Studies in the Person-World and Pre-Science (1985)

© Henry A. Flynt, Jr.

D.  Novel possibilities of integration

1.  Escaping the conformist models

a.                  Let me consider the claim that the conformist imaginative models are the only plausible and efficient means of correlating fleeting appearances.  How could one not accept the conformist models in the following cases?

i.  I close my eyes and don’t see the world delivered to vision.  Shall I believe that the world has ceased to exist?

ii.  When I become unable to see an object delivered to vision because it moves in front of a field of the same color, shall I believe that the object has ceased to exist?

iii.  If I can frame the moon with my fingers, shall I conclude that my hands are larger than the moon?

iv.  Let me hold my left forefinger vertically in the near center of my visual field and gaze beyond it so that the visible finger splits into right and leftward fingers.  I touch its tip with the tip of my right forefinger held horizontally.  At a glance, my right forefinger goes through the rightward finger and is stopped by the leftward one.  On close inspection, the right forefinger also is doubled along its length.  Should I conclude that I have two left forefingers? 

Aside:  If I bring my right fingertip down vertically on the left finger(s), I see two contacts, but feel one!  Intersensory discorrelation!  °1 

v.  Suppose I put a piece of ice in my mouth and hold it until there until it melts.  °2  In the sensuous career of the piece of ice, it is delivered to vision (and touch) as an object—then to touch alone as an object that shrinks and becomes irrecoverable.  Shall I deny the substantial unity and indestructibility of the object?

vi.  Suppose I heap stones on a ledge or platform until it collapses.  Do I deny that things outside of me interact directly with each other?

vii.  In relating to other people:  am I to maintain that there is no substantial body underlying my visual, auditory, and tactile impressions of another person?  °3  When I am in the presence of another person, where is my consciousness positioned spatially relative to that person?  At their body? 

2008:  Let two people stand side-by-side facing a mirror. 

—Where are their consciousnesses positioned spatially in this experiment? 

—Do the two people see the same thing?  Really?

viii.  Shall I believe that the tricks of a conjurer—restoring a cut rope, etc.—accomplish what they appear to accomplish?

ix.  if two unframed  mirror-squares are placed side by side, and I move my face back and forth in front of the vertical break between the mirrors, I see my face appear and disappear.  Should I conclude that my head achieves invisibiity and then loses it?

x.  I see railroad tracks at a given milepost move together as I back away from that milepost.  Should I expect that a pliable object left between the tracks will be crushed when I withdraw so far that the tracks meet?

b - c.       In 1985, I followed (i)-(x) with a critical come-back, and then proceeded to introduce D.2 as to its method and scope. 

                        Here I will anticipate a lesson of D.2If you rely on no authority, and look at “the world” (including your mind) from the vantage-point of your personal comprehension, you will find gaps everywhere.

                        In D.2, the meta-technological metamorphosis, the novel schemes of integration, are sometimes called “replacement.”

                        D.1.b - c is at the end, as an Addendum, and may be read now if one wishes.

2.  Cases

a.                  Which feels longer to you now, one year ten years ago, or one month one month ago?  My answer:  I can’t give an answer on the basis of “feeling.”  The only sense of past duration to which I could appeal to answer the question comes from the linguistically embodied chronometric conventions of the prevailing culture.  To put it another way, if somebody states dogmatically that what is called the year 1974 is the “same length” as one month in 1985, I cannot disagree with this assertion on the basis of my experiential memory or cumulative remembered sense-contents.

                        Can you tell by “feeling” whether a given past year was a leap year or not?

                        If past lapses of time are delimited, and labeled, by episodic contents in my life, then in general, even the sense of importance of events in my life does not attach independently-felt durations to them.

[Excepting cases in which calendar-determinations are an integral feature of the episode, which I cannot exclude in remembering without disrupting the memory:  e.g. the length in years of my senior high school program.]

                        Generally speaking, length comparisons of remembered lapses of time depend on language-assignments and cannot be ascertained by languageless comprehension.  I can determine lapses of time subsequent to certain events in my life only because I have memorized year-numbers as verbal information.  So <length of a time-lapse>  becomes
phenomenally free as it moves into the past.  [2008.  <the felt length of a standard time-interval>]  °4

                        Here is a determination of episodic life demanded by common sense which individualized comprehension leaves open.


