A proposition is a central concept in
semantics
Semantics (from grc, σημαντικός ''sēmantikós'', "significant") is the study of reference, meaning, or truth. The term can be used to refer to subfields of several distinct disciplines, including philosophy
Philosophy (f ...
,
logic
Logic is the study of correct reasoning. It includes both formal and informal logic. Formal logic is the science of deductively valid inferences or of logical truths. It is a formal science investigating how conclusions follow from premises ...
,
philosophy of language
In analytic philosophy, philosophy of language investigates the nature of language and the relations between language, language users, and the world. Investigations may include inquiry into the nature of meaning, intentionality, reference, ...
and related fields, often characterized as the primary
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 ...
or
falsity
Deception or falsehood is an act or statement that misleads, hides the truth, or promotes a belief, concept, or idea that is not true. It is often done for personal gain or advantage. Deception can involve dissimulation, propaganda and sleight o ...
. Propositions are also often characterized as being the kind of thing that
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." In traditional grammar, it is typically defined as a string of words that expresses a complete thought, ...
s
denote
In linguistics and philosophy, the denotation of an expression is its literal meaning. For instance, the English word "warm" denotes the property of being warm. Denotation is contrasted with other aspects of meaning including connotation. For insta ...
. For instance the sentence "The sky is blue" denotes the proposition that the sky is blue. However, crucially, propositions are not themselves
linguistic expressions. For instance, the
English
English usually refers to:
* English language
* English people
English may also refer to:
Peoples, culture, and language
* ''English'', an adjective for something of, from, or related to England
** English national ide ...
sentence "Snow is white" denotes the same proposition as the
German
German(s) may refer to:
* Germany (of or related to)
**Germania (historical use)
* Germans, citizens of Germany, people of German ancestry, or native speakers of the German language
** For citizens of Germany, see also German nationality law
**Ger ...
sentence "Schnee ist weiß" even though the two sentences are not the same. Similarly, propositions can also be characterized as the objects of
belief
A belief is an attitude that something is the case, or that some proposition is true. In epistemology, philosophers use the term "belief" to refer to attitudes about the world which can be either true or false. To believe something is to take i ...
and other
propositional attitude
A propositional attitude is a mental state held by an agent toward a proposition.
Linguistically, propositional attitudes are denoted by a verb (e.g. "believed") governing an embedded "that" clause, for example, 'Sally believed that she had won ...
s. For instance if one believes that the sky is blue, what one believes is the proposition that the sky is blue. A proposition can also be thought of as a kind of
idea
In common usage and in philosophy, ideas are the results of thought. Also in philosophy, ideas can also be mental representational images of some object. Many philosophers have considered ideas to be a fundamental ontological category of being ...
: Collins Dictionary has a definition for ''proposition'' as "a statement or an idea that people can consider or discuss whether it is true."
Formally, propositions are often modeled as
functions which map a
possible world
A possible world is a complete and consistent way the world is or could have been. Possible worlds are widely used as a formal device in logic, philosophy, and linguistics in order to provide a semantics for intensional logic, intensional and mod ...
to a
truth value
In logic and mathematics, a truth value, sometimes called a logical value, is a value indicating the relation of a proposition to truth, which in classical logic has only two possible values (''true'' or '' false'').
Computing
In some progr ...
. For instance, the proposition that the sky is blue can be modeled as a function which would return the truth value
if given the actual world as input, but would return
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
Logic is the study of correct reasoning. It includes both formal and informal logic. Formal logic is the science of deductively valid inferences or of logical truths. It is a formal science investigating how conclusions follow from premises ...
,
linguistics
Linguistics is the scientific study of human language. It is called a scientific study because it entails a comprehensive, systematic, objective, and precise analysis of all aspects of language, particularly its nature and structure. Linguis ...
,
philosophy of language
In analytic philosophy, philosophy of language investigates the nature of language and the relations between language, language users, and the world. Investigations may include inquiry into the nature of meaning, intentionality, reference, ...
, and related disciplines. Some researchers have doubted whether a consistent definition of propositionhood is possible,
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.
