Infinite and Apeiron

George Cantor is credited with the conceptual construction called transfinite numbers, an endomorphization of the concept of infinite within the system of the real numbers (ℝ). The tool for the construction was the creation of a synthetic representation of the infinite as a whole, familiar to the Platonist Weltanschauung, whose condition of possibility was the natural number, i.e., individuation: infinite is then the result of an endless aggregation. Of course such a representation is not the actual representation of an intuition but the representation of a continuing iterative process, which by its closed condition (the finite character of the algorithm of counting), seems to have a meaning. Once the infinite is an endomorphic concept of the system, any composition with it will be endomorphic, including the notion of transfinite number.

Infinite aggregates can be constructed either by endless iterative processes or by the postulation of properties to which infinite extensions must follow. But the aggregation of units is a synthesis of a different sort than the one obtained by the postulation of a property which has some supposed extension of individuals. In the first case, we proceed inductively, and the whole obtains its meaning from the finitude of the algorithm, even if it cannot be intuited in its infinite performance. In the second, we proceed holistically, and the parts obtain their meaning in relation to the a priori meaning of the whole, i.e., the property. In the first case, we reificate the whole, in the second, the units or parts.

When the parts are themselves processes of aggregation, the reification gets of second order and all sorts of paradoxes grow, for now we are violating both the intuition of iteration (iterating infinities), and the intuition of property (the finite representation of a pairing, for we apply the possibility of the construction of the concept to infinite extensions). In this framework, we meet all sort of nonsensical postulates that mathematics forces us to take dogmatically (for intuitively does not follow) under the disguise of theorems that follow from ontoteological axioms (axiom of substitution, choice, infinitude, union), such as: an infinite set has the same cardinality as one of its subsets, a postulate that can only have meaning under the reification of the extension of the set, metaphysically, or the reification of the iterative process in a non-intuitive scale, metaphysically also, beyond all life experience.

From a mythopoetical point of view, the concept of infinity is a representation of the concept of apeiron, whose form is conditioned by the ontoepistemology of the myths assigned to the space-time intuitions. When space-time is curved, infinity is bounded, i.e, finitized under a property. When space-time is linear, infinity is unbounded, finitized under a process of iteration. When space-time is liminal, infinity is just apeiron.

Matter and Idea II

In relation to the semantic operator matter/idea, my concern is with the old ontological assumptions that are inherited and assumed unnoticed in its use, its implicit reifications. Physics does not speak anymore about matter. Fermions, the particles which are thought to be matter-like (in opposition to the force carrier bosons) make only sense within the whole system, which implies that matter is not material in the traditional sense, but some sort of symbolic construction that we use to understand an apeironic experience. For instance the Weyl-fermions are massless, which means a massless matter, if such an expression has any meaning at all. In this sense is very different to old Greco-Roman atomic constructions. And things do not get any better if we try to switch the matter representation for the concept of energy. According to Maxwell’s definition: energy is the capacity of a system to perform mechanical work (1891), but in order for the definition to have any meaning we already have to know the concepts of system and mechanical work (and its associated intuitions), we need a Lebenswelt praxis to construct upon.

Psychology, on the other hand is showing that ideas are not independent of the vital process (unless we assume them a priori to be so), and that even perception is conditioned by emotional valuations, id est, the relation object/subject is more complex than it was thought to be, I would say mimetic. The reference for matter and idea is mind, but mind is not an exomorphic representation, for we can think it in terms of life processes, and for those processes we can take as an anthropological departing point the system of mythical interpretation with its economical and primitive determinations (as I have explained these concepts in Mythopoetics). In this sense ideas are determined not only by Lebenswelt butalso by what we could call Unterlebenswelt, valuations on a physiological levelprior to the symbolizations of human language. My opinion is that we need some sort of metaphilosophical system to encompass such a wide and complex scope of conceptualizations that independent sciences cannot think. It does not have to be reductionistic, neither depart from a unique ontoepistemology but simply define a basic framework for the treatment of the emergence of all these new complex relations, in myths harmonized with our ways of life.

It is not so much that matter has become more ideal and ideas more material, as a question of the obsolescence of the old semantic dual operator.

Matter and Idea

A.

1   1. A major objection to materialism: matter is a narrative construction of vital experience.

Argument: the changing conception of matter through time.

Objection: But today we have the accurate description, and therefore, somehow the description represents a morphism (even isomorphism).

Answer: we could not know it, and in any case, it would be a description, i.e., a narrative, for any communicative account is narrative.

2    2. The concept of matter is conditioned by communicative action.

B.

1     1. A major objection to idealism: ideas are compositions of concepts which have as final referents vital experience. Natural numbers and other basic concepts are basic intuitions of experience (sequence, synthesis, analysis and so on).

Argument: the sense of numerosity in animals. The intuitive set theory in the epistemologies of anima mundi (totem thinking is a basic form of set theory).

Objection: But vital experience is nothing without ideas that valuate and give it a meaning.

Answer: The valuation is done in a cognitive level previous to the human conceptualization. Ideas must have relevance for survival. In fact, they are the result of an n-aryzation (or complexification) of basic emotions (as protocols for survival), which evolve in the context of communicative action.

