Marcel Chelba: The Antinomy Of Pure Reason And Logical Paradoxes (kantinomus)

Marcel Chelba

The Antinomy of Pure Reason and Logical Paradoxes Or about antinomic schematism and his possible ontological significance.

Excerpt published in the volume of studies: Logică şi Ontologie, Ed. Trei, Bucureşti, 1999 (Logic and Ontology, Publishing Trei, Bucharest, 1999) − text revised and added to the 29 January 2009 – Translation: Marcel Chelba

Let's start with the first antinomy (first conflict of transcendental ideas), as it appears in Kant. This antinomy, and others, in fact, is reduced to two contradictory statement, called thesis and antithesis, and a so-called “demonstration” in apagogic method (reduction to absurdity), which, ultimately, the two assertion may be “deducted” one from another. The whole problem is reduced, ultimately, to understand the mechanism and significance of this logical phenomenon, by which any predication made on totality (as world) „slide” or „switch” (transcends) in its opposite. In this first antinomy is put in question the boundary problem of the world in space and time. The thesis is “The world has a beginning in time and is also limited in space” and the antithesis is “The world has no beginning, no limits in space but infinite in time and space”. (CPR, A 427-428, B 455-456)

Kant, as is known, is based, in his demonstration, in a speculative manner, on the concept of series (Reihe), a concept of mathematical provenance, which had already (at that time) a nice career. As could be seen in Kant's demonstrations, the development of infinite series takes place when outdoors, as progress, while inside, as regression of determinations. is:

Synthetic, Kant's demonstration in the first antinomy

In respect of time, if we recognize that the world has no beginning, it means that until the given world (this world now) has elapsed an eternity (a infinite series of successive states of the world), but as an infinity of states can not never be exhausted, means that the world (whereas just is) have a beginning. Conversely, if we recognize that the world has a beginning, it means that the given world, even from the first moment of its presence, has behind it (in its past) “Nothing”, an absolute vacuum, but as this given world can not result only from another state of itself, also given, it means that behind any given state of the world is an infinity of past states − so the world, through its past, is infinite (has no beginning). In respect of space, if we recognize that the world is infinite, then, as it is given, you should assume that is finished what may never be finished: the emergence („listing”, says Kant) of all its parts − so the world is finite. Conversely, if we recognize that the world is finite, then it should be bounded by anything, but as beyond its hypothetical borders is nothing on which to limit, being an absolute whole, it is infinite. Logical-philosophical literature is rife with approaches of this paradox. Unfortunately, however, they have delayed too much on their formal support, logicalmathematical, rather than looking in a manner as synthetic possible for their general schematism, as it is, I believe, essential.

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This first kantian antinomy could be presented (synthetic) so: Concerning space, given world, if is infinite, then is bordered with „Nothing”, but since everything is given, „Nothing” is „something” too − so the world is finite. Conversely, if given world is finite, it is bordered by „something”, but because it is everything, that „something” is „Nothing” − so the world is infinite. Concerning time, the scheme is the same: if the given world is infinite in the past, it is bordered by „Nothing”, but „Nothing” is „something” too, because, otherwise, the current world would have been impossible − so the world is finite; concerning the future, present world could not „volatilize” in „Nothing”, as if it were to disappear, it would disappear in „something” − so the world is finite in the future too. Conversely, if given world is finite in time, means that it is bordered in the past and future with „something”, but because it is everything, that „something” is part of it − so the world is bordered by „Nothing” − is infinite. * Finite is what borders with something. Infinite is what borders with nothing. Here's why the ontological condition of indisolubile unity and absolute freedom of Transcendent is absolute loneliness − the neighborhood with "Nothingness". Absolute freedom, to Hegel, is an exclusive prerogative of absolute being, because only absolute being, in its condition of „whole” or „historical totality of an unending self-confirmation process", lies, ontological, in absolute loneliness condition. * But look more closely at this schematism. It is noted that each time the world is „introduced” as being given, present in its entirety. This release gives

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the world, at once, all possible attributes of an object, so the world is introduced here as representation, although its concept has not resulted in a complete synthesis of the diversity given in sensibility, but clearly from a transcendental source. But any representation implies automatically a limit, a conceptual determination. From here starts the whole game. Besides the current use in relation to „sensibility”, our faculty of representation has in addition the extraordinary ability to receive in its space, as pure forms of intellect, concepts whose origin is not synthetic, based on experience, but intuitive and aprioric, as a kind of a reversed synthesis of a transcendent presence, namely, from the „synthetic a priori unity”, absolute, which appears at a time self-awareness as a determinant-self (thinking itself), not determinable-self, as „thinking subject”, so much above (or beyond) than that „I think” of Descartes. But putting the world as a given infinity in to the representation's space is the same as putting it in a limit, and asserting, in addition to it, a new concept − an „uninvited guest”, says George Enescu − namely, simple its difference from any possible determination. At this stage, put just as simple possible infinity, any determination of the world will be equal to its opposite, that the world be so, or we could say (at once) everything, as about the supreme god in oriental religions, or we can not say anything, as about the „One” of Parmenide. Since the purpose of research, in kantian antinomies, is to distinguish and determine an absolute presence (transcendent) in relation to „thinking subject”, this first step of putting the world as „possible infinity” ends poorly, with its simple determination as being indefinite. Due to the need to find the world (as representation) a sufficient determination, reason will join the world, always, with the concept of „totality” − a synthetic product of our imagination faculty − which is not a concept of empirical extraction − but a kind of cardinal

