From e83b8620bc4cd159e6e34db2bc92160afbc7e87c Mon Sep 17 00:00:00 2001 From: grr Date: Wed, 8 May 2024 19:43:11 -0400 Subject: addition of several extra essays --- extra/apprehension_of_pluraility.tex | 1265 ++++++++++++++++++++++++++++++ extra/general_acognitive_culture.tex | 29 + extra/philosophy_of_concept_art.tex | 1161 +++++++++++++++++++++++++++ extra/radicalism_of_unbelief.tex | 374 +++++++++ extra/structure_art_pure_mathematics.tex | 156 ++++ 5 files changed, 2985 insertions(+) create mode 100644 extra/apprehension_of_pluraility.tex create mode 100644 extra/general_acognitive_culture.tex create mode 100644 extra/philosophy_of_concept_art.tex create mode 100644 extra/radicalism_of_unbelief.tex create mode 100644 extra/structure_art_pure_mathematics.tex diff --git a/extra/apprehension_of_pluraility.tex b/extra/apprehension_of_pluraility.tex new file mode 100644 index 0000000..c09bcbd --- /dev/null +++ b/extra/apprehension_of_pluraility.tex @@ -0,0 +1,1265 @@ +The Apprehension of Plurality + + +Henry Flynt + + +(An instruction manual +for 1987 concept art) + + +I. Original Stroke-Numerals + + +Stroke-numerals were introduced in foundations of mathematics +by the German mathematician David Hilbert early in the twentieth +century. Instead of a given Arabic numeral such as ‘6’, for example, one +has the expression consisting of six concatenated occurrences of the +stroke, e.g. ‘III’. + +To explain the use of stroke-numerals, and to provide a back- +ground for my innovations, some historical remarks about the philo- +sophy of mathematics are necessary. Traditional mathematics had +treated positive whole-number arithmetic as if the positive whole +numbers (and geometrical figures also) were objective intangible +beings. Plato is usually named as the originator of this view. Actually, +there is a scholarly controversy over the degree to which Plato espoused +the doctrine of Forms—over whether Aristotle’s Metaphysics put +words in Plato’s mouth—but that is not important for my purposes. +For an intimation of the objective intangible reality of mathematical +objects in Plato’s own words, see the remarks about “divine” geometric +figures in Plato’s “Philebus.” Aristotle’s Metaphysics, 1.6, says that +mathematical entities + + +are intermediate, differing from things perceived in being eternal and +unchanging, and differing from the Forms in that they exist in copies, +whereas each Form is unique. + + +For early modern philosophers such as Hume and Mill, any such +“Platonic” view was not credible and could not be defended seriously. +Thus, attempts were made to explain number and arithmetic in ways +which did not require a realm of objective intangible beings. In fact, +Hume said that arithmetic consisted of tautologies; Mill that it con- +sisted of truths of experience. + +Following upon subsequent developments—the philosophical +climate at the end of the nineteenth century, and specifically mathema- +tical developments suchas non-Euclidian geometry—Hilbert proposed +that mathematics should be understood as a game played with mean- +ingless marks. So, for example, arithmetic concerns nothing but formal +terms—numerals—in a network of rules. Actually, what made arith- +metic problematic for mathematicians was its infinitary character—as +expressed, for example, by the principle of complete induction. Thus, +the principal concern for Hilbert was that this formal game should not, +as a result of being infinitary, allow the deduction of botha proposition +and its negation, or of such a proposition as 0 = 1. + +But at the same time (without delving into Hilbert’s distinction +between mathematics and metamathematics), the stroke-numerals +replace the traditional answer to the question of what a number is. The +stroke-numeral ‘IIIIII’ is a concrete semantics for the sign ‘6’, and at the +same time can serve as a sign in place of ‘6’. The problem of positive +whole numbers as abstract beings is supposedly avoided by inventing +e.g. a number-sign, a numeral, for six, which is identically a concrete +semantics for six. Let me elaborate a little further. A string of six copies +of a token having no internal structure is used as the numeral ‘6’, the +sign for six. Thus the numeral is itself a collection which supposedly +demands a count of six, thereby showing its meaning. Hans Freud- +enthal calls this device an “ostensive numeral.” + +So traditionally, there is a question as to what domain of beings +the propositions of arithmetic refer to, a question as to what the +referents of number-words are. Correlative to this, mathematicians’ +intentions require numerous presuppositions about content, and +require extensive competancies—which the rationalizations for math- +ematics today are unable to acknowledge, much less to defend. + +For example, if mathematics rests on concrete signs, as Hilbert +proposed, then, since concrete signs are objects of perception, the +reliability of mathematics would depend on the reliability of percep- +tion. Given the script numeral 1 + + +which is ambiguous between one and two, conventional mathematics +would have to guarantee the exclusion of any such ambiguity as this. +Yet foundations of mathematics excludes perception and the reliability +of concrete signs as topics—much as Plato divorced mathematics from +these topics. (Roughly, modern mathematicians would say that reliabil- +ity of concrete signs does not interact with any advanced mathematical +results. So this precondition can simply be transferred from the requi- +sites of cognition in general. But it would not be sincere for Hilbert to +give this answer. Moreover, my purpose is to investigate the possibility +of reconstructing our intuitions of quantity beyond the limits of the +present culture. In this connection, I need to activate the role of +perception of signs.) + +But the most characteristic repressed presuppositions of mathe- +matics run in the opposite, supra-terrestrial direction. Mathematicians’ +intentions require a realm of abstract beings. Again, it is academically +taboo today to expose such presuppositions.* But to recur to the +purpose of this investigation, concept art is about reconstructing our +intuitions of quantity beyond the limits of the present culture. This +project demands an account of these repressed presuppositions. To +compile such an account is a substantial task; I focus on it ina collateral +manuscript entitled “The Repressed Content-Requirements of Math- +ematics.” To uncover the repressed presuppositions, a combination of +approaches is required.** I will not dwell further on the matter here- +but a suitable sample of my results is the section “The Reality- +Character of Pure Whole Numbers and Euclidian Figures” in “The +Repressed Content-Requirements.” + +Returning to the original stroke-numerals, they were meant +(among other things) to be part of an attempt to explain arithmetic +without requiring numbers as abstract beings. They were meant as +signs, for numbers, which are identically their own concrete semantics. +Whether I think Hilbert succeeded in dispensing with abstract entities is +not the point here. I am interested in how far the exercise of positing + + +*Godel and Quine admit the need to assume the non-spatial, abstract +existence of classes. But they cannot elaborate this admission; they cannot +provide a supporting metaphysics. + +**One anthroplogist has written about “the locus of mathematical +reality” —but, being an academic, he merely reproduces a stock answer outside +his field (namely that the shape of mathematics is dictated by the physiology of +the brain). + + +stroke-numerals as primitives can be elaborated. My notions of the +original stroke-numerals are adapted from Hilbert, Weyl, Markov, +Kneebone, and Freudenthal. For example, how does one test two +stroke-numerals for equality? To give the answer that “you count the +strokes, first in one numeral and then in the other,” is not in the spirit of +the exercise. For if that is the answer, then that means that you have a +competency, “counting,” which must remain a complete mystery to +foundations of mathematics. What one wants to say, rather, is that you +test equality of stroke-numerals by “cross-tallying”: by e.g. deleting +strokes alternately from the two numerals and finding if there is a +remainder from one of the numerals. This is also the test of whether one +numeral precedes the other. So, now, given an adult mastery of quality +and abstraction, you can identify stroke-numerals without being able +to “count.” + +In the same vein, you add two stroke-numerals by copying the +second to the right of the first. You subtract a shorter numeral from a +longer numeral by using the shorter numeral to tally deletion of strokes +from the longer numeral. You multiply two stroke-numerals by copy- +ing the second as many times as there are strokes in the first: that is, by +using the strokes of the first to tally the copying of the second numeral. + +To say that all this is superfluous, because we already acquired +these “skills” as a child, misses the point. The child does not face the +question, posed in the Western tradition, of whether we can avoid +positing whole numbers as abstract beings. To weaken the require- +ments of arithmetic to the point that somebody with an adult mastery +of quality and abstraction can do feasible arithmetic “blindly”—i.e. +without being able to “count,” and without being able to see number- +names (‘five’, ‘seven’, etc.) in concrete pluralities—is a notable exercise, +one that correlates culturally with positivism and with the machine age. + +To reiterate, the stroke-numeral is meant to replace numbers as +abstract beings by providing number-signs which are their own con- +crete semantics. Freudenthal said that we should communicate positive +whole numbers to alien species by broadcasting stroke-numerals to +them (in the form of time-series of beeps). Still, Freudenthal said that +the aliens would have to resemble us psychologically to get the point. +(Lincos, pp. 14-15.) + +When Hilbert first announced stroke-numerals, certain difficulties +were pointed out immediately. It is not feasible to write the stroke- +numerals for very large integers. (And yet, if it is feasible to write the +stroke-numeral for the integer n, then there is no apparent reason why + + +it would not also be feasible to write the stroke-numeral for n+1. So +stroke-numerals are closed under succession, and yet are contained ina +finite segment of the classical natural number series.) Moreover, large +feasible stroke-numerals, such as that for 10,001, are not surveyable. + +But this is not a study of metamathematical stroke-numerals. And +I do not wish to go into Hilbert’s question of the consistency of +arithmetic as an infinitary game here; “The Repressed Content- +Requirements” will have more to say on the consistency question. The +purpose of this manual, and of the artworks which it accompanies, is to +establish apprehensions of plurality beyond the limits of traditional +civilizations (beyond the limits of Freudenthal’s “us”). Moreover, these +apprehensions of plurality are meant to violate the repressed presuppo- +sitions of mathematics. I refer back to original stroke-numerals because +certain devices which I will use in assembling my novelties cannot be +supposed to be intuitively comprehensible—certainly not to the +traditionally-indoctrinated reader—and will more likely be understood +if 1 mention that they are adaptations of features of original stroke- +numerals. Let me mention one point right away. In our culture, we +usually see numerals as positional notations—e.g. 111 is decimal +1X 102+ 1X 10!+1 or binary | X 22+ 1 X 2!+ 1. But stroke-numerals +are not a positional notation (except trivially for base 1). Likewise, my +novelties will not be positional notations; I will even nullify the refer- +ence to base 1. (Only much later in my investigations, when broad +scope becomes important, will I use positional notation.) So the fore- +going introduction to stroke-numerals has only the purpose of moti- +vating my novelties. And references to the academic canon are given +only for completeness. They cannot be norms for what I am “per- +mitted” to posit. + + +IT. Simple Necker-Cube Numerals + + +In my stroke-numerals, the printed figure, instead of being a +stroke, is a Necker cube. (Refer to the attached reproduction, “Stroke- +Numeral.”) A Necker cube is a two-dimensional representation of a +cubical frame, formed without foreshortening so that its perspective is +perceptually equivocal or multistable. The Necker cube can be seen as +flat, as slanting down from a central facet like a gem, etc.; but for the +moment I am exclusively concerned with the two easiest variants in +which it is seen as an ordinary cube, either projecting up toward the +front or down toward the front. + + +Biel] Bie] bie/ bie) in] Bie bia) + + +STROKE-NUMERAL + + +STROKE + + +Q) +O VACANT + + +Since I will use perceptually multistable figures as notations, I +need a terminology for distinctions which do not arise relative to +conventional notation. I call the ink-shape on paper a figure. I call the +stable apparition which one sees in a moment—which has imputed +perspective—the image.* As you gaze at the figure, the image changes +from one orientation to the other, according to intricate subjective +circumstances. It changes spontaneously; also, you can change it +voluntarily. + +Strictly—and very importantly—it is the image which in this +context becomes the notation. Thus, I will work with notations which +are not ink-shapes and are not on a page. They arise as active interac- +tions of awareness with an “external” or “material” print-shape or +object. + +So far, then, we have images—partly subjective, pseudo-solid +shapes. I now stipulate an alphabetic role for the two orientations in +question. The up orientation is a stroke; the down orientation is called +“vacant,” and acts as the proofreaders’ symbol © , meaning “close up +space.” (So that “vacant” is not “even” an alphabetic space.) Now the +two images in question are signs. The transition from image to sign can +be analogized to the stipulation that circles of a certain size are (occu- +rances of) the letter “o."**I may say that one sees the image; one +apprehends the image as sign. + +When a few additional explanations are made, then the signs +become plurality-names or “numerals.” First, figures, Necker cubes, +are concatenated. When this is done, a display results. So the stroke- +numeral in the artwork, as an assembly of marks on a surface, is a +display of nine Necker cubes. An image-row occurs when one looks at +the display and sees nine subjectively oriented cubes, for just so long as + + +*I may note, without wanting to be precious, that a bar does not count as +a Hilbert stroke unless it is vertical relative to its reader. +** And—the shape, bar, positioned vertically relative to its reader, is the +symbol, Hilbert stroke. + + +the apparition is stable (no cube reverses orientation). I chose nine +Necker cubes as an extreme limit of what one can apprehend ina fixed +field of vision. (So one must view the painting from several meters +away, at least.) The reader is encouraged to make shorter displays for +practice. Incidentally, if one printed a stroke-numeral so long that one +could only apprehend it serially, by shifting one’s visual field, it would +be doubtful that it was well-defined. (Or it would incorporate a feature +which I do not provide for.) The universe of pluralities which can be +represented by these stroke-numerals is “small.” My first goal is to +establish “subjectified” stroke-numerals at all. They don’t need to be +large. + +The concatenated signs which you apprehend in a moment of +looking at the display are now apprehended or judged as a plurality- +name, a numeral. At the level where you apprehend signs (which, +remember, are alphabetized, partly subjective images, not figures), the +apparition is disambiguated. Thus I can explain this step of judging the +signs as plurality-names by using fixed notation. For nine Necker cubes +with the assigned syntactical role, you might apprehend such permuta- +tions of signs as + + +a) ISCHOOCSI +by ISTSoC SH +c) IIIS DOCS +d) HINO CCTI + + +RNA ARRANN +OC) vuevvuvvuves + + +My Necker-cube stroke-numerals are something new; but (a)-(e) are +not—they are just a redundant version of Hilbert stroke-numerals +(which nullifies the base | reference as I promised). The “close up +space” signs function as stated; and the numeral concluded from the +expression corresponds to the number of strokes; i.e. the net result is +the Hilbert stroke-numeral having the presented number of strokes. So +(a) and (b) and (c) all amount to III. (d) amounts to IIIII. + +As for (e), it has the alphabetic role of a blank. My initial interpre- +tation of this blank is “no numeral present.” Later I may interpret the +blank as “zero,” so that every possibility will be a numeral. Let me +explain further. Even when I will interpret the blank as “zero.” it will +not come about from having nine zeros mapped to one zero (like a sum +of zeros). (e) has nine occurrences of “close up space,” making a blank. + + +There is always only one way of getting “blank.” (A two-place display +allows two ways of getting “one” and one way of getting “two”; etc.) +The notation is not positional. It is immaterial whether one “focuses” +starting at the left or at the right. + +Relative to the heuristic numerals (a)-(e), you may judge the +intended numerals by counting strokes, using your naive competency +in counting. (It is also possible to use such numerals as (a)-(e) “blindly” +as explained earlier. This might mean that there would be no recogni- +tion of particular numbers as gestalts; identity of numbers would uv +handled entirely by cross-tallying.) The Necker-cube numerals, how- +ever, pertain to a realm which is in flux because it is coupled to +subjectivity. My numerals provide plurality-names and models of that +realm. Thus, the issue of what you do when you conclude a numeral +from a sign in perception is not simple. We have to consider different +hermeneutics for the numerals—and the ramifications of those herme- +neutics. Here we begin to get a perspective of the mutability which my +devices render manageable. + +For one thing, given a (stable) image-row, and thus a sign-row, you +can indeed use your naive arithmetical competency to count strokes, +and so conclude the appropriate numeral. This is bicultural hermeneu- +tic, because you are using the old numbers to read a new notation for +which they were not intended. We use the same traditional counting, of +course, to speak of the number of figures in a display. + +(This prescription of a hermeneutic is not entirely straightforward. +The competency called counting is required in traditional mathematics. +But such counting is already paradoxical “phenomenologically.” I +explain this in the section called “Phenomenology of Counting” in “The +Repressed Content-Requirements.” As for the Necker-cube numerals, +the elements counted are not intended in a way which supports the +being of numbers as eternally self-identical. So the Necker-cube +numerals might resonate with the phenomenological paradoxes of +ordinary counting. The meaning of ordinary numbering, invoked in +this context, might begin to dissolve. But I mention this only to hint at +later elaborations. At this stage, it is proper to recall one’s inculcated +school-counting; and to suppose that e.g. the number of figures in a +display is fixed in the ordinary way.) + +Then, there is the ostensive hermeneutic. Recall that I explained +Hilbert stroke-numerals as signs which identically provide a concrete +semantics for themselves; and as an attempt to do arithmetic without +assuming that one already possesses arithmetic in the form of com- + + +petency in counting, or of seeing number-names in pluralities. My +intention was to prepare the reader for features to be explained now. +On the other hand, at present we drop the notion of handling identity of +numerals by cross-tallying.