Henry Flynt (original manuscript Sept. 1981)

(c) 1992 Henry A. Flynt, Jr.

Forward
I wrote this introduction to the logic of contradictions in 1981. My subsequent research has outrun this exposition. I am writing a new prospectus on logic and contradictions whose priorities will come from my latest research. What follows is an abridgement of the 1981 essay; it serves as a self-standing introduction to basic parts of the logic of contradictions. It supplements the new prospectus, and elaborates on some of the topics. I must proceed in this way, because my research is always moving into unexplored territory. I will not have a chance to organize my innovations in a comprehensive treatise.

I must assume that my readers will be trained in modern analytic philosophy and formal logic--which means mathematical logic. To these readers, it may seem that I am brutally trampling an intricately elaborated and delicately nuanced doctrine. But that is because I am starting over--starting, that is, in the midst of vernacular logic. I reject the ideology of mathematical logic in its entirety. (Even though I invoke this or that term or device or formal scheme in passing.) I reject, most of all, the goal of mathematical logic: the attainment of truth beyond a shadow of a doubt by the method of sterility--supposedly starting from nothing, and cumulating affirmative certainty in self-evident steps.[1]

I have written point-by-point critiques of mathematical logic elsewhere. It would be unsuitable to dispute such a derivative apologism here, before I have even started. After all, the analyses I will present go a long way in showing why I reject mathematical logic.

In the early phase of the discussion, I will employ heuristic explanations. That is, I will employ explanations which are somewhat pictorial, in order to identify the topic to the general reader in an accessible way. Opportunities for debates over principle will be passed up at this early stage. As I proceed, the heuristic explanations will be replaced by my own novel analyses and inventions; and some of the postponed issues of principle may become the focus of the discussion.

I. THE POSSIBILITY OF AN EXTRA-CULTURAL REORIENTATION OF LOGIC

A. The Availability of Non-Vacuous Contradictions

What does it mean intuitively to say that a term or proposition is inconsistent? The term 'unicorn' refers to a chimera. No unicorns exist; the set of actual entities to which the term refers (denotation, extension) is empty. Nevertheless, common-sensically the term is meaningful. Heuristically, this means that we can draw a picture of a unicorn even though this picture portrays no actual entity.[2]

[I cannot resist mentioning a complication. 'Napoleon', like 'unicorn', has no referent (today). Nevertheless, it is claimed that 'Napoleon' had a referent in the past. Time. Extinction of a referent. But these points are not to be pursued yet.]

The phrase 'non-equine horse', in contrast, is inconsistent. The situation is not merely that there is no actual entity to which the phrase applies. A non-equine horse cannot even be pictured or imagined, because the concept is self-annulling or self-erasing. Intuitively, inconsistency is this self-erasing character. Because the term is self-erasing, no empirical investigation is required to establish that there are no non-equine horses; "logical definition" alone guarantees that there are none.

In the same vein, the assertion 'Italy is now covered by a glacier' is meaningful but false. It pictures a logically possible state of affairs; that state of affairs is not actual.[3] The assertion 'Italy is not Italy', on the other hand, is self-erasing. It pictures nothing, and no investigation is required to determine that it is not actual.

I arrive at my reason for beginning in this way. It is known academically, although it is not well-known, that there are perceptual illusions which in effect are "pictures" of inconsistent concepts or terms. The waterfall illusion, for example, serves as a "picture" of stationary motion.[4] This point was known to Aristotle. A contemporary source is J.J. Gibson, The Perception of the Visual World, p. 133. Indeed, it is nearly a truism in perceptual psychology that we can have experiences of the logically impossible when we suffer illusions. See R.L. Gregory, Eye and Brain, p. 107. The waterfall illusion is logically an anomaly as extraordinary as a drawing of a square circle would be. So perceptual illusions provide meanings for a whole assortment of inconsistent terms or descriptions--establishing that inconsistency need not be self-annulling or self-erasing.[5]

Further remarks should be included here. The first is that it is not my judgment alone that the waterfall illusion furnishes a "picture" for a self-contradictory description. If the reader is one who cannot observe anything until authorities legitimate it in advance, let me repeat that the observation expresses a consensus among psychologists and philosophers familiar with the phenomenon. Secondly, the waterfall illusion is a sensuous-concrete experience. It is a profoundly uncanny perception. Mere stipulation can neither create such illusions nor render them inoperative. A deeper treatment will find that the waterfall illusion devolves from our instilled perceptual recognition of qualities--and the codification of these qualities in antonymous pairs.

Understand that the waterfall illusion is only a "picture" of stationary motion. This picture no more proves that stationary motion is actual than a picture of a unicorn proves that unicorns are actual.

Turning to a different subject-area, Zeno's paradoxes have long been known. For me, what Zeno's paradoxes establish, or hint at, is that the basic (and in some sense indispensable and unavoidable) concepts by which we ordinarily apprehend the world and conduct ordinary social interaction yield contradictions when they are logically "unfolded." The concepts of motion, change, continuity are self-contradictory: this has always been recognized as a challenge to thought. [Not to mention the infinity of non-negative integers.] Of course, many attempts have been made to neutralize Zeno's paradoxes--that is, to show that proofs which derive contradictions from "indispensable" concepts are themselves sophistries or fallacies. Nevertheless, Zeno's paradoxes have vexed philosophers long enough that they can be considered as the smoke which evinces fire. Subsequently I will demonstrate inconsistencies in inescapable concepts of ordinary apprehension of the world and ordinary social interaction which can in no way be dismissed as petty sophisms.

The junctures I have just mentioned, then, have been on record from the time of Aristotle. Still speaking heuristically, these junctures are known (or suspected) to belie cardinal tenets of logic such as

Inconsistent terms are vacuous (self-annulling).

and

All concepts indispensable to thinking can be embraced in consistent, flawless theories.