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that we put (by incomplete induction) at the end of the series all our representations, as a limit − as a set from that, another, larger, is not possible (such as mathematicians say). Kant called amphiboly just the usual (instinct or reflex) of the intellect to confuse representation with the phenomenon, to superimpose its pure a priori form over an given empirical content and to consider as given in the phenomenon, which actually is only in itself. In these circumstances, should be noted that the situation created by this first antinomy is not a amphiboly in the true sense of the word, since the concept „totality” can not be a genuine empirical content of the concept „world”, which is not simply a product of our productive imagination. It is rather a transcendental simulation of an amphiboly − a kind of mental experiment, that was not given to us by „mother nature”, we are entitled to believe, only to help us discover the limits of our rational thinking (Kant's „solution”), but just to help us discover something beyond the limits of reason (Hegel's „solution”). But about this, I will talk later. * For now I would like to pay my duty to clarify the concept of representation's space (or transcendental space), which, although it appears nowhere in Kant, however, may be placed in the kantiene concepts family of transcendental place, logic place, logical horizon and transcendental topic. (See CPR, A 268-270, B 324-326 and A 659, B 687.) If, after „Note to the amphiboly of reflection concepts”, Kant no longer speaks nowhere explicitly on transcendental topic is because ultimately, the whole „Critic of Pure Reason” is such a topic, meant to distinguish the reflection planes, and remove us from the vicious circle of amphiboly (transcendental illusion). This subject is an immensity that would deserve a separate research, although, in background, I talk about

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the same thing here. A deepening of this topic can be found in Critical Introduction (2004), in chapter Dilema and method of metaphisics (not yet translated into English). I hurry, therefore, to mention that the concept of space of representations, I do not refer only to common place of all representations as representations − common horizon within which they can be compared as representations and classified in some categories, which I will call plans (ontological plans). And another thing: the concept of neighborhood, in the space of representations, is the representation of difference to any possible determination of a given concept, as contingent and contiguous with respect to him (in the same ontological plane), but also necessary (hence, located in another ontological plane), there is no talking about given objects in the world of experience, but about things given only as being possible in the field of pure thinking, of reason free of any external constraints. Ontological difference, in this space of representations, is not only the limit of a given concept, but the intersection (the common place) with the opposite concept, located in an conjugate (orthogonal) plane. Or, geometrically speaking, the only „area” of space that can be „present” simultaneously in two orthogonalconjugate (perpendicular) planes is the „zero zone” − the nul element of space − the intersection of two planes. In other words, the nul element (death in the mythological vision) is the common element (the contiguity zone and crossing corridor) of opposites (of being and nothingness). Opposites (sincategorematic concepts, as they say) are not contradictory, in that geometric vision of kantian antithetik, since they „live” in different ontological plans − some plans are no longer parallel (separate), as in classical (euclidiano-artistotelian) vision, but orthogonal, as in noneuclidian geometry. (See Critical introduction, chapter Towards a new paradigm of science.) Hence the possibility of thinking an ontology in several dimensions, as a kind of generalization of classical

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ontology, dualist, built on the foundation of pairs of opposing concepts. In this hiperconsistent vision, a concept may have several opposites (an infinity). But this is another issue on which we could wear only after we conclude this. Thus, ontological terms, sincategorematic concepts are some objects that reside in transcendent plans − that just makes each other to be practically absent and intangible (the projection of each in ontological plane of the other is the nul element of the space of representations). Only in this hyperbolic architecture of our transcendental space our sincategorematic concepts may remain each ontological limit of another, without denying each other. Only on this area of intersection (of logical contiguity) between contingent and necessary, respectively, between conditionate and unconditionate, i.e., only on the ground of cosmological ideas we may assert, in eleat method, that is all that can be thought. Therefore, only in the space of representations is necessary, outside the world (as given infinity), to be something, because something is thought as a limit of the world, even by thematic proposal of Nothingness. In the space of representations even Nothingness (ontological gap) is something. The transcendent, as in theology, is the beyond world − but, as in the fairy tale „Youthfulness without oldness and life without death” or in the ballad „Mioriţa”, the transcendent is accessible by death. Nothingness (the zero element of space of representations) is the small sheepfold between earth and heaven („On the crest of the hill, at an ace of Heaven’s sill”), the threshold between transcendent and transcendental. The land is, as Kant says, full of danger and risk to stray or fall into ravine lies in ambush, waiting for us at every step. *

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To go further, however, confident in our forces, and try to arrange the data of this first antinomy in a diagram.

It can be seen at first glance how the concepts of finite and infinite (sincategorematic concepts) pass each other - that is, when one concept is applied to the world (as totality), it goes in the other, turning inside out all determinations of the world. Then, we can see how the concept of the world is superimposed over that of totality which, in turn, is integrated into the world − a amphiboly similar to that in which we look at an apple and we would seem that see in it the space itself or the cardinal points. Finally, by the ceaseless passage of something to nothing and vice versa, see how (in the sphere of totality) can produce a something from nothing, as a limit (or difference) of the world, and then the resorption of that something in nothing, as a part of the world, leaving, again, the outside world an „empty space”. Follow, again, the reasoning on chart: If the world is finite, it is neighboring to something, but because the world is all those who are, that means that something (outside world) is nothing. So the world is infinite − but carefully, only as infinite progressive activity, through the inexhaustible production and resorption of its determinations.

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Conversely, if the world is infinite, it is bordered by nothing, but because the world is given as a „totality of everything that is” anything beyond should no longer be possible, or mere implementation of the concept of neighborliness, even empty of any content, is something already existing outside world − so the world is finite − but carefully, only as representation, because only here, in the space of representations, we may consider that something necessarily exist, whereas it may be thought. On this occasion we produced, finally, that separation of plans, sought and recommended by Kant. If the first diagram, these two plans appear confused and the outcome of each approach was a flagrant contradiction of the premise, now a new chart is necessary, which will see that they are actually two planes „parallel”, which communicate among themselves through entire concept, which makes possible a tilting of the conclusion, always, in the other plane, symmetrically of the assumption was made. Here's the diagram:

It can be seen how the world, given as infinite (the premise), appears (as totality) to be finite in the other plan, and vice versa, given as finite, appears (as totality) to be infinite in the symmetric plan. Synthetic, the antinomy is as follows: Infinite world, given as totality, is finie.

