russell, 3rd Earl Russell (18 May 1872 – 2 February 1970) was a British , , , , , , , , and .Stanford Encyclopedia of Philosophy"Bertrand Russell" 1 May 2003 Throughout his life, Russell considered himself a , a and ...
held that propositions were structured entities with objects and properties as constituents. One important difference between
Ludwig Wittgenstein Ludwig Josef Johann Wittgenstein ( ; ; 26 April 1889 – 29 April 1951) was an Austrian Austrian may refer to: * Austrians, someone from Austria or of Austrian descent ** Someone who is considered an Austrian citizen, see Austrian nationali ...

Ludwig Wittgenstein
's view (according to which a proposition is the set of
possible world A possible world is a complete and consistent way the world is or could have been. They are widely used as a formal device in logic Logic is an interdisciplinary field which studies truth and reasoning Reason is the capacity of consciously ...
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).


Relation to the mind

In relation to the mind, propositions are discussed primarily as they fit into
propositional attitudes A propositional attitude is a mental state held by an agent toward a proposition In logic and linguistics, a proposition is the meaning of a declarative sentence (linguistics), sentence. In philosophy, "Meaning (philosophy), meaning" is understood ...
. Propositional attitudes are simply attitudes characteristic of
folk psychology In philosophy of mind Philosophy of mind is a branch of philosophy that studies the ontology and nature of the mind and its relationship with the body. The mind–body problem is a paradigmatic issue in philosophy of mind, although a number of ot ...
(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 Philosophy of mind is a branch of that studies the and nature of the and its relationship with the body. The is a paradigmatic issue in philosophy of mind, although a number of other issues are addressed, such as the and the nature of parti ...

philosophy of mind
and
psychology Psychology is the scientific Science (from the Latin Latin (, or , ) is a classical language belonging to the Italic languages, Italic branch of the Indo-European languages. Latin was originally spoken in the area around Rome, known ...

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
intentional Intentions are mental states A mental state, or a mental property, is a state of mind of a person. Mental states comprise a diverse class including perception, pain experience, belief, desire, intention, emotion, and memory. There is controversy co ...
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
Frege Frege is a surname. Notable people with the surname include: * Carola Frege (born 1965), German scholar *Élodie Frégé, French singer and actress *Gottlob Frege (1848 – 1925), German philosopher, logician, and mathematician. * Livia Fre ...
's view that propositions are
Platonist Platonism is the philosophy Philosophy (from , ) is the study of general and fundamental questions, such as those about reason, Metaphysics, existence, Epistemology, knowledge, Ethics, values, Philosophy of mind, mind, and Philosophy of ...
entities, that is, existing in an abstract, non-physical realm. 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 or properties of thoughts (which could be the same across different thinkers). 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 and externalismInternalism and externalism are two opposing ways of explaining various subjects in several areas of philosophy Philosophy (from , ) is the study of general and fundamental questions, such as those about reason, Metaphysics, existence, Epi ...

internalism and externalism
in philosophy of mind.


Treatment in logic

As noted above, in
Aristotelian logic In philosophy Philosophy (from , ) is the study of general and fundamental questions, such as those about reason, Metaphysics, existence, Epistemology, knowledge, Ethics, values, Philosophy of mind, mind, and Philosophy of language, langu ...
a proposition is a particular kind of sentence (a
declarative sentence In linguistics and grammar, a sentence is a linguistic expression, such as the English example "The quick brown fox jumps over the lazy dog, The quick brown fox ''jumps'' over the lazy dog." In traditional grammar, it is typically defined as a stri ...
) that affirms or denies a
predicate Predicate or predication may refer to: Computer science *Syntactic predicate (in parser technology) guidelines the parser process Linguistics *Predicate (grammar), a grammatical component of a sentence Philosophy and logic * Predication (philo ...
of a subject, optionally with the help of a copula. Aristotelian propositions take forms like "All men are mortal" and "Socrates is a man." Propositions show up in modern formal logic as sentences of a formal language. A formal language begins with different types of symbols. These types can include variables,
operators Operator may refer to: Mathematics * A symbol indicating a mathematical operation * Logical operator or logical connective in mathematical logic * Operator (mathematics), mapping that acts on elements of a space to produce elements of another sp ...
, function symbols, predicate (or relation) symbols,
quantifiers Quantifier may refer to: * Quantifier (linguistics), an indicator of quantity * Quantifier (logic) * Quantification (science) See also

