In the branch of linguistics known as pragmatics, a presupposition (or PSP) is an implicit assumption about the world or background belief relating to an utterance whose truth is taken for granted in discourse. Examples of presuppositions include:
Jane no longer writes fiction.
Presupposition: Jane once wrote fiction.
Have you stopped eating meat?
Presupposition: you had once eaten meat.
Have you talked to Hans?
Presupposition: Hans exists.
A presupposition must be mutually known or assumed by the speaker and addressee for the utterance to be considered appropriate in context. It will generally remain a necessary assumption whether the utterance is placed in the form of an assertion, denial, or question, and can be associated with a specific lexical item or grammatical feature (presupposition trigger) in the utterance.
Crucially, negation of an expression does not change its presuppositions: I want to do it again and I don't want to do it again both presuppose that the subject has done it already one or more times; My wife is pregnant and My wife is not pregnant both presuppose that the subject has a wife. In this respect, presupposition is distinguished from entailment and implicature. For example, The president was assassinated entails that The president is dead, but if the expression is negated, the entailment is not necessarily true.
If presuppositions of a sentence are not consistent with the actual state of affairs, then one of two approaches can be taken. Given the sentences My wife is pregnant and My wife is not pregnant when one has no wife, then either:
Both the sentence and its negation are false; or
Strawson's approach: Both "my wife is pregnant" and "my wife is not pregnant" use a wrong presupposition (i.e. that there exists a referent which can be described with the noun phrase my wife) and therefore can not be assigned truth values.
Bertrand Russell tries to solve this dilemma with two interpretations of the negated sentence:
"There exists exactly one person, who is my wife and who is not pregnant"
"There does not exist exactly one person, who is my wife and who is pregnant.
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Dynamic semantics is a framework in logic and natural language semantics that treats the meaning of a sentence as its potential to update a context. In static semantics, knowing the meaning of a sentence amounts to knowing when it is true; in dynamic semantics, knowing the meaning of a sentence means knowing "the change it brings about in the information state of anyone who accepts the news conveyed by it." In dynamic semantics, sentences are mapped to functions called context change potentials, which take an input context and return an output context.
Linguistic entailments are entailments which arise in natural language. If a sentence A entails a sentence B, sentence A cannot be true without B being true as well. For instance, the English sentence "Pat is a fluffy cat" entails the sentence "Pat is a cat" since one cannot be a fluffy cat without being a cat. On the other hand, this sentence does not entail "Pat chases mice" since it is possible (if unlikely) for a cat to not chase mice. Entailments arise from the semantics of linguistic expressions.
Logic is the study of correct reasoning. It includes both formal and informal logic. Formal logic is the science of deductively valid inferences or logical truths. It studies how conclusions follow from premises due to the structure of arguments alone, independent of their topic and content. Informal logic is associated with informal fallacies, critical thinking, and argumentation theory. It examines arguments expressed in natural language while formal logic uses formal language.