* For the ostensive hermeneutic, it is crucial +that the display is short enough to be apprehended in a fixed field of +vision. + +With respect to short Hilbert numerals, I ask that when you see +e.g. + +Il + + +marked ona wall, you grasp it asa sign for a definite plurality, without +mediation—without translating to the word “two.” A similar intention +is involved in recognizing + + +THLE + + +as a definite plurality, as a gestalt, without translating to “five.” + +Now I ask you to apply this sort of hermeneutic to Necker-cube +stroke-numerals. I ask you to grasp the sign-row as a numeral, as a +gestalt. (Without using ordinary counting to call off the strokes.) Fora +two-place display, you are to take such images as + + +ae + + +as plurality-names without translating into English words. (Similarly + + +BR + + +in the case where I choose to read “blank” as “zero.”) Perhaps it is +necessary to spend considerable time with this new symbolism before + + +and + + +*Because this notion corresponds to a situation in which we are unable to +appraise image-rows as numerals, as gestalts. + + +recognition is achieved. Again, I encourage the reader to make short +displays for practice. I have set a display of nine figures as the upper +limit for which it might be possible to learn to grasp every sign-row as a +numeral, as a gestalt. + +The circumstance that the apprehended numeral may be different +the next moment is not a mistake; the apprehended numeral is sup- +posed to be in flux. So when you see image-rows, you take them as +identical signs/semantics for the appearing pluralities. + +But who wants such numerals—where are there any phenomena +for them to count? For one thing, they count the very image-rows which +constitute them. The realm of these image-rows is a realm of subjective +flux: its plurality is authentically represented by my numerals, and +cannot be authentically represented by traditional arithmetic. + +A further remark which may be helpful is that here numerals arise +only visually. So far, my numerals have no phonic or audio equivalent. +(Whereas Freudenthal in effect posited an audio version of Hilbert +numerals, using beeps.) + +To repeat, by the “ostensive hermeneutic” I mean grasping the +sign-row, without mediation, as a numeral. But there is, as well, the +point that the Necker-cube numerals are ostensive numerals. That is, +the (momentary) numeral for six would in fact be an image-row with +just six occurrences of the image “upward cube.” (Compare e.g. +I 2111) The numeral is a collection in which only the “copies” of +“upward cube” contribute positively, so to speak; and these copies +demand a count of six (bicuturally). This feature needs to be clear, +because later I will introduce numerals for which it does not hold. + +Let me add another proviso concerning the ostensive hermeneutic +which will be important later. I will illustrate the feature in question +with an example which, however, is only an analogy. Referring to +Arabic decimal-positional numerals, you can appraise the number- +name of + + +1001 + + +(comma omitted) immediately. But consider +786493015201483492147 + + +Here you cannot appraise the number-name without mediation. That +is, if you are asked to read the number aloud, you don’t know whether +to begin with “seven” or “seventy-eight” or “seven hundred eighty-six.” + + +Lacking commas, you have to group this expression from the right, in +triples, to find what to call it. An act of analysis is required. + +In the case of Necker-cube numerals and the ostensive hermeneu- +tic, don’t want you to see traditional number-names in the pluralities. +However, I ask you to grasp a sign-row as a numeral, as a gestalt. | now +add that the gestalt appraisal is definitive. I rule out appraising image- +rows analytically (by procedures analogous to mentally grouping an +Arabic number in triples). (I established a display of nine figures as the +upper limit to support this.) + +The need for this proviso will be obscure now. It prepares for a +later device in which, even for short displays, gestalt appraisal and +appraisal by analysis give different answers, either of which could be +made binding. + + +The bicultural hermeneutic is applied, in effect, in my uninter- +preted calculus “Derivation,” which serves as a simplified analogue of +my early concept art piece “Illusions.” (Refer to the reproductions on +the next four pages.) Strictly, though, “Derivation” does not concern a +Necker-cube stroke-numeral. The individual figures are not Necker +cubes, but “Wedberg cubes,” formed with some foreshortening to make +one of the two orientations more likely to be seen than the other. What +is of interest is not apprehension of image-rows as numerals, but rather +appraisal of lengths of the image-rows via ordinary counting. As for the +lessons of this piece, a few simple observations are made in the piece’s +instructions. But to pursue the topic of concept art as uninterpreted +calculi, and derive substantial lessons from it, will require an entire +further study—taking off from earlier writings on post-formalism and +uncanny calculi, and from my current writings collateral to this essay. + + +1987 Concept Art — Henry Flynt +“DERIVATION” (August 1987 corrected version) + + +Purpose: To provide a simplified analogue of my 1961 concept art piece “‘IIlusions’’ which is +discrete and non-‘‘warping.’’* Thereby certain features of “‘Illusions’’ become more +clearly discernible. + + +Given a perceptually multistable figure, the ““Wedberg cube,” which can be seen in two +orientations: as a cube; as a prism (trapezohedron.) + +Call what is seen at an instant an /mage. + +Nine figures are concatenated to form the display. + + +An element is an image of the display for as long as that image remains constant (Thus, +elements include: the image from the first instant of a viewing until the image first +changes; an image for the duration between two changes; the image from the last +change you see in a viewing until the end of the viewing.) + + +The /ength of an element equals the number of prisms seen. Lengths from O through nine +are possible. Two different elements can have the same length. Length of element X +is written /(X). + + +Elements are seen in temporal order in the lived time of the spectator. | refer to this order by +words with prefix ‘T’. T-first; T-next; etc. + + +Element Y succeeds element X if and only if +i) (X) = KY), and Y is T-next after X of all elements with this length; or +ii) ¥ is the T-earliest element you ever see with length /(X) + 1. +Note that (ii) permits Y to be T-earlier than X: the relationship is rather artificial. + + +The initial element A is the T-first element. (/(A) may be greater than O; but it is likely to be O +because the figure is biased.) + + +The conclusion C is the T-earliest element of length 9 (exclusive of Ain the unlikely case in +which /(A) = 9). + + +A derivation is a series of elements in lived time which contains A and C and in which every +element but A succeeds some other element. + + +Discussion + +To believe that you have seen a derivation, you need to keep track that you see each +possible length, and to force yourself to see lengths which do not occur spontane- +ously. + + +You may know that you have seen a derivation, without being able to identify in memory the +particular successions. + + +“Derivation” is not isomorphic to “Illusions” for a number of reasons. ‘‘Illusions” doesn’t +require you to see individually every possible ratio between the T-first ratio and unity. +“Illusions” allows an element to succeed itself. The version of ‘Derivation’ pres- +ented here is a compromise between mimicking “‘Illusions”’ and avoiding a trivial or +cluttered structure. Any change such as allowing elements to succeed themselves +would require several definitions to be modified accordingly. + + +*In “Illusions,” psychic coercion, which may be called “false seeing” or “warping,” is +recommended to make yourself see the ration as unity. In ‘‘Derivation,” this warping is not +necessary; all that may be needed is that you see certain lengths willfully. + + +ABABA AAS + + +Concept Art Version of Mathematics System 3/26/6l(6/19/61) + +An "element"is the facing 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 element’s "associated +ratio") does not change. + +A "selection sequence" is asequence of elements of which the +first is the one having the greatest associated ratio, and +each of the others has the associated ratio next smallerthan +that of the preceding one. (To decrease the ratio, come to +see the vertical line as shorter, relative to the horizontal +line, one might try measuring the lines with a ruler to con- +vince oneself that the vertical one is not longer than the +other, and then 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.) +(Observe that the order of elements in a selection sequence +may not be the order in which one sees them.] + + +An elaboration of “Stroke-Numeral” should be mentioned here, +the piece called “an Impossible Constancy.” (Refer to the facing page.) +As written, this piece presupposes the bicultural hermeneutic, and that +is probably the way it should be formulated. The point of this piece, +paradoxically, is that one seeks to annul the flux designed into the +apprehended numeral. Viewing of the Necker-cube numeral is placed +in the context of a lived experience which is interconfirmationally +weak: namely, memory of past moments within a dream (a single +dream). Presumably, appraisals of the numeral at different times could +come out the same because evidence to the contrary does not survive. +So inconstancy passes as constancy. Either hermeneutic can be +employed; but when I explained the hermetic hermeneutic, I encour- +aged you to follow the flux. Here you wouldn’t do that—you wouldn't +stare at the display over a retentional interval. + + +As for the concept of equality with regard to Necker-cube numerals, +what can be said about it at this point? We have equality of numbers of +figures in displays, by ordinary counting. We have two hermeneutics +for identifying an apprehended numeral. In the course of expounding +them, I expounded equivalence of different permutations of “stroke” +and “vacant.” Nevertheless, given that, for example, a display of two +figures can momentarily count the numeral apprehended from a dis- +play of three figures,* we are in unexplored territory. Cross-tallying, +suitable for judging equality of Hilbert numerals, seems maladapted to +Necker-cube numerals; in fact, I dismissed it when introducing the +ostensive hermeneutic. + +If the “impossible constancy” from the paragraph before last were +manageable, then one might consider restricting the ultimate definition +of equality to impossible constancies. That is, with respect to a single +display, if one wanted to investigate the intention of constancy (self- +equivalence of the apprehended numeral), one might start with the +impossible constancy. Appraisals of a given display become constant +(the numeral becomes self-equivalent) in the dream. Then two displays +which are copies might become constantly equivalent to each other, in +the dream. + +Such is a possibility. To elaborate the basics and give an incisive +notion of equality is really an open problem, though. Other avenues +might require additional devices such as the use of figures with distinc- +tions of appearance. + + +*that it is not assured that copies of a numeral will be apprehended or +appraised correlatively + + +1987 Concept Art — Henry Flynt +Necker-Cube Stroke-Numeral: AN IMPOSSIBLE CONSTANCY + + +The purpose of this treatment is to say how a Necker-cube stroke numeral may be +judged (from the standpoint of private subjectivity) to have the same value at different +times; even though the conventional belief-system says that the value is likely to change +frequently. + + +This is accomplished by selecting a juncture in an available mode of illusion, namely +dreaming, which annuls any distinction between an objective circumstance, and the +circumstance which exists according to your subjective judgment. In the first instance, | +don’t ask you to change your epistemology. Instead, to repeat, | select an available juncture +in lived experience at which the conventional epistomology gets collapsed. + + +You have to occupy yourself with the stroke-numeral to the point that you induce +yourself to dream about it. + +When, in apprehending a stroke-numeral, you “judge” the value of the numeral, the +number, this refers to the image you see and to the number-word which you may conclude +from the image. + +Suppose that in a single dreamed episode, you judge the value of the numeral at two +different moments. Suppose that at the second moment, you do not register any discre- +pancy between the value at the second moment and what the value was at the first +moment. Then you are permitted to disregard fallibility of memory, and to conclude that the +values were the same at both moments: because if your memory has changed the past, it +has done so tracelessly. A tracelessly-altered past may be accepted as the genuine past. + + +Refinements. The foregoing dream-construct may be “‘lifted” to waking experience, as +per the lengthy explanations in ““An Epistemic Calculus.”’ Now you are asked to alter your +epistemology, selectively to suspend a norm of realism. + +Now that we are concerned with waking experience, a supporting refinement is +possible. Suppose | make an expectation (which may be unverbalized) that the value of the +numeral at a future moment will be the same that it is now. This expectation cannot be +proved false, if: the undetermined time-reference ‘future moment” is applied only at those +later moments when the value is the same as at the moment the expectation was made. +(Any later moment when the value is not the same is set aside as not pertinent, or forgotten +at still later moments when the value is the same.) + + +As a postscript, there is another respect in which testing a fact requires trust in a +comparable fact. Suppose | make a verbalized expectation that the value of the numeral in +the future will be the same as at present. Then to test this expectation in the future depends +on my memory of my verbalization. My expectation cannot be belied unless | have a sound + +“memory that the number | verbalized in my expectation is different from the number | +conclude from the image now. + + +HT. Inconsistently-Valued Numerals + + +As the “Wedberg cube” illustrates, a cubical frame can be formed +in different ways, altering the likelihood that one or another image is +seen. With respect to the initial uses of the Necker-cube stroke-numeral +a figure is wanted which lends itself to the image of a cube projecting +up, or of a cube projecting down, with an approximately equal likeli- +hood for the two images—and which makes other images unlikely. +Now let a Necker cube be drawn large, with heavy line-segments, with +all segments equally long, with rhomboid front and back faces; and +display it below eye level. + + +As you look for the up and down orientations, there should be +moments when paradoxically you see the figure taking on both of these +mutually-exclusive orientations at once—yielding an apparition which +is a logical/ geometric impossibility. The sense-content in this case is +dizzying. + +That we have perceptions of the logically impossible when we +suffer illusions has been mentioned by academic authors. (Negative +afterimages of motion—the waterfall illusion.) Evidently, though, these +phenomenaare so distasteful to sciences which are still firmly Aristote- +lian that the relations of perception, habituation, language, and logic +manifested in these phenomena have never been assessed academically. +For me to treat the paradoxical image thoroughly here would be too +much of a digression from our subject, the apprehension of plurality. +However, a sketchy treatment of the features of the impossible image is +necessary here. + +To begin with, the paradoxical image of the Necker cube is not the +same phenomenon as the “impossible figures” shown in visual percep- +tion textbooks. The latter figures employ “puns” in perspective coding +such that parts of a figure are unambiguous, but the entire figure + + +cannot be grasped as a gestalt coherently. Then, the paradoxical Necker- +cube image is not an inconsistently oriented object (as the reader may +have noted). It is an apparitional depiction of an inconsistently oriented +object. But this is itself remarkable. For since a dually-oriented cube (in +Euclidean 3-space) is self-contradictory by geometric standards, a +picture of it amounts to a non-vacuous semantics for an inconsistency. +Another way of saying the same thing is that the paradoxically- +oriented image is real as an apparition. + +If one is serious about wanting a “logic of contradictions”—a logic +which admits inconsistencies, without a void semantics and without +entailing everything—then one will not attempt to get it by a contorted +weakening of received academic logic. One will start from a concrete +phenomenon which demands a logic of contradictions for its authentic +representation—and will let the contours of the phenomenon shape the +logic. + +In this connection, the paradoxically-oriented Necker-cube image +provides a lesson which I must explain here. Consider states or proper- +ties which are mutually exclusive, such as “married” and “bachelor.” +Their conjunction—in English, the compound noun “married +bachelor”—is inconsistent.* On the other hand, the joint denial +“unmarried nonbachelor” is perfectly consistent and is satisfied by +nonpersons: a table is an unmarried nonbachelor. “Married” and +“bachelor” are mutually exclusive, but not exhaustive, properties. Only +when the domain of possibility, or intensional domain, is restricted to +persons, so “married” and “bachelor” become exhaustive properties. ** +Then, by classical logic, “married bachelor” and “unmarried nonbache- +lor” both have the same semantics: they are both inconsistent, and thus +vacuous, and thus indistinguishable. For exhaustive opposites, joint +affirmation and joint denial are identically vacuous. + +But the paradoxically-oriented Necker-cube image provides a +concrete phenomenon which combines mutually exclusive states—as +an apparition. We can ascertain whether a concrete case behaves as the +tenets of logic prescribe. As I have said, various images can be seen ina +Necker cube, including a flat image. Thus, the “up” and “down” cubes + + +*If I must show that it is academically permitted to posit notions such as +these, then let me mention that Jan Mycielski calls “triangular circle” incon- +sistent in The Journal of Symbolic logic, Vol. 46, p. 625. + +**] invoke this device so that I may proceed to the main point quickly. If it +is felt to be too artificial, perhaps it can be eliminated later. + + +are analogous to “married” and “bachelor” in that they are not exhaus- +tive of a domain unless the domain is produced by restriction. Then +“neither up nor down” is made inconsistent. (It is very helpful if you +haven't learned to see any stable images other than “up” and “down.”) +The great lesson here is that given “both up and down” and “neither up +nor down” as inconsistent, their concrete reference is quite different. To +see a cube which manifests both orientations at the same time is one +paradoxical condition, which we know how to realize. To see a cube +which has no orientation (absence of “stroke” and absence of “vacant” +both) would be a different paradoxical condition, which we do not +know how to realize and which may not be realizable from the Necker- +cube figure. I don’t claim that this is fully worked out; but it intimates a +violation of classical logic so important that I had to mention it. When +concept art reaches the level of reconstructing our inferential intuitions +as well as our quantitative intuitions, such anomalies as these will surely +be important. + +Referring back to the Necker cube of page 210, let us now intend it +as a stroke-numeral (display of one figure). Let me modify the previous +assignments and stipulate that “blank” means “zero,” rather than “no +numeral present.” (It is more convenient if every sign yields a numeral.) +When you see the paradoxical image, you are genuinely seeing “a” +numeral which is the simultaneous presence of two mutually exclusive +numerals “one” and “zero” —because it is the simultaneous presence of +images which are mutually exclusive geometrically.*** + +It’s not the same thing as + + +| + + +—because these are merely ambiguous scripts. In the Necker-cube case, +two determinate images which by logic preclude each other are present +at once; and as these images are different numerals, we have a genuine + + +—or as an alternative, + + +*For brevity, I may compress the three levels image, sign, numeral in +exposition. + + +inconsistently-valued numeral. + +This situation changes features of the Necker-cube numerals in +important ways, however. Lessons from above become crucial. We +transfer the ostensive hermeneutic to the new situation, and find an +inconsistent-valued numeral. But this is no longer an ostensive +numeral. We have a name which is one and zero simultaneously, but +this is because of the impossible shape (orientation) of the notation- +token. What we do not have is a collection of images of a single kind +(the stroke) which paradoxically requires a count of one and a count of +zero. “Stroke” is positively present, while “vacant” is positively present +in the same place. We will find that a display with two figures can be +inconsistent as zero and two; but it is not an ostensive numeral, because +the number of strokes present is two uniquely.* Here the numerals are +not identically their semantics: for the anomaly is not an anomaly of +counting. The ambiguous script numeral is a proper analogy in this +respect. To give an anomaly of counting which serves as a concrete +semantics for the inconsistently-valued numerals, I will turn to an +entirely different modality. + +From work with the paradoxical image, we learn that the Necker +cube allows some apprehensions which are not as commonas others— +but which can be fostered by the way the figure is made and by +indicating what is to be seen. These rare apprehensions then become +intersubjectively determinate. If one observes Necker-cube displays for +a long time, one may well observe subtle, transient effects. For exam- +ple, you might see the “up” and “down” orientations at the same time, +but see one as dominating the other. In fact, there are too many such +effects and their interpersonal replicability is dubious. If we accepted +such effects as determining numerals, the interpersonal replicability of +the symbols would be eroded. Also the concrete definiteness of my +anomalous, paradoxical effects would be eroded. So I must stipulate +that every subtle transient effect which I do not acknowledge explicitly +is not definitive, and is unwanted, when the display is intended as a +symbolism. + +Let me continue the explanation, for the inconsistently-valued + + +*Referring to my “person-world analysis” and to the dichotomy of +Paradigm | and Paradigm 2 expounded in “Personhood III,” this token which +is two mutually exclusive numerals because its shape is inconsistent is outside +that dichotomy: because established signs acquire a complication which is +more or less self-explanatory, but the meanings do not follow suit. + + +numerals, for displays of more than one figure. When the display +consists of two Necker cubes, and the paradoxical images are admitted, +what are the variations? In the first place, one figure might be seen (ina +moment) as a paradoxical image and the other as a unary image. +Actually, if it is important to obtain this variant, we can compel it, by +drawing one of the cubes in a way which hampers the double image. +(Thin lines, square front and back faces, the four side segments much +shorter than the front and back segments.) Then we stipulate that the +differently-formed cubes continue to have the same assigned interpre- +tation. + + +Reading the two-figure display, then, the paradoxical and unary +images concatenate so that the resulting numeral is in one case one and +two at the same time; and in the other case zero and one at the same +time. Of course, it is only ina moment that either of these two cases will +be realized. At other moments, one may have only unary images, so +that the numeral is noncontradictorily zero, one, or two as the case may +be. (If it is important to know that we can obtain a numeral which is +both one and two at the same time without using dissimilar figures, +then, of course, we can use a single figure and redefine the signs as “one” +and “two.”) + +Now let us consider a display of two copies of the cube which lends +itself to the paradoxical image. Suppose that two paradoxical images +are seen; what is the numeral? Here is where I need the proviso which I +introduced earlier. Every sign-row is capable of being grasped as a +numeral, as a gestalt; and the appraisal of image-rows as numerals, +analytically, is ruled out. Let me explain how this proviso applies when +two paradoxical images are seen. + +Indeed, let me begin