Mathematical Reductionism: As Case Via C. S. Peirce’s Hypothetical Realism.

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During the 20th century, the following epistemology of mathematics was predominant: a sufficient condition for the possibility of the cognition of objects is that these objects can be reduced to set theory. The conditions for the possibility of the cognition of the objects of set theory (the sets), in turn, can be given in various manners; in any event, the objects reduced to sets do not need an additional epistemological discussion – they “are” sets. Hence, such an epistemology relies ultimately on ontology. Frege conceived the axioms as descriptions of how we actually manipulate extensions of concepts in our thinking (and in this sense as inevitable and intuitive “laws of thought”). Hilbert admitted the use of intuition exclusively in metamathematics where the consistency proof is to be done (by which the appropriateness of the axioms would be established); Bourbaki takes the axioms as mere hypotheses. Hence, Bourbaki’s concept of justification is the weakest of the three: “it works as long as we encounter no contradiction”; nevertheless, it is still epistemology, because from this hypothetical-deductive point of view, one insists that at least a proof of relative consistency (i.e., a proof that the hypotheses are consistent with the frequently tested and approved framework of set theory) should be available.

Doing mathematics, one tries to give proofs for propositions, i.e., to deduce the propositions logically from other propositions (premisses). Now, in the reductionist perspective, a proof of a mathematical proposition yields an insight into the truth of the proposition, if the premisses are already established (if one has already an insight into their truth); this can be done by giving in turn proofs for them (in which new premisses will occur which ask again for an insight into their truth), or by agreeing to put them at the beginning (to consider them as axioms or postulates). The philosopher tries to understand how the decision about what propositions to take as axioms is arrived at, because he or she is dissatisfied with the reductionist claim that it is on these axioms that the insight into the truth of the deduced propositions rests. Actually, this epistemology might contain a short-coming since Poincaré (and Wittgenstein) stressed that to have a proof of a proposition is by no means the same as to have an insight into its truth.

Attempts to disclose the ontology of mathematical objects reveal the following tendency in epistemology of mathematics: Mathematics is seen as suffering from a lack of ontological “determinateness”, namely that this science (contrarily to many others) does not concern material data such that the concept of material truth is not available (especially in the case of the infinite). This tendency is embarrassing since on the other hand mathematical cognition is very often presented as cognition of the “greatest possible certainty” just because it seems not to be bound to material evidence, let alone experimental check.

The technical apparatus developed by the reductionist and set-theoretical approach nowadays serves other purposes, partly for the reason that tacit beliefs about sets were challenged; the explanations of the science which it provides are considered as irrelevant by the practitioners of this science. There is doubt that the above mentioned sufficient condition is also necessary; it is not even accepted throughout as a sufficient one. But what happens if some objects, as in the case of category theory, do not fulfill the condition? It seems that the reductionist approach, so to say, has been undocked from the historical development of the discipline in several respects; an alternative is required.

Anterior to Peirce, epistemology was dominated by the idea of a grasp of objects; since Descartes, intuition was considered throughout as a particular, innate capacity of cognition (even if idealists thought that it concerns the general, and empiricists that it concerns the particular). The task of this particular capacity was the foundation of epistemology; already from Aristotle’s first premisses of syllogism, what was aimed at was to go back to something first. In this traditional approach, it is by the ontology of the objects that one hopes to answer the fundamental question concerning the conditions for the possibility of the cognition of these objects. One hopes that there are simple “basic objects” to which the more complex objects can be reduced and whose cognition is possible by common sense – be this an innate or otherwise distinguished capacity of cognition common to all human beings. Here, epistemology is “wrapped up” in (or rests on) ontology; to do epistemology one has to do ontology first.

Peirce shares Kant’s opinion according to which the object depends on the subject; however, he does not agree that reason is the crucial means of cognition to be criticised. In his paper “Questions concerning certain faculties claimed for man”, he points out the basic assumption of pragmatist philosophy: every cognition is semiotically mediated. He says that there is no immediate cognition (a cognition which “refers immediately to its object”), but that every cognition “has been determined by a previous cognition” of the same object. Correspondingly, Peirce replaces critique of reason by critique of signs. He thinks that Kant’s distinction between the world of things per se (Dinge an sich) and the world of apparition (Erscheinungswelt) is not fruitful; he rather distinguishes the world of the subject and the world of the object, connected by signs; his position consequently is a “hypothetical realism” in which all cognitions are only valid with reservations. This position does not negate (nor assert) that the object per se (with the semiotical mediation stripped off) exists, since such assertions of “pure” existence are seen as necessarily hypothetical (that means, not withstanding philosophical criticism).

By his basic assumption, Peirce was led to reveal a problem concerning the subject matter of epistemology, since this assumption means in particular that there is no intuitive cognition in the classical sense (which is synonymous to “immediate”). Hence, one could no longer consider cognitions as objects; there is no intuitive cognition of an intuitive cognition. Intuition can be no more than a relation. “All the cognitive faculties we know of are relative, and consequently their products are relations”. According to this new point of view, intuition cannot any longer serve to found epistemology, in departure from the former reductionist attitude. A central argument of Peirce against reductionism or, as he puts it,

the reply to the argument that there must be a first is as follows: In retracing our way from our conclusions to premisses, or from determined cognitions to those which determine them, we finally reach, in all cases, a point beyond which the consciousness in the determined cognition is more lively than in the cognition which determines it.

Peirce gives some examples derived from physiological observations about perception, like the fact that the third dimension of space is inferred, and the blind spot of the retina. In this situation, the process of reduction loses its legitimacy since it no longer fulfills the function of cognition justification. At such a place, something happens which I would like to call an “exchange of levels”: the process of reduction is interrupted in that the things exchange the roles performed in the determination of a cognition: what was originally considered as determining is now determined by what was originally considered as asking for determination.

The idea that contents of cognition are necessarily provisional has an effect on the very concept of conditions for the possibility of cognitions. It seems that one can infer from Peirce’s words that what vouches for a cognition is not necessarily the cognition which determines it but the livelyness of our consciousness in the cognition. Here, “to vouch for a cognition” means no longer what it meant before (which was much the same as “to determine a cognition”), but it still means that the cognition is (provisionally) reliable. This conception of the livelyness of our consciousness roughly might be seen as a substitute for the capacity of intuition in Peirce’s epistemology – but only roughly, since it has a different coverage.