Hegel is a figure who must be mentioned. But his logic is a literary doctrine which does not challenge formal logic frontally. Hegel is no help in this investigation. (I have scholarly appraisals of Hegel in other writings.)

What my logic of contradictions proposes to do is to take the anomalies which violate cardinal tenets of logic as hints; and to explore and potentiate the logical situation they exemplify until I explode the existing discipline of logic. Logic will be replaced by a discipline beyond all scientific culture.

The waterfall illusion, if we will only seize upon it and uphold it, provides us with an extraordinary anomaly: a perception which contravenes the cardinal tenet that "inconsistent terms are vacuous." I wish to pursue this anomaly. I want, for example, to find many and stronger logic-violating illusions. [1992. And I have done so. Since they require intensive individual analysis, my treatment of them is separate from this introduction.]

I also want to draw upon techniques which depart from other received principles of logic. E.g. the principle of thinghood of tokens:

A notation-token must not appear different to different viewers or at different times.

In reference to Zeno's paradoxes, I want to sharpen the paradoxes of culturally inescapable doctrines, and to bring as many of them as possible to the forefront. [1992. There is, for example, "The Paradoxes of Common Sense" (1988).] I foresee the possibility of transformatively plunging people into an experience-world which is pervasively uncanny.

Academic logicians, when they have considered natural language and ordinary apprehension of the world, have claimed that the accompanying logic is the two-valued first-order predicate calculus--or, in any case, is one of the trite symbolic logics.

But how would academic logicians know anything about the logic of ordinary apprehension of the world and ordinary social interaction? Contemporary formal logic is mathematical logic. All of the phenomena acknowledged in mathematical logic come from the abstract world of mathematics (as conceived in the self-understanding of mathematicians, or a Fregean faction of them).[6] Quine's Mathematical Logic, p. 33, says it well: evidence that mathematical logic is not the only possible sort of inference should be disallowed if that evidence does not come from mathematics itself.

The logic of the ordinary apprehension of the world is a subject which the exponents of mathematical logic have shunned and disdained. In "Personhood II," I offered an observation which is speculative but which has sufficient basis to play a crucial role in my argument here. From personal contacts with graduate science students and beginning university instructors, I found that such "science men" somehow suppress normal experiences--when those experiences can be invoked to challenge objectivism or rationalism. In the first place, they did not confirm perceptual illusions which according to psychology textbooks are normal. In the second place, they denied having or remembering dreams. Such culturally correlated mutilations of personal faculties will be illustrative throughout my argument.

The relation between the logic of the ordinary apprehension of the world and academic logic brings us to Aristotle. To his credit, Aristotle acknowledged the perceptual illusions and dreaming. However, Aristotle's vision of logic was limited to the hypocritical ideal of a logic of consistency. Aristotle dominated for thousands of years, and was only seriously challenged when mathematicians appeared who sought an ultimate abstract justification for mathematics. The resulting mathematical logic swept the field. Mathematical logicians occasionally claim that the naive calculi of their discipline exhaust ordinary thought; we must consider that to be a witless bluff.

B. Branches of the Logic of Contradictions

1. Normative Everyday Logic and Identitarian Logic's Hypocracy

One of the first tasks of the logic of contradictions is to investigate the logic of ordinary thought; and to learn something about the baseline logic, the "logic of consistency" (also called "identitarian logic") relative to which the waterfall illusion is an anomaly. It is necessary, then, to have a strong identitarian logic as baseline. Our phenomena cannot be accounted for via a logic which is so weak that nothing can be inconsistent. So ordinary thought has a baseline logic of consistency which is a hypocritical ideal. This everyday logic is based on the interdependence of concept and perception and inculcated discriminations. It is based on interpretations in the experience-world.

Normative everyday logic must address explicitly, and from the very beginning, the ordinary experience-world or common-sense world. The cultural consensus is that there is a world outside of language. I, or part of me, belongs to this world; I also confront the world as an observer. So my place in this world is a contingency. Other topics are:

- consciousness

- the experience-world's temporality

- stability of identity in the experience-world

- my relation to other people

- intent or motives

and the emplacement of language within these world-phenomena. Modern formal logic has sought to separate logic from these questions; or else has viewed the questions through the lenses of a pre-selected logic of mathematics. (So that the topics are co-opted to pre-existing formalisms. Time, for example, is just the real line.) As I undertake this investigation, it leads into a realm qualitatively different from, and incomparable to, mathematical logic. Here, for example, is where the instilled perceptual recognition of qualities must be acknowledged (including the codification of perceived qualities in antonymous pairs).

I have an entire separate essay on the baseline logic of consistency for the experience-world: "Normative Everyday Logic." Again, this logic is a hypocritical ideal. [1992. As with the present essay, the previous version of "Normative Everyday Logic" was written in 1981. But unlike this essay, I am reworking that essay completely.] This task requires me to investigate carefully a subject-area and a complex of problems which mathematical logic never addressed (notwithstanding the claims of some mathematical logicians). The codification provided by "Normative Everyday Logic" is incomplete. That is deliberate. I do not believe that normative everyday logic can be codified as a complete and problem-free system. The significance of normative everyday logic is that it is an actually used system--a myth, if you will (one of the most inescapable myths)--which constitutes the baseline relative to which stationary motion and other compelling sensory-conceptual anomalies arise.

My approach to logic does not aim for, or expect, exhaustive flawless affirmative truth (certainty; laws of thought; codified stipulations or rules). Indeed: it is the task of another branch of this logic of contradictions to establish the metatheoretic inconsistency of any academic or mathematical logic. Specifically, the exercise consists in deriving or inducing the "Is there language?" trap[7] in the metatheory of whatever system of mathematical logic or mathematics is under consideration. ("Vertical inconsistency.") Presently I have completed "A Refutation of Arithmetic" (1988).[8] The dependence of arithmetic on the ability to count (and the ability to classify experience-world objects as notation) is important in the argument, for it means that formal arithmetic can be shown to depend on applied arithmetic. (Incidentally, note that the assertion that a tautological proposition has been recognized, understood, is not a tautology.)