                   Let me characterize the vagueness of experienced time-lapses abstractly.  (Cf. the leap-year case.)  Separate time-lapses can be delimited by a) qualitative contents of personal memory; also by b) a culturally supplied quantitative scale (clock, calendar  [designations]).  Also I have c) a subjective measure of lapsed time delimited qualitatively.  (Feeling of duration.)

                        I cannot validate the ratio of the durations, i.e. (b), on the basis of subjective duration-sense, i.e. (c), applied to personal memory (a).

                        Counting sunrises or full moons begs the question, because as a quantitative measurement of time-lapse, constancy of this qualitatively specified marker is at issue. ∆

b.                  This section may seem less accessible than the one that follows, but there is a reason for placing it first.

                        What is episodic recollection—if we don’t judge it in advance to be veridical?  It is an attribution of “past realism” to <a visualized event (a “daydream”) in a pastward context>.  By what magic do we impute past realism to a daydream at all?  We won’t inquire into that yet.

                        Take the standpoint of being inside a dream, a single specific dream.  Within a given dream, I have a visualization-or-daydream-memory, stretching a past behind the dream’s “now.”

                        Suppose that (in the dream) I leave a room in which there is a chair, and then return to find the chair gone.  At the time of returning, I remember a past situation different from the present situation, and thus judge that the chair has been removed.

                        But can it be that I am in error in thinking (remembering) that a chair was in the room at the earlier time?  Is the earlier portion of the dream objectively subsistent somewhere, so that it is meaningful to compare it with my dreamed memory of it?

                        Suppose I live through a dream event, and then later in the same dream, attribute in memory a different event to that earlier time.  In this case, there is no consciousness of a discrepancy, no disappointed expectation.  Is an error of memory possible which leaves no trace in the ongoing dream experience?

                        We underline:  this is about memory in a dream of an earlier moment in the same dream.  There are two cases:

—Conscious intertemporal disparity.  I remember a chair in the room and now it’s gone.  Surprise; perception of a deficit.  (Was a chair removed or should I question my memory?)

—Can I simply remember falsely—absent surprise or perception of a deficit?  Now the objective past is irrecoverable.  °7

                        Should a tracelessly altered past, if any, be accepted as the genuine past:  on the grounds that a mirage-event in a mirage-episode simply collapses to what you, still in the mirage-episode, now think the event to have been?  [Science might claim that the earlier phase of the dream is objectively real, in the form of brain electricity.  But in this inquiry, that claim an irrelevant hypothesis, since there is no possibility of recovering the information in personal comprehension.]

                        In the dream-realm in question, there is no independent test of episodic recollection.  It’s a dream, and I am permitted to say:  the past episode changes to correspond to what I recollect it as being.

                        Does personal comprehension assure the constancy of the past’s contents (qualitative constancy of the past)?  If “my life” includes my dreams—perhaps not.

c.                  Testing a personal prediction requires determinations which comprehension may not be able to “lock up.”

                        What guises does a prediction have? 

—A proposition.  A verbalization in my stream of thought.

—A fantasy-expectation (cf. desire, fear)—a daydreamed future. 

                        But there is a catch in the latter case.  How do you know that the daydream is future-directed or future-situated? 

                        To understand what follows, it is necessary to understand, for example, that perspective is not radial distance.  You infer radial distance from perspective, but perspective does not prove radial distance. 

                        I’m not claiming an analogy with prediction, but in both cases a sensory content is expanded with a reality-dimension. 

                        How do you intend future to a daydream?  If you can’t prove that the world will exist tomorrow, how can you project today’s fear to tomorrow semantically?


We arrive at a class of subjective phenomena in which “real depth” is ascribed, but the “real depth” is not delivered in the sensory content; it is imputed.  These have the characer of perception and language both.  (Language:  denotation and so forth).  They include:


—perception of a deficit

—perceptual illusions which cannot be identified without language

—“temporally cognitive emotions”:  desire, fear

Elsewhere, I gave these phenomena one or another label:

proto-semantic consciousness-events in perception

incipiently semantic consciousness-events

Again, these are concomitant to beliefs, about an objective world, which cannot be substantiated from the sensory content.

                        To proceed with issues of personal predictions.

i.                    You have to remember the making of a prediction in order to confirm it.  When the time arrives to which the prediction adverts, the prediction has to be remembered:  either as fantasy-expectation or as a proposition.  Confirmation of a prediction happens to require that you remember the prediction.  That is as uncertain as judging what happens in the arrived duration to which the prediction referred.