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Meillassoux, Deleuze, and the Ordinal Relation Un-Grounding Hyper-Chaos. Thought of the Day 41.0

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As Heidegger demonstrates in Kant and the Problem of Metaphysics, Kant limits the metaphysical hypostatization of the logical possibility of the absolute by subordinating the latter to a domain of real possibility circumscribed by reason’s relation to sensibility. In this way he turns the necessary temporal becoming of sensible intuition into the sufficient reason of the possible. Instead, the anti-Heideggerian thrust of Meillassoux’s intellectual intuition is that it absolutizes the a priori realm of pure logical possibility and disconnects the domain of mathematical intelligibility from sensibility. (Ray Brassier’s The Enigma of Realism: Robin Mackay – Collapse_ Philosophical Research and Development. Speculative Realism.) Hence the chaotic structure of his absolute time: Anything is possible. Whereas real possibility is bound to correlation and temporal becoming, logical possibility is bound only by non-contradiction. It is a pure or absolute possibility that points to a radical diachronicity of thinking and being: we can think of being without thought, but not of thought without being.

Deleuze clearly situates himself in the camp when he argues with Kant and Heidegger that time as pure auto-affection (folding) is the transcendental structure of thought. Whatever exists, in all its contingency, is grounded by the first two syntheses of time and ungrounded by the third, disjunctive synthesis in the implacable difference between past and future. For Deleuze, it is precisely the eternal return of the ordinal relation between what exists and what may exist that destroys necessity and guarantees contingency. As a transcendental empiricist, he thus agrees with the limitation of logical possibility to real possibility. On the one hand, he thus also agrees with Hume and Meillassoux that [r]eality is not the result of the laws which govern it. The law of entropy or degradation in thermodynamics, for example, is unveiled as nihilistic by Nietzsche s eternal return, since it is based on a transcendental illusion in which difference [of temperature] is the sufficient reason of change only to the extent that the change tends to negate difference. On the other hand, Meillassoux’s absolute capacity-to-be-other relative to the given (Quentin Meillassoux, Ray Brassier, Alain Badiou – After finitude: an essay on the necessity of contingency) falls away in the face of what is actual here and now. This is because although Meillassoux s hyper-chaos may be like time, it also contains a tendency to undermine or even reject the significance of time. Thus one may wonder with Jon Roffe (Time_and_Ground_A_Critique_of_Meillassou) how time, as the sheer possibility of any future or different state of affairs, can provide the (non-)ground for the realization of this state of affairs in actuality. The problem is less that Meillassoux’s contingency is highly improbable than that his ontology includes no account of actual processes of transformation or development. As Peter Hallward (Levi Bryant, Nick Srnicek and Graham Harman (editors) – The Speculative Turn: Continental Materialism and Realism) has noted, the abstract logical possibility of change is an empty and indeterminate postulate, completely abstracted from all experience and worldly or material affairs. For this reason, the difference between Deleuze and Meillassoux seems to come down to what is more important (rather than what is more originary): the ordinal sequences of sensible intuition or the logical lack of reason.

But for Deleuze time as the creatio ex nihilo of pure possibility is not just irrelevant in relation to real processes of chaosmosis, which are both chaotic and probabilistic, molecular and molar. Rather, because it puts the Principle of Sufficient Reason as principle of difference out of real action it is either meaningless with respecting to the real or it can only have a negative or limitative function. This is why Deleuze replaces the possible/real opposition with that of virtual/actual. Whereas conditions of possibility always relate asymmetrically and hierarchically to any real situation, the virtual as sufficient reason is no less real than the actual since it is first of all its unconditioned or unformed potential of becoming-other.

Topological Drifts in Deleuze. Note Quote.

Brion Gysin: How do you get in… get into these paintings?

William Burroughs: Usually I get in by a port of entry, as I call it. It is often a face through whose eyes the picture opens into a landscape and I go literally right through that eye into that landscape. Sometimes it is rather like an archway… a number of little details or a special spot of colours makes the port of entry and then the entire picture will suddenly become a three-dimensional frieze in plaster or jade or some other precious material.

The word fornix means “an archway” or “vault” (in Rome, prostitutes could be solicited there). More directly, fornicatio means “done in the archway”; thus a euphemism for prostitution.

Diagrammatic praxis proposes a contractual (push, pull) approach in which the movement between abstract machine, biogram (embodied, inflected diagram), formal diagram (drawing of, drawing off) and artaffect (realized thing) is topologically immanent. It imagines the practice of writing, of this writing, interleaved with the mapping processes with which it folds and unfolds – forming, deforming and reforming both processes. The relations of non-relations that power the diagram, the thought intensities that resonate between fragments, between content ad expression, the seeable and the sayable, the discursive and the non-discursive, mark entry points; portals of entry through which all points of the diagram pass – push, pull, fold, unfold – without the designation of arrival and departure, without the input/output connotations of a black boxed confection. Ports, as focal points of passage, attract lines of resistance or lines of flight through which the diagram may become both an effectuating concrete assemblage (thing) and remain outside the stratified zone of the audiovisual. It’s as if the port itself is a bifurcating point, a figural inflected archway. The port, as a bifurcation point of resistance (contra black box), modulates and changes the unstable, turbulent interplay between pure Matter and pure Function of the abstract machine. These ports are marked out, localized, situated, by the continuous movement of power-relations:

These power-relations … simultaneously local, unstable and diffuse, do not emanate from a central point or unique locus of sovereignty, but at each moment move from one point to another in a field of forces, marking inflections, resistances, twists and turns when one changes direction or retraces one’s steps… (Gilles Deleuze, Sean Hand-Foucault)

An inflection point, marked out by the diagram, is not a symmetrical form but the difference between concavity and convexity, a pure temporality, a “true atom of form, the true object of geography.” (Bernard Cache)

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Figure: Left: A bifurcating event presented figurally as an archway, a port of entry through order and chaos. Right: Event/entry with inflexion points, points of suspension, of pure temporality, that gives a form “of an absolute exteriority that is not even the exteriority of any given interiority, but which arise from that most interior place that can be perceived or even conceived […] that of which the perceiving itself is radically temporal or transitory”. The passing through of passage.