The methodology can be applied, mutatis mutandis, to the metatheory of any quasi-mathematical system you wish. The chief strategic problem for a negative universal result--or applications thereof--is to avoid having the argument defeat itself. I have explained the strategy many times elsewhere--in conjunction with my principle of astute hypocracy--and so will omit the explanation here.

If a "vertical inconsistency" can be elicited in any academic logic, then such logics pose the problem which I have identified in the everyday logic of consistency. We must account for the actual functioning of an entire range of pseudo-consistent logics--as opposed to their apologetic facades. Academic logic--mathematical logic--was originated supposedly as a codification of the logical procedures of mathematics. But that explanation is a towering misrepresentation. I gave a new assessment of mathematics in a manuscript called "Anti-Mathematics" (1980). I showed that mathematical logic, so far from exhibiting how the affirmative doctrine of mathematics is determined, is concocted for the apologetic purpose of diverting attention from how the affirmative doctrine of mathematics is determined.

For example, the doctrine of consistency in mathematical logic suggests that judgments of consistency (or strictly, inconsistency) are unbiased and immutable judgments employing an objective, mechanical test. Consistency is just the objective formal present-tense property that there is no well-formed formula A in the system such that both A and [not]A are provable. If proofs of A and [not]A are found, then this state of affairs can be verified by a purely mechanical procedure, and the system stands refuted once-for-all. Affirming the absoluteness of these judgments, Hilbert said:

Mathematics in a certain sense develops into a tribunal of arbitration, a supreme court that will decide questions of principle--and on such a concrete basis that universal agreement must be attainable and all assertions can be verified.

in From Frege to Gödel, ed. van Heijenoort, p. 384

But this dogma regarding determinations of inconsistency is misdirective. Frege's system was discovered by the first person who actually studied it (Russell) to be inconsistent, a discovery with humiliating consequences for Frege. So was the system then expunged from the proceedings of the profession, as the above dogma implies it should have been? It was not. There followed a series of contorted attempts to "save" the system. There is nothing in mathematical logic to explain this. Mathematical logic cannot explain why infinitesimal calculus was pursued as a science for about two centuries during which it was unconcealably inconsistent. (Cf. Bishop Berkeley; also L'Hôpital's 1696 textbook.) The consistency dogma does not explain why, when Galileo's paradox exposed countable infinity as inconsistent,[9] Cantor's subsequent co-optation of the contradiction as a new mathematical fact was preferred over Bolzano's treatment of equinumerousness. Mathematical logic does not explain the logical scandal surrounding divergent series, summarized by Morris Kline, Mathematical Thought from Ancient to Modern Times, p. 1120. "Anti-Mathematics" is available separately, and my subsequent research has buttressed its analysis; I shall not repeat the presentation here.

Next, mathematical logic is insincere to an entire degree beyond what I have suggested so far. Mathematics is an example of a phenomenon not infrequent in doctrinal thought: a system which is saturated with contradictions, but which uses social sanctions (so to speak) to suppress the undesired components of the contradictions and to maintain the pretense of being a consistent system. Here we arrive--in the field of doctrinal and propositional thought--at the phenomenon of the disguised tendentious contradiction-system. Here is another quite general result about ordinary thought which must be integrated with my codification of normative everyday logic to produce a comprehensive and rich account of the actual functioning of doctrinal thought. We find that a whole dimension of mathematics is not intellectual but "social." We find that mathematics and mathematical logic are disguised contradiction-systems (in the sense of demarcated doctrinal systems which happen to be thoroughly inconsistent).

In "Anti-Mathematics," I said that mathematics is so malleable that for any given theorem, the negation of that theorem can also be established. I am not referring to the cliché that if {A, B} is one axiom system, then {A, [not]B} can be chosen as a different axiom system which will yield a different theory. No, I am saying that once you understand the malleability of mathematics you can prove [not]B from {A, B} as axiom system--if you are willing to engage in salesmanship and coercive indoctrination. This is not a claim that a particular formalized theory is mechanically inconsistent, as Quine's ML was found to be. I claim that mathematical practice is malleable on a level not acknowledged by mathematical logic. [1992. This claim needed further focusing to be satisfactory. ?--Test cases of the sort of thing: the profession's co-optation of Galileo's paradox; the profession's co-optation of the conflicting solutions of Leibniz's series; Cantor versus Bolzano on the definition of equinumerousness.]

We see that mathematics and mathematical logic are disguised tendentious contradiction-systems. We see that junctures such as Galileo's paradox or infinitesimals are managed by professional negotiation and intimidation. But my encounters with mathematicians have brought to the foreground entire additional levels at which mathematics is driven by non-cognitive motivation. I speculate that these factors may explain the persistence of infinitesimal calculus during the centuries in which it was unconcealably inconsistent, and mathematicians' easy dismissal of Brouwer's inconsistency proof of real analysis.[10] The general observation (whether or not Brouwer's proof is compelling) is that the mathematician reaches the point of saying "I know it's false and I don't care." The game that is actually being played is one in which the mere circumstance that a tenet is a barefaced lie is not even an objection to it. By this point, mathematics is being sustained by processes of personhood which are non-intellectual.

Beyond this, processes of personhood are involved which are correlated to the entire culture. Modern rationality and sanity are analyzed in "Personhood II" as "delusions." Inasmuch as mathematical logic is a regime of relationships among phantom objectivities whose "lexicon" is mechanical, it is dependent on a particular sort of depersonalization. Mathematics and mathematical logic are embedded in a culture-wide deformation and mutilation of personal faculties. One manifestation is the science men's deletions of illusions and dreams from their experience-world. Another is the split between rational gratification (logic, science) and irrational gratification (poetry, emotion).