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Conversely, finite world, given as totality, is infinite. This cyclical discursive movement may continue indefinitely. Separation of plans has not led to the destruction of antinomy. By introducing a new dimension on which we can not yet pronounce, was created only the possibility to distinguish this two plans. Figure two-dimensional (1/a) can be imagined in an three-dimensional space where, rotated a little to be seen in profile, appears (under it) another plan, standing (until now) hidden. * Kant seems to be satisfied that the denial of world's determinations (given in premise), no longer produces in the same „logical place” (in the same plan), but in a symmetrical plan (complementary), it no longer a contradiction in terms but only a relationship of contrariety, his „solution” seeming to be at this point just the sepparation of antinomy in two paralogisms. Hegel seems to be pleased that this miraculous overthrow of the opposite (twisting) continue; that, in other words, despite any distinctions, the game between the two plans can not be stopped, its result is always a return to the beginning, to the premise, to the ground. „Essence came from being and concept from essence, and so from being. But this becoming has its specific effect that of returning upside-down its own way, so that the outcome is rather the unconditioned and the original” − Hegel, Science of logic (§ 1325). Hegel considered, therefore, that the two plans, although distinct, should be further held together, and let the game continue on larger spaces. Kant, on the contrary, held that separation of the two plans is sufficient to ensure peace and the smooth running of the reason in its regulative use. To observe in passing that if we want to recompose antinomy chart (1/b) and instead overlap the two plans, join them in the same plane and compresses them into

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one unit, get the famous Yin-yang diagram − and this is not a random coincidence. * But let's go further, to research with our own means unless there is a pure schematism of reason that Kant recognized as such (as natural antithetic of reason) (see CPR, A 407, B 433] but to stand not only the foundation of antinomies, but also paradoxes, in general, if not even the foundation of syllogism − the meaning of Hegel. If there is, this schematism could be establishet as pure form of totality or undeterminate in absolute sense and, as such, it could be put to the foundation of somme possible inferenţe on a global reality, possible in absolute sense. These inferences would be the only who could be admitted as exceptions to the principle of knowledge founded by Kant (and not just postulated, as in Hume) that the only way to purchase and validation of a true knowledge is experience. Since this global presence, external and objective, can not be given in any experience as such, i.e. in its entirety, this antinomic schematism of pure reason, as a form of self-consciousness (the only presence given they themselves in an absolute way and put before they themselves as being objective), which may be a genuine "model" of global presence, ie, as a priori appropriate form of an object, which does not show in the experience than by its parts and only in succession. (See Critical Introduction, chapter Towards a new paradigm of science, which says explicitly that modern physics, the unified field theory, will inevitably be a metaphysical, whereas just the subject they study, the universe in its entirety, there will never be an object of our empirical experience.) Therefore, we can not experience Totality itself, just as it is only a synthetic concept − a synthetic a priori intuition − that we associate (only under the formal title, for lack of other guide marks) with that alleged global

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presence, objective and imuabile, which, although transcendent, however, affect our senses. Even just a hypothesis, this meeting in absolute of self-consciousness with the transcendent (as a global presence), with the concept of "everything", will produce actually only ontological justification of the existence of formal compatibility between reason (the faculty of principles, says Kant) and the so-called laws of nature, promising a further elucidation of our original dilemma, on the primacy of spirit over the nature, or of nature over the spirit. With Hegel (which, however, take things to the absolute, without any critical precautions) we can see that this working hypothesis − this settlement in the mirror (face to face, one as an shattered image of the other) of being (as absolutely undetermined) and selfconsciousness (as historicaly determined state of that ineffable presence, generic called being) − is, however, an ontological productivity more than it could imagine Kant. This working hypothesis has been taken as an ontological solution since immemorial times − the texts of oriental religious tradition make the most convincing evidence that the man always had access to this idea, and that this ontological solution is intrinsically linked of human nature itself, whatever the stage of civilization that is, faith and religious thinking being for human a sufficiently strong support to sustain such a metaphysical construction. Obviously, in search of that schematism, I will not propose to me, now, a exhaustive approach to antinomies, paradoxes and Hegel's sylogistic. I will only touch the problem, treating casuistry in selectively. To conclude the discussion on first antinomy, I would not want to emphasize only that its reiteration, as relationship of the world with time, would be similar to the relationship of the world with space, and would not bring any formal news about schematism.

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Time would not appear in this algebraic entry to this problem than another space, complementary, but identical in terms of determinations (laws of composition). World, put in a unilateral report with time, behaving (logically) as in its unilaterally report with space. How could behave world in a simultaneously report to both spaces, yet it is not appropriate to discuss here. * Let's get to the second antinomy. If the first antinomy was one in which world reported themselves as absolute totality of composition, in terms of quantity, the second antinomy corresponds to a self reporting of the world as absolute totality of decomposition, in terms of quality. Therefore, the second antinomy will start the following statement: „Any composed substance in the world consists of simple parts and there is absolutely nothing anywhere than the simple or composed of simple” − thesis, and „No composed object in the world consists of simple parts and there is nowhere something simple in the world” − antithesis. (CPR, A 434-435, B 462-463] This formulation is, how you can see, something more confusing than the first antinomy. The conflict is actually between the following assertion: the world is absolutely simple or absolutely composed? This antinomy should go like this: If we assume that the given world is absolutely simple (if suppress any composition in mind − as Kant says), then would disappear every distinct thing, including world; but because given world is distinct as a totality of those who are, means that it is distinct from it, at least, this totality (even if it is an empty lot); so, since is something distinguished into the concept of the world, the world is composed. If we assume that given world is absolutely composed, then, since it is all, means that any thing is