                        I make a prediction now; later, I live through the episode that verifies (tests) it.  By the time the episode arrives, the meaningful prediction (the one made in advance) can only be retrieved in memory.  (For that matter, I could remember wrongly what I predicted.  For that matter, in using a name to equate entities, I could wrongly remember the name; or wrongly remember my criterion for applying it to an entity.)

                        A prediction would be subjectively irrefutable if memory tracelessly altered the prediction to conform to what eventuated.  So the realm of a successful prediction is as dependent on memory of a past thought as it is on the “arrival” of the appropriate event.  °8  The common-sense determination requires plural successes in linking different time-phases in order not to beg the question.

ii.                 Suppose you sit in your house, and forecast that if you go outside your house you will see the postman in front of your house.  You go outside and you don’t see the postman.  You come back in.  Then you go outside again and do see the postman.  Was your forecast verified or falsified by the arrival of a veritable experience?

This seems a mere issue of specificity.  But wait!

                        Suppose that when you go out the second time, you don’t remember the deed of going out before.  Is your forecast then unequivocally verified? 

                        Suppose it is said that a personal forecast is verified if it is fulfilled in the objective (future) time-frame to which it refers.  But how do you tell you are in the appropriate objective time-frame, except by concrete contents which locate that frame?  If you aren’t relying on hours or clock (i.e. authority), then your knowledge that your first trial to see the postman was unsuccessful depends totally on the integrity of your life-memory at the time of the “other” trial.

                        The possibility of false memory was invoked in D.2.b.  But that is not the whole point or the main point.  The point is that my ability to relate present and future unequivocally is mixed up with my memory when the future arrives—with my attribution of “past realism” to <visualizations in pastward contexts>.

[We note that in this case of the postman, I need to remember that I harbored a prediction, either a fantasy-expectation or a verbalization, and that I went to look more than once.  Three reality-types are in play, two concerning what I thought, one concerning what I did.  But let us be careful:  a verbalization would not be contextless; it would occur in my stream of thought.  A fantasy-expectation would occur in my stream of thought.  Going to look would be a deed.  Memory begins by conjuring up any of these as a “daydream.”  A daydream of a deed (i.e. a visualized event), and a daydream of a verbalization in my stream of thought—perhaps these need no comment.  But a daydream, of a fantasy-expectation, to which I attribute “past realism”?  If imputations of realism in personal consciousness are “magic,” here we have second-degree magic!]

                        Continuing with the postman, how do you know that the unique time-frame has arrived to which the prediction refers?  Do you know because, subsequently, the arrived future agrees, or disagrees, with the remembered prediction?  But a prediction can be right or wrong.  So whether it is one or the other is not a test of whether the indicated time-frame is now arrived.   Neither satisfaction nor frustration of the prediction proves that the relevant time-frame has arrived.

                        On the one hand, whether a given time-frame has arrived is a matter of whether certain time-lengths have elapsed. 

                        But unless you are relying blindly on hours or clock, don’t you have to invoke concrete event-contents to specify a future time-frame?

                        2008.  Individuated comprehension has only its own leg to stand on.  °9

[Aside:  Prediction could be explained as the surmise of a specific detail in the context of a broader event which is certain to occur (by induction?).  But—in an unfamiliar situation, this proposal is not even relevant.  Moreover, literal certainty of the future is a claim which is unacceptably rigid to common sense.]

d.                  A repeating event

                        Let me take one standard principle of lived experience literally.  Events are literally individual.  Literally, nether events nor moments of time repeat.  °10  2008. We place an earlier and a later event in an equivalence-class without claiming that they are literal duplicates.

                        Thus, a procedure can be repeated only in the sense that steps a, b may be followed by steps a', b', where a' is identified with a and b' with b.  But in no way is this a reliving of the times of a and b.  This relativization of repeatability of events to stipulation weakens common-sense causation—and can also weaken stipulation itself. Further, D.2.a is strengthened by this posture.  Now there cannot literally be a metric time:  since in the case of a so-called interpolation of moment of time c between moments a and b—actually, an inclusion of the step c in the later series a', c, b'—one does not know whether a', c, b' is more dense in time than a, b, or is instead longer.  This posture makes average velocity and incremental velocity (“acceleration”) undefinable.

e.                  Common sense (and physical science, relative to the phenomenal “world”-zone) demands that in perception, we judgmentally resolve apparitions as substantial objects via a standard scheme.  That was the conformist import of many of the cases in D.1.a above. But I can select apparitions, phenomena, which are classified by conformist thought as being wholly in the palpable object-zone [FN. unlike afterimages, which are not] which fool the standard scheme.

i.                    When a disc-shaped shadow turns edge-on, not only does it seem to vanish, it does vanish.  (Referring back to C.2.b.iv.)

ii.                 When two separated shadows are seen to meet or to cross, they do interpenetrate frictionlessly.  Or, they do cross without one covering the other (in the strict sense).

