# Fortune of the Individuals Restricted to Integers: Random Economic Exchange Between Populations of Traders.

Consider a population of traders, each of which possesses a certain amount of capital which is assumed to be quantized in units of minimal capital. Taking this latter quantity as the basic unit, the fortune of an individual is restricted to the integers. The wealth of the population evolves by the repeated interaction of random pairs of traders. In each interaction, one unit of capital is transferred between the trading partners. To complete the description, we specify that if a poorest individual (with one unit of capital) loses all remaining capital by virtue of a “loss”, the bankrupt individual is considered to be economically dead and no longer participates in economic activity.

In the following, we consider a specific realization of additive capital exchange, the “random” exchange, where the direction of the capital exchange is independent of the relative capital of the traders. While this rule has little economic basis, the model is completely soluble and thus provides a helpful pedagogical point.

In a random exchange, one unit of capital is exchanged between trading partners as represented by the reaction scheme (j, k) → (j ± 1, k ∓ 1). Let ck(t) be the density of individuals with capital k. within a mean-field description, ck(t) evolves according to

dck(t)/dt = N(t) [ck+1(t) + ck-1(t) – 2ck(t)] —– (1)

with N(t) ≡ M0(t) = ∑k=1 ck(t), the population density. The first two terms account for gain in ck(t) due to the interactions (j, k + 1) → (j + 1, k) and (j, k − 1) → (j−1, k), respectively, while the last term accounts for the loss in ck(t) due to the interactions (j, k) → (j±1, k∓1).

By defining a modified time variable,

T = ∫0dt’N(t’) —– (2)

equation (1) is reduced to the discrete diffusion equation

dck(T)/dT = ck+1(T) + ck-1(T) – 2ck(T) —– (3)

The rate equation for the poorest density has the slightly different form, dc1/dT = c2 − 2c1, but may be written in the same form as equation (3) if we impose the boundary condition c0(T) = 0.

For illustrative purposes, let us assume that initially all individuals have one unit of capital, ck(0) = δk1. The solution to equation (3) subject to these initial and boundary conditions is

ck(T) = e−2T [Ik−1(2T) − Ik+1(2T)] —– (4)

where In denotes the modified Bessel function of order n. consequently, the total density N(t) is

N(T) = e−2T [I0(2T) + I1(2T)] —– (5)

To re-express this exact solution in terms of the physical time t, we first invert equation (2) to obtain t(T) = ∫0T dT′/N(T′), and then eliminate T in favor of t in the solution for ck(T). For simplicity and concreteness, let us consider the long-time limit. From equation (4),

ck(T) ≅ k/√(4πT3) exp (-k2/4T) —– (6)

and from equation (5),

N(T) ≅ (πT)−1/2 —– (7)

Equation (7) also implies t ≅ 2/3 √(πT3) which gives

N(T) ≅ (2/3πt)1/3 —– (8)

and

ck(t) ≅ k/3t exp [-(π/144)1/3 k2/t2/3] —– (9)

Note that this latter expression may be written in the scaling form ck(t) ∝ N2xe−x2, with the scaling variable x ∝ kN. One can also confirm that the scaling solution represents the basin of attraction for almost all exact solutions. Indeed, for any initial condition with ck(0) decaying faster than k−2, the system reaches the scaling limit ck(t) ∝ N2xe−x2. On the other hand, if ck(0) ∼ k−1−α, with 0 < α < 1, such an initial state converges to an alternative scaling limit which depends on α. These solutions exhibit a slower decay of the total density, N ∼ t−α/(1+α), while the scaling form of the wealth distribution is

ck(t) ∼ N2/αCα(x), x ∝ kN1/α —– (10)

with the scaling function

Cα(x) = e−x20 du e−u2 sinh(2ux)/u1+α —– (11)

Evaluating the integral by the Laplace method gives an asymptotic distribution which exhibits the same x−1−α as the initial distribution. This anomalous scaling in the solution to the diffusion equation is a direct consequence of the extended initial condition. This latter case is not physically relevant, however, since the extended initial distribution leads to a divergent initial wealth density.

