some stuff

1 files changed, 278 insertions, 429 deletions

diff --git a/blueprint.tex b/blueprint.tex
index 49cfd11..3499bd2 100644
--- a/blueprint.tex
+++ b/blueprint.tex
@@ -2422,17 +2422,22 @@ One accepts language, one accepts logic.
 
 \section{}
 
-FROM "CULTURE" TO VERAMUSEMENT 
-Boston-New York 
-PRESS RELEASE: for March-April, 1963 
+{ 
+\raggedleft
+\textsc{From "Culture" to Veramusement} \\
+Boston--New York \\
+\textsc{Press Release:} for March--April, 1963 \par
+}
 
 
 Henry Flynt, Tony Conrad, and Jack Smith braved the cold to demonstrate 
 against Serious Culture (and art) on Wednesday, February 27. They began at 
 the Museum of Modern Art at 1:30 p.m., picketing with signs bearing the 
-slogans DEMOLISH SERIOUS CULTURE! /DESTROY ART! ; DEMOLISH 
-ART MUSEUMS! / NO MORE ART! ; DEMOLISH CONCERT HALLS! / 
-DEMOLISH LINCOLN CENTER! ; and handing out announcements of 
+slogans 
+\textsc{Demolish serious culture! / Destroy art!} ; 
+\textsc{Demolish art museums! / No more art!} ;
+\textsc{Demolish concert halls! / Demolish Lincoln Center!} ;
+and handing out announcements of 
 Flynt's lecture the next evening. Benjamin Patterson came up to give 
 encouragement. There was much spontaneous interest among people around 
 and in the Museum. At about 1:50, a corpulent, richly dressed Museum 
@@ -2463,15 +2468,10 @@ On Thursday evening, February 28, at Walter DeMaria's loft, Henry Flynt
 gave a long lecture expositing the doctrine the Wednesday demonstrations 
 were based on. On entering the lecture room, the visitor found himself 
 stepping in the face of a Mona Lisa print placed as the doormat. To one side 
-
-
-69 
-
-
 was an exhibition of demonstration photos and so forth. Behind the lecturer 
-was 2 large picture of Viadimir Mayakovsky, while on either side were the 
+was a large picture of Viadimir Mayakovsky, while on either side were the 
 signs used in the demonstrations, together with one saying 
-VERAMUSEMENT---NOT CULTURE. About 20 people came to the lecture. 
+\textsc{Veramusement---Not culture}. About 20 people came to the lecture. 
 The lecturer showed first the suffering caused by Serious-Cultural snobbery, 
 by its attempts to force individuals in line with things supposed to have 
 objective validity, but actually representing only alien subjective tastes 
@@ -2486,39 +2486,34 @@ lecture was concerned with. After the lecture, Flynt told how his doctrine
 was anticipated by little known ideas of Mayakovsky, Dziga Vertov, and 
 their group, as related in Ilya Ehrenburg's memoirs and elsewhere. He 
 touched on the Wednesday demonstrations. He spoke of George Maciunas' 
-FLUXUS, with which all this is connected. Several people at the lecture 
+\textsc{Fluxus}, with which all this is connected. Several people at the lecture 
 congratulated Flynt on the clarity of the presentation and logicality of the 
 arguments. Photos were taken. 
 
-
-5. 
-Statement of November 1963 
+\section{Statement of November 1963}
 
 
-Back in March 1963, I sent the tirst FCTB PRESS RELEASE, about FCTB's 
+Back in March 1963, I sent the first \textsc{FCTB Press Release}, about FCTB's 
 February picketing and lecture, to all the communications media, including 
 the New Yorker. It is so good that the New Yorker wanted to use it, but 
 they didn't want to give FCTB any free publicity; so they finally published 
-an inept parody of it, in the October 12, 1963 issue, pp. 49-51. They 
+an inept parody of it, in the October 12, 1963 issue, pp. 49--51. They 
 changed my last name to Mackie, changed February 27 to September 25, the 
 Museum of Modern Art to a church, changed our slogans to particularly 
-idiotic ones {although they got in 'NO MORE ART/CULTURE?' later on), 
+idiotic ones (although they got in '\textsc{No More Art/Culture?}', later on), 
 and added incidents; but the general outlines, and the phrases lifted verbatim 
 from the FCTB RELEASE, make the relationship clear.---Henry Fiynt 
 
+\section{}
 
-70 
-
-
-pee 
-
+{ \raggedleft 3/6/63 \par }
 
-Henry, 3/6/63 
+Henry, 
 
 
 Received your note this morning. I had written down a few things about the 
 lecture the very night I got home but decided they were not very clear so I 
-didn't send them. Don't know if I can make it any clearer...actually I keep 
+didn't send them. Don't know if I can make it any clearer\ldots actually I keep 
 thinking that I must have overlooked something because the objection I have 
 to make seems too obvious. You spend much time and effort locating 
 Veramusement, stating clearly wnat it is not, and stating that it is, if I get it, 
@@ -2529,7 +2524,7 @@ another or several activities. You have discredited activities---like art,
 competitive games---as pseudo work or unsatisfactory recreation by employing 
 arguments which are external to "experiencing" these activities (e.g. chess is 
 bad because why agree to some arbitrary standard of performance which 
-doesn't fit you)...weil it seems to me that Veramusement could never replace 
+doesn't fit you)\ldots well it seems to me that Veramusement could never replace 
 any cultural form because it has no external "edges" but rather by definition 
 can occur anywhere anytime anyplace (By the way I want to say here that 
 its existence as a past tense or memory I find objectionable---but I can't at the 
@@ -2540,7 +2535,7 @@ exposition of how the two things are related has been very clear. George
 Herbert Mead, an early Pragmatist (don't shudder at that word, but I can see 
 you throwing up your hands in despair) talked about this relation as a kind 
 of double aspect of the personality (which he called the "me" and the "I" 
-..can't remember his book, something like Mind, Self, and Society). 
+\ldots can't remember his book, something like \booktitle{Mind, Self, and Society}). 
 
 I thought you presented the lecture very weil, but towards the end I was 
 getting too tired to listen very carefully and I am sorry because this was the 
@@ -2548,72 +2543,66 @@ newest writing. I would like very much to read this part, i.e. that which dealt
 with the evolution of work, automation and the liberation from 
 drudgery---send me a copy if you can. 
 
