From da4c2f772d5b8b9ad6a4f5e384edd919f1bee214 Mon Sep 17 00:00:00 2001
From: phoebe jenkins <pjenkins@tula-health.com>
Date: Fri, 23 Aug 2024 02:56:50 -0400
Subject: header structure for esthetics, para-science, re-include and fix post
formalism
---
essays/post_formalism_memories.tex | 18 ++++++++++++++----
1 file changed, 14 insertions(+), 4 deletions(-)
(limited to 'essays/post_formalism_memories.tex')
diff --git a/essays/post_formalism_memories.tex b/essays/post_formalism_memories.tex
index 73477a5..0c867a2 100644
--- a/essays/post_formalism_memories.tex
+++ b/essays/post_formalism_memories.tex
@@ -3,8 +3,12 @@
\chapter{Post-Formalism in Constructed Memories}
+
\section{Post-Formalist Mathematics}
+\fancyhead{} \fancyfoot{} \fancyfoot[LE,RO]{\thepage}
+\fancyhead[LE]{\textsc{Post-Formalism in Constructed Memories}} \fancyhead[RO]{\textit{Post-Formalist Mathematics}}
+
Over the last hundred years, a philosophy of pure mathematics has
grown up which I prefer to call \enquote{formalism.} As Willard Quine says in the
fourth section of his essay "Carnap and Logical Truth,' formalism was
@@ -22,14 +26,18 @@ innovations.
The formalist position goes as follows. Pure mathematics is the
manipulation of the meaningless and arbitrary, but typographically
-well-defined ink-shapes on paper `$w$,' `$x$,' `$y$,' `$z$,' `$'$,' `$($,' `$)$,' `$\downarrow$,' and `$\in$.'
-These shapes are manipulated according to arbitrary but well-detined
+well-defined ink-shapes on paper
+`$w$,' `$x$,' `$y$,' `$z$,'
+`\texttt{'},'
+`$($,' `$)$,'
+`$\downarrow$,' and `$\in$.'
+These shapes are manipulated according to arbitrary but well-defined
mechanical rules. Actually, the rules mimic the structure of primitive
systems such as Euclid's geometry. There are formation rules, mechanical
definitions of which concatenations of shapes are \enquote{\term{sentences}.} One sentence
is `$((x) (x\in x) \downarrow (x) (x\in x))$.' There are transformation rules, rules for the
mechanical derivation of sentences from other sentences. The best known
-trasformation rule is the rule that $\psi$ may be concluded from $\varphi$ and
+transformation rule is the rule that $\psi$ may be concluded from $\varphi$ and
$\ulcorner \varphi \supset \psi \urcorner$;
where `$\supset$' is the truth-functional conditional. For later convenience, I will
say that $\varphi$ and $\ulcorner \varphi \supset \psi \urcorner$ are \enquote{\term{impliors},}
@@ -406,6 +414,7 @@ beyond the reach of past mathematics.
\clearpage
\section{Constructed Memory Systems}
+\fancyhead[LE]{\textsc{Post-Formalism in Constructed Memories}} \fancyhead[RO]{\textit{2. Constructed Memory Systems}}
In order to understand this section, it is necessary to be thoroughly
familiar with \essaytitle{Studies in Constructed Memories,} the essay following this
@@ -669,7 +678,8 @@ Knows What's Going On.} One just has to guess whether this system exists,
and if it does what it is like.\editornote{The appendix contains a presentation of this work.} The preceding remark is the
metametamathematical description, or definition, of the system.
-\subsection{Epilogue}
+\section{Epilogue}
+\fancyhead[LE]{\textsc{Post-Formalism in Constructed Memories}} \fancyhead[RO]{\textit{3. Epilogue}}
Ever since Carnap's Principle of Tolerance opened the floodgates to
arbitrariness in mathematics, we have been faced with the prospect of a
--
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