with the case of a pair of ambiguous + + +script-numerals: ] ] + + +When these numerals are formed as exact copies, and I appraise the +expression as a numeral, as a gestalt, then I see 11 or I see 22. (“Conca- +tenating in parallel”) I do not see 21 or 12—although these variants are +possible to an analytical appraisal of the expression. In the gestalt, it is +unlikely to intend the left and right figures differently. This case is +helpful heuristically, because it provides a situation in which the percep- +tual modification is only a matter of emphasis (as opposed to imputa- +tion of depth). To this degree, the juncture at issue is externalized; and it +is easier to argue a particular outcome. On the other hand, the mechan- +ics differ essentially in the script case and the Necker-cube case. + +In the Necker-cube case, one sees both the left and the right image +determinately both ways at once. This case may be represented as + + +stroke stroke +vacant vacant + + +Analytically, then, four variants are available here, + + +stroke-stroke + +stroke-vacant +vacant-stroke +vacant-vacant + + +However, to complete the present explanation, only two of these +variants appear as gestalts, + + +stroke-stroke +vacant-vacant + + +I chose to rule out the three-valued numeral which would be obtained +by analytically inventorying the permutations of the signs afforded in +the perception. The two-valued numeral arising when the sign-row is +grasped as a gestalt is definitive. + +Let me summarize informally what I have established. Relative to +a two-figure display with paradoxical images admitted, we have a +numeral which is inconsistenly two and zero. We can also have a +numeral which is inconsistently one and zero, and a numeral which is +inconsistently two and one. (In fact, these variants occur in several +ways.) But we don’t have a numeral which is inconsistently zero, one, +and two—even though such a variant is available in an analytical +appraisal—because such a numeral does not appear, in perception, asa +gestalt. + +Academic logic would never imagine that there is a situation +which demands just this configuration as its representation. Certain + + +definite positive inconsistencies are available in perception. Other defi- +nite positive inconsistencies, very near to them, are not available. Once +again, if one wants a vital “logic of contradictions,” one has to develop +it as a representation of concrete phenomena; not as an unmotivated +contortion of received academic logics. + + +But what is the use of inconsistently-valued numerals? I shall now +provide the promised concrete semantics for them. This semantics +utilizes another experience of a logical impossibility in perception. This +time the sensory modality is touch; and the experienced contradiction +is one of enumeration. Aristotle’s illusion is well known in whicha rod, +placed between the tips of crossed fingers, is felt as two rods. (Actually, +the greater oddity is that when the rod is held between uncrossed +fingers, it is felt as one even though it makes two contacts with the +hand.) I now replace the rod with a finger of the other hand: the same +finger is felt as one finger in one hand, as two fingers by the other hand. +So the same entity is apprehended as being of different pluralities, in +one sensory modality. + +Let me introduce some notation to make it easier to elaborate. +Abbreviate “left-hand” as L and “right-hand” as R. Denote the first, +middle, ring, and little fingers, respectively, as 1, 2,3, and 4. Now cross +L2 and L3, and touch R3 between the tips of L2 and L3. One feels R3 as +one finger in the right hand, and as two fingers with the left hand. As +apparition, R3 gets a count of both one and two, apprehended in the +same sensory modality at the same time. Here is a phenomenon +authentically signified by a Necker-cube numeral which is both “1” and +“> + +The crossed-finger device is obviously unwieldy. The possibilities +can, however, be enlarged somewhat, to make a further useful point. +For example, touch L1 and R3, while touching crossed L2 and L3 with +R4. Here we have a plurality, concatenated from one unary and one +paradoxical constituent, which numbers two and three at the same +time. + +Then, we may cross L1 and L2 and touch R3, while crossing L3 +and L4 and touching R4. Now we have a plurality which is two and +four at the same time. In terms of perceptual structure, it is analogous +to the numeral concatenated from two paradoxical images. As gestalt, +we concatenate in parallel. In the case of the fingers, we do not find a +plurality of three unless we appraise the perception analytically (block- + + +ing concatenation in parallel). + +If one wants the inconsistently-valued numerals to be ostensive +numerals, then one can use finger-apparitions to constitute stroke- +numerals. Referring back to the first example, if we specify that the +stroke(s) is your R3-perception, or the apparition R3, then we obtaina +stroke which is single and double at the same time. Now the +inconsistently-valued numeral is identically its semantics: it authenti- +cally names the token-plurality which constitutes it. + +I choose not to rely heavily on this device because it is so unwieldy. +The visual device is superior in that considerably longer constellations +are in the grasp of one person. Of course, if one chose to define fingers +as the tokens of ordinary counting, one might keep track of numbers +larger than ten by calling upon more than one person. The analogous +device could be posited with respect to the inconsistently-valued +numbers; but then postulates about intersubjectivity would have to be +stated formally. I do not wish to pursue this approach. + +It is worth mentioning that if you hold a rod vertically in the near +center of your visual field, hold a mirror beyond it, and focus your gaze +on the rod, then you will see the rod reflected double in the mirror. This +is probably not an inconsistent perception, because the inconsistent +counts don’t apply to the same apparition. (But if we add Kant’s +postulate that a reflection exactly copies spacial relations among parts +of the object, then the illusion does bring us close to inconsistency.) The +illusion illustrates, though, that there is a rich domain of phenomena +which support mutable and inconsistent enumeration. + + +IV. Magnitude A rithmatic + + +I will end this stage of the work with an entirely different approach +to subjectively variable numerals and quantities. I use the horizontal- +vertical illusion, the same that appeared in “Ilusions,” to form numer- +als. The numeral called “one” is now the standard horizontal-vertical +illusion with a measured ratio of one between the segments. The +numeral called “two” becomes a horizontal-vertical figure such that the +vertical has a measured ratio of two to the horizontal segment. Etc. If +“zero” is wanted, it consists of the horizontal segment only. + +The meaning of each numeral is defined as the apparent, perceived +length-ratio of the vertical to the horizontal segment. Thus, for exam- +ple, the meaning of the numeral called “one” admits subjective varia- +tion above the measured magnitude. For brevity, I call this approach +magnitude arithmetic—although the important thing is how the mag- +nitudes are realized. + + +In all of the work with stroke-numerals, numbers were determina- +tions of plurality. An ostensive numeral was a numeral formed from a +quantity of simple tokens, which quantity was named by the expres- +sion. The issue in perception was the ability to make gestalt judgments +of assemblies of copies of a simple token. + +The magnitude numerals establish a different situation. Magni- +tude numerals pertain to quantity as magnitude. They relate to plural- +ity only in the sense that in fact, measured vertical segments are integer +multiples of a unit length; and e.g. the apprehended meaning of “two” +will be a magnitude always between the apprehended meanings of +“one” and “three”—etc. + +Once again we can distinguish a bicultural and an ostensive +hermeneutic. The bicultural hermeneutic involves judging meanings of +the numerals with estimates in terms of the conventional assignment of +fractions to lengths (as on a ruler). I find, for example, that the +magnitude numeral “two” may have a meaning which is almost 3. +(Larger numerals become completely unwieldly, of course. The point of +the device is to establish a principle, and I’m not required to provide for +large numerals.) + +Then there must be an ostensive hermeneutic, a “magnitude- +ostensive” hermeneutic. Here the subjective variations of magnitude do +not receive number-names. They are apprehended (and retentionally +remembered) ostensively. + +As I pointed out, above, the concept of equality with regard to +Necker-cube numerals is at present an open problem. To write an +equality between two Necker-cube displays of the same length is not +obviously cogent; in fat, it is distinctly implausible. For magnitude +numerals, however, it is entirely plausible to set numbers equal to +themselves—e.g. + + +The point is that it is highly likely that copies of a magnitude numeral +will be apprehended or appraised correlatively. This was by no means +guaranteed for copies of a Necker-cube numeral displayed in proximity. + + +Upon being convinced that these simplest of equations are mean- +ingful, we may stipulate a simple addition, “one” plus “one” equals +“two.” (It was not possible to do anything this straightforward with +Necker-cube numerals.) Continuing, we may write a subtraction with +these numerals. There may now appear a complication in the rationale +of combination of these quantities. The “two” in the subtraction may +appear shorter than the “two” in the addition. A dependence of percep- +tions of these numbers on context may be involved. + +We find, further, that “readings” of these equations according to +the bicutural hermeneutic yield propositions which are false when +referred back to school-arithmetic—e.g. the addition might be read as + + +I'/s + 1's = 24/s + + +So the effect of inventing a context in which a relationship called “one +plus one equals two” is appraised as 1!/5 + 1!/; = 24/5 (where there is a +palpable motivation for doing this) is to erode school-arithmetic. + +Another approach to the same problem is to ask whether magni- +tude arithmetic authentically describes any palpable phenomenon. The +answer is that it does, but that the phenomenon in question is the +illusion, or rationale of the illusion. The significant phenomenon arises +from having both a measured ratio and a visually-apparent ratio, which +diverge. This is very different from claiming equations among non- +integral magnitudes without any motivation for doing so. Indeed, given +that the divergence is the phenomenon, the numerals are not really +ostensive in a straightforward way. + +One way of illustrating the power of the phenomenon which +models magnitude arithmetic is to display ruler grids flush with the +segments of a horizontal-vertical figure. + + +What we find is that the illusion visually captures the ruler grids: it +withstands objective measurement and overcomes it. We have a non- +trivial, systematic divergence between two overlapping modalities for +appraising length-ratios—one modality being considered by this cul- +ture to be subjective, and the other not. + + +In “Derivation” I used multistable cube figures to give a simplified, +discrete analogue of the potentially continuous “vocabulary” in “Illu- +sions.” I could try something similar for magnitude numerals. Take as +the magnitude unit a black bar representing an objective unit of twenty +20ths, concatenated with a row of five Necker cubes. Each cube seen in +the “up” orientation adds another 20th to the judged magnitude of the +subjective unit, so that the unit’s subjective magnitude can range to 14. +When, however, we write the basic equality between units, it becomes +clear that this device does not function as it is meant to. In particular, +the claim of equality applied to the Necker-cube tails is not plausible, +because it is not guaranteed that these tails will be apprehended or +appraised correlatively. I have included this case as another illutration +of the sort of inventiveness which this work requires; and also to +illustrate how a device may be inadequate. + + +* * * + + +This completes the present stage of the work. Let me emphasize +that this manual does little more than define certain devices developed +in the summer of 1987. These devices can surely give rise to substantial +lessons and substantial applications. + +There is my pending project in a priori neurocybernetics. Given +that mechanistic neurophysiology arrives at a mind-reading machine— +called, in neurophysiological theory, an autocerebroscope—devise a +text for the human subject such that reading it will place the machine in +an impossible state (or short-circuit it). Such a problem is treated +facetiously in Raymond Smullyan’s 5000 B.C.; and more seriously by +Gordon G. Globus’ “Mind, Structure, and Contradiction,” in Con- +sciousness and the Brain, ed. Gordon Globus et al. (New York, 1976), p. +283 in particular. But I imagine that my Necker-cube notations will be +the key to the first profound, extra-cultural solution. + +In any case, this essay is only the beginning of an enterprise which +requires collateral studies and persistence far into the future to be +fulfilled. (I may say that I first envisioned the possibility of the present +results about twenty-five years ago.) + + +Background References + + +David Hilbert, three papers in From Frege to Godel, ed. Jean van Heijenoort +(1967) + +David Hilbert, “Neubegrundung der Mathematik” (1922) + +David Hilbert and P. Bernays, Grundlagen der Mathematik I (Berlin, 1968), +pp. 20-25 + +Plato, “Philebus” + +Aristotle, Metaphysics, 1.6 + +Proclus, A Commentary on the First Book of Euclid’s Elements, tr. Glenn +Morrow (Princeton, 1970), 54-55 + +Hans Freudenthal, Lincos: Design of a Language for Cosmic Intercourse +(Amsterdam, 1960), pp. 14-5, 17, 21, 45-6 + +Kurt Godel in The Philosophy of Bertrand Russell, ed. Paul Schilpp (1944), p. +137 + +W.V.O. Quine, Mathematical Logic (revised), pp. 121-2 + +Paul Benacerraf, “What numbers could not be,” in Philosophy of Mathemat- +ics (2nd edition), ed. Paul Beneacerraf and Hilary Putnam (1983) + +Leslie A. White, “The Locus of Mathematical Reality: An Anthropological +Footnote,” in The World of Mathematics, ed. J.R. Newman, Vol. 4, pp. +2348-2364 + +Herman Weyl, Philosophy of Mathematics and Natural Science (Princeton, +1949), pp. 34-7, 55-66 + +Andrei Markov, Theory of Algorithms (Jerusalem, 1961) + +G.T. Kneebone, Mathematical Logic and the Foundations of Mathematics +(London, 1963), p. 204ff. + +Michael Resnik, Frege and the Philosophy of Mathematics (Ithaca, 1980), pp. +82, 99 + +Ludwig Wittgenstein, Wittgenstein’s Lectures on the Foundations of Mathe- +matics (1976), p. 24; but p. 273 + +Ludwig Wittgenstein, Philosophical Grammer (Oxford, 1974), pp. 330-331 + +Steven M. Rosen in Physics and the Ultimate Significance of Time, ed. David +R. Griffin (1986), pp. 225-7 + +Edgar Rubin, “Visual Figures Apparently Incompatible with Geometry,” +Acta Psychologica, Vol. 7 (1950), pp. 365-87 + +E.T. Rasmussen, “On Perspectoid Distances,” Acta Pschologica, Vol. Il +(1955), pp. 297-302 + +N.C.A. da Costa, “On the Theory of Inconsistent Formal Systems,” Notre +Dame Journal of Formal Logic, Vol. 15, pp. 497-510 + +FG. Asenjo and J. Tamburino, “Logic of Antinomies,” Notre Dame Journal +of Formal Logic, Vol. 16, pp. 17-44 + + +Richard Routley and R.K. Meyer, “Dialectical Logic, Classical Logic, and the +Consistency of the World,” Studies in Soviet Thought, Vol. 16, pp. 1-25 + +Nicolas Goodman, “The Logic of Contradiction,” Zeitschr. f. math. Logik und +Grundlagen d. Math., Vol. 27, pp. 119-126 + +Hristo Smolenov, “Paraconsistency, Paracompleteness and Intentional Con- +tradictions,” in Epistemology and Philosophy of Science (1982) + +J.B. Rosser and A.R. Turquette, Many-valued Logics (1952), pp. 1-9 + +Gordon G. Globus, “Mind, Structure, and Contradiction,” in Conciousness +and the Brain, ed. Gordon Globus et al. (New York, 1976), p. 283 + + diff --git a/extra/general_acognitive_culture.tex b/extra/general_acognitive_culture.tex new file mode 100644 index 0000000..1561bc7 --- /dev/null +++ b/extra/general_acognitive_culture.tex @@ -0,0 +1,29 @@ +\chapter{My New Concept of General Acognitive Culture} + +{\itshape [This essay was written c. May 1962 and published in \journaltitle{d\'{e}collage No. 3.} This transcription serves to correct the typographical errors. Footnotes are written in 1992.]} + +Of the adult (human) activities I discredit explicitly, consider pure mathematics (and structure art and games of intellectual skill), and Serious Culture\slash all art\slash literary culture\slash science fiction\slash music. I show that these activities (as such) should be repudiated. Now humans are likely in any case to resist this radical idea of repudiating these major institutionalized activities; but especially if nothing were to take their place, if the idea were negative only. Even when the activities' Serious Cultural pretensions have been discredited and repudiated, and their obvious confusions of purpose have been noted,\footnote{cf. \essaytitle{Concept Art} on music} humans are likely to be interested in them still, to like them in at least one respect: for their entertainment, recreational value; for their value as \enquote{ends,} in themselves. (And are thus likely to fear that to repudiate these activities without anything's taking their place would be to give up all recreation, doing things \enquote{just for fun,} doing things just liked.) Now this chapter will be first, an analysis of the concept of entertainment, recreation, of doing things just liked, which will criticize the activities even as just entertainment. (And will discredit my own initial notion of \term{acognitive culture,} as not going far enough.) + +I discredit these activities, show they should be repudiated, for \enquote{everybody,} adult humans and creeps. Now since I am a creep, my primary constructive concern is to point out something rather than these activities, for creeps: my new concept of \term{creep acognitive culture.} However, I am going to \enquote{do adult humans a favor} in the hope that it will keep them from just changing the discredited activities into something no less wrong and confused, and will encourage them to repudiate the activities. \enquote{Creep acognitive culture} is, to speak generally, a concept of \enquote{recreation} (resulting from analysis of the concept of recreation) for conscious organisms. Part of it is applicable for adult humans (as well as creeps), in replacing the discredited activities for them. I am going to give that general part here, in this book\footnote{This essay was a chapter in a book in early 1962; that book must have become From Culture to Veramusement.}---my new concept of \term{general acognitive culture.} (The specialization for creeps I will give in Creep.) The specialization of this concept for adult humans I will leave to them, since that is their concern. Incidentally, even though generally applicable, the characteristics of general acognitive culture may be reminiscent of creepiness, but they will not in any case embarrass mature adults, which is where I draw the line between the adult human and the really creep. + +To give a better idea of the major area of life, \enquote{recreation,} I am concerned with here, let me mention, along with the activities mentioned above: games, possibly athletics \enquote{for fun,} conventional entertainment and recreation, and children's play. Or \term{acognitive culture} in my initial sense. Further, let me suggest the area with respect to its place in (adult) human life today. Naively, a worker has a job, job hours, an occupation, does work (which produces material wealth), to obtain his means of consumption. His job is a \enquote{means}; even though he may like it he is pretty much forced to do it. This can be extended to apply to the whole area of his responsibilities to society. Then he has after-hours, time when he doesn't have to do anything, and does what he does more as an end, in itself, \enquote{for fun,} because he likes it: here is where recreation is included. This is when workers listen to music, read science fiction, play games, and the rest. A thing is more purely recreational the more it is done just \enquote{for fun,} the more is it is not an extension of the job, a means. This can be extended to apply to the whole area of what he does just because he likes it; and the area can now be conceived as existing (presumably as a matter of course) side-by-side what he does \enquote{for society.} All this can be said about recreation today. + +To arrive at the preliminaries of my concept of general acognitive culture, a certain concept of \enquote{recreation} applicable for any conscious organisms (my initial notion of \term{acognitive culture}), let me give some characteristics which the activities I have listed, in their recreational aspect, have in common, which would apply for any conscious organisms. No one of the activities is biologically necessary (or biologically harmful) to the organism. Probably no one is necessary for society, co-operation among the organisms. They are not technology (although they may use it). As (\enquote{mere}) recreation, they are not supposed to have cognitive value (and in particular are without associated cognitive pretensions, so that they cannot be Serious Culture). (They may use believings, especially wrong ones, as \enquote{experiences,} but these are not claimed to have cognitive value in any way.) They do not involve anything, in particular sensuous indulgence, which has sophistication-proving significance. And of course, they are entertainment, recreation, are things just liked. These characteristics are the preliminary, initial determination of the parts of life, of any conscious organism, which I am selecting out to consider as one area, a unity, that of acognitive culture. + +Having located and initially determined the area of life I am concerned with, I will now analyze, explicate the concept of pure entertainment, recreation, doing things just liked (with respect to the individual); and at the same time elaborate my new concept of general acognitive culture. Consider, for contrast, work, or the cognitive. With respect to these, there are \enquote{objective} or \enquote{intersubjective standards of value,} for ex., whether a table top is level, or whether many people like a thing. One may well make a contribution to these areas even if one doesn't like the areas, or one's contribution; one can make a level table even if one dislikes the table and finds making it tedious. It makes sense to specially exert oneself to contribute to these areas, to drive oneself to work in them even though one would just as soon do something else. Now 'recreation' connotes, \term{general acognitive culture} is defined to be, exactly the opposite. One does the latter because one likes it (now), for no other reason. It doesn't make sense to try to do acognitive culture as objectively valuable, in conformity with objective standards. If one doesn't like what one does, it can't be acognitive culture. One can't create acognitive culture as a profession. + +It is obvious, then, that Serious Cultural institutionalized activities, doing things in Serious Cultural institutional Forms, such as the Fugue, cannot be recreation, acognitive culture. What is not obvious, a point of this analysis, is that the whole institution of society's providing Forms (for the individual to do things in) supposedly for his recreation and self-expression, such as Science Fiction and Pole-Vaulting (or my Linact\footnote{ +Linguistic acognitive cultural activity. Extant examples are my \essaytitle{Poem 1} and \essaytitle{Poem 4.