Cache’s absolute exteriority is equivalent to Deleuze’s description of the Outside “more distant than any exterior […] ‘twisted’, folded and doubled by an Inside that is deeper than any interior, and alone creates the possibility of the derived relation between the interior and the exterior”. This folded and doubled interior is diagrammed by Deleuze in the folds chapter of Foucault.

Thinking does not depend on a beautiful interiority that reunites the visible ad articulable elements, but is carried under the intrusion of an outside that eats into the interval and forces or dismembers the internal […] when there are only environments and whatever lies betwen them, when words and things are opened up by the environment without ever coinciding, there is a liberation of forces which come from the outside and exist only in a mixed up state of agitation, modification and mutation. In truth they are dice throws, for thinking involves throwing the dice. If the outside, farther away than any external world, is also closer than any internal world, is this not a sign that thought affects itself, by revealing the outside to be its own unthought element?

“It cannot discover the unthought […] without immediately bringing the unthought nearer to itself – or even, perhaps, without pushing it farther away, and in any case without causing man’s own being to undergo a change by the very fact, since it is deployed in the distance between them” (Gilles Deleuze, Sean Hand-Foucault)

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Figure: Left: a simulation of Deleuze’s central marking in his diagram of the Foucaultian diagram. This is the line of the Outside as Fold. Right: To best express the relations of diagrammatic praxis between content and expression (theory and practice) the Fold figure needs to be drawn as a double Fold (“twice twice” as Massumi might say) – a folded möbius strip. Here the superinflections between inside/outside and content/expression provide transversal vectors.

A topology or topological becoming-shapeshift retains its connectivity, its interconnectedness to preserve its autonomy as a singularity. All the points of all its matter reshape as difference in itself. A topology does not resemble itself. The möbius strip and the infamous torus-to-coffe cup are examples of 2d and 3d topologies. technically a topological surface is totalized, it can not comprise fragments cut or glued to produce a whole. Its change is continuous. It is not cut-copy-pasted. But the cut and its interval are requisite to an emergent new.

For Deleuze, the essence of meaning, the essence of essence, is best expressed in two infinitives; ‘to cut ” and “to die” […] Definite tenses keeping company in time. In the slash between their future and their past: “to cut” as always timeless and alone (Massumi).

Add the individuating “to shift” to the infinitives that reside in the timeless zone of indetermination of future-past. Given the paradigm of the topological-becoming, how might we address writing in the age of copy-paste and hypertext? The seamless and the stitched? As potential is it diagram? A linguistic multiplicity whose virtual immanence is the metalanguage potentiality between the phonemes that gives rise to all language?

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An overview diagram of diagrammatic praxis based on Deleuze’s diagram of the Foucaultian model shown below. The main modification is to the representation of the Fold. In the top figure, the Fold or zone of subjectification becomes a double-folded möbius strip.

Four folds of subjectification:

1. material part of ourselves which is to be surrounded and folded

2. the fold of the relation between forces always according to a particular rule that the relation between forces is bent back in order to become a relation to oneself (rule ; natural, divine, rational, aesthetic, etc)

3. fold of knowledge constitutes the relation of truth to our being and our being to truth which will serve as the formal condition for any kind of knowledge

4. the fold of the outside itself is the ultimate fold: an ‘interiority of expectation’ from which the subject, in different ways, hopes for immortality, eternity, salvation, freedom or death or detachment.

Causality

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Causation is a form of event generation. To present an explicit definition of causation requires introducing some ontological concepts to formally characterize what is understood by ‘event’.

The concept of individual is the basic primitive concept of any ontological theory. Individuals associate themselves with other individuals to yield new individuals. It follows that they satisfy a calculus, and that they are rigorously characterized only through the laws of such a calculus. These laws are set with the aim of reproducing the way real things associate. Specifically, it is postulated that every individual is an element of a set s in such a way that the structure S = ⟨s, ◦, ◻⟩ is a commutative monoid of idempotents. This is a simple additive semi-group with neutral element.

In the structure S, s is the set of all individuals, the element ◻ ∈ s is a fiction called the null individual, and the binary operation ◦ is the association of individuals. Although S is a mathematical entity, the elements of s are not, with the only exception of ◻, which is a fiction introduced to form a calculus. The association of any element of s with ◻ yields the same element. The following definitions characterize the composition of individuals.

1. x ∈ s is composed ⇔ (∃ y, z) s (x = y ◦ z)
2. x ∈ s is simple ⇔ ∼ (∃ y, z) s (x = y ◦ z)
3. x ⊂ y ⇔ x ◦ y = y (x is part of y ⇔ x ◦ y = y)
4. Comp(x) ≡ {y ∈ s|y ⊂ x} is the composition of x.

Real things are distinguished from abstract individuals because they have a number of properties in addition to their capability of association. These properties can be intrinsic (Pi) or relational (Pr). The intrinsic properties are inherent and they are represented by predicates or unary applications, whereas relational properties depend upon more than a single thing and are represented by n-ary predicates, with n ≥ 1. Examples of intrinsic properties are electric charge and rest mass, whereas velocity of macroscopic bodies and volume are relational properties.

An individual with its properties make up a thing X : X =< x, P(x) >

Here P(x) is the collection of properties of the individual x. A material thing is an individual with concrete properties, i.e. properties that can change in some respect.

The state of a thing X is a set of functions S(X) from a domain of reference M (a set that can be enumerable or nondenumerable) to the set of properties PX. Every function in S(X) represents a property in PX. The set of the physically accessible states of a thing X is the lawful state space of X : SL(X). The state of a thing is represented by a point in SL(X). A change of a thing is an ordered pair of states. Only changing things can be material. Abstract things cannot change since they have only one state (their properties are fixed by definition).

A legal statement is a restriction upon the state functions of a given class of things. A natural law is a property of a class of material things represented by an empirically corroborated legal statement.

The ontological history h(X) of a thing X is a subset of SL(X) defined by h(X) = {⟨t, F(t)⟩|t ∈ M}

where t is an element of some auxiliary set M, and F are the functions that represent the properties of X.

If a thing is affected by other things we can introduce the following definition:

h(Y/X ) : “history of the thing Y in presence of the thing X”.

Let h(X) and h(Y) be the histories of the things X and Y, respectively. Then

h(Y/X) = {⟨t,H(t)⟩|t ∈ M},

where H≠ F is the total state function of Y as affected by the existence of X, and F is the total state function of X in the absence of Y. The history of Y in presence of X is different from the history of Y without X .

