breakout last essays

1 files changed, 283 insertions, 0 deletions

diff --git a/essays/propositional_vibration.tex b/essays/propositional_vibration.tex
new file mode 100644
index 0000000..9df1a7f
--- /dev/null
+++ b/essays/propositional_vibration.tex
@@ -0,0 +1,283 @@
+\chapter{Subjective Propositional Vibration (Work in Progress)}
+
+Up until the present, the scientific study of language has treated 
+language as if it were reducible to the mechanical manipulation of counters 
+on a board. Scientists have avoided recognizing that language has a mental 
+aspect, especially an aspect such as the 'understood meaning" of a linguistic 
+expression. This paper, on the other hand, will present linguistic constructs 
+which inescapably involve a mental aspect that is objectifiable and can be 
+subjected to precise analysis in terms of perceptual psychology. These 
+constructs are not derivable from the models of the existing linguistic 
+sciences. In fact, the existing linguistic sciences overlook the possibility of 
+such constructs. 
+
+Consider the ambiguous schema '$A\supset B\&C$', expressed in words as '$C$ and 
+$B$ if $A$'. An example is 
+
+\begin{equation}
+	\label{firstvib}
+	\parbox{4in}{Jack will soon leave and Bill will laugh if Don speaks.}
+\end{equation}
+
+In order to get sense out of this utterance, the reader has to supply it with a 
+comma. That is, in the jargon of logic, he has to supply it with grouping. Let 
+us make the convention that in order to read the utterance, you must 
+mentally supply grouping to it, or "bracket" it. If you construe the schema 
+as '$A\supset (B\&C)$', you will be said to bracket the conjunction. If you construe 
+the schema as '$(A\supset B)\&C$', you will be said to bracket the conditional. There 
+is an immediate syntactical issue. If you are asked to copy \ref{firstvib}, do you write 
+"Jack will soon leave and Bill will laugh if Don speaks"; or do you write 
+"Jack will soon leave, and Bill will laugh if Don speaks" if that is the way 
+you are reading \ref{firstvib} at the moment? A distinction has to be made between 
+reading the proposition, which involves bracketing; and viewing the 
+proposition, which involves reacting to the ink-marks solely as a pattern. 
+Thus, any statement about an ambiguous grouping proposition must specify 
+whether the reference is to the proposition as read or as viewed. 
+
+Some additional conventions are necessary. With respect to \ref{firstvib}, we 
+distinguish two possibilities: you are reading it, or you are not looking at it 
+(or are only viewing it). Thus, a "single reading" of \ref{firstvib} refers to an event 
+which separates two consecutive periods of not looking at \ref{firstvib} (or only 
+viewing it). During a single reading, you may switch between bracketing the 
+conjunction and bracketing the conditional. These switches demarcate a 
+series of "states" of the reading, which alternately correspond to "Jack will 
+soon leave, and Bill will laugh if Don speaks" or "Jack will soon leave and Bill 
+will laugh, if Don speaks". Note that a state is like a complete proposition. 
+We stipulate that inasmuch as \ref{firstvib} is read at all, it is the present meaning or 
+state that counts---if you are asked what the proposition says, whether it is 
+true, \etc
+
+Another convention is that the logical status of 
+\begin{quotation}
+(Jack will soon leave and Bill will laugh if Don speaks) if and only if (Jack 
+will soon leave and Bill will laugh if Don speaks) 
+\end{quotation}
+is not that of a normal tautology, even though the biconditional when 
+viewed has the form '$A\equiv A$'. The two ambiguous components will not 
+necessarily be bracketed the same way in a state. 
+
+We now turn to an example which is more substantial than \ref{firstvib}.
+
+Consider 
+
+\begin{quotation}
+Your mother is a whore and you are now bracketing the conditional in (2) if 
+you are now bracketing the conjunction in (2). (2) 
+\end{quotation}
+
+If you read this proposition, then depending on how you bracket it, the 
+reading will either be internally false or else will call your mother a whore. In 
+general, ambiguous grouping propositions are constructs in which the mental 
+aspect plays a fairly explicit role in the language. We have included (2) to 
+show that the contents of these propositions can provide more complications 
+than would be suggested by \ref{firstvib}.
+
+There is another way of bringing out the mental aspect of language, 
+however, which is incomparably more powerful than ambiguous grouping. 
+We will turn to this approach immediately, and will devote the rest of the 
+paper to it. The cubical frame \cubeframe\ is a simple reversible perspective figure 
+which can either be seen oriented upward like \cubeup\ or oriented downward 
+like \cubedown. Both positions are implicit in the same ink-on-paper image; it is 
+the subjective psychological response of the perceiver which differentiates 
+the positions. The perceiver can deliberately cause the perspective to reverse, 
+or he can allow the perspective to reverse without resisting. The perspective 
+can also reverse against his will. Thus, there are three possibilities: deliberate, 
+indifferent, and involuntary reversal. 