}}), is absurd. The notion that the Forms are the real right ones, represent the real right thing to do, are objectively valuable, inevitably grows up around them. As an example, consider the Form of \enquote{Composition,} as any writing of specifications of activities (supposedly) for others to do as recreation. Compositions are primarily the writings, as opposed to doing the activities specified; their existence begins when the writings are completed. They are for \enquote{others} to do (and may never be done by anyone), showing that they are thought to be objectively valuable. The tendency is to turn out and store up quantities of them no matter whether the composer or anyone else likes them. Recreation, acognitive culture, cannot include Composition. Then there is the notion that given a Form, such as I am considering, one should do things in it whether one likes to or not, until one \enquote{understands} the Form, because one will like to then; and that the Form is objectively good if this happens. This has no place in recreation, acognitive culture. People who do things in these Forms all do so largely because they have acquired the notion that the Forms are the real right ones, are objectively more valuable than just anything. A proof of this is that the Forms are so extremely \enquote{objective,} common, impersonal. This is why one can be unable to tell anything about the people themselves from what they do in the Forms. People have no idea of the extreme extent to which they are socialized even in what they do for recreation, self-expression. Even being a writer of any kind, a maker of objects, a creator of works, in the traditional, established, and common sense, is already extremely objective, impersonal, and indicates that one is extremely socialized. (This is what was wrong with my initial notion of \term{acognitive culture}.) The reader may ask, if these Forms are so impersonal, what a personal Form will be like, how personal one can get. The answer will be given below. + +Thus, an excellent determining principle is that it's pure recreation, acognitive culture only if it's what one would have done, would do, are doing, \enquote{anyway}; \enquote{prior} (to being \enquote{advanced} enough) to \enquote{know} the real, right, objective, the impersonal things to do, not from trying to contribute to an established real, right Form. Acognitive culture is not created by special exertion. One does it \enquote{anyway} \enquote{first,} and \enquote{then} it turns out to be in the category of \term{acognitive culture.} In fact, the concept of acognitive culture is only used applying retroactively. One doesn't set out to produce so many units of acognitive culture; one realizes that what one did which one would have done anyway was acognitive culture. What, then, is the reason for making the analysis, having the concept at all? Conscientious persons who have suspected the impersonality, of established Forms supposedly for their recreation and self-expression, have had great difficulty in repudiating the Forms, in not being ashamed of not contributing to them, not feeling that they have stopped doing anything. The reason for making the analysis, having the concept, is to help these persons with this difficult step, and to show those who are to give up the discredited activities what replaces them: to show that in giving them up they have not given up doing things just liked. So that they will \enquote{take seriously,} pride themselves on what they do just \enquote{for fun,} doing what they like, would do anyway; rather than being ashamed because they do not contribute to the discredited activities. The analysis, concept, is to make possible an attitude so one can thoroughly, consciously do things just liked. + +Since acognitive culture is what one would do anyway, does entirely because one likes it, is for one's liking, it excludes entertaining others, conforming to another's likes---which are an intersubjective standard, making entertaining work. Further, on analysis, being entertained by another, another's creation, becomes questionable. Can the \enquote{creation} of another be liked by oneself, be for one's liking, represent oneself, as well as the \enquote{creation} of oneself? One may admire work by another, with respect to an objective standard, as being better than one's work with respect to that standard, but all that is irrelevant to acognitive culture. If it fits oneself who's doing the liking, if one allows oneself one's likings, then oneself is the source of value and, it would seem, will as a matter of course like one's creations best. Does it make sense for me to appreciate \enquote{great} chess players, poets, pole-vaulters (if their activities are to be regarded as recreation)? My point here is quite radical, but would seem entirely plausible. To go back, analysis of the concept of entertainment shows that separation of entertainer from entertained is incompatible with a thorough-going concept of pure entertainment; entertaining as work is discredited. This does not exclude every kind of involvement of others in one's recreation. + +All this leads to the idea of (one's) acognitive culture as a part of oneself---as within oneself, at least so far as specifications are concerned. This would seem to be the opposite of contributions to impersonal Forms. Acognitive culture (being what one would do anyway) would not, it would seem, consist of artifacts built up outside of, separate from, oneself, to be gone back to (for ex. recordings, writings); or specifications one would have to be concerned about remembering. If one is wanting \enquote{what one likes, would do anyway,} one will have it; one shouldn't have to be concerned about retaining it. + +The reader may have been asking, 'But may not merely what one would do anyway be less interesting than the pseudo-recreation which is created by special exertion, such as Flynt's \essaytitle{Reproduction of the Memory of an Energy Cube Organism}?' Strictly speaking, this question doesn't make sense: how could anything be more interesting to oneself, likable, than what one just likes, than what one would do anyway \enquote{prior} to \enquote{knowing} the real, right thing to to? However, I will give a heuristic answer to the question. Asking the question shows that one has as yet no idea of what specific doings would be included by the category of \enquote{acognitive culture} as I have defined it. They may well be so different from the discredited activities, the traditional, established, common real right Forms supposedly for recreation and self-expression, as to be irrelevant to them, so to speak. They are going to be indefinitely\footnote{incalculably?} more \enquote{new,} \enquote{different,} interesting, just as individuality is more so than anonymity. It is a matter of one's realizing that what fulfills the supposed function of the discredited activities are things one would not have thought of as replacements for them. All this will become obvious, when one considers what specific doings of oneself meet all of the specifications, are included by the category of \term{acognitive culture} as I have defined it. It may further be asked whether doing just what one would do anyway won't lead to a nihilism of acognitive culture's becoming indistinct, being absorbed in undistinguished personality, life, leaving only \enquote{nature}; or a nihilism that if acognitive culture needs to happen it will just happen, a nihilism of not doing anything. Well, something disappears, namely trying to do things just liked as a real right objectively valuable Form, a profession, by special exertion. However, acognitive culture doesn't disappear, because conscious organisms in any case just do anyway things just liked, which are distinguished, and which are \enquote{then} included by the category of \term{acognitive culture,} \enquote{people have their recreation}---the category of \term{acognitive culture} represents a selecting out of things which presumably the life of any conscious organism will include, for which there will presumably be a place in any life. + +As I have mentioned the possibility that the reader may as yet have no idea of what specific doings would be included by the category of acognitive culture as I have defined it, it might seem in order for me to describe some examples of such specific doings. Actually, however, it is just not in the spirit of acognitive culture to try to describe such examples. Real acognitive culture is not likely to lend itself to reduction to words. And trying to describe examples of acognitive culture cannot but be a tendency to make them into works; actually, there is no reason why one's acognitive culture should mean anything to another, or even to oneself at another time. Thus, although I might informally describe examples in conversation, I am not going to try to write any up. The reader who does not yet understand what specific doings are included by the category will just have to study the specifications of acognitive culture some more, and then consider what specific doings meet all of them. When the reader does understand, then he can discover the parts of what he does anyway, already does, that are included by the category of acognitive culture: they are his acognitive culture. + +This completes the elaboration of the concept of general acognitive culture. My proposal can now be seen to be plausible, that one give up the discredited activities, all established real right activities which would otherwise be retained as quasi-recreation; and have in their place \enquote{nothing,} except one's acognitive culture, or rather recognition of it. Now this chapter is relatively short, and the ideas in it are intrinsically simple. At the same time, it is of major scope; and it is socially radical, counter to major entrenched interests, institutionalized chess, institutionalized art, Olympic games, and the rest. In the past, there has been a tendency for people to read, but not \enquote{notice,} such writings. I want last to say something to counter any such tendency with respect to this chapter. This chapter may be short and simple, but it is what I have been led to, my complete conclusions, after years of contributing to art and post-artistic activities and thinking about aesthetics and post-aesthetic fields (in an attempt not to waste time as a result of taking the wrong things for granted). Further, it will be outrageous if this chapter is ignored, just bypassed, merely because it discredits major entrenched interests while being short and simple. + diff --git a/extra/philosophy_of_concept_art.tex b/extra/philosophy_of_concept_art.tex new file mode 100644 index 0000000..f2431ef --- /dev/null +++ b/extra/philosophy_of_concept_art.tex @@ -0,0 +1,1161 @@ +\newcommand{\action}[1]{[\textit{#1}]} + +\newcommand{\speaker}[1]{\vskip 0.2em \textsc{#1}: } +\newcommand{\speakermod}[2]{\vskip 0.2em \textsc{#1} \textit{(#2)}: } + +\chapter{Philosophy of Concept Art (1987)} + +{ \centering \itshape +An interview with Henry Flynt \\ +by Christer Hennix \\ +Dec. 6, 1987 \par } + + +\speaker{FLYNT} I'm going to give a summary of how I originated Concept Art +in order to bring it up to the point where it's understandable why I +speak of you (Catherine Christer Hennix) as my only successor in the genre. +Summarizing briefly, I see two things coming together. One of them +was my involvement with the modern music community of the time---Stockhausen, +Cage, LaMonte Young---and the other aspect was that I +had been a mathematics major at Harvard and already knew that I +thought of myself primarily as a philosopher---that my intention had +been when I was very young, when I didn't understand the situation +that I was in---my intention had been to become a philosopher with +nevertheless a specialization in mathematics. Of course, many people +actually did that. + +So, having said that, one of the things that I began to notice about +the modern music of that time was this extremely strong pseudo- +intellectual dimension in Stockhausen---Stockhausen's theoretical +journal \journaltitle{die Reihe}---the impression that they were doing science +actually---for example Stockhausen had a long essay on how the +duration of the notes had to correspond to the twelve pitches of the +chromatic scale \ldots + +\speaker{HENNIX} "\ldots\ how time passes\ldots"\footnote{\journaltitle{die Reihe 3}} + +\speaker{FLYNT} Yes, and what is more, the other rhythms had to correspond to +the overtone structure above those frequencies as fundamentals. + +\speaker{HENNIX} Yes, I'm quite familiar with that. + +\speaker{FLYNT} Yes, I would expect you would be. I remember Bo +Nilson---you will like this---in 1958 at the same time I saw Stockhausen's +score---he went even one step further than Stockhausen because he +used fractional amplitude specifications---so this is even more than +Stockhausen, and so forth and so on. + +Cage took a considerable step further in the sense that in Cage this +kind of play with structure is carried to the point where there is an +extreme dissociation between what the composer sees and what the +performer sees in terms of the structure of the piece and what the +audience knows. They are completely divorced from one another. Cage +would compose a piece on a graph in which the time that a note begins +is on one axis and the length of the note is on another axis. What he +would do was to superimpose that on some picture like from a star +catalogue--- + + +\speaker{HENNIX} \opustitle{Atlas Eclipticalis}--- + + +\speaker{FLYNT} Yeah, well, that's the particular piece. I'm making up a +composite of his compositional techniques but the result is that when you +break up a sequential event in that way, it's not like a pitch-time graph +where there's an intuitive recognition of the way the process unfolds. +He would have one structure for beginnings and another structure for +durations. Well at any rate, already in Cage's music there was a kind of +ritual aspect to performing classical music. I mean in Cage's piece, +which is actually all silence---the only thing the pianist does is open and +close the lid of the piano or something like that. + +Then LaMonte Young comes along. His word pieces were the first +that I ever saw, composed in mid-1960. I saw them in December +1960.\footnote{Other composers have earlier dates, but for me, +Young crystallized the genre. [H.F., note added]} +It was a very different kind of structural game. It was no longer like +twelve-tone organization and so forth but rather it was like playing +with paradoxes---it was nearer to making a paradox than making some +kind of complicated network. + +And I felt that matters had reached the point where there was +some kind of inauthenticity here because the point of the work of art +had become some kind of structural or conceptual play, and yet it was +being realized under the guise of music so that the audience had no +chance of really seeing what was supposed to be the point of the +piece---the audience was actually prevented from seeing. Certainly +Cage's methods had exactly that effect. The audience receives an +experience which simply sounds like chaos but in fact what they are +hearing is not chaos but a hidden structure which is so hidden that it +cannot be reconstructed from the performed sound. It's so hidden that +it can't be reconstructed but nevertheless Cage knows what it is. So I +felt that the confusion between whether they were doing music or +whether they were doing something else had reached a point where I +found that disturbing or unacceptable. + +At the same time at that period there was a great fascination in sort +of taking the Stockhausen attitude and looking back at the history of +music from that point of view. Stockhausen's analysis in \journaltitle{die Reihe 2} of +Webern's \opustitle{String Quartet [Op. 28]} tried to show that Webern was +composing total serial music and not just twelve tone music. That was +the attitude, they were rewriting the history of music, trying to show +that all previous important figures were essentially preoccupied with +structure, that they had been complete structuralists. + + +\speaker{HENNIX} Really? I thought it was only Webern that was given that +treatment. + + +\speaker{FLYNT} Well, they were digging up all these composers from the +Middle Ages, the isorhythmic motet and everything like that---they +were sort of dredging that up because that was the previous +period---the medieval scores in the form of a circle and the use of insertion +syncopation,\footnote{My term for the rhythmic feature common to Magister Zacharias' \opustitle{Sumite Karissimi} and \opustitle{Klavierst\"{u}uck XI}. See Willi Apel, \booktitle{The Notation of Polyphonic Music} (4th ed.), p. 432 for \opustitle{Sumite Karissimi}. [H.F., note added]} +it appears with the red notes ina medieval score and then +it reappears in Stockhausen's \opustitle{Klavierst\"{u}ck XI}. They were just jumping, +they were dismissing what we would call the baroque, classical and +romantic periods periods as completely worthless. In other words, the +last music before Stockhausen was in the 14th century, this is the way +the history of music was being rewritten. And LaMonte was getting +into Leonin and Perotin and all that kind of stuff. Well, anyway, that's +quite an excursion. +At any rate there is in music, there is this preoccupation with---it +may be a kind of quasi-Pythagoreanism, I don't know\ldots + +\speaker{HENNIX} The way I looked at it was that they saw in Webern, first of +all the harmony was going away. And they saw in Webern a way of +determining the note more and more precisely, in terms of all of its +parameters, pitch, duration, timbre and all that. What was left was that +timbre was not serialized yet. And that, as far I see it, was what the +Darmstadt school did---they added--- + +\speaker{FLYNT} Stockhausen's \opustitle{Kontra-Punkte}--- + +\speaker{HENNIX} Yeah. And they all considered Webern the god of the new +music--- + +\speaker{FLYNT} Yes--- + +\speaker{HENNIX} ---and also a little bit Messiaen--- + +\speaker{FLYNT} Yes. + +\speaker{HENNIX} It was Webern and Messaien that determined the entire +fifties in Darmstadt. In other words, they were saying that Cage was no +good. He was just looking in \booktitle{I Ching}---it was a random thing. And you +cannot recover the structure, it's hidden, as you said. The problem was +that Stockhausen, when he played his \opustitle{Klavierst\"{u}ck XI}, you couldnt +recover the structure either. It was so complex now. So the complexity +of the serialist music became exactly the complexity of Cage. Cage +looked his numbers up in random number tables; the others were +sitting calculating rows of numbers. But in addition to that they also +had to fake it. Because---you find that yourself when you do serial +music---the music moves too slowly. So you change the numbers to get +the music up a little bit. + +\speaker{FLYNT} Yes. We're taking longer on this than I meant to\ldots + +\speaker{HENNIX} But I wanted to say this. The completely deterministic com- +position technique and the completely random, aleatoric technique, +gave exactly the same results. And that was the complete breakdown of +the Darmstadt school. That's when they started to improvise in Darm- +stadt. Not before that was there improvisation in Darmstadt. + +\speaker{FLYNT} When they first tried to serialize duration, they tried to pick a +fundamental unit and use multiples of it; in other words, that's not the +way you serialize pitch. You don't take one cycle per second and then +use two cycles per second, up to twelve. That's not what you do. But +that's what they did with duration. And that's what produced the +Boulez pieces that move so slowly. In other words if you treat rhythm as +multiples of like a whole note then it was moving too slowly for them. + +But Cage was for them what was wrong with America or something. +I mean, the center of what Stockhausen was doing was the +concept of scientificity. In other words at that time I fantasized the +composer appearing as performer, on the stage in a lab coat carrying a +slide rule---there were no electronic calculators at that time, it would +have to have been a slide rule---but that seemed completely approp- +riate. In other words, a composition was a laboratory experiment. I +mean they viewed Cage as a typical American---coming in a vacuum--- +American superficiality---a vacuum with no scientificity. But Cage was +actually not using a random number table, he was flipping coins, he +was using the \booktitle{I Ching}. Yet it was not even that---what Cage was doing +was much more whimsical than using a random number book. He +would just copy a leaf---in the \opustitle{Concert for Piano and Orchestra} he just +put the staff over a leaf and then the main points defining the shape of +the leaf he just copied them on and he ended up with a circle or not a +circle, but a group of notes in cyclic shape, and so the pianist was +supposed to play around the circle. This was completely whimsical +actually and yes, I remember very well these debates that they had, the +one and the other\footnote{Serial vs. chance.