The term proposition has a broad use in contemporary analytic
philosophy. It is used to refer to some or all of the following: the
primary bearers of truth-value, the objects of belief and other
"propositional attitudes" (i.e., what is believed, doubted, etc.), the
referents of that-clauses, and the meanings of declarative sentences.
Propositions are the sharable objects of attitudes and the primary
bearers of truth and falsity. This stipulation rules out certain
candidates for propositions, including thought- and utterance-tokens
which are not sharable, and concrete events or facts, which cannot be
1 Historical usage
1.1 By Aristotle
1.2 By the logical positivists
1.3 By Russell
2 Relation to the mind
3 Treatment in logic
4 Objections to propositions
5 See also
Aristotelian logic identifies a proposition as a sentence which
affirms or denies a predicate of a subject with the help of a
'Copula'. An Aristotelian proposition may take the form "All men are
mortal" or "Socrates is a man." In the first example the subject is
"men", predicate is "mortal" and copula is "are". 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 sentences to distinguish them
from what is expressed by an open sentence. In this sense,
propositions are "statements" that are truth-bearers. This conception
of a proposition was supported by the philosophical school of logical
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 of them. On the other hand, some signs 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 beliefs 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, and so on, are thus called propositional attitudes when they
take this sort of content.
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 worlds/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 that two plus two equals four is distinct on
a Russellian account from 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 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 intentional mental states.
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 (see the entry on
internalism and externalism in philosophy of mind).
Treatment in logic
As noted above, in
Aristotelian logic a proposition is a particular
kind of sentence, one which affirms or denies a predicate of a subject
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 objects of a formal
language. 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 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 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
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
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, terms must be defined. A term is
(i) a variable or (ii) a function symbol applied to the number of
terms required by the function symbol's arity. 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. A
proposition is (i) a predicate symbol applied to the number of terms
required by its arity, (ii) an operator applied to the number of
propositions required by its arity, or (iii) 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 formulas, though these
terms are usually not synonymous within a single text. This definition
treats propositions as syntactic objects, as opposed to semantic or
mental 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.
Propositions are called structured propositions if they have
constituents, in some broad sense.
Assuming a structured view of propositions, we can distinguish between
singular propositions (also Russellian propositions, named after
Bertrand Russell) 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
Two meaningful declarative sentences express the same proposition if
and only if they mean the same thing.
thus defining 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
Two meaningful declarative sentence-tokens express the same
proposition if and only if they mean the same thing.
Unfortunately, the above definitions have the result that two
sentences/sentence-tokens which have the same meaning and thus express
the same proposition could have different truth-values, e.g. "I am
Spartacus" said by Spartacus and said by John Smith; and e.g. "It is
Wednesday" said on a Wednesday and on a Thursday.
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
W.V. Quine maintained that the indeterminacy of translation
prevented any meaningful discussion of propositions, and that they
should be discarded in favor of sentences. Strawson advocated the
use of the term "statement".
^ "Propositions (Stanford Encyclopedia of Philosophy)".
Plato.stanford.edu. Retrieved 2014-06-23.
^ Propositions by Matthew McGrath
^ Singular Propositions by Greg Fitch
^ Structured Propositions by Jeffrey C. King
^ Quine, W. V. (1970). Philosophy of Logic. NJ USA: Prentice-Hall.
pp. 1–14. ISBN 0-13-663625-X.
Philosophy of language
Gottfried Wilhelm Leibniz
Wilhelm von Humboldt
Ferdinand de Saussure
Benjamin Lee Whorf
J. L. Austin
A. J. Ayer
G. E. M. Anscombe
P. F. Strawson
Willard Van Orman Quine
Causal theory of reference
Contrast theory of meaning
Descriptivist theory of names
Direct reference theory
Mediated reference theory
Theory of descriptions
Principle of compositionality
Sense and reference
Philosophy of information