From 022def0093b2674ea6240b730014f8323a726dcd Mon Sep 17 00:00:00 2001
From: grr <grr@lo2.org>
Date: Sat, 25 May 2024 18:47:44 -0400
Subject: some fixes to concept art

---
 essays/concept_art.tex | 104 +++++++++++++++++++++++--------------------------
 1 file changed, 48 insertions(+), 56 deletions(-)

(limited to 'essays/concept_art.tex')

diff --git a/essays/concept_art.tex b/essays/concept_art.tex
index 79247a6..e46d55c 100644
--- a/essays/concept_art.tex
+++ b/essays/concept_art.tex
@@ -1,24 +1,22 @@
-\chapter{Concept Art}
-{ \raggedleft (1961) \par }
-
+\chapter{Concept Art (1961)}
 
 Concept art is first of all an art of which the material is concepts, as the 
 material of e.g. music is sound. Since concepts are closely bound up with 
 language, concept art is a kind of art of which the material is language. That 
-is, unlike e.g. a work of music, in which the music proper (as opposed to 
+is, unlike e.g.\ a work of music, in which the music proper (as opposed to 
 notation, analysis, etc.) is just sound, concept art proper will involve 
 language. From the philosophy of language, we learn that a concept may as 
 well be thought of as the intension of a name; this is the relation between 
 concepts and language.\footnote{The extension of the word 'table' is all 
 existing tables; the intension of 'table' is all possible instances of a table.}
 The notion of a concept is a vestige of the notion of 
-a platonic form (the thing which e.g. all tables have in common: tableness), 
+a platonic form (the thing which e.g.\ all tables have in common: tableness), 
 which notion is replaced by the notion of a name objectively, metaphysically 
 related to its intension (so that all tables now have in common their 
 objective relation to table). Now the claim that there can be an objective 
 relation between a name and its intension is wrong, and (the word) concept, 
-as commonly used now, can be discredited (see my book, Philosophy 
-Proper). If, however, it is enough for one that there be a subjective relation 
+as commonly used now, can be discredited (see \essaytitle{Philosophy 
+Proper}). If, however, it is enough for one that there be a subjective relation 
 between a name and its intension, namely the unhesitant decision as to the 
 way one wants to use the name, the unhesitant decisions to affirm the names 
 of some things but not others, then concept is valid language, and concept 
@@ -29,10 +27,10 @@ concepts? This question can best be answered by telling where concept art
 came from; I developed it in an attempt to straighten out certain traditional 
 activities generally regarded as aesthetic. The first of these is structure art, 
 music, visual art, etc., in which the important thing is \enquote{structure.} My 
-definitive discussion of structure art is in my unpublished essay \essaytitle{Structure 
+definitive discussion of structure art is in my unpublished\editornote{We provide this for you in the appendix!} essay \essaytitle{Structure 
 Art and Pure Mathematics}; here I will just summarize that discussion. Much 
-structure art is a vestige of the time when \eg music was believed to be 
-knowledge, a science, which had important things to say in astronomy \etc
+structure art is a vestige of the time when e.g. music was believed to be 
+knowledge, a science, which had important things to say in astronomy etc.
 Contemporary structure artists, on the other hand, tend to claim the kind of 
 cognitive value for their art that conventional contemporary mathematicians 
 claim for mathematics. Modern examples of structure art are the fugue and 
@@ -49,7 +47,7 @@ trying to be music or whatever (which has nothing to do with knowledge),
 and knowledge represented by structure, structure art both fails, is 
 completely boring, as music, and doesn't begin to explore the aesthetic 
 possibilities structure can have when freed from trying to be music or 
-whatever.The first step in straightening out e.g. structure music is to stop 
+whatever. The first step in straightening out e.g.\ structure music is to stop 
 calling it music, and start saying that the sound is used only to carry the 
 structure and that the real point is the structure--and then you will see how 
 limited, impoverished, the structure is. Incidentally, anyone who says that 
@@ -64,7 +62,7 @@ performer vs. listener, playing a work. The second criticism of structure art
 applies, with the necessary changes, to this art. 
 