}---I didn't have any idea that I was going to spend +this much time competing with the music critic of the \journaltitle{New York Times} +about who remembers the 1950s the best. + +At any rate\ldots\ There is of course a larger tradition in art which has +a kind of quasi-scientific involvement in structure that does go very +much to the Renaissance, for example. Althought I was not so conscious +of that---I looked that up much later. But it was certainly there. + +So, on the one hand concept art came from the idea of lifting +structure off and makinga separate art form out of it. The structure or +conceptual aspect, and making a separate art form out of it. The other +thing that was coming---the development of my philosophical thinking +---I have to explain first that the version of mathematics that I received +at Harvard in the 1950s in which Quine was the head of the department +and editor of the \journaltitle{Journal of Symbolic Logic} and so forth and the +hottest thing in philosophy was considered to be Quine's debate with +Carnap. And I was a schoolmate of Kripke, Solovay, Goodman \etc\ +\etc, \etc. I'm just mentioning that to locate the period of time. Actually +my conversations with them were insignificant as far as the philosophy +of mathematics was concerned, there was no discussion between me +and them on any of that but it will locate the time frame that I'm talking +about.* + +\footnote{I'm being too diffident. I had quite significant discussions with Kripke and Goodman in 1961. [H.F,, note added]} + +But observing what was going on at that time, I picked up the idea +that the most plausible explanation of what mathematics is, is that it is +an activity analogous to chess, or in other words that chess captures the +characteristic features of mathematics, even though, as I have told you +privately many times, everybody knew who Brouwer was and what the +intutionist school was, but nobody studied it, and from my point of +view looking at it and knowing what it was, I felt no inclination to +pursue it further. + +The reason why this chess game explanation of mathematics +seemed so plausible---you know, at the end of the nineteenth century +they found themselves with three geometries---this is not Henry Flynt +saying this, this is the canard, the story in the text books. There were +three geometries; one of them fit the real world. They thought it was +Euclidean, but it might not be. It might be one of the others like elliptic, +for example; nevertheless, all three were consistent. Now what was the +epistemological status of the two out of the three geometries that were +true without having any correspondence to the real world, while one of +them did have a correspondence to the real world and was also true? +But what of the other two---the ones that were called true even thought +they had nothing to with the world? You know presumably Hilbert +wrote \essaytitle{Foundations of Geometry} as the original answer to that +question. + +Although---I can't pursue this here, it is much too technical---this +is now an open question for me. It has never been an open question in +the past. I just accepted what I was told---that Hilbert solved this by +seeing that a system of mathematics that has no relation to the real +world---in what does its truth consist? Its consistency as an uninterpreted +calculus as they would say---axioms, proofs, formation rules, +transformation rules. Certainly it was clear in the early twentieth +century that the concept of an abstract space was established. This was +what geometry was about. Geometry did not attempt---in Kant's time it +was assumed that when you were talking about geometry you were +talking about the geometry of the real world. That's the only geometry +that there was. The idea that there was a different agenda for geometry +other than the real world---how Kant could have moved geometry into +the constitutive subject and said that it was congenital to the mind---Euclidean geometry. +In hindsight that seems to be one of the biggest +mistakes he made, tremendously embarrassing, because by the mid-twentieth +century it was completely taken for granted that the job of the +mathematician was to study structures which do not have any reality. +And that from time to time you will give an interpretation to one or the +other of these structures, like a physical interpretation, and then it may +be found to be true or false in reality or not. Meanwhile, you have +another sense of the word "interpretation" which has to do with relative +consistency proofs by something having a model. + +This is now a completely open question for me, what they thought +they were doing. In other words what Hilbert thought that he was +doing---he interpreted one or another non-Euclidean geometry---what +was the interpretation that he used? It was a denumerable domain of +algebraic numbers.\footnote{Foundations of Geometry, pp. 27--30} + +\speaker{HENNIX} I think his ideas go back to Klein's models---which are +Euclidean in the center of the circle and then at the periphery they have +turned non-Euclidean (in the complex plane). + +\speaker{FLYNT} You had to have an explanation of how mathematics could be +true in any sense whatsoever even though any claim of a connection +with the real world had been completely severed, and it was being +pursued in some kind of vacuum. What does mathematics mean in that +case? And the answer that Hilbert gave was that it does not have to +mean anything. + +That's the answer. So it's a chess game. And the only difference +between mathematics and a chess game is that there are additional +complications created in mathematics by the fact that it deals with +infinitary games. By the way, I completely overlooked that aspect at +that time. You know, I can only see it now, kind of like two superimposed +pictures, because I see what I know now and compare it with what I knew then. + +\speaker{HENNIX} Yeah, the same for myself. I didn't know that this idea of +Hilbert's was forced by Frege until later. Frege was the one who said +that either the parallel axiom is true, or it's not. Which way do you want +it? And so he caused the big stir in the foundations of geometry in the +end of the nineteenth century and that's why he became enemies with +Hilbert. They were life enemies. + +\speaker{FLYNT} The reason I see it like two superimposed transparencies--- + +\speaker{HENNIX} But even today this debate with Frege---you have to go to a +single volume in Frege's posthumous writings---it is not mentioned in +any textbook---no lecture mentions it, and, so far, nobody has +explained it properly.\footnote{\booktitle{Nachgelassene Schriften und Wissenschaftlicher Briefwechsel}, vol. 2, Felix Meiner, Hamburg: 1976. (Gottlob Frege, The Philosophical and Mathematical Correspondence, University of Chicago Press: 1980)} + +\speaker{FLYNT} Yes, yes, yes. You're talking about an obscure origin of something +and what I'm talking about is a kind of consensus that had grown +up, since everybody agreed that mathematics should study unreal structures. + +\speaker{HENNIX} But that consensus was forced on us, that that was what we +were supposed to do. + +\speaker{FLYNT} The problem then---I thought mathematics was like chess. +What I understand now is that even a good formalist would not agree +with that. A good formalist would say that when you have a finite game +like chess, the problems of validity and soundness become transparent +or intuitively ascertainable, therefore a finite game is too trivial to be a +proxy for mathematics. At that time I did not understand that distinction. +I've read in many books since then that mathematics is the science +of infinity---that is the way mathematics is defined now in half of the +books that I look at. But at that point I did not understand. I thought +the finite game was already, I mistakenly thought, a complex enough +problem to stand for mathematics. Or that the reliability of a finite +game was sufficiently complicated to stand for mathematics so I basically +focused just on a finite game. + +\speaker{HENNIX} By the way, this was exactly the late Wittgenstein's view of +the philosophy of mathematics---it's not a complete misunderstanding, +that is to say, other people thought of it that way too. + +\speaker{FLYNT} The question then arose of even the soundness, the reliability, +the consistency of a finite game---this then is the problem for example +whether it is possible to follow a very simple rule correctly or not. The +other thing that was feeding into everything that was going on was that +Wittgenstein's \essaytitle{Remarks on The Foundations of Mathematics} was in +the Harvard Bookstore when I walked in as a freshman my very first +day there---so in other words I was looking at Wittgenstein's Remarks +on The Foundations of Mathematics from 1957--- + +\speaker{HENNIX} Ten years before me--- + +\speaker{FLYNT} ---but very cursorily. Because I had a philosophical +agenda---I passed over this material in a very cursory way because I had a +philosophical agenda. I was not involved in the distinction between a +finite and an infinite structure. I was not involved in that. + +\speaker{HENNIX} You thought there was no such distinction? + +\speaker{FLYNT} Well no, I thought that---it didn't seem that there was very +much point in worrying about that when there were much more +extreme problems to be worried about. But Wittgenstein wrote a lot +about the possibility of following very simple rules. And I assumed that +if there were epistemological questions for mathematics that this game +interpretation---this chess interpretation---had displaced the question +of the soundness and reliability of the mathematics to the possibility of +understanding a very simple rule like writing the series "plus 2". + +And having gathered that this was the way that I should picture +mathematics---I mean we understood very well that there were other +pictures of mathematics, but we thought they were philosophically +obsolete. In other words the person who believed that mathematics was +a description of a real supra-terrestrial structure, and certainly there +were people like that--- + +\speaker{HENNIX} Still today. + +\speaker{FLYNT} ---we thought that this was a philosophy that had been +exposed as superstitious by Positivism and possibly even by Ockham +several centuries earlier. So it was not that we didn't know about that. I +drew a personal conclusion that that position could not be defended by +any arguments that are acceptable by modern standards. What I really +meant was by Carnap's standards. That's what modern standards +meant to me. + +In my philosophy I was not concerned with the specifics of +mathematics; I was concerned with the problem of how I knowa world +beyond my immediate sensations. That was actually the question that I +began with---the question of propositions of material fact, like "it is raining" +or "the \textsc{Empire State Building} is at Fifth Avenue and 34th Street." + +I had read a very simplified exposition---it was actually some +lectures that Carnap gave in England in the 1930s on what Positivism +was.\footnote{R. Carnap, \booktitle{Philosophy and Logical Syntax} (1935).} +They were very simple lectures and very different from his actual +published books with all this supposed apparatus and symbols and so +forth but a very simple exposition of what it is for a proposition to be +meaningful---that it must be empirically testable and so forth and so on +and the solution of questions of metaphysics that make assertions that +are not testable are therefore meaningless---the possibility of solving +questions of what is real by declaring if there is no way of deciding them +they are therefore meaningless. That seemed to me to be, at the time, a +stunning contribution. Because I come out of a background---I was in +high school reading Kant and so forth and so on. And Carnap's +solution was much more attractive to me than trying to participate with +Kant, to experience his question and try to take one side or the other +when he already said it's not really answerable; I solve it by simply +having faith or something like that, which is what he said about the +famous God freedom and immortality---I found it immensely attractive +when Carnap came along and said that there is no way of answering +these questions; therefore, words are being used nonsensically. + +I went through a process of thinking about that without ever +having seen Carnap's \booktitle{The Logical Structural of The World}. When I +was in Israel Scheffler's philosophy of science class, I tried to write a +text which in effect gave my own empiricist constructions of what it +means to say that A causes B and so forth, to give empiricist constructive +definitions of those---which is, I suppose, in the spirit of Carnap's +program, even though I hadn't actually seen what he had written, and if +I had it would have confused me---no, I wouldn't say "confused"; I +would say it would have discredited him completely. I wouldn't say +"confused" because that's too modest. + +\speaker{HENNIX} No, I wouldn't think "confused," I would think it would +have upset you\ldots + +\speaker{FLYNT} No, I wouldn't say "confused." I would say he had been +discredited. + +I very quickly passed to the position that the propositions of +natural science were meaningless metaphysics. + +\speaker{HENNIX} On what basis? Can you pin that down? A little bit, only. + +\speaker{FLYNT} This is something I want to compress---it says a little bit about +this in \booktitle{Blueprint for a Higher Civilization}\footnote{H. Flynt, Blueprint for a Higher Civilization (Milan, 1975). Recently reissued and an expanded and corrected edition by \textsc{Salitter Workings}}---like +the proposition, "this key is made of iron" or something like that, I comment on that in the +essay \essaytitle{Philosophical Aspects of Walking Through Walls}. + +\speaker{HENNIX} I didn't recall the example actually. + +\speakermod{FLYNT}{reading} "The natural sciences must certainly be dismantled. +In this connection it is appropriate to make a criticism about the logic +of science as Carnap rationalized it. Carnap considered a proposition +meaningful if it had any empirically verifiable proposition as an +implication. But consider an appropriate ensemble of scientific propositions +in good standing, and conceive of it as a conjunction of an infinite +number of propositions about single events (what Carnap called +protocol-sentences). Only a very small number of the latter propositions +are indeed subject to verification. If we sever them from the entire +conjunction, what remains is as effectively blocked from verification as +the propositions which Carnap rejected as meaningless. This criticism +of science is not a mere technical exercise. A scientific proposition is a +fabrication which amalgamates a few trivially-testable meanings with +an infinite number of untestable meanings and inveigles us to accept the +whole conglomeration at once. It is apparent at the very beginning of +\booktitle{Philosophy and Logical Syntax} that Carnap recognized this quite +clearly; but it did not occur to him to do anything about it." + +The only point that I'm trying to make here is that I began to move +very quickly when I was still very young towards a position of extreme +disillusionment and cognitive extremism. I moved very quickly. This +was not a slow process. I just immediately took Carnap's critique of +metaphysics, decided that it applied directly to natural science---you +dismiss natural science as meaningless. The problem: is there an object +that is beyond my experience, is there a glass which is beyond what they +would call the "scopic" glass, the "tactile" glass \action{gestures toward the +glass from which he has been drinking}---is there a glass other than +those glasses---when you first think about it, that question seems to +have exactly the status of the propositions about God, freedom, and +immortality that Kant said are unanswerable and that Carnap said are +meaningless. However, there is one additional step for people who are +interested in the history of philosophy. Kant, in the second edition of +\booktitle{Critique of Pure Reason}, added this notorious refutation of idealism to +prove the existence of the real world independent of my sense +impressions---you may not know about this---this was the basis of +Husserl's phenomenology---Husserl's phenomenology was invented in +this passage and it also tremendously preoccupied Heidigger. It was +one of the sources which causes Heidigger to say that the essence of +Being is Time. Kant said that essentially it is the passage of time which +proves that there must be an external world. This is notorious in the +history of philosophy. Because on the one hand it is so deeply +influential for later thinkers; and on the other hand, for example, +Schopenhauer said it was a complete disgrace---it was such an obvious sophistry +that it was just disgusting---that it had the effect of ruining the +\booktitle{Critique of Pure Reason}. + +Actually this refutation of idealism is distributed throughout the +\booktitle{Critique of Pure Reason}, it's not in any one place---a foot note here, +a preface there, another passage somewhere else. In one of the footnotes +Kant makes the same point. In order to ask the question whether +there is a glass beyond my sense impression of it---I cannot ask that +question\ldots + +\speaker{HENNIX} Oh you mean the \term{ding an sich} question. + +\speaker{FLYNT} Well that's what Kant would have been talking about but I +don't want to fit that narrowly into Kant's controlling the terms of the +discussion. I'm trying to ask it as someone who has embraced +Logical Positivism and is now turning around to question Logical +Positivism---you see the point that I was just making there---when +you say that this key is made of iron, which is Carnap's favorite +example---and then a protocol sentence, for example +"if I hold a magnet near this key, the key will be attracted to the magnet"---it +is not clear where Carnap stands on +the question whether only my sense impressions are real---just talking +about this situation---only my sense impressions are real---or is there +supposed to be a substantial key? + +By the way, I don't know Carnap's work that well. I passed over +these people in a very offhand way, so much so that many times I've +talked to people and they've concluded in their own mind that I dont +really know philosophy because I seem to have just glanced at these +people---picked up one or two points---the reason for that is that I was +moving so quickly to my own terminus---I only needed to see the +slightest symptom from these people to know that they were spending +all their time worrying about something that it was a waste of time to +worry about since it could only be a secondary issue. Here is Carnap +with this key made of iron---while I'm trying to ask is there a key other +than the scopic key, the tactile key \emph{now}---since the past and the future +are beyond immediate experience. I mean they cannot be cited as +evidence---or whether they are evidence or not, is the same problem. +Should I believe in the past and the future even though they are not +immediates? Should I believe in the glass, even though what I +presumably have is a scopic glass---at this very moment, a visual glass +apparition, from that should I conclude a glass? + +The first reaction to that question for somebody who is coming +from Kant and Carnap and who does not mind how extreme his +answer is---that's the key thing. In other words, if I came to a +conclusion that was completely untenable as far as social circumstances---that +didn't bother me at all. At first the question whether there is a real glass +beyond the apparition would seem to be an unanswerable +question---one of Kant's metaphysical questions---but then you think---that if you +know what the question means, then there must be a realm beyond +experience, because otherwise it is unclear how the question could be +understandable. + +From my point of view---if you want to make an issue out of +semantics---this is the profound issue. What the mathematical philosophers +and philosophers of mathematics were doing, talking about +semantics, interpreting geometry as an algebra and algebra as a +geometry---really for the purposes of relative-consistency proofs or +because they found they could solve problems by using a machinery +developed in another branch of mathematics by seeing these structural +similarities---but to confuse that with what I thought the bona fide +semantic question is: how would I understand the question whether +there is a substantial glass other than the scopic glass---you know the +conclusion---I can't tell you the exact breakdown---but I am talking +now about the 1961 manuscript, \essaytitle{Philosophy Proper}\footnote{Published in \booktitle{Blueprint for a Higher Civilization}. This book.