*Quantification (disambiguation) {{disambiguation ...
, and propositional constants.(Grouping symbols such as
delimiter A delimiter is a sequence of one or more Character (computing), characters for specifying the boundary between separate, independent regions in plain text, Expression (mathematics), mathematical expressions or other Data stream, data streams. An ...
s are often added for convenience in using the language, but do not play a logical role.) Symbols are concatenated together according to
recursive Recursion (adjective: ''recursive'') occurs when a thing is defined in terms of itself or of its type. Recursion is used in a variety of disciplines ranging from linguistics Linguistics is the science, scientific study of language. It e ...

recursive
rules, in order to construct strings to which truth-values will be assigned. The rules specify how the operators, function and predicate symbols, and quantifiers are to be concatenated with other strings. A proposition is then a string with a specific form. The form that a proposition takes depends on the type of logic. The type of logic called propositional, sentential, or statement logic includes only operators and propositional constants as symbols in its language. The propositions in this language are propositional constants, which are considered atomic propositions, and composite (or compound) propositions, which are composed by recursively applying operators to propositions. ''Application'' here is simply a short way of saying that the corresponding concatenation rule has been applied. The types of logics called predicate, quantificational, or ''n''-order logic include variables, operators, predicate and function symbols, and quantifiers as symbols in their languages. The propositions in these logics are more complex. First, one typically starts by defining a term as follows: # A variable, or # A function symbol applied to the number of terms required by the function symbol's
arity Arity () is the number of arguments In logic Logic (from Ancient Greek, Greek: grc, wikt:λογική, λογική, label=none, lit=possessed of reason, intellectual, dialectical, argumentative, translit=logikḗ)Also related to (''logo ...
. For example, if ''+'' is a binary function symbol and ''x'', ''y'', and ''z'' are variables, then ''x''+(''y''+''z'') is a term, which might be written with the symbols in various orders. Once a term is defined, a proposition can then be defined as follows: # A predicate symbol applied to the number of terms required by its arity, or # An operator applied to the number of propositions required by its arity, or # A quantifier applied to a proposition. For example, if ''='' is a binary predicate symbol and ''∀'' is a quantifier, then ∀''x'',''y'',''z'' ''x'' = ''y'') → (''x''+''z'' = ''y''+''z'')is a proposition. This more complex structure of propositions allows these logics to make finer distinctions between inferences, i.e., to have greater expressive power. In this context, propositions are also called sentences, statements, statement forms, formulas, and
well-formed formula In mathematical logic Mathematical logic is the study of formal logic within mathematics. Major subareas include model theory, proof theory, set theory, and recursion theory. Research in mathematical logic commonly addresses the mathematical p ...
s, though these terms are usually not synonymous within a single text. This definition treats propositions as
syntactic In linguistics Linguistics is the science, scientific study of language. It encompasses the analysis of every aspect of language, as well as the methods for studying and modeling them. The traditional areas of linguistic analysis includ ...

syntactic
objects, as opposed to
semantic Semantics (from grc, σημαντικός ''sēmantikós'', "significant") is the study of reference Reference is a relationship between objects in which one object designates, or acts as a means by which to connect to or link to, another o ...
or
mental Mental may refer to: * of or relating to the mind Films * Mental (2012 film), ''Mental'' (2012 film), an Australian comedy-drama * Mental (2016 film), ''Mental'' (2016 film), a Bangladeshi romantic-action movie * ''Mental'', a 2008 documentary by ...
objects. That is, propositions in this sense are meaningless, formal, abstract objects. They are assigned meaning and truth-values by mappings called interpretations and valuations, respectively. In
mathematics Mathematics (from Greek: ) includes the study of such topics as numbers (arithmetic and number theory), formulas and related structures (algebra), shapes and spaces in which they are contained (geometry), and quantities and their changes (cal ...
, propositions are often constructed and interpreted in a way similar to that in predicate logic—albeit in a more informal way. For example. an
axiom An axiom, postulate or assumption is a statement that is taken to be , to serve as a or starting point for further reasoning and arguments. The word comes from the Greek ''axíōma'' () 'that which is thought worthy or fit' or 'that which comm ...

