From 7c50841fc33c3ce5e65c12bcbc85f11c2af8ba0c Mon Sep 17 00:00:00 2001
From: JJ
Date: Sun, 5 May 2024 16:36:43 -0700
Subject: meow

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 linguistics/semantics.md | 14 +++++++++++---
 1 file changed, 11 insertions(+), 3 deletions(-)

(limited to 'linguistics/semantics.md')

diff --git a/linguistics/semantics.md b/linguistics/semantics.md
index 105a0fd..96bbb17 100644
--- a/linguistics/semantics.md
+++ b/linguistics/semantics.md
@@ -23,16 +23,20 @@ This framework is [first-order/predicate logic](../mathematics/logic) and the [s
 
 ### Predicate Logic & The Lambda Calculus
 
-Formal semantics begets a formal system for such semantics, and *first-order logic* and *the lambda calculus* are a natural fit. As discussed above, language functions by composition - and what are functions but their property of composition?
+Formal semantics begets a formal system for such semantics, and *first-order logic* and *the lambda calculus* are a natural fit. Semantics is the study of meaning - and what is logic but a system for expressing meaning? As discussed above, language functions by composition - and what are functions but their property of composition?
 
-[*An Invitation to Formal Semantics*](https://eecoppock.info/bootcamp/semantics-boot-camp.pdf) covers basic logic and the lambda calculus well in its first six chapters. Otherwise, see [logic](../mathematics/logic), and [lambda-calculus](../plt/lambda-calculus).
+[*An Invitation to Formal Semantics*](https://eecoppock.info/bootcamp/semantics-boot-camp.pdf) covers basic logic and the lambda calculus well in its first six chapters. Otherwise, for a worse introduction, see [logic](../mathematics/logic), and [the lambda calculus](../plt/lambda-calculus).
 
 ## Denotational Semantics
 
-With basic logic and the lambda calculus as our base, we may simply get straight to assigning *meaning* to language.
+With basic logic and the lambda calculus under our belt, we may simply get straight to assigning *meaning* to language. We consider two *basic types* to start: the type of entities, $e$, and the type of truth values, $t$. Our function types we denote by ordered pairs: that is, a function from $e$ to $t$ is of type $⟨e,t⟩$. This is perhaps clunkier notation than the type-theoretic $e→t$, but it is what it is. (And does avoid issues of precedence.)
 
 ### Entities and Functions
 
+> I am Alice.
+> Alice is bad.
+> The blue pigeon flew away.
+
 ### Quantification
 
 ### Reference
@@ -49,6 +53,10 @@ With basic logic and the lambda calculus as our base, we may simply get straight
 
 ### Command, Request, Obligation
 
+> Alice, run!<br>
+> Alice, please run.<br>
+> Alice should run.
+
 ### Questions
 ## Resources
 - ✨ [Invitation to Formal Semantics](https://eecoppock.info/bootcamp/semantics-boot-camp.pdf)
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