<In the case of motion of a shadow, the shadow may be apprehended under the world-aspect of permanence.  But under the conventional doctrine of substantiality, that is an error:  it is nonsense to say that a shadow endures from one place to another.>

iii.               When an object and a shadow are reflected in a pool of water, a ripple wavers the reflection of the object, and the reflection of the shadow, in equal degree.  In other words, reflection transforms object and shadow to the same plane of substantiality.  [This is a surmise:  needs more confirmation.]

                        Again, what point is made by these examples?  They are cases in which the standard judgmental resolution of visual apparitions as substantial objects fails.  Thus, the scheme of immediate assessment of apparition which conformism provides is susceptible to “replacement.”

f.                   The phenomenon of nontransitivity of identity for slowly varying observables—as in the case of observing the change of position of the minute-hand of a clock—has been much discussed by academic philosophers.  I claim this phenomenon as a major substantiation of my outlook.  Indeed, the philosophers who choose to discuss this phenomenon while speaking for orthodoxy undermine their own outlook. Cf. Michael Dummett, “Wang’s Paradox,” in Truth and other Enigmas.  °11

                   Discriminations of slowly varying observables

                        Intransitivity of equality relative to slowly varying observables

                        Various authors have noted that the relation “imperceptibly different” is non-transitive.  Phenomenal sameness is a “non-transitive equality.”

                        If you watch the minute hand of an electric motor clock, you will not see it move, but by memory you will observe that its position changes. This observation will be sharper if you can observe a reference mark at the tip of the hand.  Basically, it is by recollection that you know the hand changes position, but in the case of a minute hand, retention might stretch over the interval necessary to perceive the change.  The effect is acutely uncanny.

                        Now if you can select a mark on the clock to define a position, and also count off short intervals of time (e.g. one second), or have them counted by a ticker, then you can observe what I call “ratchet intransitivity.”  Let the hand coincide with the mark at the start.  Let the mark’s position be x.  Let the hand’s position at four consecutive counts or ticks be a, b, c, d.  Let ≈ mean “not discriminably different.”  You observe

a ≈ x,

b ≈ x,

c ≈ x,

¬ (d ≈ x),


d ≈ c

For a given acuity of perception, change is observed after a definite number of ticks, but not between any two (or three) consecutive ticks.  The mark x can be the terminus as well as the start.

                        Phenomenal sameness is non-transitive.  This means that all sense-observational properties are inconsistent?!

g.                  In Blueprint, pages 201-6, I used cubical frames (Necker cubes) as notation-tokens, and so constructed phenomena “of the mode of language” which belie the notions of objectivity of language that trade on the objectivity of notation.  [FN. “Phenomena of the mode of language”:  phenomena which extend language as presupposed by the culture—in anticipation of “replacement.”  These constructions are not an absolute guarantee of language, of course.]  Here I give another case of anomalous linguistic phenomena, conceived for a rather different purpose.

                        I accept chosen means as having the mode of “a proposition” if they i) specify a state of affairs (or of the world) and ii) claim its realism.  (Propositions are not assured of truth, of course.) 

                        Now:  An experiential or episodic memory can be considered to be a proposition.  You have a “daydreamed” past, plus an attitude which attributes realism to that “daydream.”  (Again the magic of “attribution of realism.”  Here we use the magic without questioning it.  Cf. incipiently semantic consciousness-events, D.2.c.)

                        Here episodic memories become wordless private language.  An application of this proposal, on the other hand, is to transform person-world memory to an entirely linguistic memory, by identifying episodic memories as language (co-optation of episodic memory to propositions).  °12

h.                  Phenomenal aspects of counting

                        The last topic is the comprehension of quantity—i.e. enumeration.  This topic could have been included in the critical inventory of conventional mentation in Section C; or it could start a new Section E, on pre-science.  (Section E was eventually cast as “Superseding.”)  But I prefer to treat enumeration here because I want to present the Necker-cube example (Fig. 5 below) in a complete context.

i.                    Referring to Fig. 1, count the “cells” in the figure.  (Note that the figure is irregular, so that the number cannot be judged by symmetry or a symmetrical template.)