# The Concern for Historical Materialism. Thought of the Day 53.0

The concern for historical materialism, in spite of Marx’s differentiation between history and pre-history, is that totalisation might not be historically groundable after all, and must instead be constituted in other ways: whether logically, transcendentally or naturally. The ‘Consciousness’ chapter of the Phenomenology, a blend of all three, becomes a transcendent(al) logic of phenomena – individual, universal, particular – and ceases to provide any genuine phenomenology of ‘the experience of consciousness’. Natural consciousness is not strictly speaking a standpoint (no real opposition), so it can offer no critical grounds of itself to confer synthetic unity upon the universal, that which is taken to a higher level in ‘Self-Consciousness’ (only to be retrospectively confirmed). Yet Hegel does just this from the outset. In ‘Perception’, we read that, ‘[o]n account of the universality [Allgemeinheit] of the property, I must … take the objective essence to be on the whole a community [Gemeinschaft]’. Universality always sides with community, the Allgemeine with the Gemeinschaft, as if the synthetic operation had taken place prior to its very operability. Unfortunately for Hegel, the ‘free matters’ of all possible properties paves the way for the ‘interchange of forces’ in ‘Force and the Understanding’, and hence infinity, life and – spirit. In the midst of the master-slave dialectic, Hegel admits that, ‘[i]n this movement we see repeated the process which represented itself as the play of forces, but repeated now in consciousness [sic].

# Noneism. Part 1.

Noneism was created by Richard Routley. Its point of departure is the rejection of what Routley calls “The Ontological Assumption”. This assumption consists in the explicit or, more frequently, implicit belief that denoting always refers to existing objects. If the object, or objects, on which a proposition is about, do not exist, then these objects can only be one: the null entity. It is incredible that Frege believed that denoting descriptions without a real (empirical, theoretical, or ideal) referent denoted only the null set. And it is also difficult to believe that Russell sustained the thesis that non-existing objects cannot have properties and that propositions about these objects are false.

This means that we can have a very clear apprehension of imaginary objects, and quite clear intellection of abstract objects that are not real. This is possible because to determine an object we only need to describe it through its distinctive traits. This description is possible because an object is always chacterized through some definite notes. The amount of traits necessary to identify an object greatly varies. In some cases we need only a few, for instance, the golden mountain, or the blue bird; in other cases we need more, for instance, the goddess Venus or the centaur Chiron. In other instances the traits can be very numerous, even infinite. For instance the chiliedron, and the decimal number 0,0000…009, in which 9 comes after the first million zeros, have many traits. And the ordinal omega or any Hilbert space have infinite traits (although these traits can be reckoned through finite definitions). These examples show, in a convincing manner, that the Ontological Assumption is untenable. We must reject it and replace it with what Routley dubbs the Characterization Postulate. The Characterization Postulate says that, to be an object means to be characterized by determined traits. The set of the characterizing traits of an object can be called its “characteristic”. When the characteristic of an object is set up, the object is perfectly recognizable.

Once this postulate is adopted, its consequences are far reaching. Since we can characterize objects through any traits whatsoever, an object can not only be inexistent, it can even be absurd or inconsistent. For instance, the “squond” (the circle that is square and round). And we can make perfectly valid logical inferences from the premiss: x is the sqound:

(1) if x is the squond, then x is square
(2) if x is the squond, then x is round

So, the theory of objects has the widest realm of application. It is clear that the Ontological Assumption imposes unacceptable limits to logic. As a matter of fact, the existential quantifier of classical logic could not have been conceived without the Ontological Assumption. The expression “(∃x)Fx” means that there exists at least an object that has the property F (or, in extensional language, that there exists an x that is a member of the extension of F). For this reason, “∃x” is unappliable to non existing objects. Of course, in classical logic we can deny the existence of an Object, but we cannot say anything about Objects that have never existed and shall never exist (we are strictly speaking about classical logic). We cannot quantify individual variables of a first order predicate that do not refer to a real, actual, past or future entity. For instance, we cannot say “(∃x) (x is the eye of Polyphemus)”. This would be false, of course, because Polyphemus does not exist. But if the Ontological Assumption is set aside, it is true, within a mythological frame, that Polyphemus has a single eye and many other properties. And now we can understand why noneism leads to logical material-dependence.