We can now introduce the notion of action:

X ▷ Y : “X acts on Y”

X ▷ Y =def h(Y/X) ≠ h(Y)

An event is a change of a thing X, i.e. an ordered pair of states:

(s1, s2) ∈ EL(X) = SL(X) × SL(X)

The space EL(X) is called the event space of X.

Causality is a relation between events, i.e. a relation between changes of states of concrete things. It is not a relation between things. Only the related concept of ‘action’ is a relation between things. Specifically,

C'(x): “an event in a thing x is caused by some unspecified event exxi“.

C'(x) =def (∃ exxi) [exxi ∈ EL(X) ⇔ xi ▷ x.

C(x, y): “an event in a thing x is caused by an event in a thing y”.

C(x, y) =def (∃ exy) [exy ∈ EL(x) ⇔ y ▷ x

In the above definitions, the notation exy indicates in the superscript the thing x to whose event space belongs the event e, whereas the subscript denotes the thing that acted triggering the event. The implicit arguments of both C’ and C are events, not things. Causation is a form of event generation. The crucial point is that a given event in the lawful event space EL(x) is caused by an action of a thing y iff the event happens only conditionally to the action, i.e., it would not be the case of exy without an action of y upon x. Time does not appear in this definition, allowing causal relations in space-time without a global time orientability or even instantaneous and non-local causation. If causation is non-local under some circumstances, e.g. when a quantum system is prepared in a specific state of polarization or spin, quantum entanglement poses no problem to realism and determinism. The quantum theory describes an aspect of a reality that is ontologically determined and with non-local relations. Under any circumstances the postulates of Special Relativity are violated, since no physical system ever crosses the barrier of the speed of light.

Egyptology

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The ancient Egyptians conceived man and kosmos to be dual: firstly, the High God or Divine Mind arose out of the Primeval Waters of space at the beginning of manifestation; secondly, the material aspect expressing what is in the Divine Mind must be in a process of ever-becoming. In other words, the kosmos consists of body and soul. Man emanated in the image of divinity is similarly dual and his evolutionary goal is a fully conscious return to the Divine Mind.

Space, symbolized by the Primeval Waters, contains the seeds and possibilities of all living things in their quiescent state. At the right moment for awakenment, all will take up forms in accordance with inherent qualities. Or to express it in another way: the Word uttered by the Divine Mind calls manifested life to begin once more.

Growth is effected through a succession of lives, a concept that is found in texts and implied in symbolism. Herodotus, the Greek historian (5th century B.C.), wrote that

the Egyptians were the first to teach that the human soul is immortal, and at the death of the body enters into some other living thing then coming to birth; and after passing through all creatures of land, sea, and air (which cycle it completes in three thousand years) it enters once more into a human body, at birth.

The theory of reincarnation is often ascribed to Pythagoras, since he spent some time in Egypt studying its philosophy and, according to Herodotus, “adopted this opinion as if it were his own.”

Margaret A. Murray, who worked with Flinders Petrie, illustrates the Egyptian belief by referring to the ka-names of three kings (The ka-name relates to the vital essence of an individual); the first two of the twelfth dynasty: that of Amonemhat I means “He who repeats births,” Senusert I: “He whose births live,” and the ka-name of Setekhy I of the nineteenth dynasty was “Repeater of births.” (The Splendour That Was Egypt)

Reincarnation has been connected with the rites of Osiris, one of the Mysteries or cycles of initiation perpetuated in Egypt. The concept of transformation as recorded in the Egyptian texts has been interpreted in various ways. De Briere expresses it in astronomical terms: “The sensitive soul re-entered by the gate of the gods, or the Capricorn, into the Amenthe, the watery heavens, where it dwelt always with pleasure; until, descending by the gate of men, or the Cancer, it came to animate a new body.” Herodotus writes of transmigration, i.e., that the soul passes through various animals before being reborn in human form. This refers not to the human soul but to the molecules, atoms, and other components that clothe it. They gravitate to vehicles similar in qualities to their former host’s, drawn magnetically to the new milieu by the imprint made by the human soul, whether it be fine or gross. It is quite clear from the Book of the Dead and other texts that the soul itself after death undergoes experiences in the Duat (Dwat) or Underworld, the realm and condition between heaven and earth, or beneath the earth, supposedly traversed by the sun from sunset to sunrise.

The evolution of consciousness is symbolized by the Solar Barque moving through the Duat. In this context the “hours” of travel represent stages of development. Bika Reed states that at a certain “hour” the individual meets the “Rebel in the Soul,”  that is, at the “hour of spiritual transformation.” And translating from the scroll Reed gives: “the soul warns, only if a man is allowed to continue evolving, can the intellect reach the heart.”

Not only does the scripture deal with rituals assumed to apply to after-death conditions — in some respects similar to the Book of the Dead — but also it seems quite patently a ritual connected with initiation from one level of self-becoming to another. Nevertheless the picture that emerges is that of the “deceased” or candidate for initiation reaching a fork offering two paths called “The Two Paths of Liberation” and, while each may take the neophyte to the abode of the Akhu (the “Blessed”) — a name for the gods, and also for the successful initiates — they involve different experiences. One path, passing over land and water, is that of Osiris or cyclic nature and involves many incarnations. The other way leads through fire in a direct or shortened passage along the route of Horus who in many texts symbolizes the divine spark in the heart.

In the Corpus Hermeticum, Thoth — Tehuti — was the Mind of the Deity, whom the Alexandrian Greeks identified with Hermes. For example, one of the chief books in the Hermetica is the Poimandres treatise, or Pymander. The early trinity Atum-Ptah-Thoth was rendered into Greek as theos (god) — demiourgos or demourgos-nous (Demiurge or Demiurgic Mind) — nous and logos (Mind and Word). The text states that Thoth, after planning and engineering the kosmos, unites himself with the Demiurgic Mind. There are other expressions proving that the Poimandres text is a Hellenized version of Egyptian doctrine. An important concept therein is that of “making-new-again.” The treatise claims that all animal and vegetable forms contain in themselves “the seed of again-becoming” — a clear reference to reimbodiment — “every birth of flesh ensouled . . . shall of necessity renew itself.” G. R. S. Mead interprets this as palingenesis or reincarnation — “the renewal on the karmic wheel of birth-and-death.” (Thrice-Greatest Hermes)

The Corpus Hermeticum or Books of Hermes are believed by some scholars to have been borrowed from Christian texts, but their concepts are definitely ancient Egyptian in origin, translated into Alexandrian Greek, and Latin.

