65 lines
2.4 KiB
TeX
65 lines
2.4 KiB
TeX
% File: 13-09-2021.tex
|
|
% Created: 10:11:31 Mon, 13 Sep 2021 EDT
|
|
% Last Change: 10:11:31 Mon, 13 Sep 2021 EDT
|
|
%
|
|
\documentclass[letterpaper]{article}
|
|
\usepackage{amsmath}
|
|
\usepackage{graphicx}
|
|
\usepackage{cancel}
|
|
\usepackage{amssymb}
|
|
\usepackage{listings}
|
|
\usepackage[shortlabels]{enumitem}
|
|
\usepackage{lipsum}
|
|
\usepackage{soul}
|
|
\usepackage{geometry}
|
|
|
|
\geometry{portrait, margin=1in}
|
|
|
|
\date{09/13/2021}
|
|
\title{%
|
|
Notes\\
|
|
\large PHIL-205-01:Symbolic Logic}
|
|
\author{Blizzard MacDougall}
|
|
\begin{document}
|
|
\maketitle
|
|
\pagenumbering{arabic}
|
|
If we keep the concept of truth minimal, all will be fine.\\
|
|
|
|
|
|
There's three main theories on how to expand the definition of truth.
|
|
\begin{enumerate}
|
|
\item Correspondence Theory\\
|
|
"p" is true iff it corresponds to the facts.
|
|
\item Coherence Theory\\
|
|
"p" is true iff p coheres with the rest of our beliefs.\\
|
|
Don't mess with this one.
|
|
\item Epistemic Theories/Provability Theory\\
|
|
"p" is true iff p is provable, knowable.
|
|
\item Pragmatic Theory\\
|
|
"p" is true iff the belief that p works is durable, dependable, in the long run.
|
|
\item Deflationism/Minimalism\\
|
|
"p" is true iff p
|
|
\end{enumerate}
|
|
|
|
Theories of truth don't go too far. It doesn't correspond to science, it can't. There's some things you just have to experiment with.\\
|
|
|
|
Picking up from where we left off\dots \\
|
|
Translation time!\\
|
|
|
|
$\forall x(Dx\implies Kx)$ = For all x, if it's a doctor, then it is kind. = All doctors are kind.\\
|
|
|
|
Usually, the universal quantifier goes with a conditional $\implies$, and the existential quantifier goes with a conjunction $\land$. Not \emph{every} time, but this is where you should start.\\
|
|
$\forall x(Sx\implies Px)$ (all students will pass the course)\\
|
|
NOT $\forall x(Sx\land Px)$ (everything is a student who will pass the course)\\
|
|
$\exists x(Sx\land Px)$ (some things, given that they are students, will pass the course)\\
|
|
NOT $\exists x(Sx\implies Px)$ (there are some things such that if its a student, it will pass the course [This will sometimes be true at the same time as the other, but not always])\\
|
|
|
|
Parentheses are essential.\\
|
|
$\forall x(Dx\implies Kx)$ = Every doctor is kind.\\
|
|
$\forall xDx\implies Kx)$ = Everything is a doctor, and x is kind.\\
|
|
|
|
Domains of $\forall x$ need to be explicit. Otherwise, one can assume the domain is the universe.\\
|
|
|
|
"Syncategorematic adjectives" are adjectives that functions differently in the context. i.e. "expectant" in "expectant mother" is syncategorematic.
|
|
|
|
\end{document}
|