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An Epistemic Calculus: Realizing "Impossibilities" by Lifting Annulled Reality-Grades

Henry Flynt

original July 1987

© Henry A. Flynt, Jr.


A. We may distinguish between an object-like phenomenon which is "given in reality" from the same object-like phenomenon "given in an illusion." Thus we distinguish a table from a reflection of a table, or a shadow of a table, or a table appearing in a dream, or a memory of a table. So there are at least two grades of realism of "a table" depending on whether the phenomenon is a real table or a mirage (or fantasy-replica) of a table.

These distinctions and these labels are presented to represent the conventional belief-system. No other endorsement on my part of notions such as "reality" or "mirage" is implied. I allow myself to generalize the notion of illusion of an object quite loosely. This facilitates rapid extension of the analysis. As for calling a reflection or shadow or dream or memory of a table an illusion of a table, the reasons for doing so are relatively plausible in common-sense terms. It is much more problematic to explain what is meant by calling the real table "real"; and in fact one aspect of the epistemic calculus is to exploit the incoherence and weaknesses of the notion of the realism of real objects.

A case of a shadow which is especially appropriate here is a shadow which vision can mistake for a "free-standing object." In this case, the shadow is an illusory copy of the free-standing object which it resembles.

As for the standard illusions of visual psychology, I stretch the interpretation of them so that they too can be considered illusory copies of real things. Line segments which are "really" equal are placed in a visual context where they are seen as unequal–and so mimic segments which are really unequal. Lines which are really straight are placed in a visual context where they are seen as curved–and so mimic lines which are really curved. A figure which is really flat is seen as having radial extension because of the illusion of perspective–so it mimics a three-dimensional frame or surface.

I include afterimages, again stretching the interpretation to fit. It is possible for afterimages to appear precisely as copies of things seen in exterior space (with the color changed). (Dan Conrad's film "Circles.") Other afterimages may be considered as illusory copies of whatever real phenomena they resemble: e.g. a small white light floating in front of you. As for negative afterimages of motion (such as the waterfall illusion), they are logically anomalous and so do not resemble any usual real thing. Such logically anomalous perceptions have a special role in extending my scheme.

I consider passing from a real object to an illusion of it as an operation on the real object. A reflection of a table results from applying the operation of reflection to the table. A Necker cube, with its illusory three-dimensionality, results from applying to a real cubical frame an operator which represents via perspective. I will symbolize all of the illusion-making operations by one symbol, J. So J does not have a qualitatively unique meaning; it is a generic symbol.

As a last but important case, I will interpret personal memory of an episode as a fantasy-replica of that episode. Thus, personal episodic memory is also a case of operation J–here applied to a life-episode.


Look at a Necker cube displayed vertically at eye level. One application of J is already involved: the visual illusion of a three-dimensional (or radially extended) frame is produced by a figure which is really flat–via perspective. Now let us consider a reflection of the Necker cube in a mirror. This is a second application of J. Now a Necker cube is seen in the mirror-world, apparently behind the plane of the mirror. The cube appears to have radial extension in the mirror-world. Now: do we still distinguish, in the mirror-world, that although the cube seems to have radial extension, it is really flat (in the world behind the mirror)? Or may we say that the distinction between seeming radial extension and real radial extension, in the mirror-world, has been annulled? I hypothesize that reflection annuls the distinction between perspective and radial distance–since in the mirror world, all radial distance is an illusion. So the two grades of reality, those of radial distance and perspective, have been annulled or equated in the mirror-world. (Certain complications of this argument will be dealt with below.)

To generalize, I suggest that a singly illusory object and a doubly illusory object both can only be singly illusory. In symbols, J2 = J.

Let us consider a flexible mirror, such as a reflective plastic sheet. Now let the mirror reflect both an object and the shadow of that object (on some surface other than the mirror, of course). When the mirror is shaken and rippled, the reflection of the object and the reflection of the object's shadow are equally rippled. Object and shadow receive equal status in the illusion-world. The original object and shadow have different grades of realism. But this distinction of grades is annulled when both are reflected.