-Best regards, 
-
-Bob Morris 
-
-
-71 
+\signoff{Best regards,}
+\signoff{Bob Morris}
 
+\section{}
 
-Henry 3/12/1963 
+{ \raggedleft 3/12/1963 \par }
+Henry 
 
+\begin{tabular}
+	\redact{Jazz} & \redact{Cage} & \redact{"Folk Music} & \redact{Communism} & 
+		\begin{tabular}
+			(anti-art?) \\
+			------ \\
+			(communism) \\
+		\end{tabular} \\
+\end{tabular}
 
-(anti-art? } 
-Jgfz Cage "Folk Music" Communism ____...----.----- 
-(communism) 
 I've been along this road too. 
-Yes I certainly do see the harmfullness of serious culture. My favorite movies 
-are plain documentaries. 
-
-
-"Veramusement" 
-questions: the way you set it up it sound like veramusement is IT. Some 
-
+Yes I certainly do see the harmfullness of serious culture. My favorite movies are plain documentaries. 
 
-kind of Absolute good state or activity. --ie) ATHLETICS are out. 
--now my brother is a healthy athelete--he enjoys nothing so much as 
-swimming or playing tennis all! day (he likes to use his body--and he likes the 
-form--competition) 
-
-Is this "wrong" 
+\gap
 
-Should he stop.-- 
 
+"Veramusement" 
+questions: the way you set it up it sound like veramusement is \textsc{It}. Some 
+kind of Absolute good state or activity. ---ie) \textsc{Athletics} are out. \\
+---now my brother is a healthy athelete---he enjoys nothing so much as 
+swimming or playing tennis all day (he likes to use his body---and he likes the 
+form---competition) 
+
+{ \centering
+Is this "wrong" \\
+Should he stop.--- \par
+}
 
 or wouldn't your "creep theory" which lets each person be himself and 
-relish in himself--by extention from this--shouldn't the atheletic person be 
-
-
-alowed to be himself? --too. 
-I think you were opening up the world to the people at the lecture-- 
+relish in himself---by extention from this---shouldn't the atheletic person be 
+alowed to be himself? ---too. \\
+I think you were opening up the world to the people at the lecture---
 
 
+{
 making them move free-- 
-sd "ready to be themselves 
+" " ready to be themselves \par
+}
 
 
 I think you were right in not giving examples! 
 
 
-however 
-
-your absolute--statements and 'come on"--and blend with the communist 
-ideas--(My mind was pretty tired by then and I didn't follow how the 
-veramusement--was tied to communism)--this IT kind of taik.--can only shoo 
-people off-and let them wait for the next revision or explication. 
-
-people off--and let them wait for the next revision or explication. 
-
-
-Walter DeMaria 
-
+however \\
+your absolute---statements and "come on"---and blend with the communist 
+ideas---(My mind was pretty tired by then and I didn't follow how the 
+veramusement---was tied to communism)---this \textsc{It} kind of talk.---can only shoo 
+people off-and let them wait for the next revision or explication. \\
+people off---and let them wait for the next revision or explication. 
 
-72 
-
-
-8. 
+\signoff{Walter DeMaria}
 
+\section{}
 
 Dear Henry, March 18, 1963 
 
@@ -2634,15 +2623,16 @@ Yours,
 
 Diane Wakoski 
 
+\section{}
 
 "Dear Mr. Flynt...Since I may be depending on o-ganized culture for my 
 loot & livelihood I can wish you only a limited success in your movement... 
 Cornelius Cardew" [froma postcard of June 7, 1963] 
 
 
-73 
-
+\clearpage
 
+{
 2/22/1963 
 
 
@@ -2652,17 +2642,15 @@ February 22, 1963
 
 (photo by Tony Conrad) 
 
-
-74 
-
-
 Museum of Modern Art, 
+}
+\clearpage
 
 
-PARA—SCIENCE 
+\part{Para---science}
 
 
-> 9, The Perception-Dissociation of Physics 
+\chapter{The Perception-Dissociation of Physics}
 
 
 From the physicist's point of view, the human dichotomy of sight and 
@@ -2701,12 +2689,7 @@ we begin as follows. A healthy human has a realm of sights, and a realm of
 touches: and there is a correlation between the two which receives its highest 
 expression in the concept of the object. (In psychological jargon, intermodal 
 organization contributes to the object Gestalt. Incidentally, for us "touch" 
-includes just about every sense except sight, hearing, smel!.) Suppose there is 
-
-
-77 
-
-
+includes just about every sense except sight, hearing, smell.) Suppose there is 
 a change in which the tactile realm remains coherent, if not exactly the same 
 as before, and the visual realm also remains coherent; but the correlation 
 between the two becomes completely chaotic. A totally blind person does 
@@ -2716,36 +2699,38 @@ Let us define such a change. Consider the sight-touch correlation identified
 with closing one's eyes. The point is that there is a whole realm of sights 
 which do not occur when one can feel that one's eyes are closed. 
 