As we have anticipated, there must be some limitations concerning the selection of the contradictory properties; otherwise the whole theory becomes inconsistent and is trivialized. To avoid trivialization neutral (noneist) logic distinguishes between two sorts of negation: the classical propositional negation: “8 is not P”, and the narrower negation: “8 is non-P”. In this way, and by applying some other technicalities (for instance, in case an universe is inconsistent, some kind of paraconsistent logic must be used) trivialization is avoided. With the former provisions, the Characterization Postulate can be applied to create inconsistent universes in which classical logic is not valid. For instance, a world in which there is a mysterious personage, that within determined but very subtle circumstances, is and is not at the same time in two different places. In this case the logic to be applied is, obviously, some kind of paraconsistent logic (the type to be selected depends on the characteristic of the personage). And in another universe there could be a jewel which has two false properties: it is false that it is transparent and it is false that it is opaque. In this kind of world we must use, clearly, some kind of paracomplete logic. To develop naive set theory (in Halmos sense), we must use some type of paraconsistent logic to cope with the paradoxes, that are produced through a natural way of mathematical reasoning; this logic can be of several orders, just like the classical. In other cases, we can use some kind of relevant and, a fortiori, paraconsistent logic; and so on, ad infinitum.

But if logic is content-dependent, and this dependence is a consequence of the Ontological Assumption’s rejection, what about ontology? Because the universes determined through the application of the Characterization Postulate may have no being (in fact, most of them do not), we cannot say that the objects that populate such universes are entities, because entities exist in the empirical world, or in the real world that underpins the phenomena, or (in a somewhat different way), in an ideal Platonic world. Instead of speaking about ontology, we should speak about objectology. In essence objectology is the discipline founded by Meinong (Theory of Objects), but enriched and made more precise by Routley and other noneist logicians. Its main division would be Ontology (the study of real physical and Platonic objects) and Medenology (the study of objects that have no existence).

# Bayesianism in Game Theory. Thought of the Day 24.0

Bayesianism in game theory can be characterised as the view that it is always possible to define probabilities for anything that is relevant for the players’ decision-making. In addition, it is usually taken to imply that the players use Bayes’ rule for updating their beliefs. If the probabilities are to be always definable, one also has to specify what players’ beliefs are before the play is supposed to begin. The standard assumption is that such prior beliefs are the same for all players. This common prior assumption (CPA) means that the players have the same prior probabilities for all those aspects of the game for which the description of the game itself does not specify different probabilities. Common priors are usually justified with the so called Harsanyi doctrine, according to which all differences in probabilities are to be attributed solely to differences in the experiences that the players have had. Different priors for different players would imply that there are some factors that affect the players’ beliefs even though they have not been explicitly modelled. The CPA is sometimes considered to be equivalent to the Harsanyi doctrine, but there seems to be a difference between them: the Harsanyi doctrine is best viewed as a metaphysical doctrine about the determination of beliefs, and it is hard to see why anybody would be willing to argue against it: if everything that might affect the determination of beliefs is included in the notion of ‘experience’, then it alone does determine the beliefs. The Harsanyi doctrine has some affinity to some convergence theorems in Bayesian statistics: if individuals are fed with similar information indefinitely, their probabilities will ultimately be the same, irrespective of the original priors.

The CPA however is a methodological injunction to include everything that may affect the players’ behaviour in the game: not just everything that motivates the players, but also everything that affects the players’ beliefs should be explicitly modelled by the game: if players had different priors, this would mean that the game structure would not be completely specified because there would be differences in players’ behaviour that are not explained by the model. In a dispute over the status of the CPA, Faruk Gul essentially argues that the CPA does not follow from the Harsanyi doctrine. He does this by distinguishing between two different interpretations of the common prior, the ‘prior view’ and the ‘infinite hierarchy view’. The former is a genuinely dynamic story in which it is assumed that there really is a prior stage in time. The latter framework refers to Mertens and Zamir’s construction in which prior beliefs can be consistently formulated. This framework however, is static in the sense that the players do not have any information on a prior stage, indeed, the ‘priors’ in this framework do not even pin down a player’s priors for his own types. Thus, the existence of a common prior in the latter framework does not have anything to do with the view that differences in beliefs reflect differences in information only.

