Proposition

propositionspropositionalclaimlogical propositionstatementsmathematical statementstatement inquisitive propositionassumptionsclaims
A proposition is a tentative and conjectural relationship between constructs that is stated in a declarative form.wikipedia
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Analytic philosophy

Analyticanalytic philosopheranalytical philosophy
The term proposition has a broad use in contemporary analytic philosophy.
The principle that the logical clarification of thoughts can be achieved only by analysis of the logical form of philosophical propositions. The logical form of a proposition is a way of representing it (often using the formal grammar and symbolism of a logical system), to reduce it to simpler components if necessary, and to display its similarity with all other propositions of the same type. However, analytic philosophers disagree widely about the correct logical form of ordinary language.

Truth-bearer

truthbearerprimary bearerstruth bearer
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.
Truth-bearer candidates include propositions, sentences, sentence-tokens, statements, concepts, beliefs, thoughts, intuitions, utterances, and judgements but different authors exclude one or more of these, deny their existence, argue that they are true only in a derivative sense, assert or assume that the terms are synonymous,

Truth

truetheory of truthtruth theory
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.
Logic is concerned with the patterns in reason that can help tell us if a proposition is true or not.

Term logic

scholastic logicAristotelian logictraditional logic
Aristotelian logic identifies a proposition as a sentence which affirms or denies a predicate of a subject with the help of a 'Copula'.
The fundamental assumption behind the theory is that propositions are composed of two terms – hence the name "two-term theory" or "term logic" – and that the reasoning process is in turn built from propositions:

Predicate (mathematical logic)

predicatepredicatespredication
Aristotelian logic identifies a proposition as a sentence which affirms or denies a predicate of a subject with the help of a 'Copula'.
Here, P(x) is referred to as the predicate, and x the placeholder of the proposition.

Truth value

truth-valuelogical valuetruth values
For example, yes–no questions present propositions, being inquiries into the truth value of them.
In logic and mathematics, a truth value, sometimes called a logical value, is a value indicating the relation of a proposition to truth.

Propositional attitude

propositional attitudesattitudesattitude
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.
A propositional attitude is a mental state held by an agent toward a proposition.

Logical positivism

logical positivistslogical positivistlogical empiricism
This conception of a proposition was supported by the philosophical school of logical positivism.
Concerning statements, the analytic is true via terms' arrangement and meanings, thus a tautology—true by logical necessity but uninformative about the world—whereas the synthetic adds reference to a state of facts, a contingency.

Propositional calculus

propositional logicpropositionalsentential logic
These types can include variables, operators, function symbols, predicate (or relation) symbols, quantifiers, and propositional constants.
It is also called propositional logic, statement logic, sentential calculus, sentential logic, or sometimes zeroth-order logic. It deals with propositions (which can be true or false) and argument flow.

Free variables and bound variables

free variablesbound variablebound
These types can include variables, operators, function symbols, predicate (or relation) symbols, quantifiers, and propositional constants.
However, it could be confusing to use the same letter again elsewhere in some compound proposition.

Sentence (mathematical logic)

sentencesentencesclosed formula
Often propositions are related to closed sentences to distinguish them from what is expressed by an open sentence. 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.
Proposition

Willard Van Orman Quine

QuineW. V. O. QuineW. V. Quine
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.
His major writings include Two Dogmas of Empiricism (1951), which attacked the distinction between analytic and synthetic propositions and advocated a form of semantic holism, and Word and Object (1960), which further developed these positions and introduced Quine's famous indeterminacy of translation thesis, advocating a behaviorist theory of meaning.

Semantics

semanticsemanticallymeaning
This definition treats propositions as syntactic objects, as opposed to semantic or mental objects.
factors internal to language, such as the problem of resolving indexical or anaphora (e.g. this x, him, last week). In these situations context serves as the input, but the interpreted utterance also modifies the context, so it is also the output. Thus, the interpretation is necessarily dynamic and the meaning of sentences is viewed as contexts changing potentials instead of propositions.

Statement (logic)

statementsstatement
Strawson advocated the use of the term "statement".
Philosopher of language, Peter Strawson advocated the use of the term "statement" in sense (b) in preference to proposition.

Inductive reasoning

inductioninductiveinductive logic
Propositions are generally derived based on logic (deduction) or empirical observations (induction).

Belief

beliefsreligious beliefbelief system
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.

Referent

referentsco-referreference
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.

Meaning (linguistics)

meaninglinguistic meaningmeanings
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.

Sentence (linguistics)

sentencesentencesdeclarative sentence
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.

Subject (grammar)

subjectsubjectsgrammatical subject
Aristotelian logic identifies a proposition as a sentence which affirms or denies a predicate of a subject with the help of a 'Copula'.

Open formula

open sentencelogical satisfaction
Often propositions are related to closed sentences to distinguish them from what is expressed by an open sentence.

Yes–no question

yes-no questionyes/no questionpolar question
For example, yes–no questions present propositions, being inquiries into the truth value of them.

Semiotics

semioticsemioticiansemiology
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.

Bertrand Russell

RussellRussell, Bertrand16 Questions on the Assassination
Bertrand Russell held that propositions were structured entities with objects and properties as constituents.

Ludwig Wittgenstein

WittgensteinWittgensteinianCount of Wittgenstein
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.