Figure 1

Fig. 1

The number of cells is a property of the visual image which one can establish by a purely mental procedure (applied to the visual image), of which more momentarily.  After the property has been ascertained, you still can’t see it in the image immediately, but instead have to repeat the mental procedure to reverify the number.  All that can be ascertained immediately is a range in which the number might fall.  We have a mentally derived property of a wholly visible image which never becomes verifiable at a glance.

                        When you count the cells by an exclusively mental procedure, you assign to them a succession of thought-events which appear and disappear in time (exhaustively and without repetitions, which means that the procedure is also an ordering).  (This observation was anticipated in C.4.b.)  What is extraordinary, and even mad, is that one apprehends different “sides” of “the world” under mutually exclusive temporal world-aspects.

                        To avoid the use of transitory mental tokens, you could number by moving your finger along a label-row such as Fig. 2, only looking at the last step, and accepting the written number as the count.

Figure 2

Fig. 2

The crucial feature of comprehending or verifying quantity here is (still) the reviewing of the cells of Fig. 1 in temporal sequence. 

[If the items to be counted were evenly spaced in a row, you could count them with a template like a ruler:  measuring quantity as if it were magnitude.  But this is clearly a special case and a derivative case.]

                        The cells in Fig. 1 are taken as persistent (as is the label-row of Fig. 2).  (Presuming that the objects transcend your impressions, and are unchanging; and that your memory is proof that the objects endure while out of view.)  So if counting in a different order gives a different answer, the result is construed as a subjective mistake.

                        The number-labels are used transitorily in counting mentally, but the labels must comprise a fixed linguistic protocol.  The labels must be fixed in memory or elsewhere, while the mental counting-events successively happen and vanish.

ii.                 If you pair the cells in Fig. 1 with the expressions in a memorized sequence whose number-assignments you don’t know immediately, then the procedure will yield an expression, but will not of itself tell you the number.  You may use the letters of the English alphabet; or the words of a memorized speech.

[Even more instructive might be memorizing the decimal expansion of π to thirty places and then using it to count by saying the digits by rote.  Using the obtained digit together with order-of-magnitude considerations, the unique numerical count could be obtained in at least some cases.]

                        Using the English alphabet to count Fig. 1, what is it that makes “s” intend differently from the label “19”?  “s” and “19” can both be used as the count; but they don’t have the same import for comprehension.  (To the speaker of a language whose letters do not abbreviate Hilbert stroke-numerals.  [FN.  For the uninitiated, the latter amount to Roman numerals with ‘|’ only.])  What is the special import of “19”?  One guess is that the decimal numbers get their import because one has learned addition tables, etc., for them.  But the question is open—it may be, for example, that  the numbers’ phenomenal meaning invoves the metaphor of cumulation of equal lengths.  (Equal spacing—the intuitive metric of the cardinals.)

If number as opposed to <letter in a sequence> gets its meaning from the additive and multiplicative decompositions of the number, then consider that when water and alcohol are mixed, volume is not additive.

iii.               One may record the lapse of a multiplicity of full moons by marking a permanent surface at each full moon.  In this case, the transitory events are so much separated that they can only be compared in recollection; moreover, memory is not a convincing medium to cumulate the observations of dozens of full moons.  So the process is transferred to a model—to a sustained presence.  The medium of record has to be substantial and changeless for the procedure to be plausible.  So a “repeating event” (D.2.d noted that repeating events are products of stipulation) with a period far outside the scope of an experienceable time-lapse is modeled by a display of continually and simultaneously present marks.

iv.                Count the vertical strokes in Fig. 3.

Figure 3
Fig. 3

Here is an enduring display which is difficult to count reliably by a purely mental procedure because of its fineness and indistinctness.

v.                  If you regard a delimited multitude of soap bubbles (to which no more bubbles are added), and ask for the number of bubbles which are present simultaneously, that number changes in time.  Indeed, the number may decrease during the attempt to count; and bubbles which have not been reached by the count may disappear before they are reached.  In this case, effectiveness of counting may depend on the order chosen.

                        Note that photographing the display at the first instant replaces the display with a model in which the entities to be counted are persistent.