-Let T indicate tactile and V indicate visual. Let the tactiie sensation of 
-open eyes be T, and of closed eyes be To. Now anything that can be seen 
-with closed eyes--from total blackness, to the multicolored patterns produced 
+Let $T$ indicate tactile and $V$ indicate visual. Let the tactile sensation of 
+open eyes be $T_1$, and of closed eyes be $T_2$. Now anything that can be seen 
+with closed eyes---from total blackness, to the multicolored patterns produced 
 by waving the spread fingers of both hands between closed eyes and direct 
-sunlight--can no doubt be duplicated for open eyes. Closed-eye sights are a 
-subset of open-eye sights. Thus, let sights seen only with open eyes be V1, 
-and sights seen with either open or closed eyes be V>: If there are sights seen 
-only with closed eyes, they will be V3; we want disjoint classes. We are 
+sunlight---can no doubt be duplicated for open eyes. Closed-eye sights are a 
+subset of open-eye sights. Thus, let sights seen only with open eyes be $V_1$, 
+and sights seen with either open or closed eyes be $V_2$: If there are sights seen 
+only with closed eyes, they will be $V_3$; we want disjoint classes. We are 
 interested in the temporal concurrence of sensations. Combining our 
 definitions with information about our present world, we find there are no 
 intrasensory concurrences (eyes open and closed at the same time). Further, 
 our change will not produce intrasensory concurrences, because each realm 
 will remain coherent. Thus, we will drop them from our discussion. There 
 remain the intersensory concurrences, and four can be imagined; let us 
-denote them by the ordered pairs (T,, Vj), (17, V9), (To, V4), (Tp, V9). In 
+denote them by the ordered pairs $(T_1, V_1), (T_1, V_2), (T_2, V_1), (T_2, V_2)$. In 
 reality, some concurrences are permitted and others are forbidden, Let us 
 designate each ordered pair as permitted or forbidden, using the following 
 notation. Consider a rectangular array of "places" such that the place in the 
-ith row and jth column corresponds to (T;, Vj), and assign a p or f (as 
+ith row and jth column corresponds to $(T_i, V_j)$, and assign a $p$ or $f$ (as 
 appropriate) to each place. Then the following state array is a description of 
-regularities in our present world. ¢ 3 
+regularities in our present world. 
 
-
-fp 
+$$\begin{pmatrix}
+	p & p\\
+	f & p 
+\end{pmatrix}$$
 
 
 So far as temporal successions of concurrences (within the présent 
 world) are concerned, any permitted concurrence may succeed any other 
 permitted concurrence. The succession of a concurrence by itself is 
-excluded, meaning that at the moment, a Vv, is defined as lasting from the 
+excluded, meaning that at the moment, a $V_1$, is defined as lasting from the 
 time the eyes open until the time they next close. 
 
 We have said that our topic is a certain change; we can now indicate 
@@ -2754,66 +2739,74 @@ more precisely what this change is. As long as we have a 2x2 array, there are
 states. The changes we are interested in, then, are specific changes from the 
 
 
-present state'p p\to another state such ap fI\ However, 
-tp pp/ 
+present state
+$\begin{pmatrix}
+	p & p \\
+	f & p
+\end{pmatrix}$
+
+to another state such as
+
+$\begin{pmatrix}
+	p & f \\
+	p & p
+\end{pmatrix}$
 
+However, 
 we want to exclude some changes. The change that changes nothing is 
 excluded. We aren't interested in changing to a state having only f's, which 
 amounts to blindness. A change to a state with a row or column of f's leaves 
-one sight or touch completely forbidden {a person becomes blind to 
+one sight or touch completely forbidden (a person becomes blind to 
 open-eye sights); such an "impairment" is of little interest. Of the remaining 
 changes, one merely leaves a formerly permitted concurrence forbidden: 
 closed-eye sights can no longer be seen with open eyes. The rest of the 
 changes are the ones most relevant to perception-dissociation. They are 
-changes in the place of the one f ; the change to the state having only p's; 
-
-
-and finally / 
-PP) > fp 
-
-
-\f p pf 
-
+changes in the place of the one f; the change to the state having only p's; 
+and finally 
+
+
+\begin{tabular}
+	$\begin{pmatrix}
+		p & p \\
+		f & p
+	\end{pmatrix}$ &
+	->
+	&
+	$\begin{pmatrix}
+		f & p \\
+		p & f
+	\end{pmatrix}$ \\
+\end{tabular}
 
 In general, we speak of a partition of a sensory realm into disjoint 
-classes of perceptions, so that the two partitions are [Tj] and [Vj]. The 
+classes of perceptions, so that the two partitions are $[T_j]$ and $[V_j]$. The 
 number of classes in a partition, m for touch and n for sight, is its 
-detailedness. The detailedness of the product partition [T;] X [V;] is written 
-m x n. This detailedness virtually determines the (mn)? imaginable states, 
+detailedness. The detailedness of the product partition $[T_j]\times [V_j]$ is written 
+$m\times n$. This detailedness virtually determines the $(mn)^2$ imaginable states, 
 although it doesn't determine their qualitative content. Now suppose one 
 change is followed by another, so that we can speak of a change series. It is 
 important to realize that by our definitions so far, a change series is not a 
 conposition of functions; it is a temporal phenomenon in which each state 
 lasts for a finite time. (A function would be a genera! rule for rewriting 
-states. A 2X2 rule might say, rotate the state clockwise one place, fromja b 
-to/ca\. cd 
-
-ce 
-
+states. A 2X2 rule might say, rotate the state clockwise one place, from
+$\begin{pmatrix}a & b \\ c & d\end{pmatrix}$ to
+$\begin{pmatrix}c & a \\ d & b\end{pmatrix}$.
 
 But a composition of rules would not be a temporal series; it would be a new 
 rule.) Returning to the sorting of changes, we always exclude the no-change 
-changes, and states having only f's. We are unenthusiastic about 'impairing' 
+changes, and states having only f's. We are unenthusiastic about "impairing"
 changes, changes to states with rows or columns of f's. Of the remaining 
 changes, some merely forbid, repiacing p's with f's. The rest of the changes 
 are the most perception-dissociating ones. 
 
 As for changes in the succession state in the eye case, either they leave 
 the forbidden concurrence permitted; or else they merely leave permitted 
-successions forbidden--for example, in order to open your eyes in the dark 
+successions forbidden---for example, in order to open your eyes in the dark 
 you might have to open them in the light and then turn the light off. These 
 secondary changes are of secondary interest. 
 
 If we simply continue with the material we already have, two lines of 
 investigation are possible. The first investigation is mathematical, and 
-
-
-79 
-
-
-s 
-
-
 apparently amounts to combinatorial algebra. The second investigation 
 concerns the relation between concurrences and commands of the will 
 (observable as electrochemica! impulses along efferent neurons). If a change 
@@ -2843,11 +2836,7 @@ outside or only in the mind" comes to have less and less scientific meaning.
 If physics survived, it would have to recognize the touch-sight dichotomy as 
 a physical one! This scenario helps answer a question the reader may have 
 had: what is the methodological status of our states? They don't seem to be 
-
-
-either physics or psychology, yet it is quite clear how we would know if the , 
-
-
+either physics or psychology, yet it is quite clear how we would know if the
 asserted regularities had changed; in fact, that is the whole point of the 
 states. The answer is that the states are perfectly good assertions (of 
 observed regularities) which would acquire primary importance if the 
@@ -2860,24 +2849,19 @@ has to be done to the photons and electrons to produce the changes. It is the
 same as with time travel: the hard part is deciding what it is and the even 
 harder part is making it happen. 
 