 The second main antecedent of structure art is mathematics. This is the 
-result of my revolution in mathematics, presented in my 1966 \essaytitle{Mathematical 
+result of my revolution in mathematics, presented in my \essaytitle{1966 Mathematical 
 Studies}; here I will only summarize. The revolution occured first because for 
 reasons of taste I wanted to deemphasize discovery in mathematics, 
 mathematics as discovering theorems and proofs. I wasn't good at such 
@@ -101,9 +99,9 @@ for the emotions, perhaps it would be better to restrict art to apply to art for
 the emotions, and recognize my activity as an independent, new activity, 
 irrelevant to art (and knowledge). 
 
-\section*{Concept Art Version of Mathematics System 3/26/61 (6/19/61)}
+\section{Concept Art Version of Mathematics System 3/26/61 (6/19/61)}
 
-An element is the adjacent area (with the figure in it) so long as the 
+An element is the adjacent area (with figure \ref{implications} in it) so long as the 
 apparent, perceived, ratio of the length of the vertical line to that of the 
 horizontal line (the element's associated ratio) does not change. 
 
@@ -119,10 +117,14 @@ ratios and practicing judging these ratios; and so forth.)
 [Observe that the order of elements in a selection sequence may not be the 
 order in which one sees them.] 
 
+\begin{figure}
+	\centering
+	\includegraphics[scale=1]{img/implications}
+	\caption{tktk}
+	\label{implications}
+\end{figure}
 
-\img{implications}
-
-\section*{Implications---Concept Art Version of Colored Sheet Music No. 1 3/14/61 (10/11/61)}
+\section{Implications---Concept Art Version of Colored Sheet Music No. 1 3/14/61 (10/11/61)}
 
 [This is a mathematical system without general concepts of statement, 
 implication, axiom, and proof. Instead, you make the object, and stipulate 
@@ -131,84 +133,74 @@ since there is no objective relation between name and intension, all
 mathematics is this arbitrary. Originally, the successive statements, or sheets, 
 were to be played on an optical audiorecorder.]
 
-\begin{sysrules}
-The axiom: a sheet of cheap, thin white typewriter paper 
+\begin{hangers}
+The \term{axiom}: a sheet of cheap, thin white typewriter paper.
 
-The axiom implies statement 2: soak the axiom in inflammable liquid which 
+The axiom implies statement 2 ($S_2$): soak the axiom in inflammable liquid which 
 does not leave solid residue when burned; then burn it on horizontal 
-rectangular white fireproof surface---statement 2 is ashes (on surface) 
+rectangular white fireproof surface---$S_2$ is ashes (on surface) 
 
-Statement 2 implies s.3: make black and white photograph of s.2 in white 
+$S_2$ implies $S_3$: make black and white photograph of $S_2$ in white 
 light (image of ashes' rectangle with respect to white surface (that is, of the 
 region (of surface, with the ashes on it) with bounding edges parallel to the 
 edges of the surface and intersecting the four points in the ashes nearest the 
-four edges of the surface) must exactly cover the film); develop film---s.3 is 
+four edges of the surface) must exactly cover the film); develop film---$S_3$ is 
 the negative.
 
-s.2 and s.3 imply s.4: melt s.3 and cool in mold to form plastic doubly 
+$S_2$ and $S_3$ imply $S_4$: melt $S_4$ and cool in mold to form plastic doubly 
 convex lens with small curvature; take color photograph of ashes' rectangle 
-in yellow light using this lens; develop film---s.4 is color negative.
+in yellow light using this lens; develop film---$S_5$ is color negative.
 
-s.2 and s.4 imply s.5: repeat last step with s.4 (instead of 3), using red 
-light---s.5 is second color negative 
+$S_2$ and $S_4$ imply $S_5$: repeat last step with $S_4$ (instead of $S_3$), using red 
+light---$S_5$ is second color negative 
 
-s.2 and s.5 imply s.6: repeat last step with s.5, using blue light---s.6 is third 
+$S_2$ and $S_5$ imply $S_6$: repeat last step with $S_5$, using blue light---$S_6$ is third 
 color negative 
 