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infinitely composed and in turn integrated into the composition of something with an infinity of other things; but given world, as all of those who are, is no more composed with anything else, so that, as totality, world is completly indistinct; being completely indistinct, it is absolutely simple. It is noted that the first demonstration of the thesis, the world appears finally to be composed and that this is based on the very fact that it is given (the premise). Because the world is given, however, in the thesis and antithesis, Kant had the impression that he must begin, in the thesis and antithesis, from something composed. That is why Kant chose the wording quoted above; they are practically equivalent to the following statement: there is absolutely nothing anywhere than simple things, or what is composed of simple parts, so the world, as a compound thing, is composed of simple parts (thesis) and there is absolutely nothing anywhere than compound things or what is composed of compound parts, so the world, as a compound thing, is composed of compound parts (antithesis). If, in Kant’s wording, antithesis is tautological, thesis is contradictory. Indeed, if there is anything anywhere than simple things, this means that there is no compounded things and vice versa, if there is nowhere only compound things, this means that there is no simple things. But in antinomy, if the world is given as being simple, it appears to be composed and vice versa, if is given as being composed, it must appear to be simple. It is true, world's limit (its composition) is given in thesis, but it still lies hidden in the premise, it coming to the surface only after application of the totality concept. The wording: „Any composed substance in the world consists of simple parts”, is even the amfiboly that thesis and antithesis to be dismantled. This little slip of formulation has puzzled many commentators, including Kant. To recover algorithm that antinomy it is necessary, first, to postulate two definitions:

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Definition 1: Tell about something that is absolutely simple, if not within his or outside his relative to him, we can no longer distinguish anything. In this release, an absolutely simple thing is completely blurred, it is given in a complete shutdown in itself, completely inaccessible, lacking any relationship to anything inside or outside it. In this release, the world will appear as a completely closed space, whose interior is not different from its exterior (since they are empty, are identical); the world appears as an catabasic space (like said Lucian Blaga), a monad completely closed and hazy, which, besides the fact that it is, we can not know anything. Definition 2: Tell about something that is completely composed, whether in relation to him, we can distinguish as many things, both inside and outside its limits. One thing, put that way, there will instantly grind to an infinity of distinctions, both in relation to his inside, and its outside, this distinction „inside-outside” being for us even the first possible distinction. World, put that way, it will appear as a completely open space − a anabasic space (in Blaga’s terminology), ie an infinitely lull and infinitely extended space. In both definitions, taken separately, the world appears in some hypostases non-contradictory. The problem occurs when we want to define the world as totality. In the definition of „the world is the totality of what is and ever will be” amfiboly is produced, whereas we identified in definition the synthetic concept of the world with analitic concept of totality. Therefore, the representation of world will appear a contradiction, due to the overlap of the two images of his emergence as a completely closed space, and as absolutely open space. Reason to try to get out of this situation in creatively combining the two representations of intellect: The world, given as an absolutely simple thing, so that an absolutely closed space, put as totality will appear to be open, so composed. The proposed image will be that of a world which closure appears as a limit in relation to

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an infinity of things disticte in it, so in relation to an inner infinite divisibility. Conversely, the world, given as an absolutely composed thing, so that an absolutely open space, put as totality will appear to be closed, so simple. The proposed image will be that of a world whose openness appears as a infinite expansion in relation to a possible limited distinction of things inside it, so in relation to a limited interior divisibility. What to do reason in this situation? To reject these two representations to be false or to simply recognize the functionality of their practice? Regarding the schematism of that antinomy I think it may be reduced to that of the first antinomy. Indeed, if we associate the concept of simplicity to that of infinity and that of the composition with that of finity, then we can associate the concept of absolute closure to that of the neighborhood with a “zero” which becomes “something” by the decomposition of the world as totality (a process called catabolism, in biology) and that of absolute openness with the neighborhood with a “something” that is always passed through assimilation (a process called, in biology, anabolism). It's simply irresistible temptation to join in a systematic way the concept of metabolism (in biology) with dynamic stability of the antinomic game studied here - but this is another problem * Now we get to the third antinomy, therefore, after Kant, corresponds to a self-reporting of the world as absolute totality of genesis, from the point of view of the relationship. Kant launches discussion on this antinomy with the following statement: „Causation by the laws of nature not only of which can be derived all world phenomena. To explain them is necessary to assume a causality through freedom” − the thesis, and: „There is no freedom, but everything in the

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world happens only by laws of nature” − antithesis. [CPR, A 444-445, B 472-473]. Again we are forced to notice that the sentence, Kant "filed" in fact the whole amfiboly apparently resolved even by a difference of degree or weight distribution of the two forms of determinism. Thesis, to be in a perfect symmetry with the antithesis, should be: no determination by external and objective laws of nature, but only through freedom as absolute spontaneity. Synthetic, the unfolding this antinomy could be as follows: If the world is subject to natural determinism, then everything is subject to a natural determination, outer and objective, ie every given thing exist only through another thing, given as a condition or cause of it. Should the world itself have given something beyond, something that they cause, a premium cause or a first engine. But since the world is everything, outside is not something else, so it is free, its occurrence is spontaneous, a result of his own freedom. Conversely, if given world is free, then everything is free, ie, every given thing exists only as effect of his own freedom, the world would be absolute chaos − possibly all, not could provide anything. But the world as a whole can not be something given separately and outside of this anarchy, it is only and only as a whole of this anarchy, so the world is caused by something, and that is determined by all other existing things, the former or possible once, it means that it is subject to natural determinism, namely to a rule that maintain (in the general chaos) its unity. But if there is this natural law of conservation of the world, then everything is subject to natural determinations and ... the cycle of such paradoxical judgments is taken from the beginning. (All modern cosmology spins around these two hypotheses.) It is noted that this antinomy can be placed in the same schematism: Raised to be absolutely determined, the world ask (outside) a first motor, but as totality the world is

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bordered by nothing, so it will appear to be absolutely free (self-determined). Conversely, released as absolutely free, the world makes possible absolute spontaneity of things, but as their entirety, the world appears to be determined and always exceeded by its infinity. Again we see how the world, by reporting it to themselves, because identification of the two complementary plans in which it is given − once as absolutely free and, sometimes, as absolutely determined − enters in relation to its proximate genus: the totality, wich establishes itself as specific difference and contingency, turning inside-out all initial determinations of the world. * Now we get to the fourth antinomy, which corresponds to a "self-reports of the world" as "absolute totality" of its dependence in terms of modality. This antinomy of necessity seems to be a summary of the first three, such kantian category of modality appears to be some kind of synthesis of the other three categories: quantity, quality and relationship. Therefore, in this antinomy, Kant put global problem if the world is related to something existing as a determinant of them and completely independent of it, something which, by its presence as a supreme legislative court, to submit the World to its need, or who, by his absence, to let the world drift hazard. Obviously, the subtext, Kant thinks there is the presence of God, but in „Note to fourth antinomy”, referring euphemistic to the deity as a supreme being, however, Kant states that in this antinomy is not about trying to find evidence of the existence of God (see CPR, A 456, B 484). In Kant’s formulation, the thesis and antithesis of the fourth antinomy are following statements: „World implies something that, either as a part of it or as a cause of it, is a absolutely necessary being” and

