diff options
| -rw-r--r-- | papers/2.tex | 12 | ||||
| -rw-r--r-- | papers/3.tex | 4 | ||||
| -rw-r--r-- | papers/figures/2-1.pdf | bin | 0 -> 116208 bytes |
3 files changed, 7 insertions, 9 deletions
diff --git a/papers/2.tex b/papers/2.tex index 82a2c67..79915af 100644 --- a/papers/2.tex +++ b/papers/2.tex @@ -1,6 +1,8 @@ \chapter{Supervaluationism, Dynamic Supervaluationism, and Higher-Order Vagueness} \chaptermark{Supervaluationism, Dynamic Supervaluationism, and Higher-Order Vagueness} - +\chapterauthor{Wiktor Przybrorwski, \textit{ +University of St Andrews +}} \renewcommand*{\thesection}{\arabic{section}.} \renewcommand*{\thesubsection}{\arabic{section}.\arabic{subsection}.} @@ -255,13 +257,9 @@ true at all precisifications - and by the same reasoning, so is ${D^{*}D}^{*}F$. Therefore, the S4 principle effectively applies to $D^{*}$ (see diagram below). -%\includegraphics[width=3.97674in,height=4.66543in]{media/image1.png} \begin{center} - \begin{tikzpicture} - \node at (0, 0) {\texttt{[GRAPHICS FORTHCOMING]}}; - \end{tikzpicture} - \end{center} - +\includegraphics[width=3.97674in,height=4.66543in]{papers/figures/2-1.pdf} +\end{center} Consequently, Williamson concludes that higher-order vagueness disappears.\footnote{Williamson, \emph{Vagueness}, 160.} This is because, for supervaluationism to succeed, each metalanguage must be diff --git a/papers/3.tex b/papers/3.tex index 6066649..84a52f1 100644 --- a/papers/3.tex +++ b/papers/3.tex @@ -205,7 +205,7 @@ $\forall x (Xx \ba x=y), Haec(X)(z) \wedge z \neq y \vdash Xy \ba y=y \\ \end{quote} Then, from $\vdash Haec(X)(y) \ra Tra(X)(y)$, we can observe that: \\ \begin{quote} -\begin{tabulary}{\textwidth}{Lr} +\begin{tabulary}{\textwidth}{LR} $\vdash \Box Haec(X)(y) \ra \Box Tra(X)(y)$ & (K) \\ $\vdash \Box \forall x (Xx \ba x=y) \ra \Box \Box \forall x (Xx \ba x=y)$ & (\textbf{4})\\ $\vdash Haec(X)(y) \ra \Box Haec(X)(y)$ & (Chaining conditionals) \\ @@ -214,7 +214,7 @@ $\vdash Haec(X)(y) \ra \Box Tra(X)(y)$ & \end{quote} \subsection{The proof for (o-Tracking)} \begin{quote} -\begin{tabulary}{\textwidth}{Lr} +\begin{tabulary}{\textwidth}{LR} $\vdash Haec(X)(o) \ra Tra(X)(o)$ & (Proved above) \\ $\vdash \exists X Haec(X)(o) \ra \exists X Tra(X)(o)$ & (Derivable from $\forall$ rule) \\ $\vdash \Box \exists X Haec(X)(o) \ra \Box \exists X Tra(X)(o)$ & (K)\\ diff --git a/papers/figures/2-1.pdf b/papers/figures/2-1.pdf Binary files differnew file mode 100644 index 0000000..35cd50a --- /dev/null +++ b/papers/figures/2-1.pdf |