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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. + |