"A Refutation of Arithmetic" (1988) is evidence enough that mathematical logic is not upheld by intellectual integrity. Personhood theory brings us closer to the non-intellectual motives and cultural mutilation which uphold academic logic. In general, personhood theory's analysis of "ideological theory,"[11] and of the mutilation of faculties which can be entailed by a civilization's thought-modality, adds to our understanding of the basis of the everyday logic of consistency and of disguised tendentious contradiction-systems (of which mathematics and mathematical logic are the chief formalistic instances).

There is a wing of mathematical logic which I call logical purism. Let me consider what the purists have to say to me. The purists define logic as the way of perfect truth (i.e. the science of avoiding error). They avow that contradictions are untrustworthy sources of knowledge, that contradictions are the garbage of cognition. (Let us be thankful to them for confessing that the principle of the "automatic falsity" of an inconsistency is still sacrosanct.) So, the purists say, my logic of contradictions would be a logic of untrustworthy sources of knowledge, a logic of cognitive garbage. They ask, why wallow in the garbage of natural-language thought, looking for a logic of untrustworthy sources of knowledge, when mathematics and its logic rise above the entire profane world to achieve exhaustive, flawless affirmative truth (certainty; laws of thought; codified stipulations or rules).

To this indictment I give a dual answer. On the one hand, a non-judgmental, anthropological account of a failed sectarian doctrine might indeed be a waste of time to the extent that the doctrine itself had been abandoned as worthless. But in no way is this the case with the contradictions I find worth studying. The perceptual illusions (and later, world-states in dreams) which I study are uncanny, transformative experiences which academic logic has made taboo. The whole point is that they show that inconsistency need not be "failure." Then, the belief-systems with which my logic is concerned are not abandoned parochial doctrines, but rather socially indispensable belief-systems. Like natural language, they will not disappear even if analytic philosophy scorns them.

That leads to the second part of my answer. The purists live in a fantasy of exhaustive, flawless affirmative truth, the fantasy that "logic is true" because of transcendent intellectual relationships, the fantasy that logic can be a self-grounded truth unaffected by the person-world. To define logic as the way of perfect truth (i.e. the science of avoiding error) epitomizes a delusion. The "Is there language?" trap manifests that stable, affirmative non-error, in any remotely recognizable sense (certainty; laws of thought; codified stipulations or rules) is a deluded goal. (Again, skipping the strategy needed to avoid the discourse's defeating itself.) That is why this exposition does not defer to mathematical logic.

2. Analysis of the Logic of the Non-Vacuous Contradictions

To summarize the first phase of the logic of contradictions, it consists in establishing baselines concerning the actual functioning of everyday categorization and reasoning procedures, doctrinal systems, etc. The next phase of the logic of contradictions develops the collection of anomalies which provided the initial impulse for the new discipline. A concomitant task is to develop our account of disguised tendentious contradiction-systems (of which mathematics and mathematical logic happen to be formalistic instances).

When I first began to envision a logic of contradictions, I accepted that logic's unique instrumental achievement was to furnish a calculus of the consequence relationship. (To me, the philosophical "problem of knowledge" is epistemology and not a branch of logic.) Logic provides a priori judgments as to what you concede or do not concede in consequence of conceding certain propositions initially. I tried to associate my sensory-conceptual logical anomalies with a new calculus of the consequence relationship--or at least with an algorithm-like formal calculus. While the manuscripts I produced in the late Seventies contained some useful material, their approach represented a major error of judgment.

What needs to be done is to attend to the anomalies in their concreteness and let them suggest the investigative agenda. I am now convinced that at least one of the following alternatives obtains.

i. My logic of contradictions will never become a formal calculus of the consequence-relationship.

ii. It is hopelessly premature to attempt a formal calculus of the consequence-relationship for the logic of contradictions. It will take an entire generation just to accept that we are going to have to live with the waterfall illusion, etc., and to become familiar with their concrete ramifications.

iii. The logic of contradictions should yield a calculus: in the sense of a system of procedures for plunging the experience-world into pervasive and intense uncanniness. We need a system which can foresee anomalies, rather than waiting to stumble over them. But this calculus will unfold in a qualitatively different realm from the realm of mathematical logic. It will always be connected to perception, inculcated discriminations, and interpretations in the experience-world.

One reason why a calculus would be wanted is so that the results could be transferred to natural science. Certainly I look forward to doing that. But it would be premature to speculate on how that will be accomplished.

2.a. Experiences of the logically impossible in perceptual illusions

Thus, the study of non-vacuous contradictions will begin with the anomalies themselves, in their concreteness, piecing together many specific investigations. I will establish what the conditions are for saying that an illusion gives an experience of the logically impossible. (As examples, the waterfall illusion does. The common Necker cube and simple crossed-fingers illusion do not.)

For this introduction, the conditions are as follows.

i. Mutually exclusive attributes, a quality and its negative, have to be overtly and simultaneously present in the same channel or modality of experience, in the same perception or world-state.

ii. The phenomenon must evoke an inconsistent term, or ensemble of sentences, as its authentic description.

In the theory proper, these conditions will be replaced with deeper and more exact conditions connected with results from the everyday logic of consistency.

The investigation will be guided by such questions as the following.

- Can a mere stipulation render the anomalies inoperative, or create the anomalies?

- What becomes of the anomaly in a state of radical unbelief and namelessness?

- Could different perceptual habituation modify the anomalies?

Then, particular illusions are topics.