Let me add an example which I have not yet integrated in the analysis: a reflection not correlated to its object, a double illusion achieved in one step. Hold a rod vertically in the near center of your visual field, hold a mirror behind it, and focus your gaze on the rod. Behind the rod (flanking it) you will see twin rods in the mirror. (If we accept Kant's postulate that a reflection exactly copies spatial relations among parts of the object, then this illusion brings us close to inconsistency.)

Suppose that you usually throw the morning's newspaper away before you leave your house. Suppose that today you leave without throwing the paper away. However, suppose you return and find the paper gone. And at this moment, suppose you remember yourself to have thrown the paper away. There is a distinction of realism between what happened, and a personal memory of it. In this hypothetical example, moreover, your memory is untrue to what really happened. However, you experience no immediate discrepancy in consciousness, because the situation you find fits your false memory. And you might never experience any discrepancy. Nevertheless, if in reality the paper was discarded or carried off by a roommate, say, then evidence would subsist in the real world that your memory was inaccurate–even though the discrepancy might never confront you.

But now let this same sequence of events occur in a single continuous dream-episode. (And suppose that no dream roommate confronts you about having thrown the paper away.) Your memory has altered a past which was only your subjective "hallucination" to begin with; and you are not confronted by any discrepancy. Shall we uphold that the earlier portion of the dream-episode is objectively subsistent somewhere–so that it acts as a norm of reality which invalidates my memory? Or: should we accept a tracelessly altered past as the real past of the dream, on the grounds that the past of a dream-episode collapses to one's memory of it later in the episode? Can different grades of realism be ascribed to "the" past and your memory of it, after J is applied to both the past and your memory?

Let us consider some of the complications of the foregoing ideas. Consider the length illusion known as the horizontal-vertical illusion or bisection illusion.

Now pass to a reflection of it as we did with the Necker cube. Is it again the case that two applications of the illusion operator produce only one degree of illusion? That is, are we allowed to say that in the mirror-world, the segments may be considered to be unequal? It seems that in this case there is an argument against this conclusion. In the case of the Necker cube, the illusion concerned radial distance; and in a reflection, all radial distance is an illusion. But the bisection illusion extends in a plane parallel to the mirror surface; and this extension is genuine or realistic in some sense. Why, for example, couldn't one place ruler grids flush with the two segments of the figure? Then the ruler grids would appear in the reflection and show that the segments are in reality equal in length.

Let me introduce my answer with yet another case. Take the version of the Müller-Lyer illusion in which two coIlinear straight segments are seen as unequa1 even though in reality they are equal. Display a ruler grid flush with the segments.

What happens is that not only do the segments continue to look unequal; lengths marked as equal on the ruler now look unequal too. The illusion has captured the norm of reality applied to expose it. We have here a particular instance of direct annulling of a reality-distinction in the real world. (A sort of automorphism of the real world which subverts it. But I'm not ready to formalize operations in this dimension yet.)

In the case of the reflection of the bisection illusion, if ruler grids are placed flush with the segments that get reflected, the rulers will appear unequal also (even if the effect is less pronounced). Reflection preserves the capture of the norm of reality by the illusion.

The kinesthetic procedure of using a single ruler, applying it to one and then the other of the real segments that get reflected, might be taken as proof that the reflected segments are really equal. But since the reflected ruler is an illusion, who is to say that the reflected ruler stays the same size when it is moved? In fact, the reflection palpably changes size concomitantly with some movements of the real ruler. The decisive kinesthetic procedure for proving that the reflected segments of the illusion were equal would be to enter the mirror-world while remaining real, and to measure the reflection with a real ruler. But you can't do that. So the argument that a reflection of the bisection illusion gives us an illusion of the second degree, in which the two degrees of illusion remain distinct, runs into a surprising amount of difficulty.

Afterimages may be of special interest because they appear to be located in exterior space, in the object-zone; and yet are insubstantial, move with your gaze, and have neither reflections nor shadows. These circumstances await a more thorough review for the purposes of the epistemic calculus.

