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diff --git a/ling/semantics.md b/ling/semantics.md index 747d9c3..15e4227 100644 --- a/ling/semantics.md +++ b/ling/semantics.md @@ -3,18 +3,87 @@ layout: linguistics title: linguistics/semantics --- -# notes on semantics +# semantics and pragmatics + +>! These notes are **incomplete**! Proceed with caution, or better yet, not at all. Semantics is the study of **meaning**. -How do we know what sentences are true and which are false?<br> +How do we know what sentences are *true* and which are *false*?<br> What does it *mean* for a sentence to be true?<br> -What conditions must hold for a sentence to be true? - -Formal semantics attempts to answer those questions by providing a *framework* for determining what *conditions* must hold for a sentence to be true. - -This framework is [first-order/predicate logic](../math/logic) and the [simply-typed lambda calculus](../plt/lambda-calculus). On top of this, we often build set theory, relying on *characteristic functions* of the lambda calculus as denotations of *set membership*. - +What *conditions* must hold for a sentence to be true? + +<br> + +<details> +<summary>table of contents</summary> + +- History +- Prerequisites +- Basic Principles + - Compositionality + - Substitution + - Predicate Logic & The Lambda Calculus +- Denotational Semantics + - Entities and Functions + - Quantification + - Reference + - Numbers and Plurality + - Event Semantics + - Situation Semantics +- Possible Worlds + - Necessity and Possibility + - Knowledge and Belief + - Command, Request, and Obligation + - Drawing Distinctions + - Tense and Aspect +- Beyond Truth + - Intuitionistic Logic + - Questions + - Utterances +- Pragmatics + - Impliciture + - Presupposition + - Performative Acts +- Lexical Semantics + +</details> + + +## History + +> the dirty secret of semantics is that 2/3rds of it was created by philosophers +> and the remaining third is angelika kratzer +> +> -- partialorder + +Modern approaches to semantics largely fell out of historical work in logic... +- c.i. lewis +- paul grice +- richard montague +- irene heim +- angelika kratzer +- judith butler + +## Prerequisites + +Formal semantics builds atop a bevy of concepts in formal logic. +Comfortability with the following concepts will be assumed: +- object languages and meta languages +- zeroth-order/propositional logic +- first-order/predicate logic +- the lambda calculus +- simple types +- logical models +- modal logic + - possible worlds + - accessibility relations +- second-order/higher-order logic +- intuitionistic logic + +If this is not the case, there are a variety of wonderful resources for learning such topics. I am partial to *An Introduction to Non-Standard Logics* myself, and think it gives a good, syntactic motivation for possible worlds and accessibility relations. I have heard praise for *Boxes and Diamonds* (which is free and open!) but have yet to look at it myself. Wikipedia is also a wonderful reference. Best of all, however, is finding yourself a friend who is a nerd about logic! (thanks alex) + +$$∧ ∨ + × ⊕ ↑ ↓ ∼ ¬ ⇁ → ⇒ ⊃ ⊐ ⥽ > ⊢ ⊨$$ ## Basic Principles @@ -39,7 +108,7 @@ With basic logic and the lambda calculus under our belt, we may simply get strai ### Entities and Functions > *I am Alice.* <br> -> *Alice is bad.* <br> +> *Alice is pretty.* <br> > *The blue pigeon flew away.* - Noun: $⟨e,t⟩ ↝ λx.Noun(x)$ |