- I invented a paradoxical experience which combines effects noted by Protagoras and by Mach. Have three tanks of water--in order, hot, lukewarm, cold. Put your hands in the outer tanks. Then put both hands in the middle tank. You experience the same water as cold in the left hand and hot in the right. (The same water is discretely hot and cold at the same time to the same observer in the same sensory modality.) Does this satisfy my conditions for an experience of the logically impossible?

- The apparitions of stationary motion, stationary expansion, etc. can be produced by negative afterimages of motion. Stationary motion or "swimming" can also be produced by narcotic drugs (sodium pentothal?). (Note that the psychedelics, while they produce delusions, among other effects, do not produce experiences of the logically impossible.) Contradiction-logics in drug-modulated psyches.

- The Necker cube has a paradoxical version, in which a frame is seen to have both of two mutually exclusive orientations simultaneously.[12]

- I invented a paradoxical variant of Aristotle's crossed-fingers illusion.[13] It becomes a tactile realization of inconsistent enumeration ("1 = 2"). (It's more than a picture, because a picture of duality comprises a substantial interpretation for the number two.)

- A separate investigation which overlaps with this one is counting on imputed orientations of Necker cubes. "The Apprehension of Plurality," in Io #41.

In closing this section, let me again remind the reader that I found "science men" to repress the illusions in their experience--at least during intellectual confrontations when the illusions were cited to challenge objectivism and rationalism.

2.b. Paradoxes of common sense

Turning to the area represented by Zeno's paradoxes, I investigate this area by sharpening the paradoxes of common sense. It is not unheard-of in mathematical logic for newly proposed axiom-systems to have contradictions: Frege's system, Quine's ML, etc. But in the case of the perceptual illusions, there was the great novelty that we experience uncanny perceptions which are "pictures" of contradictions and indicate that the contradictions so pictured are non-vacuous, that is, non-"self-erasing." In the case of the paradoxes of common sense, what is important is that concepts which we must use in ordinary social interaction--concepts which are in the core of natural language, concepts which have been indispensable in providing the child with communicative conceptual capacity--are inconsistent. (Examples of such concepts are change, motion, continuity, transition, time, objectivity, other minds, language, incrementation without pre-selected limit, free will vs. causation.) More rigorously, I mean that these concepts, when elaborated deductively in conjunction with basic tenets of common sense such as

Motion does occur.

Time passes.

There are other minds.

There is language.

yield inconsistent conclusions.

A paradox such as "I always lie" is a contingent paradox because the initial thesis which leads us into trouble is a gratuitous one which we can feasibly refuse to propound.[14] The paradoxes of common sense are non-contingent paradoxes, inasmuch as the theses which lead us into trouble are theses which cannot be rejected in ordinary social interaction--or in the enculturation of the child--except as a pose. (I don't mean that established common sense can never be transcended. I mean that one of the prerequisites to transcending it is to grant that presently it is fundamental to communicative conceptual capacity.)

A subsequent stage of this investigation is to attempt to reduce the paradoxes of common sense to a few very sharp archetypal paradoxes. We should further be mindful that when we study the paradoxes, we are studying the functioning of a tendentious contradiction-system as already mentioned in B.1. (Whether the contradictoriness of common sense should be considered disguised or not is debatable.) Another ramification to be studied is the close relation between the paradoxes of common sense and the incoherences of the person-world (and in particular the conceptual machinery of depersonalization, e.g. the notion of an objectivity).

2.c. Dreams and inconsistent world-descriptions

There is a realm of logical anomalies which could have been mentioned after the illusions, but which I held back--because, unlike the illusions and the common-sense paradoxes, they have no academic recognition. In dreams, we experience many anomalies, two of them being deluded states of behavior and logically impossible world-states. Let me give examples of the latter. In one dream, I was in two quite separate cities at the same time. In my dream of Dec. 19, 1973, my father was dead and buried, but he and I were sitting in a house looking through magazines for his obituary.

The paradoxical character which the common-sense concepts of change, motion, continuity, time, etc. have in waking life is obscured or forced into the background in our normal use of the concepts. Somehow, in waking life we avoid explicitly avowing A&[not]A inconsistencies in ordinary thought. We know that it is proper to avow A, and improper to declare [not]A, even though both A and [not]A are deducible. The full and embarrassing conclusion A & [not]A becomes visible only when a gadfly like Zeno harasses us with it. And these remarks provide additional explanations of what it means for a contradiction-system to be disguised and "tendentious" (also, "biased").

But logically impossible world-states in dreams are "world-states" (cross-sections of the life-world at moments which are "nows" for the subject) which are overtly experienced as contradictory. The world-state which one is in is experienced as inconsistent. Curiously enough, there is not the shock of uncanniness as there is with waking perceptual illusions. I speculate that this is an aspect of the dream's delusiveness: the norms of what is reasonable are suspended, and outright contradictions in one's world-state no longer appear unreasonable.

It is unfortunate that I am the only person who has discerned and reported these dream states, because they demonstrate many important principles. Let me again remind the reader that I found "science men" to deny having or remembering dreams--at least during intellectual confrontations when dreams were cited to challenge objectivism and rationalism.

The waterfall illusion was only a "picture" of stationary motion; such a picture no more proves that stationary motion is actual than a picture of a unicorn proves that unicorns are actual. But the contradictory dream states go a degree beyond the perceptual illusions. Indeed, relative to an objectivist judgment of dreams as private hallucinations, the dreamed states in question still only "picture" contradictions. But now, to the extent that a dream is a life-world, the contradictions are installed in the life-world. That is, they are actual from within the dream. They illustrate what a logically impossible world would be like as an experience. They further illustrate what it is to exist in a world-state which requires an avowedly inconsistent description for its faithful portrayal.