• • •

B.1. Summarizing the discussion so far, when the J operator is applied to a real object and an illusion of that object, it sends the pair into an illusion-world. There the difference in grades of realism is not preserved or maintained–because the illusion nullifies some source of "objective" evidence, some norm of realism. Now: Given the annulment of grades of realism in consequence of the transfer to an illusion-world, can we mimic this parity of real object and illusory object in the real world? That is, can we "lift" parity to the real world?

How do we send the Necker cube from the mirror-world back to the real world so that the distinction between radial distance and perspective remains annulled? We have to selectively shrink the belief-system through which we apprehend real-world objects. The value of sending the Necker cube into the illusion-world is that it rehearsed or modelled the effect which we now want in the real world. Let the Necker cube be displayed at eye level "across the room" from me. The cube has perspective; it looks like it extends radially–that is, that some of its edges are farther from me than others. Now the point is this: if I just stand and look at a visible array, there is nothing in my experience at the moment that proves the distinction between perspective and radial distance. In the moment, to impute or to deny radial distance where perspective is seen is an act of faith. Of course, it will immediately be objected that I could walk over to the surface on which the cube appears, and look at the surface minutely or probe it by touch, thus establishing that the figure is flat. But the point is that this has changed the originally given situation. (In the reflection case, compare wanting to step past the plane of the mirror while remaining real.) What I invoke, if I invade the intervening space, is an intricate collation which allows one situation to prove characteristics of another situation–relying heavily on memory, conceptual integration of a unique homogeneous space apprehended from different perspectives and in different moments; etc. (Hence, faith in the conventional spatio-temporal coherence of a world.) If, in the original situation, I suspend faith in the conventional judgments of radial distance–and in the integration of kinesthetic probing which destroys the original situation–then the distinction between perspective and radial distance as regards the Necker cube becomes unprovable.

But of what advantage is this? Let me introduce my answer with another example. We say that things seem, to vision, to get smaller as they move away from us; but that in reality they remain the same size.

(Note that what is being said here is that real-world objects participate in illusions at all times; or always have features that are illusory.)

If we were prepared to revise our belief-system to suit, though, then this interpretation could be inverted. We could insist that things really shrink as they move away from us; and that the reason they appear to remain the same size to our kinesthetic procedures of scaling or mensuration is because that is where the illusion occurs: the kinesthetic procedures are deceived.

B.2. The preceding point may seem outlandish to the casual reader. Nevertheless, the observation that any discrepancy called an illusion is capable of reciprocal resolutions is not unknown in technical philosophy and foundations of science. And it is on that level–the level at which framework beliefs are scrutinized explicitly–that I conduct this investigation.

Let me give two quotes regarding the reciprocity of interpretation of empirical evidence.

the theory itself can result in necessary deviations from the original ideas about measurement; the theory may give a specification and an adjustment of the pre-theoretical definitions of the measurable quantities. This gives the theory a conventionalist element: If it is allowed to be semantically inconsistent with the original definitions of measurement, then there could be several such theories, and it is not at once clear which adjustment of the original definition is the right one.

(Michael Drieschner, "The Structure of Quantum Mechanics," Foundations of Quantum Mechanics and Ordered Linear Spaces (1974), p. 253.)

... conventionalism arises from isolating the notions or the facts of a field of knowledge from each other ... Isolating some parts of knowledge or language from their context is not bad in itself. It may even be very useful for analysis ...

(Hans Freudenthal, Lincos: Design of a Language for Cosmic Intercourse, p. 37.)

On the other hand, while it is a tradition in philosophy to point out, in effect, that illusions are capable of reciprocal resolutions, such talk from philosophers has been understood as mere fancifulness, as attitude conditioning. For thousands of years, the arena in which deliberate reconstitution of beliefs about factual reality has gone on is the arena of abstract fictions–an invisible world beyond palpable life. For example, seventeenth-century mechanics announced that motions of matter were driven by forces (in the physicist's sense). But forces in this sense are not palpable; sense-evidence cannot establish their existence–at least not uniquely. So there was a debate among European natural philosophers which continued to the twentieth century over whether physics ought to posit the reality of forces, or to cancel them out of mechanics because they were chimeras. Perhaps the debate really ended when Spengler said that force is a Faustian metaphor, a modern European world-myth.