+
+Suppose that each of the positions is assigned a different meaning, and 
+the figure is used as a notation. We will adopt the following definitions 
+because they are convenient for our purposes at the moment. 
+
+$$ \cubeframe \left\{\parbox{4in}{for '3' if it appears to be oriented like \cubeup \linebreak
+for '0' if it appears to be oriented like \cubedown}\right\} $$
+
+We may now write 
+
+\begin{equation}
+	\label{cubefour}
+1+\cubeframe = 4 
+\end{equation}
+
+We must further agree that \ref{cubefour}, or any proposition containing such 
+notation, is to be read to mean just what it seems to mean at any given 
+instant. If, at the moment you read the proposition, the cube seems to be 
+up, then the proposition means $1+3=4$; but if the cube seems to be down, 
+the proposition means $1+O=4$. The proposition has an unambiguous 
+meaning for the reader at any given instant, but the meaning may change in 
+the next instant due to a subjective psychological change in the reader. The 
+reader is to accept the proposition for what it is at any instant. The result is 
+subjectively triggered propositional vibration, or SPV for short. The 
+distinction between reading and viewing a proposition, which we already 
+made in the case of ambiguous grouping, is even more important in the case 
+of SPV. Reading now occurs only when perspective is imputed. In reading 
+\ref{cubefour} you don't think about the ink graph any more than you think about the 
+type face. 
+
+in a definition such as that of '\cubeframe', '3' and 'O' will be called the 
+assignments. A single reading is defined as before. During a single reading, \ref{cubefour}
+will vibrate some number of times. The series of states of the reading, which 
+alternately correspond to '$1+3=4$' or '$1+O=4$', are demarcated by 
+these vibrations. The portion of a state which can change when vibration 
+occurs will be called a partial. It is the partials in a reading that correspond 
+directly to the assignments in the definition. 
+
+Additional conventions are necessary. Most of the cases we are 
+concerned with can be covered by two extremely important rules. First, the 
+ordinary theory of properties which have to do with the form of expressions 
+as viewed is not applicable when SPV notation is present. Not only is a 
+biconditional not a tautology just because its components are the same when 
+viewed; it cannot be considered an ordinary tautology even if the one 
+component's states have the same truth value, as in the case of '$1+\cubeframe\neq2$'. 
+Secondly, and even more important, SPV notation has to be present 
+explicitly or it is not present at all. SPV is not the idea of an expression with 
+two meanings, which is commonplace in English; SPV is a double meaning 
+which comes about by a perceptual experience and thus has very special 
+properties. Thus, if a quantifier should be used in a proposition containing 
+SPV notation, the "range" of the "variable" will be that of conventional 
+logic. You cannot write '\cubeframe' for '$x$' in the statement matrix 
+'$x=\cubeframe$'.
+
+We must now elucidate at considerable length the uniqué properties of 
+SPV. When the reader sees an SPV figure, past perceptual training will cause 
+him to impute one or the other orientation to it. This phenomenon is not a 
+mere convention in the sense in which new terminology is a convention. 
+There are already two clear-cut possibilities. Their reality is entirely mental; 
+the external, ink-on-paper aspect does not change in any manner whatever. 
+The change that can occur is completely and inherently subjective and 
+mental. By mental effort, the reader can consciously control the orientation. 
+If he does, involuntary vibrations will occur because of neural noise or 
+attention lapses. The reader can also refrain from control and accept 
+whatever appears. In this case, when the figure is used as a notation, 
+vibrations may occur because of a preference for one meaning over the 
+other. Thus, a deliberate vibration, an involuntary vibration, and an 
+indifferent vibration are three distinct possibilities. 
+
+What we have done is to give meanings to the two pre-existing 
+perceptual possibilities. In order to read a proposition containing an SPV 
+notation at all, one has to see the ink-on-paper figure, impute perspective to 
+it, and recall the meaning of that perspective; rather than just seeing the 
+figure and recalling its meaning. The imputation of perspective, which will 
+happen anyway because of pre-existing perceptual training, has a function in 
+the language we are developing analogous to the function of a letter of the 
+alphabet in ordinary language. The imputation of perspective is an aspect of 
+the notation, but it is entirely mental. Our language uses not only 
+graphemes, but "psychemes" or "mentemes". One consequence is that the 
+time structure of the vibration series has a distinct character; different in 
+principle from external, mechanical randomization, or even changes which 
+the reader would produce by pressing a button. Another consequence is that 
+ambiguous notation in general is not equivalent to SPV. There can be mental 
+changes of meaning with respect to any ambiguous notation, but in general 
+there is no psycheme, no mental change of notation. It is the clear-cut, 
+mental, involuntary change of notation which is the essence of SPV. Without 
+psychemes, there can be no truly involuntary mental changes of meaning. 
+
+In order to illustrate the preceding remarks, we will use an SPV 
+notation defined as follows. 
+
+\begin{equation*}
+	\cubeframe \left\{\parbox{4in}{is an affirmative, read "definitely," if it appears to be oriented 
+	like \cubeup\linebreak
+	is a negative, read "not," if it appears to be oriented like \cubedown}\right\}
+\end{equation*}
+
+The proposition which follows refers to the immediate past, not to all past 
+time; that is, it refers to the preceding vibration. 