-
-* * * 
-
-
-80 
-
+\breatk
 
 However, the foundations of our qualitative theory are not yet 
 satisfactory, We have assumed that the physicist will be able to identify the 
 subjective concurrences of perceptions, and will be able to identify his 
 perceptions themselves, even if sense correlation becomes completely 
 chaotic. We have assumed that the physicist will be able to say "I see a book 
-in my hand but I concurrently feel a pencil.' These assumptions may not be 
-justified at all. It is quite likely that the physicist will say, 'I don't even 
+in my hand but I concurrently feel a pencil." These assumptions may not be 
+justified at all. It is quite likely that the physicist will say, "I don't even 
 know whether the sight and the touch seem concurrent; I don't even know 
 whether I think I see a book; I don't even know whether this sensation is 
 visual." In fact, the anomalies may cause the physicist to decide that books 
-never looied like books in the first place. In this case, the occurrence of the 
+never looked like books in the first place. In this case, the occurrence of the 
 changes would render meaningless the terms in which the changes are 
 defined. Alternately, if the changes produce a localized chaos, so that 
 everything fits together except the book seen in the hand, the physicist may 
@@ -2911,11 +2895,6 @@ modification, he may not even know whether two perceptions seem
 simultaneous. 
 
 This criticism of the changes defined earlier is important, but it may 
-
-
-81 
-
-
 not be insurmountable. Although Stratton became used to his trick 
 eyeglasses, the image continued to seem distorted. There is some stability to 
 our identification of our perceptions. Also, the physicist in our earlier 
@@ -2947,6 +2926,7 @@ empirical importance of Alten's idea is thet it raises the question of what the
 perceptual frustration of the will (as we defined it) would do to the sense of 
 futurity. 
 
+\breatk
 
 We now come to some considerations which will help us develop the 
 state descriptions, and which also show that from one point of view, the 
@@ -2957,11 +2937,6 @@ plastic. He touches the clear plastic, but from what he sees, he believes he is
 touching the colored plastic. The lighting is then changed and his error is 
 exposed. In some sense, the sight-touch concurrence identifying an object 
 was a mere coincidence. Next, we produce another colored sheet for the 
-
-
-82 
-
-
 subject to touch, and we are able to convince him that this time the 
 object-identifying concurrence is more than a coincidence. 
 
@@ -2994,34 +2969,25 @@ concurrences are forbidden. We suggest that the physicist ultimately handles
 touch-sight concurrences in just this way. The operational basis of the 
 physicist's activity comes down to our states. (But note that the physicist 
 has tests, which do not rely directly on his hearing, to determine whether the 
-clicks come from the metronome! ) One way to develop our states, then, 
+clicks come from the metronome!) One way to develop our states, then, 
 may be to develop substates which express the differences between those 
 object-identifying concurrences that are coincidental and those that 
-aren't--the differences illustrated by the plastic sheet experiment. 
-
-
-83 
-
-
-2/22/1963 
-
-
-Henry Flynt and Jack Smith demonstra 
-February 22, 1963 
-(foto by Tony Conrad) 
-
-
-te against the Metropolitan Museum of Art, 
+aren't---the differences illustrated by the plastic sheet experiment. 
 
 
-84 
-
+\clearpage
+{ 2/22/1963 
 
-10. 1966 Mathematical Studies 
 
+Henry Flynt and Jack Smith demonstrate against the Metropolitan Museum of Art, 
+February 22, 1963 \\
+(foto\footnote{sic} by Tony Conrad) 
+} \clearpage
 
-QO. Introduction 
+\chapter{1966 Mathematical Studies}
 
+% TODO start these section numbers at 0? (this should work)
+\section*{0. Introduction}
 
 Pure mathematics is the one activity which is intrinsically formalistic. It 
 is the one activity which brings out the practical value of formal 
@@ -3046,7 +3012,7 @@ All the more reason, then, not to limit mathematics to the normal concept
 of logical truth. 
 
 Once it is realized that mathematics is intrinsically formalistic, and need 
-not adhere to the norma! concept of logical truth, why hold back from 
+not adhere to the normal concept of logical truth, why hold back from 
 exploring the possibilities which are available? There is every reason to 
 search out the possibilities and present them. Such is the purpose of this 
 monograph. 
@@ -3056,44 +3022,42 @@ has practical applications. I believe that the approaches presented on a very
 abstract level in this monograph will turn out to have such applications. In 
 order to be applied, the principles which are presented here have to be 
 developed intensively on a level which is compatible with applications. The 
-results will be found in my two subsequent essays, 'Subjective Propositional 
-Vibration" and "The Logic of Admissible Contradictions." 
-
-
-85 
+results will be found in my two subsequent essays, \essaytitle{Subjective Propositional 
+Vibration} and \essaytitle{The Logic of Admissible Contradictions}.
 
-
-1. Post-Formalism in Constructed Memories 
-1.1 Post-Formalist Mathematics 
+\section{Post-Formalism in Constructed Memories}
+\subsection{Post-Formalist Mathematics}
 