Again, the philosophers who have noted that illusions are capable of reciprocal resolutions have not called for any focused, programmatic reconstruction of common sense. When Wittgenstein said "But after all neither does the solipsist want any practical advantage when he advances his view!" that summed up the impotence of philosophers’ radicalism. There is a sort of territorial allocation, such that deliberate reconstitution of beliefs about factual reality is confined to an invisible world beyond palpable life. Common sense is not directly confronted–because the philosophical-scientific élite does not wish to change the mode of everyday life. As Brouwer declared in "Mathematik, Wissenschaft und Sprache," the will to science is a will to mundane power on the part of certain élites. These élites are better served if the subversion of reality is confined to a world which is invisible and beyond palpable life, and in addition entirely abstract and mechanomorphic. Everyday life, plebeian life, continues undisturbed; except as the theoretical novelties are applied in technology and then in commerce (and the plebeians find themselves buying and making things they never imagined).

To propose that common sense should directly be reconstituted is to propose a reconstitution of factual reality in the life-world. As I have just said, the scientific intention does not seek any such change, and cannot motivate such a change. Direct reconstitution of common sense is at the level of the appearance of civilization in the first place; or perhaps of the rise of major religions as modes of life. (Well, there were major religions before the ones that are still practiced.)

As for my investigations, here and elsewhere, my purpose is, in the first place, a purely theoretical one of showing that there is no inanimate or impersonal barrier to realizing certain "impossibilities." I contemplate what "physical" laws could be escaped in the absence of a specific oligarchic, mechanistic pragmatism.

Then, theoretical scientists could find the ideas I present here suggestive in an analogical way: since scientists continually use common-sense analogies to get a handle on the choices they have to make between abstract fictions.

On the other hand, I envision the supersession of the present culture of scientific depersonalization by a higher, post-scientific culture. If this is to happen, it will not be enough to proceed as in past and present revolutions. In particular, it will not be enough to want "knowledge" (nongullible thinking-integration) only as a means to industrial technology, limiting the reconceptualization of factual reality to the abstract fictions of an invisible world. Human self-image and the mode of life must be addressed by nongullible thinking-integration; and factual reality must be reconstructed at the level of common sense or the life-world.

My writings provide various studies to this end; the epistemic calculus presented here is one of them.

Returning to my exposition and to size constancy, the question was whether there is any advantage in positing that things change size in actuality as their distance from oneself changes. Indeed there may be no practical advantage in this–in positing that size-constancy is an illusion suffered by our kinesthetic mensuration procedures. There may be no particular gain in disrupting the conventional belief-system at this one point. The example serves to make a theoretical point. At present, many of my examples serve mainly to re-educate our judgments about what is possible. Arriving at a reconstruction of common sense which we are motivated to adopt requires an integrated envisioning, a vantage point for which human "life" is unified. Relative to such an envisioning, the present examples only convey techniques.

B.3. Let me continue the exposition with another case of lifting parity of reality-grades to the real world. Recall the case for which we could say that "the past changes to fit your memory of it," because the memory occurred in a dream-episode and referred to an earlier moment in the same dream-episode. Actually, one of my earliest statements of the notion of lifting was made in this connection, in "The Choice Chronology Project" (the 1985 draft):

The possibilities that I will find in dreams can be "lifted" to waking life by noting that reality cannot be proved to be less personally relative in waking life than in dreams.

To lift the annulled distinction between memory, and the past, to waking life, then, we again have to find a norm of realism which involves an act of faith, and to selectively suspend it. In fact, the solution is to adopt a sort of solipsist standpoint–or (to use a term from another of my investigations), a person-world standpoint; and to refuse to count anything other than one's private episodic memory as evidence about "the past."