                        The question about the number of bubbles can be changed:  over time, what is the maximum number of distinct bubbles seen?  In this case, the answer, when arrived at, may not correspond to a simultaneous presence of the entities counted.  (Also it is difficult to ensure a count which is exhaustive and non-repetitive.)  Again in this case, effectiveness of counting may depend on the order chosen.

                        The soap bubbles are treated as (enduring) objects for the purpose of the count, yet may vanish during the sequential procedure of counting.  So juggling the world-aspects of flux and permanence satisfactorily is exceptionally tricky in this case.

counting and shadows

                        Shadows are like a liquid in the sense that if two shadows become contiguous, they unite — so for two shadows to become one admits several cases.  See Fig. 4.

Figure 4

Fig. 4


hen one shadow covers another, does one shadow cease to exist?

                        If you see two discrete shadows and then abruptly there is only one of the shadows (under whatever circumstances), is 2 ≠ 1 false?  Has one shadow ceased to exist while the other endured?

                        If you were to put three identical marbles in a sack, and then to put four marbles in the sack, and then to count the marbles in the sack, and were to find six marbles, how would you interpret the result?  That 3+4 = 7 is false?  That one of the marbles had vanished?

vi.                Consider the row of Necker cubes, Fig. 5, and try to count how many cubes are oriented “upward.”

Figure 5
Fig. 5

There is now a difficulty of what is “the entity”—since the same figure may change from moment to moment as image while persisting as figure.  Indeed, the image may change as you look at it.  What is more, the orientation can be affected by your fleeting intentions to find one or the other orientation:  the object interacts with self-fulfillment or frustration.  Even though I have defined clearly what is to be counted, one is likely to feel that enumeration is not meaningful for such “entities.”

In 1985, I offered Fig. 5 as an anomalous assembly of entities to be counted, not as a number-notation. (But see below.)  You are supposed to already know the abstract natural numbers.

vii.             What has the analysis uncovered about quantity as a property so far?  Let me start with Fig. 5.  If you see a figure as “upward” and count it as such, and then e.g. glance at it a split instant later and find it “downward,” you may have serious reservations about whether a count of such apparitions is meaningful. 

                        But the sensuous world—the world that is regarded when the phenomenal analysis looks through common-sense perceptual interpretation or cognition—has much similarity to the row of Necker cubes.  I speculate that for quantity to be felt to be a reliable property, one must be surrounded by phenomena conceived as enduring and changeless (and discrete).  But one’s sensuous experience of even a stone is fluid—and intermittent—so that at the least, an interpretation is required to extract the enduring, changeless stone from the impressions.

                        Moreover, the counting labels have to comprise a fixed protocol, accessible by repetition.  Yet “the world” has to be a flux for enumeration to be a process of comprehension.  Moreover, the concocting of the stable entities which allow quantity to be a meaningful property is not only a matter of discerning stones or tables in one’s surroundings, but is an active technique.  If

—you count a fixed display by using a numbered template

—you count soap bubbles by counting bubble-pictures in a photograph

—you count full moons by recording their occurrence on a tablet

—you count a cluttered display like Fig. 3 by using a magnifying glass and other aids

then you actively substitute, for the given problem, a different problem which has the character of inertness and discreteness.  (This is also a profound observation in the phenomenal review of physical science:  science often analyzes an I-it relationship by substituting an it-it relationship and analyzing that.)  Indeed—as is patent with the photograph and the recorded count—the establishment of equinumerousness between phenomena having different reality-types is crucial in supporting quantity as a property.

                        Conventional wisdom says that the enumerated world is “just there”—the number of fingers and toes, the number of visible planets—so that as human culture develops we finally consent to count the world in order to align ourselves with it (and with the hard-wiring of our brains).  But on the contrary, the enumerated world is a structure which defies the contours of sensuous experience.  The required permanent, discrete objects, and their required relationship to the flux-aspect and to repetition, have to be willfully imputed.  The conventional thesis is the result of inverting the person-world so that the conceptualized and hypostatized (and even self-contradictory) structure is taken as elemental.

                        Mathematics wishes to define positive whole numbers which are so ideal that they do not reflect phenomenal considerations or reality-features.  (Why is this desirable?!)

                        In any case, even though mathematics now claims to address ideal numbers which can therefore have any assigned content or no content, mathematics is completely dependent on “real-world” enumeration at the level of counting notations (e.g. reading Hilbert stroke-numerals).  This circumstance guarantees the general observation that mathematicians would not be able to imagine their ideal numbers if they could not interpret their surroundings as allowing permanence and flux and their interconvertibility, as I have discussed.