Historical usage
By Aristotle
Aristotelian logic
In philosophy, term logic, also known as traditional logic, syllogistic logic or Aristotelian logic, is a loose name for an approach to formal logic that began with Aristotle and was developed further in ancient history mostly by his followers, t ...
identifies a
categorical proposition
In logic, a categorical proposition, or categorical statement, is a proposition that asserts or denies that all or some of the members of one category (the ''subject term'') are included in another (the ''predicate term''). The study of arguments ...
as a sentence which affirms or denies a
predicate
Predicate or predication may refer to:
* Predicate (grammar), in linguistics
* Predication (philosophy)
* several closely related uses in mathematics and formal logic:
**Predicate (mathematical logic)
**Propositional function
**Finitary relation, o ...
of a
subject
Subject ( la, subiectus "lying beneath") may refer to:
Philosophy
*''Hypokeimenon'', or ''subiectum'', in metaphysics, the "internal", non-objective being of a thing
**Subject (philosophy), a being that has subjective experiences, subjective cons ...
, 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 formula An open formula is a formula that contains at least one free variable.
An open formula does not have a truth value assigned to it, in contrast with a closed formula which constitutes a proposition and thus can have a truth value like ''true'' or ' ...
. In this sense, propositions are "statements" that are
truth-bearer
A truth-bearer is an entity that is said to be either true or false and nothing else. The thesis that some things are true while others are false has led to different theories about the nature of these entities. Since there is divergence of o ...
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, is a movement in Western philosophy whose central thesis was the verification principle (also known as the verifiability criterion o ...
.
Some philosophers argue that some (or all) kinds of speech or actions besides the declarative ones also have propositional content. For example,
yes–no questions present propositions, being inquiries into the
truth value
In logic and mathematics, a truth value, sometimes called a logical value, is a value indicating the relation of a proposition to truth, which in classical logic has only two possible values (''true'' or '' false'').
Computing
In some progr ...
of them. On the other hand, some
sign
A sign is an object, quality, event, or entity whose presence or occurrence indicates the probable presence or occurrence of something else. A natural sign bears a causal relation to its object—for instance, thunder is a sign of storm, or me ...
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 that something is the case, or that some proposition is true. In epistemology, philosophers use the term "belief" to refer to attitudes about the world which can be either true or false. To believe something is to take i ...
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 mathematician, philosopher, logician, and public intellectual. He had a considerable influence on mathematics, logic, set theory, linguistics, ...
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-British philosopher who worked primarily in logic, the philosophy of mathematics, the philosophy of mind, and the philosophy of language. He is considere ...
'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. Possible worlds are widely used as a formal device in logic, philosophy, and linguistics in order to provide a semantics for intensional logic, intensional and mod ...
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. 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
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 other issues are addre ...
and
psychology
Psychology is the scientific study of mind and behavior. Psychology includes the study of conscious and unconscious phenomena, including feelings and thoughts. It is an academic discipline of immense scope, crossing the boundaries betwe ...
, 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 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
Friedrich Ludwig Gottlob Frege (; ; 8 November 1848 – 26 July 1925) was a German philosopher, logician, and mathematician. He was a mathematics professor at the University of Jena, and is understood by many to be the father of analytic phil ...
's view that propositions are
Platonist 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 externalism
Internalism and externalism are two opposite ways of integration of explaining various subjects in several areas of philosophy. These include human motivation, knowledge, justification, meaning, and truth. The distinction arises in many areas of de ...
in philosophy of mind.
Treatment in logic
Aristotelian logic
As noted above, in
Aristotelian logic
In philosophy, term logic, also known as traditional logic, syllogistic logic or Aristotelian logic, is a loose name for an approach to formal logic that began with Aristotle and was developed further in ancient history mostly by his followers, t ...
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." In traditional grammar, it is typically defined as a string of words that expresses a complete thought, ...
) that affirms or denies a
predicate
Predicate or predication may refer to:
* Predicate (grammar), in linguistics
* Predication (philosophy)
* several closely related uses in mathematics and formal logic:
**Predicate (mathematical logic)
**Propositional function
**Finitary relation, o ...
of a
subject
Subject ( la, subiectus "lying beneath") may refer to:
Philosophy
*''Hypokeimenon'', or ''subiectum'', in metaphysics, the "internal", non-objective being of a thing
**Subject (philosophy), a being that has subjective experiences, subjective cons ...
, optionally with the help of a
copula.
Aristotelian propositions take forms like "All men are mortal" and "Socrates is a man."