} +---I may have +already come to the conclusion at that time---that the question itself +forces a yes answer. This does not mean that a proof of the existence of +the external world has been given. It meant that the proposition of the +existence of the external world would verify itself even if it were false! + +\speaker{HENNIX} I find this extremely interesting and rewarding, what you are +saying now, because I never heard you say it this way before. I just want +to ask you one question before you go on: namely, I see something for +the first time which I hadn't seen before---but before you go on I just +want to ask you one leading question: the simple existential statement, +"there is a glass on the table." You include that also in what will be +doubtable here. In other words not just "there is a glass on the table" +but "there exists a glass," the existential statement. I guess I wasn't very +clear now. + +\speaker{FLYNT} No, the thing is, the approach that I'm taking doesn't break it +down the way that you're talking about. Let me tell you. You may not +be \emph{sympatico} with empiricism. When you are trying to deal with +philosophy at all---you have to make some allowance for the +fact---you have to understand that the philosopher may be carving up +problems in a way that is temperamentally alien to you. + +\speaker{HENNIX} Yeah\ldots + +\speaker{FLYNT} You have to understand that. This is why somebody like +Carnap would read Hegel and say it's not saying anything. Actually, +Hegel is saying something. In fact, you might go so far as to make a case +that Hegel is actually rebutting Carnap, becaue if you understand what +Hegel is doing you realize even more than one would realize anyway +that Carnap has an untenable position---that he's sort of---that he +wants what he cannot have. He has made a set of rules that does not +allow him to have the thing that he demands to have. Hegel would have +seen that immediately. Carnap thinks that the problem of a logic of +consistency is an easy problem and a solved problem. In effect, Hegel +was saying there is something very misleading in thinking that that is a +solved problem. I'm trying to give you a sense of misunderstandings +between philosophers that are the results of temperamental incompatibilities. + + +\speaker{HENNIX} What you are giving me is a two-step way to skepticism. You +ask a certain question---is there something beyond this perception of +the glass? And you say the answer "yes" is forced on me, but then you +realize this was a meaningless question. + +\speaker{FLYNT} No, it's the other way around. + +\speaker{HENNIX} Oh, okay, but here's where you have to explain in detail +because here's where I miss you. + +\speaker{FLYNT} Let me go through the series of steps again. The series of steps +was\ldots\ I'll have to doit all at the same time. You have to understand---I +don't think that you even understand what an empiricist is. It's a +peculiar attitude. And one of the reasons why you have very little +training in this attitude is because people who claim to be +empiricists---it's always a fraud. All people who appear in public and say they are +empiricists, they are all lying all of the time. The reason that they're +lying is that they have this doctrine of the construction of the world +from sense impressions. That is their doctrine. But they do not stay with +that doctrine. And the reason why they do not stay with that doctrine is +because in addition to having the doctrine of the construction of the +world from sense impressions, they also want to have things like +science--- + +\speaker{HENNIX} Ethics\ldots + +\speaker{FLYNT} No, not ethics---one of the characteristics of the twentieth- +century philosopher was the appearance of the tough-guy philosopher +who rejects all of ethics as meaningless, which Carnap certainly did and +people who are close to him like A.J. Ayer---no, they did not want +ethics. But they wanted science. And the problem with wanting the +construction of the world from sense impressions on the one hand and +wanting science on the other is that the two finally have nothing to do +with each other at all---and when they said that the two were the same +thing as Carnap did---he was lying---I made a hero out of Carnap---I +derived some kind of positive impulse from him or something like that +without---I never actually read---my serious reading of Carnap was like +three or four pages of excerpts in a paperback popularization. I owned, +I had in my library Carnap's so-called real books, like +\booktitle{Logical Foundations of Probability} and \booktitle{Meaning and Necessity} and all the rest of them +and I never read them.\footnote{Again I'm being too diffident. I thoroughly studied portions of the +Carnap books I owned---beginning with \booktitle{The Logical Structure of Language}, +which I bought while in high school [H.F., note added].} +And in hindsight that was good, because I took +his slogan seriously and assumed that he meant what he said and drew +the necessary consequences of it. If I had actually read his books I +would have been thrust into this massive hypocrisy, and I must say +stupidity, because the man did not realize that his answers were not +adequate, did not realize how preposterous his constructions of the +world were--- + +\speaker{HENNIX} I would say vulgar. + +\speaker{FLYNT} Yes, yes. And\ldots\ what is even worse about empiricism is, in the +case of somebody like Mach, not only does he want to have his sense +impressions and does he want to have his science, but he wants to have +science explain sense impressions! And nevertheless it was supposed to +be the sense impressions that were primary, not the science. Mach is +seriously telling you, I will tell you why you see a blue book---because +the frequency of blue light is---and then he gives some uncountable +number, I mean some number that is pragmatically infinite, or something +like that. And how do you know that blue light is exactly +$3.2794835\mathrm{e}{15}$ and not one more or less---? Well, +certainly not by just looking, I'll guarantee you that! You have to go +into a laboratory with a few million dollars' worth of equipment or +something. But that's what it is to see that the book is blue. + +I'm trying to give you the sense of what it would be to be an +authentic empiricist. You ask does a glass exist; an authentic empiricist +would have to say that he already has a problem with that---that he has +to regard that as an undefined question or statement. It's undefined, +because if you are asking me if at this moment I quote unquote +have---interesting word there, "have"---that is what our ordinary +language gives us as the idiom for this. + +\speaker{HENNIX} Or "suffer!" + +\speaker{FLYNT} Yes, "have" or "suffer," that's right. I have or I suffer a scopic +glass or visual glass apparition---then that is identically true. That is +identically true. If you express any surprise at that, we have a problem +here. I have a scopic glass. If I say I have an apparitional glass, would +that be okay?---I mean from this point of view the sense impression is +not open to dispute. It's meaningless to dispute it. It's an impression, an +apparition---the sense impression is that for which seeming and being +are identical. For the empiricist the phase of the world or range of the +world for which seeming and being are identical is the sense impression. +If that seems strange to you then maybe I can make it less strange by +pointing out to you to make this as clear as possible---for the empiricist +to say that I have an apparitional glass is to say nothing about Reality +with a capital R at all! This is the so-called subjective psychological +moment---although an empiricist would never say that---the reason an +empiricist would never say that is that even to call it subjective is +already much too strong because that implies that you can guarantee +an objectivity to compare it to. And a bona fide empiricist would not +agree that my sense impression is subjective---subjective in comparison +to \emph{what}? + +\speaker{HENNIX} So an empiricist would be a person who would not doubt +whether he had a toothache or not. In other words, if he had a +toothache\ldots + +\speaker{FLYNT} You would regard it as being a mistake to do what? I'm not +sure about the word "toothache"---if you mean that he would not +doubt whether he had a toothache sensation. Whether there is an +organic---in the language of medicine---whether there is an organic +substrate for the toothache impression---this in a medical sense is a +question of what is called hysteria or something like that\ldots + +\speaker{HENNIX} Suppose I have a toothache. But now I'm an empiricist so I +say I'm doubting this impression. I probably don't have a toothache. + +\speaker{FLYNT} No, no\ldots + +\speaker{HENNIX} I have to accept the toothache? + +\speaker{FLYNT} No, you don't have--- + +\speaker{HENNIX} The glass you said was---I couldn't doubt the perception of +the glass. You said that was beyond doubt, in some sense, for the +empiricist. + +\speaker{FLYNT} It would be some kind of logical mistake to think that there +was anything there to be doubted. + +\speaker{HENNIX} Okay. And the same with the toothache. + +\speaker{FLYNT} Yes, yes. I mean the point is not so much that we have come +into an area in which the empiricist is prepared to have faith---that +would be completely missing the point. No faith is required---that's the +point. The point is that it would be some kind of logical error. Once you +understand what a sense impression is, the terminology of doubt does +not apply to that level. + +\speaker{HENNIX} I see. Just that was my question. + +\speaker{FLYNT} The terminology of doubt does not apply to apparitions. It +doesn't make sense to doubt subjective apparitions. The empiricist is +already nervous when you ask does a glass exist. If you are asking +whether I have a "scopic" glass, it's identically true. Wait, wait. There +are already problems there. I'll come back to them. But when you +say---it sounds like what you're asking me is whether the fact that I see a +glass is sufficient to prove an objective glass---that sounds like \ldots + +\speaker{HENNIX} No, no, that's not what--- + +\speaker{FLYNT} Well, ok. Most people when they say: +"do you concede that there is a glass on the table---I'm sitting here looking at it," what they +mean is: "do you concede that from your visual glass apparition you should conclude an objective glass, a substantial glass?" I'm taking it for +granted that you know enough about philosophy to have a sense of the +full weight those two words "substantial" and "objective" have in +philosophy. + +\speaker{HENNIX} Yes. + +\speaker{FLYNT} That at great length is my reaction to your question about +doubting "there is a glass on the table" versus doubting "there exists a glass." +A bona fide empiricist would say, "Why are you asking me this?" +The scopic glass is simply here for me. As far as concluding that an +objective glass exists from the existence of that apparition---the traditional +problem of concluding whether the apparition is a symptom of +some transcendent world---I think the word "transcendent" is sometimes +used in that sense in philosophy---the world beyond any sense +impression--- + +\speaker{HENNIX} This is why I used the example of the pain---because it +would be senseless for me to claim that \emph{I} can have \emph{your} toothache! + +\speaker{FLYNT} Now just a minute. An empiricist---what you're really getting +at what you're sort of squeezing out of me here---I'm glad to have it +squeezed out of me---I have no embarrassment about this---is that with +empiricism either you must be prepared immediately to depart +absolutely from the conventional world view, or else you will just plunge +yourself into a quicksand of hypocrisy. When you're asking me, can l +have your toothache\ldots\ A good empiricist would say, +\textquote{I have not established so-called other people except the other-people apparitions +that occur for me from time to time in waking life \emph{as they do in my +dreams!} And are you now going to ask me can I have the toothache of a +person who appears to me in a dream?} Then the spotlight would be +turned on you---what kind of an issue are you trying to make there? +What do you believe is the reality status of the furniture in my dreams? +For the empiricist, nothing remotely like that question has arisen yet, +because I haven't got outside of my own quote unquote head yet. + +Maybe you're just squeezing more and more. Either the empiricist +must be a "madman" or else he must be insincere. I took the alternative +of the madman. This is important not for me but for the general public +to be told---something which the general public has never been +told---and I know why they have never been told---maybe it is necessary to +complete this point. The point is that empiricism was contrived to +paper over a kind of---I mean there was sort of this +epistemological---Science epistemologically was resting on some sort of very shaky +foundation---they saw that. They brought in this empiricism in the +hope that it would solve a problem, that it would substantiate science +while at the same time it would cut away the common-sense notion of +causality as being unnecessary to science. Empiricism was going to give +you a more sophisticated science that did not need the traditional +metaphysical or common-sense notion of causality. It told you how to +get along without that, but at the same time it validated everything that +the scientist needed. And, at the same time, empiricism was supposed to +be---in the case of Neurath---he wanted to make some kind of unification +of empiricism with Marxism and make it like a complete demythified view of society. + +\speaker{HENNIX} There was even an attempt to bring ethics into it. + +\speaker{FLYNT} Well, in Neurath's case, yes. + +\speaker{HENNIX} Schlick too, I think---Schlick, I recall, did something in +ethics.\bootnote{\booktitle{Fragen der Ethik}, Vienna, 1930.} + +\speaker{FLYNT} I was talking about why empiricism is not portrayed honestly +in the general picture that exists of philosophy---the public picture of +philosophy---it was brought in to solve the problem of what is a base +for science---namely, sense impressions are going to be taken as +elemental. Science is going to arise from sense impressions by construction. +Nevertheless it is required that both scientific knowledge and the +common-sense social world be produced by this approach--- + +\speaker{HENNIX} Neurath, you mean. + +\speaker{FLYNT} No, no. Well, Carnap did not deny the existence of other +people. All of the positivists\ldots + +\speaker{HENNIX} Rather, he had nothing to say about it. + +\speaker{FLYNT} I didn't say ethics---I said the common-sense social world. I +wasn't talking about anything ethical\ldots + + +\speaker{HENNIX} The existence of tables and cars and--- + +\speaker{FLYNT} Well, what I'm saying is that the existence of other people is on +the same level as the existence of tables and automobiles. And what is +even worse than that is that the ones who were scientists in fact wanted +to see perception itself as the product of the abstract and quantified +sequence that the biophysicist or the psychophysicist sees---the light, +the lens, the retina, the optic nerve, the visual cortex, and so forth and +so on---they wanted to have that as prior to the sense impression but at +the same time they wanted to have all that constructed up from the +sense impressions. Why would this remain in place? Because it was a +more palatable---it's just like why would formalism remain in place? +Everybody learns that formalism died with Godel's incompleteness +theorems---it certainly didn't die for me; it isn't even clear what the +incompleteness theorems are supposed to have done or not to have +done---the fact remains that if you don't explain mathematics as an +uninterpreted calculus, then for us there was nothing left but +superstition. Those are the choices that you are given. If you don't explain that +science is constructed up froma ground of sense impressions, then how +do you want it to be constructed, down from God? You see, we don't +take that \emph{seriously} anymore. + +As a matter of fact Hume wrote two philosophical works and in +the first work\footnote{\booktitle{Treatise on Human Nature}} +there is the notorious passage in which he himself +understands what it means to be a genuine empiricist.\footnote{Book I, Part IV, VII "Conclusion"} +He says, \textquote{I feel that I am an outcast from the human race,} and so forth in this famous +passage---he says, +"I do not know if the glass continues to exist after I've looked away from it." +That line in Hume should have told you +whatever you wanted to know about the existence of the glass. You +should be able to ascertain the appropriate answer to your question. +Hume says: "I do not know if the glass exists when I look away from it." + +Hume's second book\footnote{\booktitle{An Enquiry Concerning Human Understanding}}, +when he was trying to vindicate himself, +when he had dropped the whole business of being a madman, it was +much nearer to what empiricism means today: an attempt to construct +science from a more meager inventory of elements, namely sense +impressions. And that is where Hume presents his doctrine that science +does not need and should not invoke metaphysical causation, that it +should replace the old-fashioned causation with some sort of construction +which is more flat or more network-like. + +Well, at any rate, I'm going into this long thing---this is why it's +never dealt with in public in a sincere way---the only time it was was by +the guy who invented it, Hume, in the book that he wrote when he was +twenty-three years old. That's the only honest version of it and everything +after that is a fraud. + +The way it goes is this: I ask the question whether there is a +substantial glass, an objective glass, a material glass, something that is +over and above the visual glass of the moment. When first considered +this seems to be a question which I have no method of answering. That +would seem to place it like a Kantian metaphysical question which +doesn't have a provable solution, though interestingly enough Kant +thought that the existence of the external world in general could be +proved but only in the second edition. And in that second edition in +those little passages, Kant did really get into the existence of this +individual thing like a unicornand how that would or would not fit into +the general proof of the existence of the world and also the question of +how dreams would affect the validity of the proof. He touches on all of +those in a way which is just awful. It's a disgraceful performance. But he +had the issue there, actually. + +Well, your first reaction is, "I have no way of answering this." Your +second reaction is, that \emph{if I understand the question}, then there must be +an external world. So it would seem that I have actually proved the +external world---that's what Kant actually said. Or he came very near +to saying something like that. The third step is the realization that the +statement would validate itself not only if it's true---but if it's false it +validates itself equally well! + +\speaker{HENNIX} Given this method of understanding the question. And the +method remained unspecified so far---as far as I know nobody has been +able to do very well at specifying it. + +\speaker{FLYNT} What? Do you mean if somebody asks whether there is an +external world---my last remark is a comment about semantics---the +genuine semantic issue, as I said, and it's very different from the sort of +thing that Tarski is going on about which I think is just ridiculous. + +Maybe I'd better stop and tell you why I think it's ridiculous. It's +because I'm now talking about things which are exactly the fundamen- +tal issues. If Tarski thinks that he can talk about the theory of chess +before the question of whether the universe exists or not has been +answered---they are deliberately creating specialized problems which in +their minds do have answers and then they are proceeding to answer +them. The larger question of whether the work has any meaning at +all---it's like somebody spending his whole life working on the King's +Indian defense in chess or something like that, and thinking that +somehow that makes it unnecessary to answer such questions as does +the chess board exist or is it only apparitional? If it's only apparitional +then there is no guarantee of the continuity of the position of the pieces +in the absence of moves. What happens is that people treat those basic +questions as if they are so basic that it's sort of preposterous to make an +issue of them. Kripke said very clearly in his book on Wittgenstein that +once the question, "Does language exist?" has been asked, not to give +an affirmative answer is "insane and intolerable."\footnote{S. Kripke, +\booktitle{Wittgenstein on Rules and Private Language}, p.60} +It's the same reaction as there is to solipsism---that solipsism is the philosophy of the +man in the lunatic asylum. + +The thing that may come before all the discussion so far is the +question of \emph{what is my position on being classified as insane} is the +beginning This of philosophy for me. + +\speaker{HENNIX} Well, this is the classical beginning of philosophy. + +\speaker{FLYNT} Because if you're not willing to face up to being classified as +insane---if you want to avoid that confrontation---you can't be a +philosopher. That confrontation is at the center of bona fide philosophy. + +\speaker{HENNIX} Or was\ldots + +\speaker{FLYNT} Yes. At any rate, I had reached this point in something like +1961. I had not yet done \essaytitlte{The "Is There Language?" Trap}. But I had reached +the point of saying that to claim the existence of a world beyond +experience is untenable. However I understood very well that it begins +to create problems for me to say, \textquote{I have a visual glass apparition,} +because there is a lot of structure in that sentence. And it's not clear +what is supporting that structure after the world has been cut away. +Even the use of the idioms like "have" and "suffer." The use of the word +"I"---after the objective world has been cut away it's unclear what is the +basis for all of that. And this is the point I had reached in 1961 and this is +the point when I did \essaytitle{Concept Art}. + +On the one hand you have an art which is about structure and +conceptual things. On the other hand this art is not going to \emph{affirm} +traditional doctrines of structuredness and conceptualization. It is +deliberately in every case going to violate them. It is going to express the +fact that there has been a philosophical discovery made. I would have +said chess is not a sound game. It's not well founded. It can't be. The +whole problem of Wittgenstein's famous question---what is the meaning +of a rule? My answer would be it doesn't have one. When you look +at it from the standpoint of Hume when he says I have become a +monster, I am outside the human race---the standpoint of the person +who chooses insanity as opposed to intellectual dishonesty! + +The person who chooses being a madman---even chess doesn't +work. The whole question of its consistency. The point of Concept Art +is on the one hand to transmit the tradition from the isorhythmic motet +and the five Platonic solids, in Leonardo---and on the other it's to blow +it up because each work of concept art must be a counter-example to +that tradition. And at the same time to say that it is art means---when I +passed to \essaytitle{Concept Art} I left behind many things that traditionally +would have been considered crucial features of art, like sentiment, for +example. Let me just leave it at that. + +When the Renaissance people did study geometry and art, they +developed perspective to paint people, not to paint abstractions. And +you know I have to admit quite bluntly, my Concept Art was already +the product of the acceptance of an abstract art. And now, many years +later I can see that that was an historical juncture, to consider it +tolerable that art should break with sentiment and with the representation +of people. It's like moving toward an Islamic view of art. And then +saying, now however, in the future, instead of Mosque decoration we +will do a piece that has the visual, sensuous delectation, but it's completely +abstract. But whereas Islamic art was trying to express the +\emph{truth} of a certain theorem in group theory, Concept Art must express +that you can't have that---that that theorem fails. Now I'm formulating +an unsolved problem---I never did a concept piece the purpose of which +was to rebut the symmetry involved in a visual pattern, with that as the +opponent to be hit. I mean I very well could and perhaps should. + +All of my pieces were uninterpreted calculi. Because I accepted +that that was the only way of explaining what mathematics is: that it +consists of a body of truth about a world that does \emph{not} exist, and +explicitly so. And that all of the traditional explanations of mathematical +content are now seen to be anachronistic superstitions. They are just +indefensible in the modern world. Put those two things together and +mathematics becomes a chess game, an uninterpreted calculus. + +All of my Concept pieces are using the terminology of Carnap's +\booktitle{Logical Syntax of Language}---the formation rule, the transformation +rule---but in each case they wish to express the violation, the failure of +some traditional organizing principle of these uninterpreted calculi, +For instance there is one where, among other things, the very notation +itself has an undisplaced active interaction with the subjectivity of the +quote unquote reader.