Looking at Walter Scott’s translation of Poimandres, it states that “At the dissolution of your material body, you first yield up the body itself to be changed,” and it will be absorbed by nature. The rest of the individual’s components return to “their own sources, becoming parts of the universe, and entering into fresh combinations to do other work.” After this, the real or inner man “mounts upward through the structure of the heavens,” leaving off in each of the seven zones certain energies and related substances. The first zone is that of the Moon; the second, the planet Mercury; the third, Venus; fourth, the Sun; fifth, Mars; sixth, Jupiter; and seventh, Saturn. “Having been stripped of all that was wrought upon him” in his previous descent into incarnation on Earth, he ascends to the highest sphere, “being now possessed of his own proper power.” Finally, he enters into divinity. “This is the Good; this is the consummation, for those who have got gnosis.” (According to Scott, gnosis in this context means not only knowledge of divinity but also the relationship between man’s real self and the godhead.)

Further on, the Poimandres explains that the mind and soul can be conjoined only by means of an earth-body, because the mind by itself cannot do so, and an earthly body would not be able to endure

the presence of that mighty and immortal being, nor could so great a power submit to contact with a body defiled by passion. And so the mind takes to itself the soul for a wrap

In Hermetica, Isis to Horus, there is the statement:

. . . . For there are [in the world above, two gods] who are attendants of the Providence that governs all. One of them is Keeper of souls; the other is Conductor of souls. The Keeper is he that has in his charge the unembodied souls; the Conductor is he that sends down to earth the souls that are from time to time embodied, and assigns to them their several places. And both he that keeps watch over the souls, and he that sends them forth, act in accordance with God’s will.

There are many texts using the term “transformations” and a good commentary on the concept by R. T. Rundle Clark follows:

In order to reach the heights of the sky the soul had to undergo those transformations which the High God had gone through as he developed from a spirit in the Primeval Waters to his final position as Sun God . . .” — Myth-And-Symbol-In-Ancient-Egypt

This would appear to mean that in entering upon physical manifestation human souls follow the path of the divine and spiritual artificers of the universe.

There is reason to believe that the after-death adventures met with by the soul through the Duat or Underworld were also undergone by a neophyte during initiation. If the trial ends in success, the awakened human being thereafter speaks with the authority of direct experience. In the most ancient days of Egypt, such an initiate was called a “Son of the Sun” for he embodied the solar splendour. For the rest of mankind, the way is slower, progressing certainly, but more gradually, through many lives. The ultimate achievement is the same: to radiate the highest qualities of the spiritual element locked within the aspiring soul.

Mutational Law of Karma (कर्म)?

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During the preparation for cell division, for example, before the formation of the gametes or reproductive cells, the chromosomes may “cross over” so that material which originated from the male parent interchanges with that from the female parent. To quote from a standard work on evolutionary theory and genetics, Ernst Mayr’s Evolution and the Diversity of Life:

At some time prior to the formation of the gametes, the two homologous chromosomes exchange equivalent pieces with each other by a process called “crossing over.” By and large (there are many exceptions) no laws seem to determine where the chromosomes will break or how large the pieces will be that are exchanged. Which particular combination of pieces of maternal and paternal chromosomes making up the new chromosome will enter a given egg or spermatozoon is largely a matter of chance, at least in most chromosomes and most species. Likewise, it is largely a matter of accident which chromosomes will go into which germ cell, provided only that each cell receives its full set of chromosomes.

It is easy to attribute events to chance, but this only expresses scientific ignorance as to the real cause.

Another phenomenon is mutation: sometimes genetic codes suddenly change. This, too, is usually attributed to accident or chance, but then it is difficult to explain why any progression is made at all once biological systems have evolved to a certain level of complexity and perfection. The chance of a mutation leading to fatal, or at least less fit, properties is far greater than of a mutation making the individual fitter. Besides “crossing over” and mutation at one or several places on the chromosomes, another uncertain factor that Mayr and others mention is the distribution of chromosomes during reduction division (meiosis) to form reproductive cells. This process affects which side in the gamete the originally paternal or maternal genetic material goes to. Moreover, there are other opportunities for the course of events to be influenced from within: only part of the cell’s genetic code is active at certain times and under certain circumstances. Other parts are not active and may never become so during the present life. Thus, there are many secrets not yet unveiled by science, but nevertheless attributed to “chance.”

Chance, however, has no place in the theosophical view. Whatever happens is karmic, that is, it can be attributed to a cause, and this cause comes from within. In theosophy the different combinations of hereditary qualities in individuals are governed by psychomagnetic attractions inherent in the skandhas (‎स्कन्ध) of the reincarnating entity. Skandhas are the individual’s aggregates of properties — such as higher and lower mental consciousness, feelings, attractions, and physical characteristics — carried over from former lives. Thus, the specific magnetism of the soul, formed by its store of properties, determines which combinations of hereditary qualities will manifest in a particular incarnation. “It is . . . unquestionable that in the case of human incarnations the law of Karma, racial or individual, overrides the subordinate tendencies of ‘Heredity,’ its servant” (The Secret Doctrine).

The Occultic Brotherhood

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Millions upon millions of years ago in the darkness of prehistory, humanity was an infant, a child of Mother Nature, unawakened, dreamlike, wrapped in the cloak of mental somnolence. Recognition of egoity slept; instinctual consciousness alone was active. Like a stream of brilliance across the horizon of time, divine beings, manasaputras, sons of mind, descended among the sleeping humans, and with the flame of intellectual solar fire lighted the wick of latent mind, and lo! the thinker stirred. Self-consciousness wakened, and man became a dynamo of intellectual and emotional power: capable of love, of hate, of glory, of defeat. Having knowledge, he acquired power; acquiring power, he chose; choosing, he fashioned the fabric of his future; and the perception of this ran like wine through his veins.

Knowledge, more knowledge, and still greater knowledge was required by the maturing humans who looked with gratitude to the godlike beings who had come to awaken them. For many millennia they followed their guidance, as children lovingly follow the footsteps of their mother.