 Over the last hundred years, a philosophy of pure mathematics has 
 grown up which I prefer to call "formalism." As Willard Quine says in the 
 fourth section of his essay "Carnap and Logical Truth,' formalism was 
 inspired by a series of developments which began with non-Euclidian 
 geometry. Quine himself is opposed to formalism, but the formalists have 
-found encouragement in Quine's own book, Mathematical Logic. The best 
-presentation of the formalist position can be found in Rudolph Carnap's The 
-Logical Syntax of Language. As a motivation to the reader, and 
+found encouragement in Quine's own book, \booktitle{Mathematical Logic}. The best 
+presentation of the formalist position can be found in Rudolph Carnap's 
+\booktitle{The Logical Syntax of Language}. As a motivation to the reader, and 
 as a heuristic aid, I will relate my study to these two standard books. (It will 
 heip if the reader is thoroughly familiar with them.) it is not important 
-whether Carnap, or Quine, or formalism--or my interpretation of them--is 
+whether Carnap, or Quine, or formalism---or my interpretation of them---is 
 "correct," for this essay is neither history nor philosophy. I am using history 
 as a bridge, to give the reader access to some extreme mathematical 
 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,' %,? "7 *),° fy and 'e.' 
+well-defined ink-shapes on paper 'w,' 'x,' 'y,' 'z,' '{}',' '(,' '),' '\downarrow,' and '$\in$.' 
 These shapes are manipulated according to arbitrary but well-detined 
 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 "sentences." One sentence 
-is '{((x) (xex}) I (x) (xex)).' There are transformation rules, rules for the 
+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 may be concluded from yand"™y> w" ; 
-where '>' is the truth-furctional conditional. For later convenience, I will 
-say that y and "y D yw are "impliors," and that y is the "implicand." 
-Some sentences are designated as "axioms." A 'proof' is a series of 
+trasformation 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 "impliors," 
+and that $\psi$ is the "implicand." 
+Some sentences are designated as "axioms." A "proof" is a series of 
 sentences such that each is an axiom or an implicand of preceding sentences. 
 The last sentence in a proof is a "theorem." 
 
@@ -3101,17 +3065,13 @@ This account is ultrasimplified and non-rigorous, but it is adequate for
 my purposes. (The reader may have noticed a terminological issue here. For 
 Quine, an implication is merely a logically true conditional. The rules which 
 are used to go from some statements to others, and to assemble proofs, are 
-rules of inference. The relevant rule of inference is the modus ponens; wW is 
-tie ponential of pand "yD W7. What I am doing is to use a terminology of 
+rules of inference. The relevant rule of inference is the modus ponens; $\psi$ is 
+the ponential of $\varphi$ and $\ulcorner \varphi \supset \psi \urcorner$. What I 
+am doing is to use a terminology of 
 implication to talk about rules of inference and ponentials. The reason is 
 that the use of Quine's terminology would result in extremely awkward 
 formulations. What I will be doing is sufficiently transparent that it can be 
 translated into Quine's terminology if necessary. My results will be 
-
-
-86 
-
-
 unaffected.) The decisive feature of the arbitrary game called "mathematics" 
 is as follows. A sentence-series can be mechanically checked to determine 
 whether it is a proof. But there is no mechanical method for deciding 
@@ -3128,19 +3088,19 @@ system can be "interpreted," or given a meaning within the language of a
 science such as physics. So interpreted, it may have scientific value, or it may 
 not. But as pure mathematics, all the systems have the same arbitrary status. 
 
-By "formalist mathematics' I will mean the present mathematical 
+By "formalist mathematics" I will mean the present mathematical 
 systems which are presented along the above lines. Actually, as many authors 
-have observed, the success of the non-Euclidian "tmaginary' geometries 
+have observed, the success of the non-Euclidian "imaginary" geometries 
 made recognition of the game-like character of mathematics inevitable. 
 Formalism is potentially the greatest break with tradition in the history of 
-mathematics. In the Foreward to The Logical Syntax of Language, Carnap 
+mathematics. In the Foreward to \booktitle{The Logical Syntax of Language}, Carnap 
 brilliantly points out that mathematical innovation is still hindered by the 
-Widespread opinion that deviations from mathematical tradition must be 
-justified--that is, proved to be "correct" and to be a faithful rendering of 
+widespread opinion that deviations from mathematical tradition must be 
+justified---that is, proved to be "correct" and to be a faithful rendering of 
 "the true logic." According to Carnap, we are free to choose the rules of a 
 mathematical system arbitrarily. The striving after correctness must cease, so 
-that mathematics will no longer be hindered. 'Before us lies the boundless 
-ocean of unlimited possibilities." In other words, Carnap, the most reputable 
+that mathematics will no longer be hindered. \said{Before us lies the boundless 
+ocean of unlimited possibilities.} In other words, Carnap, the most reputable 
 of academicians, says you can do anything in mathematics. Do not worry 
 whether whether your arbitrary game corresponds to truth, tradition, or 
 reality: it is still legitimate mathematics. Despite this wonderful Principle of 
@@ -3157,64 +3117,45 @@ systems. My sentences are physically different from concatenations of
 ink-shapes. My transformation rules have nothing to do with operations on 
 ink-shapes. 2. My systems do not necessarily follow the axiomatic-deductive, 
 sentence-implication-axiom-proof-theorem structure. Both of these 
-
-
-87 
-
-
-possibilities, by the way, are mentioned by Carnap in "Languages as 
-
-Calculi." A "post-formalist system," then, is a formalist system which differs 
-
-physically from  an_ ink-on-paper system, or which lacks the 
-
+possibilities, by the way, are mentioned by Carnap in \papertitle{Languages as 
+Calculi.} A "post-formalist system," then, is a formalist system which differs 
+physically from an ink-on-paper system, or which lacks the 
 axiomatic-deductive structure. 
 
 As a basis for the analysis of post-formalist systems, a list of structural 
 properties of formalist systems is desirable. Here is such a list. By 
-"Implication" I will mean simple, direct implication, unless I say otherwise. 
-
-1. Asentence can be repeated at will. 
+"implication" I will mean simple, direct implication, unless I say otherwise. 
+\begin{enumerate}
+\item A sentence can be repeated at will. 
 
-2. The rule of implication refers to elements of sentences: sentences 
+\item The rule of implication refers to elements of sentences: sentences 
 are structurally composite. 
 
-A sentence can imply itself. 
-
-4. The repeat of an implior can imply the repeat of an implicand: an 
+\item A sentence can imply itself. 
 
+\item The repeat of an implior can imply the repeat of an implicand: an 
 implication can be repeated. 
 
-Different impliors can imply different implicands. 
-
-6. Given two or three sentences, it is possible to recognize 
+\item Different impliors can imply different implicands. 
 
+\item Given two or three sentences, it is possible to recognize 
 mechanically whether one or two directly imply the third. 
 
-No axiom is implied by other, different axioms. 
+\item No axiom is implied by other, different axioms. 
 