\footnote{dated 6/19/61---later titled "Illusions."} +And that determines the structure of the derivation, the proof. +It was pointed out to me many years later that it's not +just that you don't get this in schoolbook mathematics---this is what +they are most concerned to exclude. + +I had another one, in which there was no general transformation +rule.\footnote{\essaytitle{Transformations}, retitled \essaytitle{Implications} in the second edition.} +There were only completely nominalistic transformation rules, +In other words, for each step you are told, for that step only and for this +moment only, what the transformation rule is. And by the time you are +ready to take the next step, that rule is forgotten and inoperative. + +\speaker{HENNIX} This is the \essaytitle{Energy Cube Organism}? + +\speaker{FLYNT} No, no. \essaytitle{The Energy Cube Organism} was not Concept Art at +all. No, no. It was a different genre. That one was the piece called +\essaytitle{Transformations}. + +\essaytitle{The Energy Cube Organism} and the \essaytitle{Perception-Dissociator} in my +own classification are not Concept Art. Only the pieces labeled +"Concept Art" are Concept Art. And I only did four of them until 1987. +Three of them are in \booktitle{An Anthology}, and the fourth was published in +\journaltitle{dimension 14} (1963). \essaytitle{The Energy Cube Organism} and the +\essaytitle{Perception-Dissociator} were in other genres. I drew these distinctions of genre +rather narrowly, actually. + +This is the one \action{pointing to 6/19/61 in \booktitle{An Anthology}} where there +is, in an uninterpreted calculus, interaction between notation and the +subjectivity of the quote unquote reader. + +This is \essaytitle{Transformations.} You are just taking these objects, you +are burning them, melting them, doing all sorts of things to them. The +point of this is that each step in the proof---you have to think of it as a +proof---you see it has the tree structure of a proof. This is my nominalistic +transformation rules, because each rule is stipulated only at that +step, and then it is thrown away. The point that I was trying to express +was that's what they do in all of it---even in chess, when you move the +pawn to King's Bishop 3, you think that you are conforming to a +general rule written in Heaven. But in fact there isn't any general rule, +and when you move the pawn to Bishop 3, you're just making up what +you are doing right at that moment, and there isn't any general rule. + +\speaker{HENNIX} You would label this ad hoc? + +\speaker{FLYNT} That's right. That would be perhaps a better word for it. All +transformation rules and probably even all formation rules are ad hoc, +yes, yes. + +I said "nominalistic" because they are only there individually. +They do not add up to any general--- + +\speaker{HENNIX} System of rules? + +\speaker{FLYNT} No---not that---they do not add up to any generality, to a +general rule that covers all cases of a certain class. + +What is inadequate about this---and I realized very quickly that +it's inadequate---is that this does not actually give some profound +reason in concrete practice for questioning chess. That's what the +inadequacy of the original Concept Art pieces is. That they don't really +give you some kind of operative situation where you can see that +following the chess rules is failing. I don't provide that. I only provide +something that's ritualistic. Saying this is how you would behave if you +realized that following any rule is ad hoc. + +A conventional mathematician would say, you have not proved +that the world that this is designed for is the world that I have to live in. +\textsc{That}'s the inadequacy. He would say that I am only ritualizing the +world of impoverishment or disorganization. I'm not showing that +that's the world that people in general have to live in because it's in +force. That's the difference between then and now. The reason that I +want meta-technology would be to give a situation where somebody +can actually see that you \textsc{Can't} play a game of chess---or that you want +to play one and that I, by putting it in the appropriate context, make it +clear that the general rules on which playing it depends are not in fact +available. + +But to show that in a serious way. From the prevailing point of +view I would be talking about contriving a miracle. In other words, to +actually substantiate any of these---what is interesting is not so much +\essaytitle{Transformations}---but it would be some situation that would substantiate +that the conventional view is actually unavailable. And to do +that you have to violate what are considered today to be the soundest +laws of science. I'd need a miracle to manifest that I'm right, so to +speak. So by the time I get to meta-technology I'm in the job of +constructing miracles, I mean constructing situations that are +absolutely physically impossible (or in some cases logically impossible) by +currently accepted scientific and commonsense views of what is the real +world. + +\essaytitle{Innperseqs} is the one that is visually sensuously the best. You are +making a rainbow halo that you can get by breathing on your glasses +and looking at a point light---you get a rainbow halo around the light. +Eventually I will set it up so that you don't need glasses or anything so +that the whole business of seeing the rainbow halo is moved out and +does not require any special preparation by the spectator. The rainbow +halo is the sensuous delectation. The derivation, the proof, the +specification of propositions, is something that you do as the halo is fading. +You have to quickly specify---I never analyzed exactly what was going +on there but it was as if---you have a notation which is externally +changing, and therefore the quote unquote reading of a mathematical +system has to be a process that is taking place in experienced time. + +By acts of attention you have to choose sentences, to choose +implications---it's a display. You are given an external display which is +changing out there, not in your head. And you have to place a structure +on it by specified rules. + +You know another point that can be made is, that \essaytitle{Innperseqs} is +philosophically inconsistent with \essaytitle{Transformations}---that these pieces +are mocking each other. + +At the time that I did this, I did not have the kind of maturity that I +would have today to put it together in a strong way. These were +gestures. And they are not even uniform ona question like whether a +rule exists or not. Well actually, frequently I'm too hard on myself. I +think that in the essay \essaytitle{Concept Art} I do say something like, objective +language doesn't exist, but I'm still free to work with what you think the +text says---I can use that in \emph{art}: this is \emph{art}! + +There are three ways that the art part comes in. One is the visual +display, the delectation. The second way the art part comes in is---well, +if LaMonte Young's Word Pieces are art, then this is art too. But the +third thing is that this does not claim to have objective truth. It is a +construction for the world-hallucination or the world-apparition or +even a construction for the private world-apparition. + +\speaker{HENNIX} You are actually extending the world by new constructions. + +\speaker{FLYNT} But it's the world-apparition. In a sense if I believed that these +rules were objectively established, then it would almost indicate that I +had not learned the lesson of the very piece which sits beside it on the +page!\footnote{\essaytitle{Innperseqs} versus \essaytitle{{Transformations,} second edition.} +And what am I doing talking about a page and a text? So the +answer is that I have abandoned the provision of truth as the purpose of +this activity and I have moved to the provision of experiences where the +possibility of these experiences is a surprise. + +\speaker{HENNIX} And you don't have to be an empiricist to be surprised. + +\speaker{FLYNT} Yes. Yes. But the truth claim that you would have from a +Kripke or a Goodman has been dropped. The meaning of the text is the +meaning that the reader associates to it. And the thing is, that in +conventional intellectual work that's an unacceptable answer, because +usually you are trying to get independent of the reader's +distortion---that's the whole hope---that you can make something that is +independent of the reader's distortion of it. This is a different game. This is not +classical mathematics; it's not classical science. It's like giving a +Rorschach blot. Then I don't mind if you have a unique subjective reaction. +If my purpose is to make Rorschach blots, then I do not object, I have +not failed, if you have a unique personal reaction. + +These pieces are designed for the individual reaction rather than in +spite of it. + +The only other Concept Art piece---in \journaltitle{dimension 14}---\enquote{one just +has to guess whether this piece exists and if it does what its definition +is.} That was the piece. And that was a response to Cage's dissociation +of what the composer sees, the performer sees, the audience sees. +Starting from that, going through all the games that LaMonte had +played with the idea of performance, where we were performing pieces +first and composing them second, maybe many months later. So finally +with the Concept Art piece, even whether the piece exists is completely +indeterminate, but I meant for people to try to take that seriously. I was +having a joke with the person who thinks that concepts form an +objective world, which the individual who cognizes only discovers bit +by bit. In effect, 1am giving him this: thank you for believing that there +is a piece here---I'm leaving it to you to find it. I wash my hands of that +Problem---\emph{you} find it! + +Well, there's a natural pause that comes here because I think that +I've summarized perhaps fairly thoroughly where I was when I did the +work published in 1963. The entire subsequent career of the label +Concept Art, its misapplication to Word Pieces and all the rest of it, we +have not begun with. After that, we can go on to the discussion of your +visual pieces of the 70s and how they resume the genre of Concept Art. + diff --git a/extra/radicalism_of_unbelief.tex b/extra/radicalism_of_unbelief.tex new file mode 100644 index 0000000..702faef --- /dev/null +++ b/extra/radicalism_of_unbelief.tex @@ -0,0 +1,374 @@ +112 + + +UNBELIEF “H + + +LISM OF +enry Flynt + + +If we are going to talk about enlightenment and deliverance, 1 do not see that +enlightenment and deliverance can come from anything as straightforward as an +individualistic search for happiness, or a mental hygiene of happiness. To me, the +life ] have now, which unfolds through ongoing interaction with other people —and +within this definite culture — is the arena that matters. In other words, | am located +in a shared basis of life. To me this circumstance is of outstanding importance. +While the medium of thought, the capabilities, the skills which are possible for me +are interior to me, at the same time they engage me with other people in cons- +ciousness—and | must regard other people as their source in most cases. (In other +words, | do not invent the English language, etc.) My consciousness and my +capabilities are, by and large, a fragment of a culture. The most worthy capabilities +in the culture become possible capabilities of mine. The most profound dilemmas +or failures in the culture, in the interpersonal arena, become my personal dilemmas. + + +What I have just said is not the same as the idolatry of “society.” I do not accept +the sociologists’ notion of reality, or conformism as a goal, or the obligation to pay +homage to societal abstractions like The Nation. Indeed, one of our culture's +extreme dilemmas and failures is its idolatry of society, an idolatry which aggres- +sively underestimates and devalues both the scope of the self and also the interper- +sonal arena. One of the most far-reaching questions posed by our contemporary +era is whether inter-subjectivity (community) will evolve beyond “society” as it is +defined by sociology (a sort of statistical mechanics applied to bodies). Here is an +outstanding reason why I do not see how enlightenment and deliverance can come +from an individualistic hygiene of happiness. The modalities necessary for enlight- +enment are novel and uncommon; and they are outside the scope of the ordinary +person's struggle for happiness in everyday existence. The necessary modalities +have to be achieved by dealing with dilemmas which arise from the culture as a +totality: enlightenment requires a “rotation” (transformation) of the entire culture. +Life is worthless unless I can inject whatever personal vision | have into the +ostensible, interpersonal arena, and seek to influence that arena so that it becomes +conducive to my sincerity and concern. + + +In order to express whatever sincerity and concern | have in the ostensible, +interpersonal arena, I must engage with the ostensible world; | must incur the risk +of realized choices; and I must “grant other people's right to exist.” + + +Whiekh + + +What I seek is a transformation of the ostensible world and of the shared basis of life. +This is to be accomplished on the basis of two enterprises which will eventually be +fused: a theory of palpable interrelations of the entirety of immediate constituents +of “my world” called “the personhood theory”; and a new instrumental modality +called “meta-technology.” In this introduction, I will focus on meta-technology +without bringing in the dimensions added to it by the personhood theory — largely +because the latter is as yet tentative. But I have another reason as well for under- +lining the contribution of meta-technology. There can be no genuine transformation +of the shared basis of life as long as the community's technological means is restricted to the +material technology we know today. The instrumental modality must come to embody the +takeover of technology by the psyche, by personhood. There is no genuine transformation +of the shared basis of life unless instrumental efficacy is at stake in that transformation, +unless the challenge to the prevailing basis of life is carried into the domain of material +technology. + +As of now, I have assembled many meta-technological elements or procedures. +These elements, however, are isolated and limited. What | have accomplished is +analogous to Becquerel's discovery that uranium fogs photographic film, My pro- +cedures are effective as curiosities. But they will not be any more than curiosities +until they are subjected to an entire phase of extension and interconnection —an +undertaking which requires collaborative effort on a wide scale. + +On the other hand, the analogy to Becquerel is misleading in that a meta- +technological procedure is of an entirely different species from Becquerel’s dis- +covery. Radioactivity occurs in the exterior realm of things (objectivities): it is an +effect of a thing on another thing. But generally speaking, a meta-technological +procedure is based not on a relation between things, but on an interdependency +between subjectivity and things. + +Because I am located in a shared basis of life, a culture, that culture is of +overwhelming importance both as a source of possible capabilities and as a source +of dilemmas and limitations. To respond to this state of affairs, the meta-technology +must accumulate information which is of more than personal significance. It must +address dilemmas which are shared and which are culture-wide. That is why | +investigate mathematics, “real-world” logic, etc. It is also why my interest in +dreamed experience relates to a proposal to modify the shared basis of life — rather +than to the familiar purposes of divination and psychiatry. + +I disregard all claims of sorcery or miraculous feats which inherently come as +reports by a second person about what a third person did (tall tales, fish stories, +legends). lam not interested in miracles which are always performed by somebody +else somewhere else. Indeed, my objections to occultism go much further than this. +But the principle which I want to emphasize now is that every meta-technological +procedure is required to be formulated as an instruction to be carried out first-hand. + +Below | will explain that a starting-point of meta-technology is an adver- +sary attitude towards credulity. One aspect of this phased unravelling of credulity +is a critical examination of claims of meaningfulness for reportage which intrinsically +precludes first-hand testing. + + +Weve ever + + +113 + + +114 + + +Whar then is my attitude to the immediate, overt, ostensible world? I have little +use for the doctrine that the ostensible world is a sham which conceals another, +perfect world behind it—a perfect world which can only be known by hypothesis. +In other words, I do not treat the ostensible world as a facade for something lying +behind it, as a front for another world which is unperceivable. And [ have little use +for the notion of a perfect world which is hypothetical and imaginary. This present +life, which unfolds through ongoing interaction with other people, and w ithin this definite +culture, is my arena of concern. Imaginary lives and gratification in fantasy are unim- +portant to me. | accept the ostensible world as the arena of my concern, and as one of the +raw materials of enlightenment and deliverance. + +The attitude I have just expressed does not imply that 1 admire whatever +ostensible world we inherit. Quite the opposite. Precisely because the ostensible world +matters to me, the arrival of enlightenment or deliverance has ta be demonstrated by a +transformation of the ostensible world and by a transformation of the shared basis of life. +Further, while I do not view the ostensible world as an illusion standing between +me and some perfect world which must be known by hypothesis, there is a sense in +which I view the ostensible world as a delusion. It is a delusion in that the very +perceptions which characterize it are palpably affected and sustained by emotions +of anticipation, by emotional dependence on other people, by morale, by esteem, +by knowing self-deception, etc etc. Everyday existence is the hallucination produced +by the so-called socialization process. Morale, esteem, etc. are co-determinate with +“perception.” + +Thus, again, the arrival of enlightenment or deliverance has to be demonstrated +by a transformation of the ostensible world and of the shared basis of life. But what +| propose is not to strip off the ostensible world to reveal a unique perfect world +behind it. Rather, | want the ability to consciously “mutate” or plasticize the +ostensible world itself. + + +Yevevew ye + + +Inasmuch as I demand that enlightenment and deliverance should be evinced +by transformation of the ostensible world, | am a kind of secular revolutionary. + +To me, the means of enlightenment and deliverance must begin with an adver- +sary attitude toward credulity and toward phenomena whose existence is solely a +product of credulity. In the Seventies, there was a rash of novels in the U.S. about +demonic possession. The protagonists in these novels were always Catholics. The +novelists knew that Catholics were protagonists who could plausibly be liable to +visitations by demons. If you do not want to see demons in your living room, +all you have to do to escape them is to stay outside the subculture that believes +in them. + +The lesson of this example, properly understood, is the starting point of enlight- +enment and deliverance for me. If it is obvious that a phenomenon can be +abolished by unbelief, then the “reality” of that phenomenon is of a very low order. +The phenomenon has only the reality of chimera or fantasy. (On the other hand, it +is obvious that a lor of people enjoy their chimeras, and do not want to escape +everything that can be abolished by unbelief.) | make it a principle to disregard +phenomena whose existence depends so obviously on credulity. The attitude + + +which is encouraged by all kinds of superstition and propaganda is “How many lies +can | (manage to) believe?" The question which | always ask is "How much of what +I am expected to believe is a lie?" + +On the other hand, the tssue of whether the existence of a phenomenon is +a product of cretlulity is not necessarily straightforward. In the first place, we have to +distinguish between getting rid of phenomena by unbelief and getting rid of them by +suppression or censorship. | often encounter situations in which scientists refuse the +opportunity to experience an anomalous phenomenon. Nobody denies that the +phenomenon is “real,” that is, accessible at first hand. The phenomenon is disre- +garded or suppressed because it is a nuisance, because it conflicts with the scien- +tist’s ideology. + +In the same vein, I am not asking anybody to deny his or her own experience just +because it is abnormal, anomalous, or singular. But | am asking that such exper- +iences not be misrepresented and inflated through knowing self-deception — +especially in reporting them to others. | have long speculated that reports of +so-called astral projection etc. might have an experiential basis in hypnagogic +hallucinations etc. Unfortunately, the sort of person who relishes reporting such +episodes is also prone to inflate them via culturally supplied