Here we come upon another new topic--another facet of everyday language-use, of natural language. With natural language, one describes, one portrays a specified world-state, a moment of the life-world, by means of an ensemble of natural-language declarative sentences or propositions. We find this in all reportage; and we see the fantasy-equivalent in fiction. So now we have an instance in which the faithful portrayal of a specified world-state by an ensemble of sentences requires the inclusion of propositions which contradict each other. For this discussion, I will call such an ensemble of sentences a description-set (for a logically impossible world-state). It no longer makes sense to say that the value a sentence must have to qualify for inclusion in a description-set is "truth," because the description-set includes inconsistent sentences. So the value "true" must be replaced by the value descriptively authentic. [1992. All this is tentative until I complete "Normative Everyday Logic."]

We have now reached the point where we are considering sets of propositions which have been collected together because each of the propositions in a set contributes to the description of a specified world-state. This is a totally unexamined situation, and we cannot assume that any traditional logical principle will apply to it. I think I can give an illustration which will make my point clearly. Traditionally it is true that if it is meaningful to write reportage, then it is also meaningful to write fiction. If it is meaningful to write that Sputnik was launched in 1957, then it is also meaningful to write about a fictitious Sputnik which was launched in 1956.

But the logically impossible world-states comprise a realm in which such principles fail. I dreamed that I was in New York and Greensboro at the same time. Does it follow that I could write about a card that was in two different post office boxes at the same time? No, it does not so follow. (Even with the paradoxical Necker cube as another, different realization of impossible geometry.)

A novel which started off "John was a bachelor, but he was married" would be just as meaningless to me as to anybody else, even though I am steeped in non-vacuous contradictions. That is because nobody has found an interpretation in the experience-world for the verbally posited "married bachelor."[15] The step from the waterfall illusion to the phrase "stationary motion" is sufficiently natural that numerous psychologists have made it. The step from the phrase "married bachelor" to the corresponding world-state is, for academic logic, a senseless, absurd problem. And to me it will be an utterly mysterious problem until somebody finds some new experience (which I cannot anticipate).

One might imagine that once we have arrived at description-sets, we could pose such issues as the following.

- Are there consequence-relations among the propositions in a description-set?

- What is the semantic effect of the conjunction operator & in A & [not]A when that proposition is non-vacuous?

But the issue which surfaced just now is so much deeper that it exposes these latter questions as superficial and at best extremely premature. To have a calculus of the consequence relationship, a semantics for the logical operators, etc., would mean that we knew how to assign meanings mechanically to arbitrary inconsistent terms, propositions, description-sets. But on the contrary, knowing how to provide such meanings would be a culminating and final achievement of the theory, an achievement which we must expect to be very far away. And to suppose that the production of these meanings would be "mechanical" would be a complete misjudgment. As my research program proceeds, we will learn something about how non-vacuous meanings can be produced for inconsistent statements for which we initially have no such meanings. Some of the methods, those presented in Part II below, employ utterly unmechanical phenomena of the person-world. In general, the map from inconsistent linguistic expressions to non-vacuous and vacuous meanings (depending on a system's bias) comprises a family of abstruse problems.

The academic logicians will oppose my research program on the following grounds. Logic begins with formation rules, individual logical operators and their semantics, = and epsilon, and atomic formulas. Logic begins--for logicians who believe that a language can be established artificially--with a meager and pristine inventory of artificial, formal operators, variables, predicates, and relations. These are then progressively assembled into an exhaustive, flawless language.[16] Complete sentences appear because they are built up from elements which are posited and substantiated first.

Flynt's logic, it will be objected, gives endings without beginnings: starting with syntactical composites which make assertions before any elements have been provided for. A logical theory cannot begin, my detractors will say, by taking such a pair of propositions as "My father is alive. My father is not alive."--or the sentence "My father is alive and my father is not alive."--as a given. And then investigating this given. I have not defined or demonstrated the formation of A&[not]A. I haven't given a foundation for A, &, (not). I haven't defined and demonstrated A&[not]A as a self-inconsistency. I haven't proved that A&[not]A is satisfied.

Here as elsewhere, the professionals would use their monopoly of public discourse to impose a sectarian definition of what is avant-garde. They are looking for the vanguardism in the wrong place. I start in the present instance with the experiential actuality of the dreamed world-states, which appear with an already-established relation to verbal description. I let the phenomena suggest the direction of investigation; I do not allow sectarian definitions of vanguardism to rule out the phenomena.

In finishing with the topic of dream states, let me give an example of the sort of detail we have to discern and inquire about. I refer to the dream in which my father was alive and dead at the same time. What was happening in this world-state at the experiential level (prior to any description of the state which I gave in natural-language propositions)? I was sitting with my father, but I had an experiential memory of my father's demise and burial. ("Phenomenology" of an experiential memory: an imagining like a daydream, which however is conjoined to the attitude of assertion "this did happen.") Was one component of the experiential inconsistency present occurrence, while the other was memory-dependent?

In my dream of Jan. 1, 1992, a tall building lay on its side, like a long hall, and I was "descending" in an elevator which travelled on top of the topmost side of the "hall." Then the building was suddenly upright, and I finished the ride descending in the normal manner. Either the building's orientation was inconsistent; or else it metamorphosed from one moment to the next in a physically impossible manner.

We must be attentive to this sort of detail. The investigation must begin with a qualitative investigation of the experience-world phenomena which support the given descriptions.

1992. In the Eighties, I added an avenue to my logic of contradictions. I have said above that norms of what is reasonable are suspended in dreams, and that outright contradictions in one's world-state need not appear unreasonable. There is a delusive modulation of logical norms. In the Eighties, I undertook a study of hypnosis, and found that suggestion can modulate logical norms in a similar manner. This discovery ties in which something I intimated in B.1 above and will expand on below. Mathematics proceeds by co-opting contradictions; and the process involves something like a warping of norms of reasonableness. Let me proceed to a sweeping conclusion: Norms of inference are instilled by suggestion to begin with; they are psychic modulations or deformations (which may be called delusive). As a further example, I gave sitting on a sidewalk bench and counting people passing a corner. The apprehension of world-flux required to make such a count is highly incoherent.