As the ages rolled by, a circulation of divine instructors succeeded these primeval manasaputras and personally supervised the progress of child-humanity: they initiated them in the arts and sciences, taught them to sow their fields with corn and wheat, instructed them in the ways of clean and moral living — in short, established primeval schools of training and instruction open and free to all to learn of things material, intellectual, and spiritual. At this early period there were no Mystery colleges: the ancient wisdom was the common heirloom of all mankind, for as yet there had been no abuse of knowledge, and hence no need for schools kept hid and sacred from the world. Truth was freely given and as freely accepted in that golden age. (H. P. Blavatsky Collected Writings)

The race was young; not all were adept in learning. Some through past experience in former world periods learned quickly and with ease, choosing intuitively the path of spiritual intellection; others, less awake, were good though wayward in progress; while a third class of humans, drugged with inertia, found learning and aspiring a burden and became laggards in the evolutionary procession. To them, spiritual apathy was preferable to spiritual exertion.

Mankind as a whole progressed rapidly in the acquisition of knowledge and its subsequent use. Some obviously wrought evil — others good. What had been latent spirituality now became active good and active evil. Suffering and pain became nature’s most merciful method of restoring the heart to its primeval instinct, that of spiritual choice. As mind developed keener potentialities and the struggle for mental supremacy overcame the spiritual, the gift of intellect became a double-edged weapon: on the one hand, the bringer of spiritual awareness and undreamed of intellectual ecstasy; and on the other, the wielder of a weapon of destruction, of horror and, in the worst cases, of deliberate spiritual wickedness — diabolism. As H. P. Blavatsky wrote:

The mysteries of Heaven and Earth, revealed to the Third Race by their celestial teachers in the days of their purity, became a great focus of light, the rays from which became necessarily weakened as they were diffused and shed upon an uncongenial, because too material soil. With the masses they degenerated into Sorcery, taking later on the shape of exoteric religions, of idolatry full of superstitions, . . . — The Secret Doctrine  

Nature is cyclical throughout: at one time fertile in spiritual things, at another barren. At this long-ago period of the third root-race, on the great continent of Lemuria, now submerged, the cycle was against spiritual progress. A great downward sweep was in force, when expansion of physical and material energies were accelerated with the consequent retardation and contraction of spiritual power. The humanities of that period were part of the general evolutionary current, and individuals reacted to the coarsening atmosphere according to their nature. Some resisted its down- ward influence through awakened spirituality; others, weaker in understanding, vacillated between spirit and matter, between good and evil: sometimes listening to the promptings of intuition, at other times submerged by the rushing waves of the downward current. Still others, in whom the spark of intellectual splendor burned low, plunged headlong downstream, unmindful of the turbulent and muddy waters.

As the downward cycle proceeded, knowledge of spiritual verities and living of the life in accordance with them became a dull and useless tool in human hearts and minds. Such folly was inevitable in the course of cosmic events, and all things were provided for. Just as there are many types of people — some spiritual, others material, some highly intelligent, others slow of thought — so are there various grades of beings throughout the universe, ranging from the mineral, through the vegetable, animal, and human kingdom, and beyond to the head and hierarch of our earth.

During these first millennia the spiritual head and guardian of the earth had been stimulating wherever possible the individual fires of active spirituality. Gradually as knowledge of divine things became abused by those strong in will but weak in morality, truth was increasingly veiled. The planetary watcher now felt the need of selecting a band of co-workers to act as bodyguard and protector of the ancient wisdom. Alone a handful of spiritually illumined human beings, in whom the divine fervor burned bright, acknowledged wholehearted allegiance to their planetary mentor — the spiritual hierarch of humanity. Through long ages certain individuals had been watched over and guided, strengthened and tested in innumerable ways, and those who passed the test of self-knowledge and self-sacrifice were gathered together to form the first association of spiritual-divine human beings — the Great Brotherhood. As G. de Purucker elaborates:

Then was formed or established or set in operation the gathering together of the very highest representatives, spiritually and intellectually speaking, that the human race as yet had given manifestation to; . . .

. . . the Silent Watcher of the Globe, through the spiritual-magnetic attraction of like to like, was enabled to attract to the Path of Light, even from the earliest times of the Third Root-Race, certain unusual human individuals, early forerunners of the general Manasaputric “descent,” and thus to form with these individuals a Focus of Spiritual and Intellectual Light on Earth, this fact signifying not so much an association or society or brotherhood as a unity of human spiritual and intellectual Flames, so to speak, which then represented on Earth the heart of the Hierarchy of Compassion. . . .

Now it was just this original focus of Living Flames, which never degenerated nor lost its high status of the mystic center on Earth through which poured the supernal glory of the Hierarchy of Compassion, today represented by the Great Brotherhood of the Mahatmans, . . . Thus it is that the Great Brotherhood traces an unbroken and uninterrupted ancestry back to the original focus of Light of the Third Root-Race. — The Esoteric Tradition  

Hence the elder brothers of the race remain

the elect custodians of the Mysteries revealed to mankind by the divine Teachers . . . and tradition whispers, what the secret teachings affirm, namely, that these Elect were the germ of a Hierarchy which never died since that period” (Secret Doctrine)

— since the foundation and establishment of the Great Brotherhood some 12 million years ago. From this center for millions of years have been streaming in continuous procession rays of light and strength into the world at large and, more specifically, into the hearts of those whose lives are dedicated to the service of truth. From this Fraternity have gone forth messengers, masters of wisdom, to inspire the grand religions of the past, and they will continue to send forth their envoys as long as mankind requires their care.

Industrial Semiosis. Note Quote.

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The concept of Industrial Semiosis categorizes the product life-cycle processes along three semiotic levels of meaning emergence: 1) the ontogenic level that deals with the life history data and future expectations about a single occurrence of a product; 2) the typogenic level that holds the processes related to a product type or generation; and 3) the phylogenic level that embraces the meaning-affecting processes common to all of the past and current types and occurrences of a product. The three levels naturally differ by the characteristic durational times of the grouped semiosis processes: as one moves from the lowest, ontogenic level to the higher levels, the objects become larger and more complicated and have slower dynamics in both original interpretation and meaning change. The semantics of industrial semiosis in industry investigates the relationships that hold between the syntactical elements — the signs in language, models, data — and the objects that matter in industry, such as customers, suppliers, work-pieces, products, processes, resources, tools, time, space, investments, costs, etc. The pragmatics of industrial semiosis deals with the expression and appeal functions of all kinds of languages, data and models and their interpretations in the setting of any possible enterprise context, as part of the enterprise realising its mission by enterprising, engineering, manufacturing, servicing, re-engineering, competing, etc. The relevance of the presented definitions for infor- mation systems engineering is still limited and vague: the definitions are very general and hardly reflect any knowledge about the industrial domain and its objects, nor do they reflect knowledge about the ubiquitous information infrastructure and the sign systems it accommodates.