It is agreed by everyone that for most (real-world) problems there is no prior stage in which the players know each other’s beliefs, let alone that they would be the same. The CPA, if understood as a modelling assumption, is clearly false. Robert Aumann, however, defends the CPA by arguing that whenever there are differences in beliefs, there must have been a prior stage in which the priors were the same, and from which the current beliefs can be derived by conditioning on the differentiating events. If players differ in their present beliefs, they must have received different information at some previous point in time, and they must have processed this information correctly. Based on this assumption, he further argues that players cannot ‘agree to disagree’: if a player knows that his opponents’ beliefs are different from his own, he should revise his beliefs to take the opponents’ information into account. The only case where the CPA would be violated, then, is when players have different beliefs, and have common knowledge about each others’ different beliefs and about each others’ epistemic rationality. Aumann’s argument seems perfectly legitimate if it is taken as a metaphysical one, but we do not see how it could be used as a justification for using the CPA as a modelling assumption in this or that application of game theory and Aumann does not argue that it should.

# Causality

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

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.

# Why Deleuzean Philosophy Begins at Hegel and Becomes a Correctional Footnote Thereafter ? Note Quote.

That philosophy must be an ontology of sense is a bold claim on Deleuze’s part, and although he takes it from a Hegelian philosophy, the direction in which he develops it across the rest of his work is resolutely, if not infamously, opposed to Hegel. Whereas Hegel will construct a logic of sense which is fundamentally a logic of the concept, Deleuze will deny that sense is reducible to signification and its universal or general concepts. Deleuze will later provide his own logic of the concept, but for him, although the concept will posit itself, this will not be as the immanent thought of the sense or the content of the matter itself, but will rather function to extract or capture a pure event, or the sense at the surface of things. Similarly, although Deleuze will agree that “sense is becoming”, this will not be a becoming in an atemporal logical time, opposed to a historical time that would play it out, but a pure becoming without present, always divided between past and future, without arrow or telos, and actualised in the present while never strictly ‘happening’. The most distinctive difference, however, will be Deleuze’s invocation of a nonsense that cannot be simply incorporated within sense, that will not be sublated and subsumed in the folds of the dialectic, a nonsense that is itself productive of sense. Moving beyond Hegel, Deleuze will deny the reducibility of sense not only to the universal meanings of signification, but also to the functions of reference or denotation. Moreover, he will deny its reducibility to the dimension of manifestation, or the meanings of the subject of enunciation – the ‘I’ who speaks. Sense can neither be found in universal concepts, nor reference to the individual, nor in the intentions of the subject, but is rather that which grounds all three.

# ++ Occult/Esoteric ++

The Greeks were adept in the use of imagery to convey profound esoteric truths, often using the form of sport; or, for instance, they would read into the exercises of the stadium inner significance. One of the best known examples of this was their portrayal through the torchbearer race of the mystic line of succession of great teachers.

In the torch-race, the torch-bearer ran from post to post. On reaching the end of his stage he handed the lighted torch which he carried to the one there waiting, who immediately took up the race and in his turn handed it to the one waiting for him. This exercise of the arena or stadium was taken by many Greek and Latin writers as symbolizing the carrying on of Light from age to age, and as pointing to the spiritual Torch-bearers who pass the Torch of Truth from hand to hand throughout unending time…. This handing on of the light of truth “throughout unending time” has formed the theme of many Mystery parables. The Greeks also referred to this spiritual succession as the Golden Chain of Hermes which they believed to stretch far into the realms of Olympus, to “Father Zeus downwards through a series or line of spiritual beings and then through certain elect and lofty human beings to ordinary men” (Esoteric Tradition).

Purucker described this mystic succession as the guruparampara. This is a Sanskrit compound literally meaning “teacher beyond beyond.” The term signifies a line of teachers reaching beyond the beyond, through past, present, and into the distant future, whose sublime purpose is ever the same: the work of spiritualization.

The ancient Mystery-Schools of every country of the globe and of whatever epoch in time, have had each one a Succession of Teachers trained and authorized by their training to teach in their turn; and as long as this transmission of the light of Truth was a reality in any one country, it was in every sense a truly spiritual institution.

An outstanding example of this ancient transmission is the succession of “living buddhas” of Tibet, which “is a real one, but of a somewhat special type, and it is by no means what Occidental scholars mistake it to be or have frequently misunderstood it to be” (Esoteric Tradition).