-8. The definition of 'proof' is the standard definition, in terms of 
+\item The definition of "proof" is the standard definition, in terms of 
 implication, given early in this essay. 
 
-9. Given the axioms and some other sentence, it is not possible to 
-recognize mechanically whether the sentence is a theorem, 
+\item Given the axioms and some other sentence, it is not possible to 
+recognize mechanically whether the sentence is a theorem.
 Compound indirect implication is a puzzle. 
+\end{enumerate}
 
 Now for the first post-formalist system. 
 
+{ \centering \large "\textsc{Illusions}" \par}
 
-wo 
-
-
-a 
-
-
-~ 
-
-
-"TY Hlusions" 
-
-
+\begin{sysrules}
 A "sentence" is the following page (with the figure on it) so long as the 
 apparent, perceived ratio of the length of the vertical line to that 
 of the horizontal line (the statement's "associated ratio") does not 
@@ -3233,27 +3174,20 @@ lengths are equal. One can correct one's perception, come to see
 the vertical line as shorter relative to the horizontal line, decrease 
 the associated ratio, by measuring the lines with a ruler to convince 
 oneself that the vertical line is not longer than the other, and then 
-
-
-88 
-
-
 trying to see the lines as equal in length; constructing similar 
 figures with a variety of real (measured) ratios and practicing 
 judging these ratios; and so forth. 
+\begin{sysrules}
 
+\img{illusions}
 
-"IIlusions" has Properties 1, 3-5, and 7-8. Purely to clarify this fact, the 
+"IIlusions" has Properties 1, 3--5, and 7--8. Purely to clarify this fact, the 
 following sequence of integers is presented as a model of the order in which 
 associated ratios might appear in reality. (The sequence is otherwise totally 
-inadequate as a model of "Iilusions.") 4 2 1; 4 2;5421;43 1. The 
+inadequate as a model of "Illusions.") 4 2 1; 4 2; 5 4 2 1; 4 3 1. The 
 implication structure would then be 
 
-
-4<> 
-s—-TXp>s SZ Lo ZN 
-4<> 4 oo yD der 1 
-
+\img{illusionstructure}
 
 The axiom would be 4, and 5 could not appear in a proof. "IIlusions" has 
 Property 1 on the basis that one can contro! the associated ratio. Turning to 
@@ -3261,24 +3195,16 @@ Property 4, it is normally the case that when an implication is repeated, a
 given occurrence of one of the sentences involved is unique to a specific 
 occurrence of the implication. In "Illusions," however, if two equal 
 sentences are next smaller than X, the occurrence of X does not uniquely 
-belong to either of the two occurrences of the implication. Compare 'the', 
-
-
-e 
-
-
-89 
-
-
+belong to either of the two occurrences of the implication. Compare '\begin{tabular} t & h & e \\ h &   &   \\ e &   & \end{tabular}', 
 where the occurrence of 't' is not unique to either occurrence of 'the'. 
-Subject to this explanation, "lilusions" has Property 4. "Illusions" has 
-Property 8, but it goes without saying thut the type of implication is not 
+Subject to this explanation, "Illusions" has Property 4. "Illusions" has 
+Property 8, but it goes without saying that the type of implication is not 
 modus ponens. Properties 3, 5, and 7 need no comment. As for Property 2, 
 the rule of implication refers to a property of sentences, rather than to 
 elements of sentences. The interesting feature of "IIlusions" is that it 
 reverses the situation defined by Properties 6 and 9. Compound indirect 
 implication is about the same as simple implication. The only difference is 
-the difference between being smaller and being next smalier. And there is 
+the difference between being smaller and being next smaller. And there is 
 only one axiom (per person). 
 
 Simple direct implication, however, is subjective and illusive. It 
@@ -3293,56 +3219,50 @@ theorem. What is difficult is grasping the steps in between, the simple direct
 implications. If the brain contains a permanent impression of every sensation 
 it has received, then the implications objectively exist; but they may not be 
 thinkable without neurological techniques for getting at the impressions. In 
-any case, "proof" is well-defined in some sense--but proofs may not be 
-thinkable. "I!lusions" is, after all, not so much shakier in this respect than 
+any case, "proof" is well-defined in some sense---but proofs may not be 
+thinkable. "Illusions" is, after all, not so much shakier in this respect than 
 even simple arithmetic, which contains undecidable sentences and 
 indefinable terms. 
 
-In The Logical Syntax of Language, Carnap distinguishes pure syntax 
+In \booktitle{The Logical Syntax of Language}, Carnap distinguishes pure syntax 
 and descriptive syntax; and says that pure syntax should be independent of 
 notation, and that every system should be isomorphic to some ink-on-paper 
 system. In so doing, Carnap violates his ov'n Principle of Tolerance. Consider 
 the following trivial formalist system. 
 
+{ \centering \large "\textsc{Order}" \par}
 
-"Order" 
+\begin{sysrules}
+A "sentence" is a member of a finite set of integers. 
 
-
-A"sentence" is a member of a finite set of integers. 
-
-Sentence Y is "implied by" sentence X it and only if Y=X, or else of all the 
+Sentence Y is "implied by" sentence X if and only if Y=X, or else of all the 
 sentences, Y is the one next smaller than X. 
 
 Take as the axiom the largest sentence. 
+\end{sysrules}
 
 
-js the pure syntax of "Iilusions' insomorphic to "Order"? The preceding 
+Is the pure syntax of "\textsc{Illusions}" insomorphic to "\textsc{Order}"? The preceding 
 paragraph proved that it is not. The implication structure of "Order" is 
-
-
-90 
-
-
 mechanical to the point of idiocy, while the implication structure of 
 "Illusions" is, as I pointed out, elusive. The figure 
 
 
-Axlom 6 eles gt abe eae eek Theorem 
+\img{orderstructure}
 
 
 where loops indicate multiple occurances of the same sentence, could 
 adequately represent a proof in "Order," but could not remotely represent 
-one in "Illusions." The essence of 'Illusions' is that it is coupled to the 
+one in "Illusions." The essence of "Illusions" is that it is coupled to the 
 reader's subjectivity. For an ink-on-paper system even to be comparable to 
 "IIlusions," the subjectivity would have to be moved out of the reader and 
 onto the paper. This is utterly impossible. 
 