A product (as concept) starts its development with initially coinciding onto-, typo-, and phylogenesis processes but distinct and pre-existing semiotic levels of interpretation. The concept is evolved, and typogenesis works to reorganize the relationships between the onto- and phylogenesis processes, as the variety of objects involved in product development increases. Product types and their interactions mediate – filter and buffer – between the levels above and below: not all variety of distinctions remains available for re-organization as phylos, nor every lowest-level object have a material relevance there. The phylogenic level is buffered against variations at the ontogenic level by the stabilizing mediations at the typogenic level.

The dynamics of the interactions between the semiotic levels can well be described in terms of the basic processes of variation and selection. In complex system evolution, variation stands for the generation of a variety of simultaneously present, distinct entities (synchronic variety), or of subsequent, distinct states of the same entity (diachronic variety). Variation makes variety increase and produces more distinctions. Selection means, in essence, the elimination of certain distinct entities and/or states, and it reduces the number of remaining entities and/or states.

From a semiotic point of view, the variety of a product intended to operate in an environment is determined by the devised product structure (i.e. the relations established between product parts – its synchronic variety) and the possible relations between the product and the anticipated environment (i.e. the product feasible states – its potential diachronic variety), which together aggregate the product possible configurations. The variety is defined on the ontogenic level that includes elements for description of both the structure and environment. The ontogenesis is driven by variation that goes through different configurations of the product and eventually discovers (by distinction selection at every stage of the product life cycle) configurations, which are stable on one or another time-scale. A constraint on the configurations is then imposed, resulting in the selective retention – emergence of a new meaning for a (not necessarily new) sign – at the typogenic level. The latter decreases the variety but specializes the ontogenic level so that only those distinctions ultimately remain, which fit to the environment (i.e. only dynamically stable relation patterns are preserved). Analogously but at a slower time- scale, the typogenesis results in the emergence of a new meaning on the phylogenic level that consecutively specializes the lower levels. Thus, the main semiotic principle of product development is such that the dynamics of the meaning-making processes always seeks to decrease the number of possible relations between the product and its environment and hence, the semiosis of product life cycle is naturally simplified. At the same time, however, the ‘natural’ dynamics is such that augments the evolutive potential of the product concept for increasing its organizational richness: the emergence of new signs (that may lead to the emergence of new levels of interpretation) requires a new kind of information and new descriptive categories must be given to deal with the still same product.

Moishe Postone: Capitalism, Temporality, and the Crisis of Labor. Note Quote.

Moishe Postone: Capitalism, Temporality, and the Crisis of Labor from The American Academy in Berlin on Vimeo.

Moishe Postone’s work establishes a crucial distinction between the critique of capitalism from the standpoint of labour and the critique of labor in capitalism.The former implies a transhistorical account of work, while the latter situates labor as a consistent category – capable of “social synthesis” – within the capitalist mode of production. But, does this distinction require us to abandon any form of ontological account of labour? As Postone would say,

It depends what you mean by an ontological account of labour. It does force us to abandon the idea that transhistorically there is an on-going development of humanity which is effected by labour, that human interaction with nature as mediated by labour is a continuous process which is led to continuous change. And that labour is in that sense a central historical category. That position is closer actually to Adam Smith than it is to Marx. I think that the centrality of labour to something called historical development can be posited only for capitalism and not for any other form of human social life. On the other hand, I think one can retain the idea that humanity’s interaction with nature is a process of self-constitution.

One of the most important contributions of Time, Labour and Social Domination is a novel theory of impersonal domination in capitalist society. To him “traditional Marxism” is a criticism of capitalism from the standpoint of labor. Postone’s Marxism, by contrast, is a critique of labor in capitalism. Since Marx’s theory refers to capitalism, not society in general, labor cannot be a transhistorical category. Instead, it must be understood as an integrated part of capitalism. This means that labor cannot provide a standpoint from which to criticize capitalism, and neither can the proletariat: “the working class is integral to capitalism, rather than the embodiment of its negation”. The struggle, then, should not be a struggle of labor against capital, as traditional Marxists thought, but a struggle against labor seen as an integral part of the valorization of capital.  This conclusion has implications for Postone’s understanding of domination in capitalism. Rather than being a matter of class relations, it takes the form of domination by impersonal and quasi-objective mechanisms such as fetishism, in the construction of which labor is deeply implicated. The benefit of this reinterpretation, according to Postone, is that it shows the usefulness of Marx’s theory not only in a criticism of liberal nineteenth-century capitalism but also in a criticism of contemporary welfare-state capitalism or Soviet-style state-capitalism. The latter forms of capitalism are just as capitalist as the former since they all build on the valorization of capital built on labor. Abolishing private ownership or rearranging the distribution of goods is not enough to escape capitalism. Postone both builds on and criticizes the approaches of Lukács and the Frankfurt School. There is much in his book that shows his affinities especially to the latter – such as the criticism of welfare state capitalism or the stress on fetishism – but he nevertheless criticizes these earlier thinkers for being bound to a transhistorical conception of labor. Lukács in particular is singled out for heavy criticism since he saw the proletariat as the Subject of history, as capable of grasping totality and hence offering the standpoint of critique. Engaging with the Hegelian legacy, or should I quip lunacy in Lukács, Postone arrives at one of his most important and provocative arguments. “Marx suggests that a historical Subject in the Hegelian sense does indeed exist in capitalism, yet he does not identify it with… the proletariat”. Instead it is capital that is portrayed as a Hegelian Geist – as a subject and self-moving substance, following its own immanent historical logic. Hegelian dialectics, then, is specific to capitalism and is not a tool for grasping history in general. Thus, to Marx, the “totality” was not the whole in general, and certainly not a standpoint which he affirmed. Instead, he identified totality with the capitalist system and made it the object of his critique: “the historical negation of capitalism would not involve the realization, but the abolition, of the totality”, Postone argues. The working class cannot lead history towards this negation. In fact, it is only by breaking with the logic consitutive of this totality, in which the working class forms part, that a different, post-capitalist society can be born.