3. The Absorbing of Contradictions

A further phase of my logic of contradictions is called the absorbing of contradictions. This phase applies the subject-matter already outlined in a way which reverses the direction of investigation. Previously, I discovered images or world-states which happened to require inconsistent terms or description-sets for their faithful portrayal. I started with the waterfall illusion, noted that it provides an image of stationary motion, and then tried to understand the ramifications of this anomaly. But in absorbing contradictions, I start with an inconsistent term or text which is given in name only--which is only a verbal shell. The problem is then to find an image, world-state, or compelling doctrinal system which provides a meaning or a realization for the inconsistency. So the absorbing of contradictions includes the very problem of mapping inconsistent expressions to non-vacuous meanings which we encountered in B.2.c.

Actually, the absorbing of contradictions in an ignominious way is a frequent task of theologians, philosophers, political ideologists, etc. Theologians struggle with the Trinity. Philosophers try to reconcile free will with causation. Adolf Grünbaum makes a massive effort to overmaster Zeno's paradoxes with the arcana of measure and dimension theory. In these cases, the ideologists accept that consistency is the prestigious posture, and they want to furnish contexts and interpretations so that inconsistency can be represented as consistent.

As I already intimated in B.1 above, something rather more interesting occurs in mathematics. Mathematics routinely discovers contradictions in its subject-matter, and reacts by co-opting and embracing them as new subject-matter. This is not a trivial or nominal process. The inconsistency is preserved and actually gives the new mathematical subject-matter its mystified quality and its "power." Nevertheless, there is a change of attitude--almost a warping of the norms of reasonableness--so that the new subject-matter is imagined to be consistent and so that the contradictions are displaced into a subliminal zone. Two great historical examples are calculus and transfinite arithmetic. An even more dramatic example, hardly known to laypersons, is divergent series. [And I hold that Yessenin-Volpin's logic is a sort of system for absorbing contradictions which he calls Zenonian situations or catchings.] The broad lesson is that most of the content of mathematics has this character.

So far I have spoken about the neutralizing of contradictions by ideologists. However, since I am the originator of the rubric "absorbing a contradiction," it is my privilege to define it as I please; and I now wish to define it so as to exclude all the above ignominious instances. The honorable instances of absorbing a contradiction are as follows. Given an inconsistent verbal paradigm, one wishes to find an image or world-state which provides a meaning or realization for the inconsistency, and which preserves, manifests, the paradoxical tension or uncanniness of the verbal inconsistency. For example, given the linguistic expression "stationary motion," to discover the waterfall illusion. Given the equality "1 = 2", to realize it with a paradoxical version of the crossed-fingers illusion. Given the specification of a material body wholly within each of two separated spatial regions, to realize it with my dream of being in two cities at once. Given the notion of a frame which has mutually exclusive spatial orientations at the same time, to picture it with the paradoxical Necker cube.

Some of the most visionary meta-technological projects which I have proposed to date involve absorbing contradictions. An example is "The Choice Chronology Project." Realization of the "Choice Chronology" world-state in the consensus realty might require unexpected constructions involving wordless languages, a drug-modulated state of consciousness, etc. In fact, I make a start on the project in "An Impossible Constancy,"[17] involving numbering with Necker-cube notations in a dream: to make a past enumeration agree with a present one by "changing the past."

But I speculate that there can be a further approach to absorbing a contradiction which is not as direct as finding a picture for the given term. We can absorb contradictions by finding compelling doctrinal systems which assimilate them. As I said, mathematics already produces most of its discoveries by this procedure--but only in a shamefaced way, because it must pretend to be mechanically consistent. What I suggest now is the avowed creation of new biased contradiction-systems. But what a suggestion--what could possibly motivate acceptance of such a system? I suggest that a collective might accept a replacement for common sense which was known to be a biased contradiction-system. To put the same proposal in a different guise, it might accept a new human self-image or perspective-of-totality. [1992. Was I trying to assess the prospects of the person-world framework? Cf. what I say about personhood theory in Part II.]

II. PERSONHOOD AND EXTREME DEPARTURES

Operations even more dramatic than my last example of absorbing a contradiction are suggested by personhood theory. Incoherences and knowing self-deception are normal features of ordinary personhood. They are sustained by the culture-correlated mutilation of faculties, etc. The entire life-world which seems to face the individual can be a "delusion" as explained in "Personhood II." In this context, the very existence of "logic" is part of a rationalistic delusion. If we knew how to consciously intervene transformatively in person-worlds, then the very possibility of logic could be turned off as suddenly as a light switch.

After all, as I mentioned in I.A, the enculturation of "science men" already suppresses two sources of non-vacuous contradictions in their person-worlds: perceptual illusions and dreams.

And as I mentioned above, when mathematics co-opts a contradiction, there is a warping of the norms of reasonableness such that the contradiction is imagined to be consistent.

Such effects as these are exceptionally strong, and show how far logic is from being "up in the sky" or "above the world." The notion that logic can properly be described as the laws of thought or the science of avoiding error--as if logic were a self-grounded truth unaffected by personhood--has no place here.

Imagine, then, the power over logic that would come with being able to induce sources of contradiction in the person-world. (Re-sensitization of science men to illusions and dreams.) Imagine the power over logic that would come with being able to reverse-warp the norms of reasonableness. (So that, for example, Galileo's paradox is seen as an inconsistency proof of denumerable infinity./The Hausdorff-Banach-Tarski paradox is seen as an inconsistency proof of the Axiom of Choice.)

Operations at the level of liquidating the "me" (as discussed in my essay "The Identity of the Self") could cause the very possibility of logic to vanish.