2     2. The notion of idea is conditioned by communicative action.

C.

The concepts of matter and idea are communicative concepts, mythic actions which render vital experience (as exomorphic, final, or literal, or liminal representation) within a symbolic system, i.e., as endomorphic, or metaphorical or liminoid representations.

Continues in Matter and Idea II

Historical Consciousness and Mythologization Paper presented at the 65th North West Annual Philosophy Conference. October, 5th. 2013. Pacific University, Forest Grove, Oregon.

The thesis of this lecture is that any historical reflection is an interpretative construction of the experience of the passage of time which is ontoepistemologically conditioned by the determinations of human material existence. Such a construction is an endomorphic process of representation of experience, a metaphorical rendering of the world in familiar terms, a mythologization. This process is not unique to traditional myths and history, but also to science and philosophy, in fact, philosophy of history is a mythologizing action.

Let me construct an argument for this thesis.

Canon and Narratives of Domination

 The idea of a literary canon is a variation of traditional censorship that makes only sense in the general processes of enculturation and development of narratives of domination. It certainly helps the teacher to reduce the number of candidates to be read on a classroom, but does a poor service to creativity endlessly repeating a transcendental pattern of inspired geniuses giving the law (literary or otherwise) to an ignorant humankind. When some years ago Harold Bloom made his famous top-ten hits in the History of Literature, leaving Hamlet and Don Quixote to play a very disputed final, after a disqualifying process of other literary works, he was consciously marking a censorship general reference, a nihil obstat for future works that creates an unreasonable mortgage for future generations. Media industry (publishing houses and general audiovisual ones) benefits from this trivial pursuit endeavors as much as the lover of literature is impaired. We do not read the way people read 100 years ago or 1.000. In fact, the web is reshaping the publishing world and the art of literature faster than ever before. The ratio et auctoritas of the censor has only place in medieval societies where the citizen remains forever a child, not in a society centered around the narratives of the human law. The idea of the canon would finally disappear once it is understood that to a desert island is better to bring paper and pen than any particular book, for writing and reading are self-constructing tools (both socially and individually) that expand our memory capabilities, allowing the construction of more rich and deeper realities. 

Haikai and Zen

 

My relation to Japanese aesthetics began with a course in Zen that I took at the University of Buffalo, back in another lifetime, in the land of the Tonawandas. The teacher was a Korean ex-monk sent to the West by his master to spread Buddhism. I actually dropped the course during the first week, for the main book was Nature (yes, he wrote it on the board with a capital N), and I believed him. I invited him over for tea and discussed the Capture of the Ox, an allegory of the spiritual quest wonderfully depicted in ancient drawings on a book by Dasetz Suzuki. In those days, I still believed in the idea of finding oneself, as if I was a pair of lost keys in the sands of time, and therefore, in the idea of stages in an imaginary trip to the nowhere land of bliss and truth, precisely the theme of the Ox Hunt. I asked him in which of the 10 stations of the spiritual journey was thriving and answered -to my delight- that sometimes in 5, others in 10, but then again dropping to 1, and so on. We laughed for quite a while. I never saw him again, I did not call him or went back to his classes at the University, for I did not want to break the lightning clarity of that sparkling moment.

  As I understand the Haikai, they are about such lightning clarity, a rare phenomenon in the poetic arena that requires both effort and spontaneity, a combination that can only be synthesized in the limits of the human psyche.

What Makes a Text to be a Poem

With this question I do not imply the distinction between true poem and false poem, for I don’t believe in it, but rather, what properties must have a text to be identified as a poem? It is a subject that I have entertained for long and I would like to open a debate giving some possible answers.

Traditionally, it was meter and rhyme, or, in a broader sense, formal properties of sound the reference frame for our qualification. Archaic poetry was still linked to the constraints of memory of oral tradition, and formal properties gave an easy and understandable protocol. Such a categorization opens up a clear understanding of early poetry, its connexion with shaman incantations and magic, long before writing, in the world of the myths of anima mundi. But the question became a bit more entangled when philosophy entered the scene. The philosophical poems of Parmenides, Empedocles, and other presocratics had the formal properties of sound of, say, Homer, or Ibicus, but the subject matter was so different that it was rather arbitrary to assign them to a same genre.

    But is there an specific content which we can call poetic? I have identified the beginnings of an inner realm of expression in Egypt and Mesopotamia derived from the recitation of the ritual texts which ended up giving the core of an emotional dimension generally accepted and identified as poetic. I call this the lyrical citizen, and as I have analyzed it somewhere else, is related to the extensions of the idea of immortality to all citizens at large which begun in Egypt after XVI B.C. as a narrative creation of the Priests of Osiris. The realm of the lyrical citizen is constituted by the difference between his/her social persona (the persona linked to a specific economic activity) and a narrative transcendental persona which he or she considers to give a deeper form of identity. The lyrical citizen is the lyrical I, which is independent of the economic action, a persona invested with all the properties created by immortality myths.

