+1 graphic

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
new file mode 100644
index 0000000..35cd50a
--- /dev/null
+++ b/papers/figures/2-1.pdf