 Here is the next system. 
 
+{ \centering \large "\textsc{Innperseqs}" \par}
 
-"I nnperseqs" 
-
-
+\begin{sysrules}
 Explanation: Consider the rainbow halo which appears to surround a small 
 bright light when one looks at it through fogged glass (such as 
 eyeglasses which have been breathed on). The halo consists of 
@@ -3353,7 +3273,7 @@ happens on one contracting radius of the halo, and specifically
 what happens on the segment of that radius lying in the vague 
 outer ring: the outer segment. 
 
-A "sentence" {or halopoint) is the changing halo color at a fixed point, in 
+A "sentence" (or halopoint) is the changing halo color at a fixed point, in 
 space, in the halo; until the halo contracts past the point. 
 
 Several sentences "imply" another sentence if and only if, at some instant, 
@@ -3374,96 +3294,59 @@ No sentence appears as a non-first member more than once. 5. The
 last sequence has one member. 
 
 In the diagram on the following page, different positions of the vague outer 
-
-
-91 
-
-
-Successive bands represent the vague outer ring at successive times as it fades in toward the small bright light. 
-
-
 ring at different times are suggested by different shadings. The 
 outer segment moves "down the page." The figure is by no means 
 an innperseq, but is supposed to help explain the definition. 
-Innperseqs Diagram 
-"Sentences" at 
-
-
-I time: a1 8 a3 aq ap ag a7 b 
-44,89 > bh 
-
-
-timeg: a9 a3 a4 a5 ag a7 be 
-ag —— eee ( 
-
-
-eS 
-SS Sos 
-Saas 
-SSS 
-
-
-WS 
-
-
-U4 yy (VY) Mi Wy i 
-Mey ae 
-AAA AL ELH i wae aan Se tl 
-peeling tatatsegZee 4,45 
-
-EL DAMA ATLL 
-
-Lita, YAP 
-
-VALE RELAY AL 
-
-LAA B68 94622 
-
-VP AO 
-
-WAL ALLL 
-
-RINE, SALA ALIIY 
-
-LAA 6 LAs 
 
-eines: Yihks 
+\ccw{Successive bands represent the vague outer ring at successive times as it fades in toward the small bright light.}
 
+Innperseqs Diagram 
 
-PT I SSS . m 
-
-ar ee oe —— timeg: ag a7 bede 
-Feo, Weak rds gis 
-ROBES I) Ronee SSS times: ayb ede f 
-KT g . 
-Snes eaiiens Pa PASE, SS a 
+\img{innperseqs}
 
-PPT PS SL RISE Os a7,c +f 
-CER I PRR 
-FS re pa oon a 
-ST RS EXER WS gat en gs 
-SAE VE er 
+"Sentences" at 
 
+	\begin{tabular}
+		\img{time1} & $time_1$: & $a_1 a_2 a_3 a_4 a_5 a_6 a_7 b$ \\
+		& & $a_1,a_2 \rightarrow\ b$ \\
+	\end{tabular}
 
-"Axioms" ay a9 a3 a4 a5 ag a7 
+	\begin{tabular}
+		\img{time2} & $time_2$: & $a_2 a_3 a_4 a_5 a_6 a_7 b c$ \\
+		& & $a_3 \rightarrow\ c$ \\
+	\end{tabular}
 
+	\begin{tabular}
+		\img{time3} & $time_3$: & $a_4 a_5 a_6 a_7 b c d$ \\
+		& & $a_4,a_5 \rightarrow\ d$ \\
+	\end{tabular}
 
-Innperseq 
-(a3,49,a4) 
-(b, a3) 
+	\begin{tabular}
+		\img{time4} & $time_4$: & $a_6 a_7 b c d e$ \\
+		& & $a_6,b \rightarrow\ e$ \\
+	\end{tabular}
 
-(c, a5, aq) 
-(d, b, ag) 
-(e,c,a7) 
-(f,e, d) 
+	\begin{tabular}
+		\img{time5} & $time_5$: & $a_7 b c d e f$ \\
+		& & $a_7,c \rightarrow\ f$ \\
+	\end{tabular}
 
-(g) 
+	\begin{tabular}
+		\img{time6} & $time_6$: & $c d e f g$ \\
+		& & $d,e \rightarrow\ g$ \\
+	\end{tabular}
 
+"Axioms" $a_1 a_2 a_3 a_4 a_5 a_6 a_7$
 
-small bright light 
 
-
-92 
+Innperseq \\
+$(a_3,a_2,a_1)$
+$(b,a_3)$
+$(c,a_5,a_4)$
+$(d,b,a_6)$
+$(e,c,a_7)$
+$(f,e,d)$
+$(g)$
 
 
 In "Innperseqs," a conventional proof would be redundant unless al! 
@@ -3488,7 +3371,7 @@ that an inner endpoint implies itself. The system also has Properties 5 and 7;
 and lacks Property 2. But, as before, Properties 6 and 9 are another matter. 
 Given several sentences, it is certainly possible to tell mechanically whether 
 one is implied by the others. But when are you given sentences? If one can 
-think the sentences, then relating them is easy--but it is difficult to think the 
+think the sentences, then relating them is easy---but it is difficult to think the 
 sentences in the first place, even though they objectively exist. The diagram 
 suggests what to look for, but the actual thinking, the actual sentences are 
 another matter. As for Property 9, when "theorems" are identified with last 
@@ -3502,9 +3385,8 @@ indeterminacies. Precisely because of the difficulty of thinking sentences, I
 will give several subvariants of the system. 
 
 
-Indeterminacy 
-
-
+{ \centering \large \textsc{Indeterminacy} \par}
+\begin{sysrules}
 A "totally determinate innperseq" is an innperseq in which one thinks all the 
 sentences. 
 
@@ -3512,13 +3394,9 @@ An "implior-indeterminate innperseq" is an innperseq in which one thinks
 only each implicand and the outer segment it terminates. 
 
 A "sententially indeterminate innperseq" is an innperseq in which one thinks 
-
-
-93 
-
-
 only the outer segment, and its inner endpoint, as it progresses 
 inward. 
+\end{sysrules}
 
 
 Let us return to the matter of pure and descriptive syntax. The interest 
@@ -3529,53 +3407,40 @@ am trying to break through to unheard of, and hopefully significant, modes
 of implication; to define implication structures (and derivation structures) 
 beyond the reach of past mathematics. 
 