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„There is nowhere a absolutely necessary existence, not in the world, nor outside the world, as a cause of the world” (CPP, A 452-454, B 480-482). As can be seen, although conscious, Kant left seduced him once (in problem formulation) of transcendental illusion of divine connotations, that this antinomie can not, however, avoid, namely that God exists, and as such He is a „part” of the world, is contingent in relation to it, is its specific difference, but as supreme court, He is completely separate from it, „lives” outside world, is transcendent, is its proximate genus. So, the amfiboly called into question is, inevitable, this paradoxical image of a unilateral relationship between world and God, where God is the only determinant for the world, the reverse being not possible any determination. But Kant berth holistic vision that would have to assimilate God to the world − of course, for reasons of dogmatic caution − the transcendence of God had provided in any case − but also convinced that this antinomy, as seen above, it is not about the divine attributes, since it can not preach on this issue nothing more than an uncertainty. Indeed, if we make the thesis: the world involves something that, either as a part or cause, either as totality, is an absolutely necessary being, and antithesis: there is nothing necessary, nor into the world, nor outside it, even the world itself, we see that the whole issue is actually transferred, as in other antinomies, on the concept of the world as pure representation. Thus we can also recast thesis that antinomy, not because of doctrinal caution, but that, indeed, the issue of God, if we may say so, must be raised elsewhere. So, the unfolding this antinomy could be as follows: If given world is absolutely necessary, then (since everything is necessary) it is necessary to have a supreme court, but this instance (since it is necessary) may not exist as such, so the world is not necessary. Conversely, if the world is not necessary, then, given as chaos, it is bordered in a necessary way with

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something different, which is by its own will and can not be controlled, but because the world is totality, it means that in the world is a will or a supreme court, which thus made to be something necessarily, so the world is necessary. As we see here, defining the world as a whole and identifying (in representation) synthetic concept of the world with analytical concept of totality, is going the same continuous upheaval of the world's attributes into their opposite. Schematism is the same: Put as being absolutely necessary, the world possesses necessary in it, as being contingent, a supreme court. Identified with totality world is split into two parts: interior and exterior. The place of court will be sent outside, just so it will retain its required attributes in relation to given world, namely noncontingecy and indetermination. But world, as totality of those who are, absorbed in themselves this court also, whereas just there. Therefore: if the world is given as necessary, then it is not possible a authentic (absolute) court or, for lack of an absolute court, means that nothing can be necessary, therefore, the given world is not necessary. Conversely, if the world is put as absolutely chaotic (anarchic), then identified with totality, it will split again into two parts: interior and exterior. If inside the world can continue to remain as placed at the top, anarchic, the outside world should be (necessary) something different from it. Outside world will therefore be something absolutely necessary, subject to a supreme court. But as the world is all those who are, means that outside world with the supreme court are present in it. So the world is absolutely necessary. At this point we can say that all four kantian antinomies are subject to the same schematism. We can represent them in a single diagram:

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In summary, we could present the whole picture of kantian antinomies as follows: 1. Put as completely finished, composed, determined and necessary, the world is put (hidden) in an appropriate relationship with its own infinity as inner limit. Identified with totality the world is split into two parts: interior and exterior. Everything was determinant for the world will be sent outside themselves, as in a transcendent neighborhood containing something: its own limit. In that place will find infinite space and eternity, simple alterity of the world, the prime engine and the supreme court. Only this external position, which is transcendent in relation to given world, can ensure their condition of determinants and indeterminate factors, ie non-contingent in relation to the given world. But world (like totality of those who are) also embodies the outside of it, whereas once with it. Consequently, outside world remains always vacuum that its authentic (absolute) limits does not exist. So, the given world is not finite, composed, determined and necessary. If the world is not finite, composed, determined and necessary, it can not be other than infinite, simple, free and chaotic.

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To see that only in the latter inference is actually reaches the so-called apagogic demonstration and that it is based also on the totality concept, which divide absolute infinity of possible in symmetrical pairs of sincategorematic categories (one as reverse the other), third category being excluded. Only under this originating division we can infer that since there is only predicate pairs a and non-a, p and non-p, etc., if an object exists and he has no property a, then he certainly has the property of non-a etc. Or vice versa. Underlying principle is: an existing object should be linked in one way or another to all existing predicate − provided that it be all (or totality). In other words, the entire apodictic certainty is based on a categorial holism or sincategorematic exclusivity of predicate, and they are based in turn on the natural limits of intellect, that of not being able to operate than bipolar distinctions, no another knife at hand than the totality concept that cut the determined presence of any object in an interior and an exterior. 2. Conversely, if the world is put as being infinite, simple, free and chaotic, then, identified with totality or released as totality, it will split again into two parts: interior and exterior. If inside the world can continue to remain as it was put, infinite, simple, free and chaotic, outside world must necessarily be something different from it. Outside them, even nul in relation to the world (as world filled everything in its infinity) will be necessarily something, something different than the given world, ie completely limited, composed, determined and necessary, which contains an implicit and absolute landmark, a rule or a absolute court. But as the world is all those who are, means that its absolutely determined outside (together with the absolute determining court) are present in it. So if world can not be absolutely infinite, simple, free and chaotic, it is absolutely limited, composed, determined and necessary. And here, world, put as infinity, enters a kind of dialogue with its diversity (with the totality concept). At first world puts out its diversity, then, that outer world,