There is another operation, at about the same level as liquidating the "me," which traditionally would not be thought of as technological but which could undercut the very possibility of logic. Let me introduce this operation by pointing out that the exponent of logic probably could not be confounded by a running debate which invoked logical derivations to educe a logical flaw in the exponent's position. As the flaw was educed, the logicist, being blind to the overall absurdity of his cognitive esteem, would keep restating his position in a way which displaced the flaw from one juncture or level and back again. That is the way professional philosopers responded to my "Is there language?" trap in the Sixties.

Let me introduce the word enchantment for impartial unbelief's opening of the shared life-world to foundationless uncanniness and mutability. The accession to enchantment cannot be computed by logical derivations: because that accession annuls and transcends reason and logic (in the sense of the need for foundational consistency, stability, certainty). To debate the identitarian logician would be to accept that the outcome of the debate could be accomplished within the logical channel. But on the contrary, enchantment can be admitted only when a sensitivity can be awakened which transcends the modern cultural dichotomy between scientific and poetic gratifications. This sensitivity may have to be induced suddenly, without benefit of logical arguments--in a total crisis in which pressures are not limited to those of logical argumentation. A person functioning under the pressures referred to may suddenly--without any logical arguments--see the overall absurdity of his or her cognitive esteem.--And see the possibility of merging with enchantment--rather than denying and blocking it.

The role of personhood in sustaining and shaping logical principles is overriding. If we could tune in to personhood's functioning or dynamic balance, we could gain a power which would outrun even the original procedures of the logic of contradictions: the specialized, stepwise procedures. The original logic of contradictions might lead us to suppose that obtaining non-trivial violations of 1 [not equal] 2 would involve abstruse and tortuous logico-mathematical calculations. But intricate cerebration need not be the only avenue by which 1 [not equal] 2 can be contravened. [As I have said, I invented a paradoxical version of the crossed-fingers illusion which realizes 1 = 2.] If there were a community determined to indulge 1 = 2 systematically as a consenting sham, that would be sufficient.

[1992. I have left this observation in because it is provocative. Apparently what I meant in 1981 was correlative to what I said in I.B.1 about proving [not]B from {A, B}. A "1 = 2" arithmetic which is as honorable as real analysis could be installed socially as a consenting sham. But the observation presupposes further distinctions. I am not referring to the disgrace of using a scientific doctrine as a political symbol, and imposing it by police terror--as with Lysenkoism. The crazed doctrine would have to be promulgated by people devoted to mathematical ideas. Then what we get, in sum, is the actual history of mathematics: Newton's infinitesimals, Cantor's paradise, Brouwer's mysticism, and all.[18] ]

Strict meta-technology (including Part I of this essay) is a collection of analyses of local instabilities in established shared determinations of reality. These analyses deliberately refrain from positing a doctrine of the totality; they propose to gain wider applicability by being agnostic about the totality.

Personhood theory, on the other hand, posits a doctrine of the whole vertical organization of one's ordinary "composure" around such axes as

- self-presence and centered activation

- esteem

- morale

- "reliability" of the experience-world

- culture-correlated configuration of faculties

- objectification

- the "why" of one's preoccupations

- the possibility for sublime self-assertion.

I don't have anything but a few hints for a way of conscious transformative intervention in person-worlds, but if I did have a genuine way of this sort, again, it would outrun the original meta-technology. A way of intervening in person-worlds could turn entire logics off and on like light-switches. The notion that logic is an autonomous and elemental human faculty has no place here. [But I still have major reservations about personhood theory. Is it more credulous than meta-technology inasmuch as it posits a doctrine of the whole vertical organization of ordinary "composure"? Is it an attempt to find a way of regularizing the totality which can replace the common objective world--an attempt which is fated to be futile? Note that in I.B.3, I speculated that such a new perspective-of-totality would have to be a biased contradiction-system.]

[1992. To speak of turning logic off like a light switch is extraordinary. On the other hand, I came to realize that such ideas could be misused. It spoils people to tell them that they are entitled to dismiss a entire tradition--in this case, scientific rationalism--without any effort on their part. Meta-technology can be realized only in the disintegrating structures of an advanced civilization. My indictment of science as a reductionist half-fantasy and a consenting sham is a great step forward; but it does not mean that we could have dispensed with the scientific phase, or that "scientific maturity" is not worth having.

I proposed the sudden nullification of logic at a time when the counter-culture of the Sixties had infected academic philosophy and psychology with a fad of tossing reality out the window. That fad had a bad influence on the tone of my writing. What I wrote in 1981 was not abstractly false; or conversely, it was nominally legitimate. But the tone was indulgent. There are far more obscurantists, demagogues, and sadists than there are principled revolutionaries. Conventional reality, debased and traumatizing as it is, is less damaging than the alternatives to it which politically would be the easiest to realize. I did not stress enough that disillusionment militates most of all against superstition. I did not stress enough that superstition and sadism are the lowest types of degradation. I did not stress enough that my alternative to consensus reality requires, first of all profound integrity, and secondly, immense mental sharpness--albeit of a new type.

After all, one of the motivations of personhood theory was to find an appropriate way to conceive integrity relative to cognition--since the greatest obstructions to my perspective were derelictions on that score.]

Let me return to the problem of mapping inconsistent expressions to meanings which surfaced in I.B.2.c. Remember that I said that the solution of this family of problems would be a culminating and final achievement of the theory. I also said that the required production of meanings would not be a mechanical craft. I hope that my references to personhood suggest just how remote the mapping envisioned would be from an inherited algebraic combinatorics. Whatever I finally decide about the semantic effects of the logical operators, the consequence-relationships, etc., in description-sets, it will never be an algebraic combinatorics--not when we are concerned with perceptual illusions, pentothal-modulated states of consciousness, dreams, suggestibility and deformation of norms of reasonableness, etc.