The abolition of the totality would, then, allow for the possible constitution of very different, non-totalizing, forms of the political coordination and regulation of society.

In a question asked about if the capitalist form of domination not better defined as the appearance of truly abstract relations as if they were concrete, personal relations? Furthermore, does this inversion, or at least the recognition of the crucial role of abstraction in capitalism, render a definition of class struggle untenable, or are we rather in need of a concept of class that takes this distance from the concrete into consideration? Postone says,

I am not sure that I would fully agree with the attempted reformulation. First of all, with regard to the quote “relations between people appearing as relations between things” what is left out of this version of what Marx said is that he adds that relations among people appear as they are, as social relations between things and thingly relations between people. Marx only explicitly elaborated the notion of fetishism with the fetishism of commodity. All three volumes of Capital, are [our change] in many respects, however, a study on fetishism even when he doesn’t use that word. And fetishism means that because of the peculiar, double character of the structuring social forms of capitalism, social relations disappears from view. What we get are thingly relations: we also get abstractions. However, one dimension of the fetish is, as you put it, that abstract relations appear concrete.They appear in the form of the concrete. So, for example, the process of creating surplus value appears to be a material process, the labour process. It appears to be material-technical, rather than moulded by social forms. And yet there are also abstract dimensions and regularities that don’t appear in the form of the concrete. I am emphasising this is because certain reactionary forms of thought only view capitalism in terms of those abstract regularities and refuse to see that the concrete itself is moulded by, and is really drenched with, the abstract. I think a lot of forms of populism and anti-Semitism can be characterised that way. Now I am not sure that this appropriation of the categories of Marx’s critique of political economy renders a definition of class struggle untenable, but it does indicate that class struggle occurs within and is moulded by the structuring social forms.This position rejects the ontological centrality or the primacy of class struggle, as that which is truly social and real behind the veil of capitalist forms. Class struggle rather is moulded by the capitalist relations expressed by the categories of value, commodity, surplus value, and capital.

Postone’s approach only seems far-fetched if we continue to equate capitalism with the economy. Not if we think of it as a form of life. For example, after Darwin wrote, natural processes, such as adaptation or sexual selection, came to be seen as operating within history. This gave us the naturalist novel of Zola or Norris. “Nature” was seen to structure history (the Rougon-Marcquet saga, the strike in Germinal etc.) as well compel individuals from within. For Postone, it is not “natural” Darwinian processes that do this but an historic process, capitalism. Another example of the same idea is Max Weber’s “spirit of capitalism.” Weber can be read, and wanted to be read, as saying that there are forces outside capitalism on which capitalism depends, such as religious ethics. However, Postone is suggesting that such “spiritual” Weberian forces as asceticism, compulsivity and hypocrisy (Weber’s famous triad) are internal to capitalism, structuring its motion. But, there are ambivalences to his theory, and especially ones concerning science and technology. Postone rejects the view, associated with traditional Marxism, that sees industrial production as a neutral, purely technical process that could be salvaged from capitalism and carried on in similar form in socialism. To criticize capitalism, he argues that we also need to criticize industrial production, or at least the form it has assumed in capitalism. The problem is that he simultaneously argues – based primarily on a famous passage in Grundrisse – that science and technology creates the preconditions for an overcoming of capitalism, since they enable human beings to create unprecedented “material wealth” in a way that relies less and less on human labor. Since in capitalism “value” can only be created by labor, capitalism increasingly comes to be characterized by a contradiction between the processes generating “wealth” and “value”. Unlike “value”, Postone appears to think that “wealth” is a category that it is fine to apply transhistorically. “Wealth” existed in precapitalist societies and must also be imagined as something that can exist in post-capitalist, socialist societies. What happens with capitalism is that the creation of “wealth” can only take place through the production of “value”, i.e. through the exploitation of labor and valorization of capital. However, by showing that “wealth” can be produced in abundance without relying on labor, science and technology open up possibilities of overcoming capitalism. Here Postone portrays science and technology, not as irremediably implicated in capitalism, but as potentially liberating forces that point beyond capitalism. That is of course fine, but the question then becomes how to distinguish the good and bad moments of science and technology. Postone calls for a transformation of not only of “relations of production” but also of the “mode of production”, but without giving us much in the way of explaining how much or how radically the latter needs to be changed.

Then there is the problem of dialectics. As mentioned, Postone confines Geist and totality to capitalism. This claim has some antecedents in earlier critical theory. Adorno, for instance, claims that the role of Spirit in capitalism is taken by “value”: “The objective and ultimately absolute Hegelian spirit [is] the Marxist law of value that comes into force without men being conscious of it” (Adorno). The posture of taking up arms against “totality” itself is of course also familiar from older critical theory. Adorno, however, never confined dialectics in toto to capitalism. Although Postone does allow for some forms of dialectical interaction (e.g. people changing their own nature reflexively through acting on nature or the reciprocal constitution of social practice and social structure), he argues that such interaction only becomes “directionally dynamic” in capitalism. In other words, dialectics in the sense of a historical logic or necessity only exists in capitalism. This raises the question of how capitalism can be overcome. If there is no Geist but capital, then dialectics cannot point the way out of capitalism. Liberation can only mean liberating oneself from dialectics, by creating a world in which it is no longer dominant.

The indication of the historicity of the object, the essential social forms of capitalism, implies the historicity of the critical consciousness that grasps it; the historical overcoming of capitalism would also entail the negation of its dialectical critique.

However, sometimes Postone himself seems to grasp the relation between capitalism and its outside dialectically, as when he uses the term “determinate negation” for the movement whereby capitalism is transcended. But if the overcoming of capitalism is a determinate negation, doesn’t that require the premise of a totality transcending the capitalist system, as Lukács thought?  Sometimes Postone writes as if the totality of capitalism were driven towards its own abolition by its inner contradictions. However, apart from the discussion of technology and wealth referred to above, it is hard to see that he specifies anywhere what kind of contraditions might bring about this self-abolition.