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given simultaneously with the world (in its infinity and absolute spontaneity), is absorbed in the world, moment in which (in the world) appears the absolute benchmark of an determination, and all initial determinations of the world are turned inside-out: it now becomes absolutely limited, composed, determined and necessary. If, in the first case, when the world is put as finity, its determination (as totality) falls outside them, in the second case, when the world is put as infinity, its determination (as totality) falls within them. But, as totality, world found themselves as an outrunning its own infinity (in the first case), respectively, as being exceeded by its own infinity (in the second case). Given as being finite, world will transcend in its own infinity, and given as being infinite, it will fall in its own finity, leaving it again exceeded by its own infinity. So the game is how the world as representation (ie, put as totality into a limit of the intellect), related to its infinity, which occurs when inside, when outside it. Amfiboly appears in juxtaposition of the two hypostases of the world: with „infinity inside” and „infinity outside” − such as said Constantin Noica (see Marcel Chelba: Last ideea of Constantin Noica and endless road of philosophy). From this identity will result a situation of indetermination in which we can say that the world is both finite and infinite, so determined and so indeterminated and so on. This amfibolie is so profound that it even born in field concept of existence. To call antinomy of existence. It can be unfold so: If the world is, then, as it is, it is neighboring (as totality) winth nothing. But, whereas nothing is, the world is not. Conversely, if the world is not, then, as it is still given as nothing, it is neighboring with something that is. But, as it is something, the world (as totality) is.

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It is noted that all these amfibolies works on the permanent confrontation of two principles: „what limits should be different from what is limited” − the analytical principle, also formulated by Kant (A 515, B 543), that the world throw out its determinations as specific differences, setting in fact they limit as proximate genus and transcendent alterity, and I say, the eleat principle of absolute identity: what limits should be identical whith what is limited, that limit again becomes contingent in relation to limited, its proximate genus now becomes its specific difference, and so giving the concept of world, by resorption they limit, the ability to climb, row on row, all its possible determinations − a principle that applies in respect of any something given in the absolute sense, as world (in the case of kantian antinomies) or One (in the case of Parmenide). Moreover, this principle of diversity identity or oposites contingency has been recognized and used as such by Kant. In Note to the Fourth antinomy, from which I quoted, it calls euphemistic: „another principle of reason”, ie a principle which, operating with the concepts of „contingent beings in general (since they are considered only as objects of understanding), [...] link through simple concepts these beings by a necessary being.” (A 456, B 484) A discussion on this principle, Kant finds it appropriate not only in a „transcendent philosophy” −

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that Kant has not ever given it − because its founding principle was unable to be substantiated (but thus left open field for Hegel). This principle should be the „transcendental ideal”, ie the concept of „absolute necessity” (A 607, B 635) and, I would add, of simplicity, freedom and absolute indetermination, all linked in one single: „absolute unconditioned” or „unconditioned necessity” − but all these concepts, as Kant, can not be found as such since they can not be found by any possible experience and therefore they can not be authentic source of knowledge. Here's what he says: “Unconditioned necessity, which, as the ultimate support and stay of all existing things, is an indispensable requirement of the mind, is an abyss on the verge of which human reason trembles in dismay. Even the idea of eternity, terrible and sublime as it is, as depicted by Haller, does not produce upon the mental vision such a feeling of awe and terror; for, although it measures the duration of things, it does not support them. We cannot bear, nor can we rid ourselves of the thought that a being, which we regard as the greatest of all possible existences, should say to himself: I am from eternity to eternity; beside me there is nothing, except that which exists by my will; whence then am I? Here all sinks away from under us; and the greatest, as the smallest, perfection, hovers without stay or footing in presence of the speculative reason, which finds it as easy to part with the one as with the other.” (A 613, B 64 − translation of Meiklejohn) Therefore, Kant considered that since this concept of an absolute indetermination can not be linked to anything under the aesthetic principles of knowledge, that is, through sensibility and experience, he is doomed to remain a simple „ideal” of pure reason. *

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Before going further, to see that in these judgments concept of the World appeared in two hypostases, respectively, with two purposes: 1. One of these hypostases is the concept of a transcendent object, absolutely unconditioned, possible in general as „regressive synthesis of the diversity in phenomenon”. Put in this way, the world appears as an absolute and problematic totality (taken only as possible) of an infinite series of conditions, fully given in it. „The absolute totality of the series of conditions to a given conditioned is always unconditioned; because beyond it there exist no other conditions, on which it might depend. But the absolute totality of such a series is only an idea, or rather a problematical conception, the possibility of which must be investigated – particularly in relation to the mode in which the unconditioned, as the transcendental idea which is the real subject of inquiry, may be contained therein” [A 417, B 445]. So, the totality, as a synthesis or limit of an infinite series, is not contingent with the terms thereof, but is part of another plan, transcendent. The world is in this sense, the concept of a transcendent object which can not enter the field of experience but whose infinity is given inside of it and can be found as such in any of its parts. The world appears to be suspended over its possible infinity. 2. Other hypostases of the concept of the world is that it appears as Nature, as aggregate, as an unfinished amount (and therefore finite) of all its possibilities, the series of all phenomena, that seems to continue forever outside world as a „dynamic whole”. World (given in this way) appears as a welldetermined attendance. As such it admits a limit, a first term of the series, which is called „in relation to past time, the beginning of the world; in relation to space, the limit of the world; in relation to the parts of a given limited whole, the simple; in relation to causes, absolute