Further, in the Eleusinian Mysteries of Greece,

hierophants were drawn from one family, the Eumolpidae, living in Athens, and the torchbearers were drawn from another family, the Lycomidae, living in Athens; and we have reason to believe that the Mysteries of Samothrace, the seat of an older rite, and which were, like the Mysteries of Eleusis, a State function, were also conducted in the same manner by the passing on of the tradition held sacred and incommunicable to outsiders; and the bond of union between the initiates of these so-called Mysteries was considered indissoluble, impossible of dissolution, for death merely strengthened the tie.– Fundamentals of the Esoteric Philosophy

In Persia as well as Egypt, we find this line of succession manifesting in another form. For example, there were the thirteen or more Zoroasters whose esoteric contribution to Persia’s history was the inspiration of that once mighty civilization:

The number of Zoroasters who have appeared from time to time is confusing, so long as we consider, and wrongly consider, these Zoroasters to be reimbodiments of one single ego, instead of different egos imbodying what we may interpret from the occult records as the “Zoroaster-spirit.” The truth of the matter is that in the scheme and terminology of Zoroastrianism, every Root-Race and sub-race, and minor race of the latter, has its own Zoroaster or Zoroasters. The term Zoroaster means in Zoroastrianism, very much what the term Buddha does in Buddhism, or Avatara does in Brahmanism. Thus there were great Zoroasters, and less Zoroasters — the qualificatory adjective depending upon the work done by each Zoroaster, and the sphere of things. Hence we can speak of the Zoroasters as being thirteen in number from one standpoint, or fourteen from another; or like the Manus in Brahmanism, or like the Buddhas in Buddhism, we can multiply each of these by seven again, or even fourteen if we take in every little branchlet race with its guiding Zoroaster-spirit.– Studies in Occult Philosophy.

In Egypt, Hermes Trismegistus (“Hermes the thrice greatest”) stands out from the long Hermes line, whose writings and teachings were founded on the ancient Mystery doctrine. In Greece also we find the Orphic Mysteries, from whose halls of esoteric instruction came forth many who bore the name of Orpheus.

What impelled these pupils to take the names of their teachers? Why did they sign their work, or give oral instruction, in the name of Orpheus, Hermes, or Zoroaster? Was it a kind of spiritual plagiarism, or was it rather because of a compelling gratitude to the teacher who had given them ALL, who had lighted the flame of esoteric fire in their hearts? Surely the latter, for whatever message they had of inspiration and light they deemed not theirs, but “his who sent me” — “As we have received it, thus shall we pass it on.” This practice is distressing to later historians who struggle always to attach correct labels to things, yet one cannot help but love these old disciples for that loyalty of soul which banishes all thought of individual greatness.

The relationship between disciple and teacher is a most sacred bond of spiritual intimacy. Gratitude wells up from the disciple commensurate with greatness of soul: the little of heart feel only resentment when guidance and protection are offered; but the large of heart burn with the flame of loving and inextinguishable gratitude. The links in this Golden Chain of Hermes are joined by gratitude. As each link is coupled with its brother link, heart with heart, teacher with pupil, pupil with teacher — each teacher a pupil to the one above, each pupil a teacher to the one below — all bonded by unbreakable links of love, fidelity, and gratitude to the teacher, to the Brotherhood, to the esoteric wisdom:

Like signal-fires of the olden times, which, lighted and extinguished by turns upon one hill-top after another, conveyed intelligence along a whole stretch of country, so we see a long line of “wise” men from the beginning of history down to our own times communicating the word of wisdom to their direct successors. Passing from seer to seer, the “Word” flashes out like lightning, and while carrying off the initiator from human sight forever, brings the new initiate into view. — Isis Unveiled

This “long line of `wise’ men” has been kept unbroken since the middle of the third root-race by two methods: (a) the actual reincarnation of adepts, and (b) the birth of the initiate out of the disciple. In this way the Brotherhood revitalizes its membership through the rebirth of hierophants, and the “second birth” of recruits from the ranks of the Mystery chambers. The “Passing of the Word” was the final rite of the solar initiation: without it no transmission of occult authority could be made from initiator to disciple.

Hence the line of esoteric authority and wisdom advances in serial order through grade after grade of chelaship to the adepts; from adepts to high mahatmas; from high mahatmas to buddhas; from buddhas to dhyani-buddhas; from dhyani-buddhas to the spiritual guide and protector of the planetary chain of earth; from the earth planetary spirit to the heart of the sun. Truly a line of luminous glory linking the humblest of disciples of wisdom with the solar logos.