The anomaly which has been lifted to waking life can be buttressed further. We may put another epistemic restriction on waking life, for the purpose of making futures fit your expectation of them. Suppose I form an expectation (which may be unverbalized) that such-and-such will be the case at a future moment. This expectation cannot be proved false, if: the undetermined time-reference "future moment" is applied only at those later moments when such-and-such is the case. (Any later moment when such-and-such is not the case is set aside as not pertinent; or is forgotten at yet later moments when such-and-such is the case.) [1999. But that solution is weak–too much like a bad stock market prediction–imprecision wielded in a self-serving way.]

To summarize, when the J operator is applied to a real object and an illusion of that object, it sends the pair into an illusion-world in which reality-grades are annulled because the illusion nullifies some source of "objective" evidence. We lift this parity of reality-grades back to the real world by finding that some real-world source of objective evidence requires faith, and/or requires destroying the given situation in order to use the source of evidence.

• • •

C. To finish this examination, which is only a prospectus, I will add some more phases to the scheme I have established so far. What I am concerned with, in general, is realizing "impossibilities" by reconstructing or mimicking them at a more realistic level than would be expected.

For example, I note in my writings on dreams and epistemology that in dreams, one may experience two mutually exclusive states of the world simultaneously. (This is rare, but it happens.) So here we have an anomaly of a different sort from those which are the main topic in this investigation. Without digressing to give a lengthy substantiation, dreams allow a non-vacuous logically impossible state–evidently because of the specific character of dreaming as a mode of illusion.

Now the next step is not to lift this state to waking life, but to create a sort of analogue in waking life by passing to another mode of illusion. We note that a paradoxical view of the Necker cube is possible in which the cube appears to be projecting in both of two mutually exclusive directions at once. (The cube must be drawn strongly as in §A.)

The astute reader will note that this example does not provide an inconsistently orientated object at all. Rather, it amounts to an apparitional depiction of an inconsistently orientated object. But that is all right: that is already an important step. Nobody has seen a unicorn, but we have seen pictorial depictions of unicorns, which can serve as a proxy for a semantics for "unicorn." This solves the problem of giving a meaning to a word which has no referents. Now "one-horned horse" is not ruled out on grounds of consistency, and so a picture of a unicorn is logically no anomaly or discovery. But the impossibly oriented cube is self-contradictory by prevailing standards; so even to have a picture or a nonvacuous semantics for it is extraordinary. (I may also mention that as far as material realization is concerned, the impossibly oriented cube does not have a different status from other objects of pure geometry. Nobody has ever seen a "consistent" circle or straight line; only "pictures" of them.)

We may take another step and do still better. Let the Necker cube be reflected in a mirror. Now, by the foregoing theory of the action of J, the seeming paradoxical extension of the Necker cube is not less real than any radial extension that is seen in the mirror-world. We have made a full analogue of the impossible dreamed state in a waking mode of illusion.

Now we may carry the exercise to the end. We suspend faith in judgments of radial distance–so "lifting" the paradoxically extended Necker cube from the mirror-world to the (epistemically modified) real world. This completes the construction of an analogue of the logically impossible dreamed state in the real world.

• • •

D. I want to end by mentioning very briefly that the real world is highly problematic even when illusions in the foregoing sense are not involved. Actually, at the end of §B.1 we found that real-world objects have illusory features at all times–such as our perception of them as self-identical at different distances and in different orientations. (That is, the apprehended real object, the object-gestalt, in phenomenological and psychological jargon.)

But now consider the experiential encounter of a slowly varying observable such as the minute hand of a large clock. Your judgments, in perception, over time, of whether the hand is in the same position or not will be found to have a paradoxical character and to depend entirely on your imaginative integration of present moment with memory.

Finally, I repeat a point I have made elsewhere about actual counting of an assembly of simultaneously present things. You apprehend the assembly under the world-aspect of persistence of entities through time; but you count them via "utterances," the number-words, which are required to arise and disappear in time (as they are spoken or thought). So even in simple counting, you intend emplacement of the world in time in two different and probably inconsistent ways.