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spontaneity (liberty); and in relation to the existence of changeable things, absolute physical necessity” [A 418, B 446]. The distinction appears, therefore, between the concept of a world possible in general (necessary, but undeterminate) and the problematic concept of a world possible in particular (contingent, but determinate). Kant does not look too sure of the importance of this distinction, but it meets (fortunately) with another Kant's distinction of the rum ending of Analitic. „Before ending this transcendental analytic, we must make an addition, which, although in itself of no particular importance, seems to be necessary to the completeness of the system. The highest conception, with which a transcendental philosophy commonly begins, is the division into possible and impossible. But as all division presupposes a divided conception, a still higher one must exist, and this is the conception of an object in general – problematically understood and without its being decided whether it is something or nothing” [A 290, B 346]. But I have suspicion that these ideas about pure uncondiţionate and original division possible-impossible (interior-exterior, transcendent-transcendental etc.) are essential. Before, however, we decide on their ontological significance, have yet to investigate whether antinomic schematism can be high indeed to the rank of an universal schematism, ie, whether it is present in all paradoxical forms of our thought. * Therefore to go ahead and let us now recall the well known sentences of Epimenide's paradox, so-called liar paradox: Epimenide, the Cretan, says:

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All Cretans are liars. How is Epimenide, honest or a liar? That is the theme. The deployment of this paradox is as follows: If Epimenide is sincere, then the truth about Cretans is that they are liars. But Epimenide is Cretan, therefore, he is a liar. Conversely, if Epimenide is a liar, then the truth about Cretans is that they are sincere. But Epimenide is Cretan, so he is honest. Also, in pursuit of this paradox, we can observe a movement of the concepts similar to that of kantian antinomies, which can be represented in a similar chart, where Epimenide falls in the position of the „world” and Cretan in the position of „totality”. The first sequence of thought, with serenity of a true politician, I would say, Epimenide separates itself from the rest of Cretans, as a rest of a set of which, however, he belongs, and which thus appears as one's neighborhood (specific difference). Then, considering himself a privileged part of the Cretan, so completely separated from it, exercises its right to issue categorical judgments on it. If Epimenide had said that „all Cretans are sincere”, everything would be okay, but he put himself in a negative relationship with the Cretans (Class of Cretans, which he belongs), precisely because otherwise no distinction between him and the Cretans (Class of Cretans) could not be possible. But the next sequence, that Epimenide's semantic rest (neighborhood or specific difference of Epimenide's concept) become what should have been from the beginning, namely: general class of Cretans (Epimenide's proximate genus). In this new position of Cretans, all that was true about them become true about Epimenide: if Epimenide is placed in the premises to be honest, will appear at the end to be a liar and vice versa. To have a structure of Epimenide's paradox identical to that of Kantian antinomies, we are entitled to believe that this unceasing reversal in their opposite of determinations of a concept (given absolutely, ie in relation only with itself, to be given) should be manifest if

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we question the determination, not of Epimenide, but the Cretan, so if we change Epimenide's position with that of the Cretan and vice versa.

In this case, the deployment of the paradox should be the following: If all Cretans are liars (if to be Cretan means to be a liar), then what Epimenide said is true, so Epimenide is sincere, but (carefully!) Epimenide is Cretan, so Cretans are sincere. Obviously it does not work. Backside would collide with the same difficulty. We see now that in this new release of the problem, last inference (from the particular to general) occurs only if beyond Class of Cretans there is no other category, and this, indeed, put so, absolutely, no longer be any difference in her womb, is identical with any part of it (here Epimenide's person) − only under this condition, any attempt to determine the Class of Cretans will be continually converted into its opposite. This „defect” of the liar paradox is also present in the first formulation of the problem: 1. Even if Epimenide is honest, we are not entitled to believe that his statement is absolutely true, whereas, on the one hand, he can not provide a global or exhaustive experience on Cretans, in other words, his generalization may be legitimate (absolutely) only upon a complete induction, which is impossible, and on the other hand,

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Class of Cretans is not a transcendental category, but a empirical one, which supports inside any other specific differences. Therefore, we must accept the conventional way, otherwise the paradox does not work, namely, an absolute identity (a perfect isomorphism) between Epimenide (as a part) and Cretan Class (as a whole) in the definition of the premise, because only under these conditions is possible the inference from particular to general and only in this way Epimenide's statements can be extrapolated to the class of all Cretans. (Both induction and deduction, in Aristotle's sense, can take place only in terms of topological paradox Banach-Tarski-Hausdorff. But this is a subject which I have reserved for the Antinomy of pure reason and ontological antinomy − a work started in 1998 and still under development.) 2. Conversely, even though we know that Epimenide is a liar, we could not conclude that, in respect of the Cretans, the opposite of his assertion is true, because, on the one hand, between honest and lying are practically a lot of possible nuances and can not qualify any man absolutely alone with these two attributes, and, on the other hand, is again the same distinction, namely, failure to reduce the Class of Cretans to these specific differences (honest Cretans and liar Cretans). So in this case, too, is an agreement: that there is only pair of honest-lying sincategorematic categories and Class of Cretans, as being given, must necessarily be determined by one of these categories. This paradox of a well-deserved fame, has the gift to show us a much clearer, even with its flaws, the training of the antinomy of pure reason and its place in the landscape of thought. What is Convention (in this paradox), as observed, namely, the identity of Epimenide with the Class of Cretans, in the antinomy of pure reason is the very nature of transcendental concepts. This identity of the individuals (as two ways of introducing the same concept, in his attempt to determine itself by a negative reporting to itself) is very indefinite and problematic nature of pure concepts, cosmological essentially, as refers to an

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absolute totality, and can be put in an absolute solitude, in space of representations, only in themselves. Hegel was right when he says that the antinomy of pure reason is not only about the four Kantian categories, but about any other concept or category. Socrates (the greatest lifting to ideas man of all time, as I like to tell) was wont to put all the concepts in reflection with themselves − asking: how is beautiful, beautiful or ugly? − how is good, good or bad? − then pointing thinking of his interlocutors, with an unmatched dexterity, to the pure idea of the absolute untying. * Parmenides, in Plato's dialogue, in the discussion on One, seeking the same thing: a release of absolutely undeterminate in front of knowing consciousness. The whole parmenidean issue is guided by a single underlying principle: something given absolutely, as presence, can not tolerate anything else besides himself − absolute presence (global) can not adjoin to anything, any distinction in her itself, otherness or multiplicity, is impossible. Developing the idea, a little, that absolute presence can not be neighboring even with absolutely vacuum, may be at most replaced with absolute vacuum, with absolute absence, as being equivalent, in their absolute indeterminacy, in front of the consciousness, but this route is impractical and therefore unproductive for thinking. Here's what Parmenides says in a passage: „I want to tell you (but you have now attentively) How many roads may wish to learn the truth: One, that Being is, and may not not be; This is the way of faith (and its follow the truth); The other − that Being is not, nor it should be. This way it (tell you) can not be investigated, For non-Being can not know it (try is futile) Nor talking about it.” (Fragment 4, Diels, Vorsocratiker 4, I, 152 − rendered in its own translation