axiom
can be conceived as a proposition in the loose sense of the word, though the term is usually used to refer to a proven mathematical statement whose importance is generally neutral by nature. Other similar terms in this category include: *
Theorem In mathematics, a theorem is a statement (logic), statement that has been Mathematical proof, proved, or can be proved. The ''proof'' of a theorem is a logical argument that uses the inference rules of a deductive system to establish that the the ...
(a proven mathematical statement of notable importance) *
Lemma Lemma may refer to: Language and linguistics * Lemma (morphology), the canonical, dictionary or citation form of a word * Lemma (psycholinguistics), a mental abstraction of a word about to be uttered * Headword, under which a set of related dict ...
(a proven mathematical statement whose importance is derived from the theorem it aims to prove) *
Corollary In mathematics Mathematics (from Ancient Greek, Greek: ) includes the study of such topics as quantity (number theory), mathematical structure, structure (algebra), space (geometry), and calculus, change (mathematical analysis, analysis). It h ...
(a proven mathematical statement whose truth readily follows from a theorem). Propositions are called structured propositions if they have constituents, in some broad sense. Assuming a structured view of propositions, one can distinguish between singular propositions (also Russellian propositions, named after
Bertrand Russell Bertrand Arthur William Russell, 3rd Earl Russell (18 May 1872 – 2 February 1970) was a British , , , , , , , , and .Stanford Encyclopedia of Philosophy"Bertrand Russell" 1 May 2003 Throughout his life, Russell considered himself a , a and ...
) which are about a particular individual, general propositions, which are not about any particular individual, and particularized propositions, which are about a particular individual but do not contain that individual as a constituent.


Objections to propositions

Attempts to provide a workable definition of proposition include the following:
Two meaningful declarative sentences express the same proposition, if and only if they mean the same thing.
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:
Two meaningful declarative sentence-tokens express the same proposition, if and only if they mean the same thing.
Unfortunately, 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 First-order logic—also known as predicate logic, quantificational logic, and first-order predicate calculus—is a collection of formal system A formal system is an used for inferring theorems from axioms according to a set of rules. These rul ...
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 Semantics (from grc, σημαντικός ''sēmantikós'', "significant") is the study of reference Reference is a relationship between objects in which one object designates, or acts as a means by which to connect to or link to, another ...
. W. V. Quine, who granted the existence of sets in mathematics, maintained that the indeterminacy of translation prevented any meaningful discussion of propositions, and that they should be discarded in favor of sentences. Strawson, on the other hand, advocated for the use of the term "
statement Statement or statements may refer to: Common uses *Statement (computer science), the smallest standalone element of an imperative programming language *Statement (logic), declarative sentence that is either true or false *Statement, a Sentence_(lin ...
".


See also

*
Categorical proposition In logic Logic is an interdisciplinary field which studies truth and reasoning Reason is the capacity of consciously making sense of things, applying logic Logic (from Ancient Greek, Greek: grc, wikt:λογική, λογική, label= ...
* Main contention * Probabilistic proposition


References


External links

* {{Authority control Logical expressions
Philosophy of languagePhilosophy of language In analytic philosophy, philosophy of language investigates the nature of language A language is a structured system of communication used by humans, including speech (spoken language), gestures (Signed language, sig ...
Semantic units Statements Syntax (logic) Semantics Propositional attitudes Mathematical logic Propositional calculus Ontology Formal semantics (natural language)