hyperbole. Reports of +abnormal experiences could have serious uses if the reportage did not surround the +experiences with chimerical objectivities, and if it took a painstakingly critical +attitude toward the “ontological” assumptions built into descriptive language. + +Another consideration is that a thorough and ruthless effort to repudiate all pheno- +mena whose existence depends on credulity will begin to undermine phenomena which +our culture defines as legitimate and plausible. Unbelief does not just dissolve supersti- +tions and chimeras; it begins to affect phenomena which rational authority defines as +valid. At this point rational authority has to step in and disparage unbelief as a +social blunder. Here the role of community intimidation in sustaining the osten- +sible world comes to the surface. But I do not shrink from this consequence of +unbelief. Indeed, the radicalism of unbelief is a basis of my ability to obtain results which +are novel and astonishing relative to the established culture. + + +Yerevan de + + +Let me give some examples of meta-technological investigations: + +A priori neurocybernetics! deals most directly with interdependencies between +awareness and objectivity. As one example, it uses perceptually multistable fig- +ures? as logical notations. The result is to establish awareness-objectivity inter- +dependencies in language which are tangible and inescapable and can be analyzed +and potentiated. The technique can be applied to break the framework of scientific +objectivism in many ways. As another example, | note that our “perception of +objects” is actually a mental collation of visual and tactile apparitions. There are +many cases in which the normal intersensory correlations are disrupted (the per- + + +1 Neurocybernetics is an existing branch of neurophysiology which seeks to explain thought by investigating the brain +as a “bionic computer.” + + +2-eg the Necker Cube. + + +115 + + +116 + + +ceptual illusions). If we take the illusions as a paradigm and reinterpret “normal” +phenomena in accord with that paradigm we are in a different reality, disjoined +along the sight-touch frontier. Bode's Law that two material bodies cannot occupy +the same position in space at the same time ceases to be usable, because the +determination of what is a material bady is seen to involve a vicious circle. + +The evaluational processing of experience studies, as one example, the circumstance +that different levels of reality are attributed to waking experience and dreamed +experience even though both are equally vivid, equally palpable. What is at issue +here is the fabrication of an “impersonal order of nature”; the inter-subjective +character of reality; and the choice of rules for testing the objectivity of phenomena. +Again, once these elements are understood consciously, they can be consciously +altered. + +The logic of contradictions is a wide-ranging, umbrella discipline. The unifying +theme of the discipline is the recognition that inconsistent conceptualizations, sa +far from being vacuous mistakes which can be eliminated from thought, are +pervasive and inescapable in thought as we know it. Conscious control of this state +of affairs is an extremely powerful achievement. The investigation begins with the +interdependency between traditional logic and perceptual habits in the real-world +logic of consistency. It then considers perceptions or events which are faithfully +described by inconsistent descriptions, such as illusions and dreams. I characterize +these apparitions as contradictory because that is the characterization given them +by shared language and paradigmatic real-world logic —as all the perceptual psy- +chology textbooks agree. Then, | study contradictions which are cognitively im- +plicit in our most authoritative or obligatory propositional thought. (Paradoxes of +common sense; the meta-theoretic inconsistency of arithmetic and set theory.) +Finally, I study how the communal milieu and its influence on esteem enables +people to assent to openly inconsistent doctrine. (Mathematics’ co-optation of its +own inconsistencies; etc.) This research yields a very wide-ranging capacity to +produce anomalies or uncanny world-states. + +My recent investigations into personhood have shown that meta-technology can +be significantly widened and deepened by studying not only linkages of perception +and descriptive language, but their co-determination by morale, esteem, ete. +Studying the entire “vertical” organization of self or self-image could result in the +realm of perception being transformed. + + +Vee Het + + +Our civilization has long been characterized by the way it molds human faculties +to produce a cleavage between scientific functioning, on the one hand, and poetic, +emotional “human” functioning on the other. Meta-technology is beyond this + + +cleavage of faculties. Also, it is worth repeating that meta-technology does not + + +3 An example of an intemensory discorrelation ix Aristotle's tactile Husian: wuch the tips of crossed forefinger +and middle finger at the left hand te a projecting dowel while also looking at the dowel. You see ane dowel and feel +two The perceptions the wo fingersare notanly disjained. they are inverted The subjectaririhures tithe index finger +what ts touched by the middle finger and tuce versa, as cin be shown by applying two distinct stimult ns the finger - +a point and a ball, for example + +Even better: try the experiment first with eves claved, and then open the eyes. Sight captures ouch, and the fingers +are switvhed withoutany motion taking place. (Adapted from Merleau-Ponry, The Phenamenalagy of Perception, pg. 105.4 + + +consist of the sort of magic tricks attributed to pre-scientific religious figures. What +is a religious miracle like changing water into wine? It is — purportedly —an object- +ively consequential manipulation of the thing-world, a type of cause-and-effect +technology. It takes place “out there,” replacing a thing with another thing. + +Meta-technology does not appear as hearsay; and it does not make any special +appeal to credulity. Rather the contrary. Its primitive procedures are given as +instructions to be carried out at first-hand. Presupposing a conventionally indoc- +trinated individual, it achieves anomalies by a decrease of the conventional level of +credulity. It is not centered on thing-to-thing relationships or causation “out there.” +It is centered on the interdependencies between subjectivity (awareness, self- +image) and things. + +In addition, there is a third constituent important enough to be mentioned +separately: the communal milieu, and especially its influence on esteem—as when +intimidation by community authorities maintains the legitimacy of ridiculous +beliefs. It is at the juncture I have just sketched that “the world” is synthesized, that +the determination of reality occurs. Meta-technology attacks the credulities which are +elements of this juncture. It works with the linkages among ‘‘perception,” descriptive +language, and abstract cognition (logic, mathematics.) Currently | am extending the +research to include linkages to personhood —the high integrative level, the vertical" +organization of self or self-image. + +There is a big gap between the primitive meta-technological procedures which I +have already formulated, and the communally implemented, culturally imple- +mented meta-technology which | envision. The primitive procedures can be +carried out by an isolated individual (and yield a sort of insight of sensibility); butat +that level they are, in a sense, only curiosities. The whole point is that meta-technology +acts on the cultural determination of reality as such. Unlike a miracle or magic trick, +which wants to remain a one-shot event in an otherwise lawful everyday world, meta- +technology must be extended through a community and a culture to realize its promise. It +is not a one-shot event bura “rotation” of an entire culture. + + +What is more, to reach its full potential, meta-technology will probably have to be +tied into existing natural science. But meta-technology would give a shock to +natural science which must not be underestimated. Natural science would be con- +ceptually shattered, and reorganized so drastically as to become unrecognizable. + + +vane + + +If meta-technology were implemented at the level of an entire community, +that community would have the power to consciously modulate what is now +thought of as the objective world. To speak of walking through walls would not be a +mere joke, Both the physical universe and mental acts as its antithesis would +disappear, in the sense of becoming inapplicable concepts. It would be possible to +achieve sustained, composed uncanniness, to live in a state of consciously modu- +lated enchantment. In this regard, the impulse underlying meta-technolgy is an +impulse toward an ecstatic form of life. (It must be understood, however, that the +rational mentality produced by modern Western civilization might experience the +enchanted community as a nightmare.) + + +117 + + +118 + + +When meta-technology shifts the focus from the thing-world to the interdepen- +dencies between subjectivity and things, it leads us to our whole humanness. It +carries out a takeover of technology by the psyche or by personhood. For a +community to attain a consciously modulated uncanniness would tend toward an +ecstatic form of life —an achievement which the prevailing culture would classify as +esthetic or spiritual, not scientific. That is what must be conveyed: acceding to +one’s whole humanness is neither science nor poetry because it is beyond both. + + +Postscript: The foregoing is not meant to promise a salvation which is blind +to economics and politics. The present article is limited to giving a few rudiments +of the meta-technology: my proposed extension or replacement for the physical +and exact sciences. My views on the social context are at least as unusual as my +views on science and form an entire line of argument in their own right. The +transformation I speak of would clearly be in conflict with the capitalist formation. +On the other hand, I hold that historical experience has obsolesced Marx's original +timetable and game plan for the supersession of capitalism. + + +Readers seeking more information or exchange of ideas are invited to write the +author care of Ikon Magazine. + + diff --git a/extra/structure_art_pure_mathematics.tex b/extra/structure_art_pure_mathematics.tex new file mode 100644 index 0000000..dd8cb61 --- /dev/null +++ b/extra/structure_art_pure_mathematics.tex @@ -0,0 +1,156 @@ +\chapter{Structure Art and Pure Mathematics (1960)} + +In some art---music, visual art, poetry, and the rest---there is a tendency for +"structure" to predominate. When structure tends to predominate in art, then \emph{if} the +artist wants the interest of the structure to predominate, wants to communicate the +interest of the structure, I will say that the art is "structure art." Much structure +art is a vestige of Serious Art; for exemple, of medieval music, which was conceived +to be a metaphysical science. Now consider, for example, a piece of structure music, +a serial piece. The "structure" of the piece is \emph{not} (in) the sounds in (a performance +of) the piece. It is a categorization of the sounds, that represented by the score +together with that typically given in the first instance by the composer in an "analysis" +of the "piece" (actually the analysis is more a part of the piece). Thus if I speak +of the "intended structure" of a piece it will be the composer's categorization; and I +will speak of others' categorizations, the audiences' categorizations, as "associated +structures" of the piece. (To some extent the composer can work to the audience's +background so that one association is more probable than another.) Many structure +artists do claim "that the structure (particulerly the intended structure) is in the +sounds" in that, for example, there is an objective relation between the categorization +and the sounds. This claim is unjustifiable; I will return to it later. There is an +important division of structure art into two kinds, exemplified by the fugue and total +serial music, according to how the structure is "appreciated." In the case of a fugue, +one is aware of its structure in listening to it; one mentally imposes "reletionships," +a categorization (hopefully the intended one) on the sounds while listening to them +that is, there is an "associated artistic structuring by oneself." In the case of total +serial music, the structure is such that this cannot be done; one just has to read an +"analysis" of the music, a specification of relationships. Incidentally, there is +another, less important kind of art in which the important thing is categorization; +the art involving conceptual cleverness, play with the concepts of the art-form such as, +in music, "the score," "performer versus listener," "playing a composition." In +structure poetry, there is a lack of concern with syntacticel structure. The poetry +is mere phonemes or graphemes with an artistic structure. + +The following is an attempt at a formal definition of "artistic structure." +The artistic structure of a production is a division or segmentation of the raw work +(the body of material), a grouping of the segments, and a "weighting" of the subgroupings +in this grouping (according to their"structural importance"); that is, it is a system +of definitions. When structure is regarded as the most important aspect of the +production, the production is merely a diagram illustrating the description of its +structure. Certain pieces of music are merely acoustical diagrams of their structures. +Such a production consists of the production proper together with a concept poem, a +body of definitions. Here is a canonical method of specifying such structures. +Given the raw work, the informal description of its structure is as follows. The +segments are blocks of color; the first two are grouped together, and each of the +others is grouped separately; the weights of the successive groups are $5, 2, 4, 2, 4$ +(2 is the weight of \eg\ a bridge passage in music). The formal specification is +$(AB)_5(C)_2(D)_4(E)_2(F)_4$; that is, the production is structurally a "$(AB)_5(C)_2(D)_4(E)_2(F)_4$." + + +The method, then, is that the terminology for a certain structure is formed from +letters corresponding to segments, parentheses to indicate grouping, and numerical +subscripts to indicate weights. (Does the method need to be elaborated to take into +account relations between segments?) It can be seen that this kind of structure is +definitional, stipulational, like logical syntax; it is not intuitive and statistical +like an individual's use of inflection in speech. I now turn to the analyses of +the structure of a production made by critics, what I call "associated definitions of the +structure" (in line with the terminology of the previous paragraph), Consider the +following examples. + +\includegraphics[width=4in]{img/structure_art} + +In each example, the actual sounds, the body of material, is exactly the same. +The difference is in the different structures defined on the material. The examples +substantiate my contentions thet the structure is not in the sounds; that the composer's +analysis of the piece is really a definition and a part of the piece; and that the +critics' analyses of the structure are definitions attached to the piece, not discoveries +of intrinsic properties of the sounds. As another example, consider the difference +between hearing the "Sanctus," \opustitle{Missa Prolationum} of Ockhegem, in no meter (by +a non-European listener), in one meter (by a lay European listener), and in four +meters (the intended structure). Arguments such as the one over whether the structure +of Webern's music is "really" motivic or serial are absurd, since Webern himself did not +define this point. Many academic structural analyses of art have been irrelevant +to the aesthetics of the works. + +The purpose throughout all this art is dual; structure or concept art tries to be, +first, music, visual art, or whatever (which suggests that it is to be listened to, or +looked at), \emph{and}, something else entirely, to be valuable for its structure or conceptual +cleverness. Then when the structure is "hidden," "unexperiencable," when it can only be +appreciated by reading the "analysis," why put emphasis on the body of sound, light, or +whatever, why listen to structure music, why look at structural visual art, why even call +them "music," "visual art"? Why not throw away the bodies of sound, light, or whatever, +and keep the "analyses" of the structure as the works of art? In general, logic, and +experience (with the results of the artists' efforts), show that the dual purpose of +structure art consists of irreconcilable objectives; that one can be attained only at the +other's expense. Which objective are the structure artists trying to attain?---they +obviously have no idea. Structure art represents obsolete, confused categories of +activities, categories which by now are obscurantist. Structure (or concept) music, +for example, needs straightening out, first, by ceasing to call it "music," and starting +to say thet the sound (or activity) is used only to carry the structure or conceptual +cleverness, and that the real point is the structure or conceptual cleverness---the +categorization---and then it will be seen how limited, impoverished the structure of +these productions trying to be music are. When you make the change, then you are led +to a far more consistent, integral activity, the same one arrived at below through +a consideration of pure mathematics. Games of intellectual skill such as chess fall +into this same category; since, after all, they can be regerded as formalist mathematics. + +Neryt I will discuss pure mathematics. Originally, mathematics was a system of +beliefs, a doctrine, about the entities numbers, points, polygons, and so forth (Pythagoras, +Euclid, Platonic geometry). As mathematicians became skeptical, and thus less desirous +of resting the importance of mathematics on the validity of these beliefs, they changed +their minds about what the purpose of mathematics is. The purpose became for the theorems +to be true if the axioms are. In the nineteenth century, as a result of e.g. the ideas +of Riemann, they became unconcerned to claim that their axioms are true. They began +to say that the value of mathematics is "aesthetic." Here is when mathematics becomes +a subject for this essay; when it becomes pure mathematics, when its value is not claimed +to be that of technology or natural science, but rather more an aesthetic value, when it +becomes "adoctrinal culture." Mathematics becomes something to be considered alongside art. +When I became interested in contributing to pure mathematics, for reasons of taste I wanted +to de-emphasize discovery in mathematics, mathematics as discovering theorems and proofs. +(Such discovery bored me.) The first way I thought of to de-emphasize discovery was that +since the value of pure mathematics is now regarded as conceptual interest, aesthetic +rather than scientific value, why not try to make up aesthetic theorems, without considering +whether they are true. The second way was to find that the conventional claim that +theorems and proofs are discovered is unjustifiable; I will return to this point later. +In the twentieth century, as a result of the ideas of Hilbert, and then Carnap, +mathematicians became unconcerned to claim that mathematical "statements," the +mathematical object language, are (substantive) assertions having truth value (as are +English statements). Rather, they are "merely" series of signs formed according to +certain rules: formalist mathematics. Then my third way of de-emphasizing discovery was +to open up unexplored regions of formalist mathematics. The resulting mathematics still +had statements, theorems, proofs, but the latter weren't "discovered" the way they +traditionally were. + +Now exploration of the wider possibilities of pure mathematics opened up by me +tends to lead beyond the form of "making statements," "proving," and the like, so thet +the term "pure mathematics" becomes completely incongruous. The category of pure +mathematics---a vestige ultimately of the old system of beliefs canonized by Plato +(hence the form of statements, proving, and the like)---is an obsolete category. My +contributions to pure mathematics lead to an integral, general activity of which the +point is categorizations (having the value of being "well-formed"); the contributions +need to be classified as such an activity rather than as pure mathematics to escape +confusion, Traditional mathematics (mathematics as discovery), reformulated, explicated +to take my findings into account, would be an untypical, small but intensively developed +part of such an activity. + +The proponents of structure art, pure mathematics, and chess make similar claims +for them. I have mentioned the claims that structure is an objective property of things; +and that mathematical theorems and proofs are discovered; and there is a similar claim for +games of intellectual skill. Two important notions associated with these fundamentally +identical claims require comment. There is the notion that contribution to structure +art, pure mathematics, and chess requires high intelligence, the discovery of implications; +the notion of intelligence as the ability to discover implications. Then, there is the +notion that structure (as in mathematics pre-eminently) is an objective property of things, +capable of discovery, demonstration, rational cognition---with particular reference +to language, art, and the like---whereas meaning, expression, and emotion are not. +(These pretensions are traditionally an essential aspect of structure art, pure mathematics, +and chess.) Both notions come down to the belief that there can be an objective relation +between a name and its referents; for example, an objective relation between the +metamathematical term "true theorem" and certain theorems, or an objective relation +between "having serial structure" and a body of sound, or between "checkmate" and +checkmates. As I said, these notions are discreditable, as can be seen from my +\essaytitle{Philosophy Proper} and \essaytitle{Primary Paradox}. Thus the notion of intelligence, pretension +of intellectual superiority, as what mathematicians, chess players, and the like have; +and the prejudice in favor of structure; cannot be defended. It is about time that +these notions be discarded. + + -- cgit v1.2.3