-s.2 and s.6 imply s.7: make lens from s.6 mixed with the ashes which have 
+$S_2$ and $S_6$ imply $S_7$: make lens from $S_6$ mixed with the ashes which have 
 been being photographed; make black and white photograph, in white fight, 
 of that part of the white surface where the ashes' rectangle was; develop film 
---- s.7 is second black and white negative 
+--- $S_7$ is second black and white negative 
 
-s.2, s.6, and s.7 imply the theorem: melt, mold, and cool lens used in last 
-step to form negative, and make lens from s.7; using negative and lens in an 
+$S_2$, $S_6$, and $S_7$ imply the theorem: melt, mold, and cool lens used in last 
+step to form negative, and make lens from $S_7$; using negative and lens in an 
 enlarger, make two prints, an enlargement and a reduction--enlargement and 
 reduction together constitute the theorem. 
-\end{sysrules}
+\end{hangers}
 
-\section*{Concept Art: Innpersegs (May--July 1961)}
+\section{Concept Art: \sysname{Innperseqs} (May--July 1961)}
 
 \begin{sysrules}
-A \enquote{halpoint} iff whatever is at any point in space, in the fading rainbow halo 
+	A \enquote{h\u{a}lpoint} iff whatever is at any point in space, in the fading rainbow halo 
 which appears to surround a small bright light when one looks at it through 
 glasses fogged by having been breathed on, for as long as the point is in the 
 halo. 
 
-An \enquote{init`point} iff a halpoint in the initial vague outer ring of its halo. 
+An \enquote{init`point} iff a h\u{a}lpoint in the initial vague outer ring of its halo. 
 
 
-An \enquote{inn`perseq} iff a sequence of sequences of halpoints such that all the 
-halpoints are on one (initial) radius of a halo; the members of the first 
-sequence are initpoints; for each of the other sequences, the first member (a 
+An \enquote{inn`pers\u{e}q} iff a sequence of sequences of h\u{a}lpoints such that all the 
+h\u{a}lpoints are on one (initial) radius of a halo; the members of the first 
+sequence are init`points; for each of the other sequences, the first member (a 
 consequent) is got from the non-first members of the preceding sequence 
 (the antecedents) by being the inner endpoint of the radial segment in the 
 vague outer ring when they are on the segment, and the other members (if 
-any) are initpoints or first members of preceding sequences; all first members 
+any) are init`points or first members of preceding sequences; all first members 
 of sequences other than the last [two] appear as non-first members, and 
-halpoints appear only once as non-first members; and the last sequence has 
+h\u{a}lpoints appear only once as non-first members; and the last sequence has 
 one member. 
 \end{sysrules}
 
-\section*{Indeterminacy}
+\section{\sysname{Indeterminacy}}
 
 \begin{sysrules}
-A $\ulcorner$totally determinate innperseq' iff an innperseq$\urcorner$ in which one is aware of 
-(specifies) all halpoints. 
+	A $\ulcorner$totally determinate inn`pers\u{e}q$\urcorner$ iff an inn`pers\u{e}q in which one is aware of 
+	(specifies) all h\u{a}lpoints. 
 
-An $\ulcorner$antecedentally indeterminate innperseq' iff an innperseq$\urcorner$ in which one is 
+	An $\ulcorner$antecedentally indeterminate inn`pers\u{e}q$\urcorner$ iff an inn`pers\u{e}q in which one is 
 aware of (specifies) only each consequent and the radial seqment beyond it. 
 
-A $\ulcorner$halpointally indeterminate innperseq' iff an innperseq$\urcorner$ in which one is 
+	A $\ulcorner$h\u{a}lpointally indeterminate inn`pers\u{e}q$\urcorner$ iff an inn`pers\u{e}q in which one is 
 aware of (specifies) only the radial segment in the vague outer ring, and its 
 inner endpoint, as it progresses inward. 
 \end{sysrules}
-
-\subsection*{Innperseqs Diagram}
-
-In the diagram, different positions of the vague outer ring at different times 
-are suggested by different shadings. The radial segment in the vague outer 
-ring moves down the page. The figure is by no means an innperseq, but is 
-supposed to help explain the definition. 
-
-\img{innperseqsdiagram}
-
-- 
cgit v1.2.3