Syntactic characterization
In modern logic, the term "proposition" is often used for sentences of a formal language. In this usage, propositions are formal
syntactic
In linguistics, syntax () is the study of how words and morphemes combine to form larger units such as phrases and sentences. Central concerns of syntax include word order, grammatical relations, hierarchical sentence structure (constituency), ...
objects which can be studied independently of the meaning they would receive from a
semantics
Semantics (from grc, σημαντικός ''sēmantikós'', "significant") is the study of reference, meaning, or truth. The term can be used to refer to subfields of several distinct disciplines, including philosophy
Philosophy (f ...
. Propositions are also called sentences, statements, statement forms, formulas, and
well-formed formula
In mathematical logic, propositional logic and predicate logic, a well-formed formula, abbreviated WFF or wff, often simply formula, is a finite sequence of symbols from a given alphabet that is part of a formal language. A formal language can be ...
s, though these terms are usually not synonymous within a single text.
A formal language begins with different types of symbols. These types can include
variables,
operators,
function symbols,
predicate (or relation) symbols,
quantifiers, and
propositional constants.(Grouping symbols such as
delimiter
A delimiter is a sequence of one or more characters for specifying the boundary between separate, independent regions in plain text, mathematical expressions or other data streams. An example of a delimiter is the comma character, which acts a ...
s are often added for convenience in using the language, but do not play a logical role.) Symbols are
concatenated together according to
recursive rules, in order to construct strings to which
truth-values
In logic and mathematics, a truth value, sometimes called a logical value, is a value indicating the relation of a proposition to truth, which in classical logic has only two possible values (''true'' or '' false'').
Computing
In some progra ...
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 or operands taken by a function, operation or relation in logic, mathematics, and computer science. In mathematics, arity may also be named ''rank'', but this word can have many other meanings in mathematics. In ...
.
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.
Semantic characterization
Propositions are standardly understood semantically as
functions which take a
possible world
A possible world is a complete and consistent way the world is or could have been. Possible worlds are widely used as a formal device in logic, philosophy, and linguistics in order to provide a semantics for intensional logic, intensional and mod ...
and return a truth value. For example, the proposition that the sky is blue could be represented as a function notated as
. Then if there is a possible world
where the sky is blue and another world
where it is not, we would have that
and
. Via the notion of a
characteristic set, propositions can be modeled equivalently as a set of possible worlds, namely those where the proposition is true. For instance, if
and
are the only worlds in which the sky is blue, the proposition that the sky is blue could be modeled as the set
.
Numerous refinements and alternative notions of proposition-hood have been proposed including
inquisitive propositions and structured propositions.
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 mathematician, philosopher, logician, and public intellectual. He had a considerable influence on mathematics, logic, set theory, linguistics, ...
) 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.
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
Ambiguity is the type of meaning in which a phrase, statement or resolution is not explicitly defined, making several interpretations plausible. A common aspect of ambiguity is uncertainty. It is thus an attribute of any idea or statement ...
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
Semantics (from grc, σημαντικός ''sēmantikós'', "significant") is the study of reference, meaning, or truth. The term can be used to refer to subfields of several distinct disciplines, including philosophy
Philosophy (f ...
.
W. V. Quine
Willard Van Orman Quine (; known to his friends as "Van"; June 25, 1908 – December 25, 2000) was an American philosopher and logician in the analytic tradition, recognized as "one of the most influential philosophers of the twentieth century". ...
, 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.
P. F. Strawson
Peter Frederick Strawson (; 23 November 1919 – 13 February 2006) was an English philosopher. He was the Waynflete Professor of Metaphysical Philosophy at the University of Oxford (Magdalen College) from 1968 to 1987. Before that, he w ...
, on the other hand, advocated for the use of the term "
statement".
See also
*
Categorical proposition
In logic, a categorical proposition, or categorical statement, is a proposition that asserts or denies that all or some of the members of one category (the ''subject term'') are included in another (the ''predicate term''). The study of arguments ...
*Main contention
*
Probabilistic proposition
A probabilistic proposition is a proposition with a measured probability
Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The p ...
References
External links
*
{{Authority control
Logical expressions
Philosophy of language
Semantic units
Statements
Syntax (logic)
Semantics
Propositional attitudes
Mathematical logic
Propositional calculus
Ontology
Formal semantics (natural language)