                        By potentating such examples as that of Fig. 5, in accord with the remarks of the preceding paragraphs, we should be able to invent profound “computational” means for novel cognitive appropriation.  These means will also constitute profound counter-examples to the scientistic-formalistic doctrines of language, number, and logic.

                        New idea:  Use Fig. 5 as anomalous stroke-record for an abstract number which has to be read or evaluated.  Upward is stroke; downward is blank.  The blank is not even read as a position; it is disregarded.

                        Could the changing image be provided by a cinema?  Necker cubes are profound for two reasons.

a) the flux is “in the mind” — not changes embodied in an external object like a film.

b) the changes of image are not solely tied to volition.  It’s not like mentally parenthesizing a written phrase.

                        The claim of the objective realism of modern arithmetic (including all the infinitary properties of the natural number series, which outrun all phenomenal considerations, and whose explicit treatment forms much of the content of pure mathematics) is a fantasy that has grown out of the repression of the phenomenal character of enumeration. 

                        A milestone in the promulgation of this fantasy came in 1960 with Hans Freudenthal’s elaborate scheme for broadcasting human knowledge to advanced extraterrestrial civilizations in Lincos:  Design of a Language for Cosmic Intercourse.  Freudenthal is not a materialist fool.  He realizes that human culture is a fiction which drastically transforms phenomenal modalities, in many dimensions at once.  Yet he posits that any intelligent being will make the transformations the way we do, implicitly, and will only want to communicate about the end-fiction:  symbolic logic and scientific physicalism.  Thus a time-sequence of signals is meant to be “written” in an enduring and unchanging array.  An intelligent addressee who has transcribed the sequence “.....=5” will intuit that “.....” means five by [meaning itself].  From a limited number of arithmetic examples, an intelligent receiver will intuit uniquely the infinite text known as classical arithmetic. 

                        “Mathematics is … a subject that may be supposed to be universally known to humanlike intelligent beings.”  “If I ask anybody to continue the sequence 1, 3, 5, 7, 9, 11, I may be sure that he will do it with 13, 15, 17 and so on.”  (page 21)  Let us not soft-pedal Freudenthal’s absolutism.  Thinking has brought us to objective reality for adaptive reasons:  and that reality devolves from ideas which have the rigidity of stones or diamonds, only more so, since they persist unchanged forever.  The postitive integers are “what is out there.”  Then any creature will know the same abstractions we do because it, too, will adapt.  (And will the creature be brought to “our” religious mythology because it is urgently obligatory for “all of us”?)

                        So we initiate contact with advanced extraterrestrial beings by broadcasting number theory to them.  I am not worried that advanced intelligent beings might fail to understand the transmission because of their “stupidity” or culture-boundedness.  My point is that Freudenthal enshrines the arithmetical (and scientific) end-fiction as a cosmic ultimate for us—even though he is way above average in understanding that fictiveness is implicated in it.  Freudenthal’s most dangerous presumption is that advanced intelligent beings will admire us for sending this transmission.


                        Insofar as mathematics uses real-world enumeration while relentlessly denying it, mathematics has produced a series of abstract explanations of number which amount to circular solutions of spurious problems. 

Foundations of mathematics has to be seen to be mathematics.  Its exponents have to be seen to be doing mathematics.  So they explain simple computations by difficult computations.  Foundations of mathematics should be called Explanation of Simple Computations by Difficult Computations.

                        Let us leave aside the claims that the whole numbers outrun any concrete notation, and in fact comprise an infinite series—which claims outrun phenomenal analysis (P notwithstanding).  After ruling out what are pejoratively called psychological explanations, [FN. Frege. Beth and Piaget, Mathematical Epistemology and Psychology.], mathematics comes to identify the non-negative whole numbers with any ordered series of labels that has a first member and an infinite tail (a' after z, etc.).  It dismisses as unnecessary the requirement that the whole numbers be “equally spaced” (the intuitive metric of the cardinals); and it purports to determine the whole numbers without defining addition.  If this doctrine were sound, then giving “s” as the count of Fig. 1, as discussed above in 2.h.ii, would be the same as “19” to immediate comprehension.  What we learn is that the most “basic” branch of modern pure mathematics is a nonsensical fantasy that has grown out of the repression of the phenomenal character of enumeration.