+
+\begin{quotation}
+You have \cubeframe deliberately vibrated (4). (4) 
+\end{quotation}
+
+
+This proposition refers to itself, and its truth depends on an aspect of the 
+reader's subjectivity which accompanies the act of reading. However, the 
+same can be said for the next proposition. 
+
+\begin{quotation}
+The bat is made of wood, and you have just decided that the second 
+word in (5) refers to a flying mammal. (5) 
+\end{quotation}
+
+
+Further, the same can be said for (2). We must compare (5), (2), and (4) in 
+order to establish that (4) represents an order of language entirely different 
+from that represented by (5) and (2). (5) is a grammatical English sentence 
+as it stands, although an abnormal one. The invariable, all-ink notation 'bat' 
+has an equivocal referental structure: it may have either of two mutually 
+exclusive denotations. In reading, the native speaker of English has to choose 
+one denotation or the other; contexts in which the choice is difficult rarely 
+occur. (2) is not automatically grammatical, because it lacks a comma. We 
+have agreed on a conventional process by which the reader mentally supplies 
+the comma. Thus, the proposition lacks an element and the reader must 
+supply it by a deliberate act of thought. The comma is not, strictly speaking, 
+a notation, because it is entirely voluntary. The reader might as well be 
+supplying a denotation io an equivocal expression: (5) and (2) can be 
+reduced to the same principle. As for (4), it cannot be mistaken for ordinary 
+English. It has an equivocal "proto-notation," '\cubeframe'. You automatically 
+impute perspective to the proto-notation before you react to it as language. 
+Thus, a notation with a mental component comes into being involuntarily. 
+This notation has an unequivocal denotation. However, deliberate, 
+inditferent, and most important of all, involuntary mental changes in 
+notation can occur. 
+
+We now suggest that the reader actually read (5), (2), and (4), in that 
+order. We expect that (5) can be read without noticeable effort, and that a 
+fixed result will be arrived at (unless the reader switches in an attempt to 
+find a true state). The reading of (2) involves mentally supplying the comma, 
+which is easy, and comprehending the logical compound which . results, 
+which is not as easy. Again, we expect that a fixed result will be arrived at 
+(unless the reader vacillates between the insult and the internally false state). 
+In order to read (4), center your sight on the SPV notation, with your 
+peripheral vision taking in the rest of the sentence. A single reading should 
+last at least half a minute. If the reader will seriously read (4), we expect that 
+he will find the reading to be an experience of a totally different order from 
+the reading of (5) and (2). It is like looking at certain confusing visual 
+patterns, but with an entire dimension added by the incorporation of the 
+pattern into language. The essence of the experience, as we have indicated, is 
+that the original imputation of perspective is involuntary, and that the reader 
+has to contend with involuntary changes in notation for which his own mind 
+is responsible. We are relying on this experience to convince the reader 
+empirically that (4) represents a new order of language to an extent to which 
+(5) and (2) do not. 
+
+To make our point even clearer, let us introduce an operation, called 
+"collapsing," which may be applied to propositions containing SPV 
+proto-notation. The operation consists in redefining the SPV figure in a given 
+proposition so that its assignments are the states of the original proposition. 
+Let us collapse (4). We redefine 
+
+\begin{equation*}
+	\cubeframe \left\{\parbox{4in}{for 'You have deliberately vibrated (4)' if it appears to be oriented 
+	like \cubeup\linebreak
+	for 'You have not deliberately vibrated (4)' if it appears to be oriented 
+	like \cubedown}\right\}
+\end{equation*}
+
+(4) now becomes 
+
+\begin{quotation}
+\cubeframe (4) 
+\end{quotation}
+
+
+We emphasize that the reader must actually read (4), for the effect is 
+indescribable. The reader should learn the assignments with flash cards if 
+necessary. 
+
+The claim we want to make for (4) is probably that it is the most 
+clear-cut case yet constructed in which thought becomes an object for itself. 
+Just looking at a reversible perspective figure which is not a linguistic 
+utterance---an approach which perceptual psychologists have already 
+tried---does not yield results which are significant with respect to "thought." 
+In order to obtain a significant case, the apparent orientation or imputed 
+perspective must be a proposition; it must be true or false. Then, (5) and (2) 
+are not highly significant, because the mental act of supplying the missing 
+element of the proposition is all a matter of your volition; and because the 
+element supplied is essentially an "understood meaning." We already have an 
+abundance of understood meanings, but scientists have been able to ignore 
+them because they are not "objectifiable." In short, reversible perspective by 
+itself is not "thought"; equivocation by itself has no mental aspect which is 
+objectifiable. Only in reading (4) do we experience an "objectifiable aspect 
+of thought." We have invented an instance of thought (as opposed to 
+perception) which can be accomodated in the ontology of the perceptual 
+psychologist. 
+