Montague Semantics (Stanford Encyclopedia of Philosophy)
First published Mon Nov 7, 2011; substantive revision Wed Apr 14, 2021 Montague semantics is a theory of natural language semantics and of its relation with syntax. It was originally developed by the logician Richard Montague (1930–1971) and subsequently modified and extended by linguists, philosophers, and logicians. The most important features of the theory are its use of model theoretic semanti
Presupposition (Stanford Encyclopedia of Philosophy)
Now consider the following example: (12) If there is a knave, then the knave stole the tarts. Let’s ignore all presupposition triggers in (12) save “the knave”, and show that Strong Kleene predicts that the sentence as a whole does not presuppose that there is a knave. Using Definition 1, it suffices to find at least one model where (12) has a classical truth value, but in which there is no knave.
Liar Paradox (Stanford Encyclopedia of Philosophy)
First published Thu Jan 20, 2011; substantive revision Mon Dec 12, 2016 The first sentence in this essay is a lie. There is something odd about saying so, as has been known since ancient times. To see why, remember that all lies are untrue. Is the first sentence true? If it is, then it is a lie, and so it is not true. Conversely, suppose that it is not true. We (viz., the authors) have said it, an
Sentence Connectives in Formal Logic (Stanford Encyclopedia of Philosophy)
First published Tue May 4, 2010; substantive revision Tue Jan 28, 2020 Natural language sentence-linking words (like “and”, “or”) have traditionally had aspects of their use simulated by corresponding connectives in various systems of formal logic. (In fact we use the word “connective” more generously, so that there don’t have to be two or more sentences linked, allowing us to consider the analogu
Truth Values (Stanford Encyclopedia of Philosophy)
First published Tue Mar 30, 2010; substantive revision Tue Nov 3, 2020 Truth values have been put to quite different uses in philosophy and logic, being characterized, for example, as: primitive abstract objects denoted by sentences in natural and formal languages, abstract entities hypostatized as the equivalence classes of sentences, what is aimed at in judgements, values indicating the degree o
Defaults in Semantics and Pragmatics (Stanford Encyclopedia of Philosophy)
First published Fri Jun 30, 2006; substantive revision Wed May 18, 2022 ‘Default’ can mean many different things in theories of meaning. It is so not only because of the multiplicity of approaches and dimensions from which meaning can be studied but also due to the fact the theoretical landscape is changing swiftly and dynamically. First, there is the dimension of the ongoing debates concerning th
David Lewis (Stanford Encyclopedia of Philosophy)
First published Thu Jul 23, 2009; substantive revision Thu Nov 18, 2021 David Lewis (1941–2001) was one of the most important philosophers of the 20th Century. He made significant contributions to philosophy of language, philosophy of mathematics, philosophy of science, decision theory, epistemology, meta-ethics and aesthetics. In most of these fields he is essential reading; in many of them he is
Quotation (Stanford Encyclopedia of Philosophy)
First published Sat Jul 16, 2005; substantive revision Wed Apr 19, 2023 Starting with Frege, the semantics (and pragmatics) of quotation has received a steady flow of attention over the last one hundred or so years. It has not, however, been subject to the same kind of intense debate and scrutiny as, for example, the semantics of definite descriptions or of propositional attitude verbs. Many philo
Set Theory: Constructive and Intuitionistic ZF (Stanford Encyclopedia of Philosophy)
Note that in IZF the schema of separation is unrestricted. In CZF, Collection is strengthened to compensate for restricted separation. Subset collection is a strengthening of Myhill’s exponentiation axiom, thus substituting for ZF’s Powerset. 4. Constructive Choice Principles When discussing the role of classical set theory as a foundation for mathematics, one usually considers the theory ZFC, tha
Logical Form (Stanford Encyclopedia of Philosophy)
First published Tue Oct 19, 1999; substantive revision Wed Sep 1, 2021 Some inferences are impeccable. Examples like (1–3) illustrate reasoning that cannot lead from true premises to false conclusions. (1) John danced if Mary sang, and Mary sang; so John danced. (2) Every politician is deceitful, and every senator is a politician; so every senator is deceitful. (3) The detective is in the garden;
Propositional Attitude Reports (Stanford Encyclopedia of Philosophy)
First published Wed Feb 16, 2000; substantive revision Thu Feb 14, 2019 Propositional attitude reporting sentences concern cognitive relations people bear to propositions. A paradigm example is the sentence ‘Jill believes that Jack broke his crown’. Arguably, ‘believes, ‘hopes’, and ‘knows’ are propositional attitude verb and, when followed by a clause that includes a full sentence expressing a pr
Reference (Stanford Encyclopedia of Philosophy)
First published Mon Jan 20, 2003; substantive revision Mon Feb 12, 2024 Reference is a relation that obtains between a variety of representational tokens and objects or properties. For instance, when I assert that “Barack Obama is a Democrat,” I use a particular sort of representational token—i.e. the name ‘Barack Obama’—which refers to a particular individual—i.e. Barack Obama. While names and ot
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Justification Logic (Stanford Encyclopedia of Philosophy)
Typelogical Grammar (Stanford Encyclopedia of Philosophy)
Intensional Transitive Verbs (Stanford Encyclopedia of Philosophy)
Structured Propositions (Stanford Encyclopedia of Philosophy)