    We then have the formal properties of sound and the realm of the lyrical citizen that put together would give a criterion to answer our question. Modern poetry, like modern music, changed the sound properties very dramatically extending the rhythmic, harmonic and formal realms far beyond tradition, so we should, of course, consider formal properties of sound in this extended sense. Even the realm of the lyrical citizen has been extended to encompass a vast world of emotions which, although rooted in them, not necessarily follow the transcendental patterns established by old poetry.

Nonetheless, we could find examples of prose works which could defy such a simple characterization. Lezama Lima’s Paradiso is a clear example, among others of an extended list. A third criterion could be added which modifies both the two aforementioned giving an hypothetical  continuum of literary works: the semantic density of the images. Ceteris paribus, we tend to consider more poetic a text that builds a denser web of semantic relations.

The Taming of the Artist

 Over the past century, the performing arts have tried to abandon the traditional social settings in favor of new scenarios for the representation of the work of art. This simple action increases the liminality of performance, for the ritual needs closed and well established scenarios. The resistance to such changes comes mainly from the general public, which needs to identify the performative actions within a mythical-ritual axis in order to give it credit. Such an authority valuates art from the point of view of ancient mythological actions. This produces a curious paradox. On the one hand, the general public desires and looks for the unanimity of criteria in relation to the work of art, it is the desire for a universal law. We need judgments like: “Beethoven's immortal symphonies”, even when we never took the time to listen to all of them in order to justify such a criterion. On the other, we want the artist to be original, which implies the impossibility of a consensus in relation to his/her work, for there are not clear grounds for the judgment. This way, the artist is tamed by the whip of traditional art forms. His/hers only escape is the neurosis of an excessive individuality, which is always judged in relation to the traditional art form, so even his individuality becomes part of the same whip. The only way out for the artist is the direct work over the narratives of identity, but this implies a form of art which is not yet recognized as such.

On the Beautiful and the Sublime

  I have heard a peasant calling beautiful the ordered disposition of his farm, or what he called ordered, an invisible pattern of work superimposed to the land, together with its expectancies, projects and dreams. Homer came to mind, calling beautiful the wind when it blew the sail in a propitious manner. How conditioned to our basic emotions our sense of beauty! The best poets have n-arized them so much that they seem new entities. And these entities, when they are related to the social emotions give the ground for our modern sense of beauty. Sexual attraction, the tool for the perpetuation of the species, became the cosmic force of a blessed existence, the rewards of paradise, the inexhaustible fountain of energy and delight. Motherhood, no less divine and beautiful in our songs, gave a model for the understanding of the universe, and we contemplate it through the eyes of art in religious ecstasy, i.e., in a self-reassuring communal action.

  What do we mean when we say that a person is beautiful? Besides the mating intentions, conscious or unconscious, it is basically an statement of approval, the fact that someone fits in our plans, in a narrative about life and ourselves that can be more or less transcendentalized, but that expresses basically the emotion of the peasant in relation to his land. And what do we mean when we say that a thing or an action is beautiful? Well, the very same statement of approval. The concept of beautiful is related to property and possession, to the actions of pertaining and belonging, which imply a narrative of identity, which demand the reassurance of identity. In this sense is opposed to the experience of the sublime, which annihilates identity. Our concept of beautiful shows our limitations, the frontiers of our individuation, our narrative of identity, and therefore, is a secondary concept for the artist of the limen, like a subsidiary reference frame forgotten when the adventure of creation begins. 

Composición Liminal

Podríamos clasificar las obras musicales en tres grandes grupos conforme a que sus estéticas sean duales, formales, o liminales, que se corresponden, más o menos, con los grupos que Lorca llamara del ángel, la musa y el duende.

Biological and Astronomical Time

The intuition of the passage of time is linked to the action performed. Physiological actions condition the pacing of the economical actions we perform in the world, actions whose purpose is the homeostasis of the social and individual organism, i.e., to maintain the physiological actions going on. Our sense of time is constituted by the morphisms between our individual physiology (actually, the common physiology we share with the others) and the physiology of the group, which in turn is conditioned by the environment, and therefore, by the astrobiological frame. This basic sense of time is modified by the narratives about time, by the symbolic structures that we construct to evaluate our vital experience, which include either consciously (Überlebenswelt) or unconsciously (Lebenswelt and Unterlebenswelt) notions about time and its intuition. From the point of view of continuous rationality, our formal scientific theories about time are just n-aryzations of our basic emotions and therefore projections of our basic intuitions and biological processes. Astronomical time is but an endomorphism of biological time. This is observable in the traditional narratives of immortality. The other worlds are but images of this one, realms where biological time and economical actions mimic those of our ordinary life, family relations and economic activities. In the cases where a more astronomical sense of time is included, those Ba narratives in which the deceased subject is not a human or a biological being anymore (began in Egypt by the Osiris Priests), the scenarios become inevitably fuzzy. But something analogous happens with the scenarios of cosmology of modern physics, when numbers enter the realm of the continuum of the first second, and there is no more a subject (for those temporalities are not biological) but a metaphysical narrative of a neverland.