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by S. Bezdechi in his introduction to Parmenides, 1943 edition, p. 9) Therefore, the discussion can only begin from the assumption „be One” − ie the belief that Something is. That hypothetical release of One (the assumption that there is something) will prove to be, at the end, all that remains from the demonstration approach. Put in relation to any other concept, the One, or breaks, or multiply itself, denying its original status of absolute and unique presence. But, as the One must remain so, are rejected, one by one, all attempts of determination: The One is not like or unlike − not with the other or the self − not with the other, because it would multiply, not with the self, because it would divide and would lose its absolute unity. Similarly, the One can not be either identical or non-identical, or equal or unequal, nor with another or with itself, it is not located, either in space or time, neither a whole nor composed of something, has no size or shape, is not at rest or in motion, because if One had any of these determinations would require something else besides him: the One, as object, besides of the One, as his own measure, as norm, as archetype or absolute landmark in space or time, and thus would be jeopardized its absolute unity. What is the meaning of that negative henology, as he calls Sorin Vieru? In my opinion, this parmenidean demonstration, which has undoubtedly his tragic grandeur, has its subject beyond itself. Its significance lies not in the demonstration technology, which are hidden, in my view, Kant's antinomies (the larval state), nor in the conceptual package that Parmenides is applied on One. This endeavor of knowing consciousness, seemingly endless and futile, to put somehow in front of her the absolute unity, as real presence, it always running ahead and always escape from any attempt of catching it within the limits of a representation, is invaluable precisely through its failure. Under this tragic disclosure of powerlessness of intellect to capture in its forms the

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Undeterminate, under the predestination of intellect to forever fail in any attempt to represent in any way the Undeterminate, knowing consciousness still get, finally, a victory: the fact that she, despite any failure, do not miss the Undeterminate theme, but can put it in front of her again, and again, indefinitely. Ultimate result of this parmenidean exercise is that, through him, knowing consciousness notes precisely her ultimate ability to grasp the absolute being in it themselves, not capture it, not catch it, because each attempt ends in a closing, a determination of it in space of representations, but only to notice its presence. The mere implementation „be One” − find us at the end − is already one of its determination, but one which, apart to its mere metaphysical presence, we can not make any other statement. Thus, negative henologia of Parmenides, that no-no of the One (or neti-neti of the appearance of divine beings, in Eastern mysticism), ending not with a uncertainty, but with the only possible certainty: the thematic presence of One (read Being). The result is, therefore, absolute determination of One to be absolutely undeterminate. But can be man satisfied, ever, only with this alert, only with this indirect determination of Being, namely through its negativity, considering himself too weak to enter in one way or another in possession of Being? Is it enough for humans to stay only in the near of Being and sniff it (as Heidegger says) within the philosophical practice? Absolutely not! Same nature (of the womb that we encountered) has planted in our souls the desire and courage to step forward, namely, to transform that result of a simple thematic disclosure of Undeterminate in front of consciousness, in a ontological disclosure of consciousness as pure Undeterminate − single step that can make possible human connection to a transcendent existence, given absolutely.

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Kant also counted on this overturned result when told about determined consciousness (as ego) that it is the only thing in itself we can observe from the inside, or when he postulated human reason the only possible reason for any intelligent beings in the world, so that universal intelligence. We are, therefore, in front of an authentic amfiboly, ie, one in which determined consciousness (as ego) it overflows its own determinations on another determined consciousness (as collective consciousness), given as a multiple of its, so that as contingent neighborhood, or on the absolute Being, given as proximate genus or as absolute and indefinite presence of a transcendent neighborhood. This amphiboly is already present in the actual formulation of the so-called solution given above, namely that, by Undeterminate, conscience „sees” absolute being in itself. Indeed, this result can be interpreted in two ways: 1. whether as a thematic referral of Being, within the determined consciousness, 2. whether as a ontological referral of Being, in which the consciousness has penetrated, so to speak, by the gate of Undeterminate. The synthetic deployment of this antinomy is that, absolute Being (as pure Undeterminate) is consciousness and consciousness (as pure Undeterminate) is Being. The thematic center is therefore the Undeterminate. Being and consciousness are only two sincategorematic determinations of Undeterminate. Source of the antinomy is the double release of Undeterminate: as absolute absence (no, no − in the Parmenidean release) and as absolute presence, as pure schematisme (and, and − in the Kantian release) − the two equipolent hypostasis (thematic and ontological) of Undeterminate. Here is the diagram:

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The synthetic deployment of this antinomy − which we will call ontological antinomy, since it is not surprising in fact only how determined consciousness relates to itself as a transcendental object − could be the following: Pure Undeterminate, as being, is the pure theme, but since there is nothing outside of him, he is his own conscience or ontological self-reporting. Conversely, if pure Undeterminate is consciousness, ie ontological reference to something, therefore, since there is nothing outside of him, he is thematical reporting to itself as to his own object; is therefore being. Obviously I will not develop here this subject, but I will content to observe that Kantian antinomies sketchiness appeared in ontological antinomy in the posture of a universal sketchiness of Undeterminate in general, put in dialogue with the other form of his indetermination: the absence itself − by taking his play not only the ontological perspective of a presence related to conscience, as in Kant's view, but also the ontic or thematic perspective of a presence reported to itself, as in Hegelian vision, where consciousness arises only as nothingness of being, or in the Heideggerian vision, where self-awareness is raised, as self-ity, in Dasein, to the rank of an absolute determining presence.

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