                        This sort of analysis is what I meant when I asked for, in “Reorienting Mathematics,” the phenomenology of mathematical competence.   I develop it in other manuscripts on mathematics.

There is a 1985 Appendix correlative to the above Note:  “Hilbert’s stroke-numerals and Freudenthal.”


Addendum:  1985 D.1.b – c

b.                  Let me reply to (i)-(x) of D.1.a in a roundabout way.  The achievement of Section C was to demolish the conformist integration of phenomena in awareness and action.  An ironic byproduct of this exercise was that by emphasizing comprehension at the phenomenal level, I uncovered a level at which common sense and physical science, supposedly antithetical, must proceed identically:  opposing the prospect of demolition.  Indeed, the questions in D.1.a identify a zone of the totality toward which common sense and physical science have to take identical positions.  Supporting this observation is the convergence of common sense and physical science [uncovered in C.7.a.iii].  If science posits subliminal beliefs, even as electrochemical facts, then they must have natural-language transcriptions.  [Because they are beliefs.]

                        The project of demolition in Section C opened the possibility of a free play of judgment relative to apparitional experience.  But I want a new way of cognitive appropriation.  Thus, it is necessary to provide definite novel schemes of integration (original devices).  Of course, it is out of the question to provide here a scheme that satisfies the global purposes of a new culture.  What I will do is quite modest but not negligible.  I will show that novel integration of the personal world is possible in isolated instances.  These schemes will be drastically unconventional. 

Yet they cannot be faulted by the conformist reality-picture, because they make less, not more, demands on conscious credulity [FN. with claims for unconscious credulity being downgraded to hypothetical or derivative status]; and because they utilize indeterminacies and paradoxes in the conformist reality-picture.

2008.  This all-important observation brings us to a supplementary remark.  One devastating difficulty in disseminating this work has been that when I announce “reintegration of subjectivity” as a topic, some people want to hurl well-worn crackpot agendas into the discussion, like theosophy.  The ghosts and goblins are like a sweetener without which they refuse to eat anything.  Obviously, they are ruined and I am not going to un-ruin them.  But if everybody is like that, then I am left beached on a wretched planet.

In fact, I am addressing a subject-matter known to academic philosophers — Michael Dummett (“Wang’s Paradox,” in Truth and other Enigmas), Tim Crane (“The Waterfall Illusion,” Analysis, 1988), etc.  It is just that unlike them (unlike Crane especially), I do not bludgeon my consciousness to the ground to make it conform to scientific orthodoxy.

c.                  °13  Our method shall be to survey the personally comprehended world selectively, and to expose junctures of three sorts.

i.  Junctures at which phenomenal contents are insufficient to determine relationships which nevertheless are obligatory for conformism.

ii.  Junctures at which conformist imaginative models impose so much structure (relative to phenomenal contents) that they already impose inconsistent determinations.

iii.  Obligatory constituents of common sense which are pure dogmas, such as induction from past to future.

                        So the illustrations in D.2 make it conceivable that a way of cognitive appropriation (at the elemental level of perception and action) could be found to satisfy the global purposes of a culture beyond the present one.  

                        But other departures will be required that I only hint at here.  Modern science attempts to treat objective fact, and comprehension, as two separable and independent realms.  It makes genuine, i.e. personal, comprehension an unmentionable ancillary to pure logic.  In fact, science often switches off:  analyzing an I-it relationship by substituting an it-it relationship and analyzing that.  (Compare D.2.h.vii.)

                         “Studies” is largely organized (Sections A – C) as a commentary on science—not e.g. on personalistic syntheses such as thematic identity and morale.  So, something gets underplayed.  We also need to search out crucial junctures in a realm uniting “objective fact” and comprehension as interactive. 

                        For example, I require that


“computation,” and


be reintegrated from the phenomenal level in personalistic waysD.2.h will provide two indications in this connection. 

2008.  What were the indications?  One was the Necker cubes.  I don’t see the other.  For completeness, an indication not in D.2.h was the co-optation of life-experience to language.  The shadow-aggregations of Fig. 4 came in a supplement, not in the body text.

In 1985 I made reference to Blueprint, pages 86-100.  What does that material lead to besides Necker cubes?  Well, to “constructed memories.”  And to assertions made in a thought-stream which refer to their own time-placement.  (Proposition with durations, whether they are rehearsed mentally or spoken aloud.)

‘I started speking a half-second ago.’

‘So-and-so will happen a second after this assertion begins.’