-
-1.2 Constructed Memory Systems 
+\subsection{Constructed Memory Systems}
 
 In order to understand this section, it is necessary to be thoroughly 
-familiar with "Studies in Constructed Memories," the essay following this 
-one. {I have not combined the two essays because their approaches are too 
+familiar with \essaytitle{Studies in Constructed Memories,} the essay following this 
+one. (I have not combined the two essays because their approaches are too 
 different.) I will define post-formalist systems in constructed memories, 
 beginning with a system in an M*-Memory. 
 
+{ \centering \large "\textsc{Dream Amalgams}" \par}
 
-"Dream Amalgams" 
-
-
-A "sentence" is a possible method, an Ag. with respect to an M*-Memory. 
-I 
-
-
-The sentence A, "implies" the sentence A, if and only if the agth 
-
-
-M*-assertion is actually thought; and either A, = Ag.» or else there is 
-q p 
-
-
-cross-method contact of a mental state in Mag with a state in Pa 
+\begin{sysrules}
+A "sentence" is a possible method, an $A_{a_i}$. with respect to an M*-Memory. 
+The sentence $A_{a_p}$ "implies" the sentence $A_{a_q}$ if and only if the $a_q$th 
+M*-assertion is actually thought; and either $A_{a_q} = A_{a_p}$, or else there is 
+cross-method contact of a mental state in $A_{a_q}$ with a state in $A_{q_p}$\footnote{sic?}
 
 The axioms must be chosen from sentences which satisfy two conditions. 
 The mental states in the sentences must have cross-method contact 
 with mental states in other sentences. And the M*-assertions 
 corresponding to the sentences must not be thought. 
 
-Explanation: As "Studies in Constructed Memories" says, there can be 
+Explanation: As \essaytitle{Studies in Constructed Memories} says, there can be 
 cross-method contact of states, because a normal dream can 
 combine totally different episodes in the dreamer's life into an 
 amalgam. 
+\end{sysrules}
 
-"Dream Amalgams" has Properties 1-5. For the first time, sentences are 
+"\textsc{Dream Amalgams}" has Properties 1-5. For the first time, sentences are 
 structurally composite, with mental states being the relevant sentential 
 elements. Implication has an unusual character. The traditional type of 
 implication, modus ponens, is "directed," because the conditional is 
-directed. Even if "yDwW" is true "YDy" may not be. Now implication is also 
-directed in 'Dream Amalgams," but for a very different reason. 
-
-
-94 
-
-
+directed. Even if $\ulcorner\varphi\supset\phi\urcorner$ is true 
+$\ulcorner\varphi\supset\phi\urcorner$ may not be. Now implication is also 
+directed in "\textsc{Dream Amalgams,}" but for a very different reason. 
 Cross-method contact, unlike the conditional, has a symmetric character. 
 What prevents implication from being necessarily symmetrical is that the 
 implicand's M*-assertion actually has to be thought, while the implior's 
@@ -3583,13 +3448,10 @@ M*-assertion does not. Thus, implication is both subjective and mechanical,
 it is subjective, in that it is a matter of volition which method is remembered 
 to have actually: been used. It is mechanical, in that when one is 
 remembering, one is automatically aware of the cross-method contacts of 
-states in Ag . The conditions on the axioms ensure that they will have 
-
-
+states in $A_{a_q}$. The conditions on the axioms ensure that they will have 
 implications without losing Property 7. 
 
-
-As for compound implication in "Dream Amalgams," the organism 
+As for compound implication in "\textsc{Dream Amalgams,}" the organism 
 with the M*-Memory can't be aware of it at all; because it can't be aware 
 that at different times it remembered different methods to be the one 
 actually used. (In fact, the organism cannot be aware that the system has 
@@ -3614,43 +3476,30 @@ study post-formalist modes of inference which are anything but deductive.
 To aid in understanding the next system, which involves infalls in a 
 D-Memory, here is an 
 
+{ \centering \large \framebox[1.1\width]{"Exercise to be Read Aloud"} \par}
 
-mn 
-
-
-"Exercise to be Read Aloud" 
 (Read according to a timer, reading the first word at O' O", and prolonging 
 and spacing words so that each sentence ends at the time in parentheses after 
 it. Do not pause netween sentences.) 
 
+\begin{tabular}
+	($event_1$) &  All men are mortal. (17") \\
 
-(event) Ail men are mortal. (17°) 
-
-(Sentence; =eventy) The first utterance tasted 17" and ended at 17"; and 
-lasted 15" and ended 1" ago. (59") 
-
-(Sp=event3) The second utterance lasted 42" and ended at 59": and 
-lasted 50" and ended 2" ago. (1' 31") 
+	($Sentence_1=event_2s$) &  The first utterance lasted 17" and ended at 17"; and lasted 15" and ended 1" ago. (59") \\
 
+	($S_2=event_3$) & The second utterance lasted 42" and ended at 59": and lasted 50" and ended 2" ago. (1' 31") \\
 
-95 
-
-
-(S3=eventy) The third utterance lasted 32" and ended at 1' 31"; and 
-lasted 40" and ended 1" ago. (2' 16") 
-
-Since '32' in $3 is greater than '2' in S9, S9 must say that S4 (=eventg) 
-
-ended 30" after Sy began, or something equally unclear. The duration of Sy 
+	($S_3=event_4$) & The third utterance lasted 32" and ended at 1' 31"; and lasted 40" and ended 1" ago. (2' 16") \\
+\end{tabular}
 
+Since '32' in $S_3$ is greater than '2' in $S_2$, $S_2$ must say that $S_1$ ($=event_2$)
+ended 30" after $S_2$ began, or something equally unclear. The duration of $S_2$
 is greater than the distance into the past to which it refers. This situation is 
-
 not a real infall, but it should give the reader some intuitive notion of an 
-
 infall. 
 
 
-"Infails" 
+"Infalls" 
 
 
 A "sentence" is a D-sentence, in a D-Memory such that event) + 4 is the first