The Mathematics of Plato's Academy: A New Reconstruction

 https://www.amazon.co.uk/Mathematics-Platos-Academy-New-Reconstruction/dp/0198539126 

The author speculates about the use of Euclid's algorithm as a way to represent rational numbers and even real numbers.

Proclus in 114 propositions

1. The transcendent One is the supreme principle of all things.
2. The world is imperfect and derived from a total perfect reality.
3. There is a reality of the intellect consisting in the pure being of ideal forms.
4. But absolute perfection must coincide with total unity and hence not coincide with intellect .
5. The one cannot have positive characteristics because this would render it limited and
imperfect.
6. The One is totally undefinable, incomprehensible and ineffable and only admits negative
descriptions.
7. The One is extremely distant from the human state, separated by multiple levels of being.
8. But at the same time is is immediately present at all levels and in all beings.
9. Gnoseological principles coincide with ontological ones.
10. Hence all multiplicity and totality must participate in and be cause by Unity
11. The universe is a hierarchically ordered totality imbued with the One.
12. Matter in the human world is what is most distant from the One.
13. The One is the measure of perfection of all things, duality and multiplicity is the principle
of imperfection.
14. Hence there is a hierarchy of perfection of levels of being from the closest to the One to
the furthest away.
15. The One is also the teleological principle, the Supreme Good to which all beings aspire.
16. The Supreme Principle as an efficient cause is the One, as a final cause is the Good .
17. The imperfect and limited being has the desire of the superior perfect good which is also
its efficient cause which it participates in.
18. Limit is the principle of existence and coherence and at the same time the cause of
imperfection that leads to the desire for the Good of superior perfection which is infinite .
19. The One imbues everything but does not mix with what participates in it: it maintains
its pure transcendence .
20. The indefinable One is not truly One but superior to unity e and to any relation, cause or
limit. It is One considered as the principle of being which is the primordial limitation .
21. The One is truly infinite.
22. All discourse about the One is approximate, conjectural and by analogy .
23. Divine faith unifies the soul with the Supreme Good in an ineffable way. It cannot be
sought by cognition or with the intellect .
24. We should close our eyes and surrender ourselves to the divine light and become established in the incognizable secret of the Principle of all beings.
25. Theurgic rites are necessary to reach Divine Union as is catharsis, the soul’s shedding all
faculties and positive limited determinations .
26. But a preliminary detailed theoretical philosophical preparation is necessary
27. The One is providential in all levels of being.
28. The principles that immediately succeed the infinite and ineffable One, the Henads, can
be known by their effects .
29. The One is absolutely perfect, complete and self-sufficient. Hence it overflows, irradiates
and causes to proceed exteriorly. But it is not affected or altered in this .
30. In all being of a given level there is first an indefinite flowing forth prohodos from form of
a potency that distancing itself from its source becomes more imperfect and hence reverts
again epistrophê to its original source, longing to attain again the lost perfection .
31. A cause is the source of being and paradigm of its effect. The effect is both different and
similar to the cause .
32. Reversion is effected by renewal of similarity .
33. This re-assimilating reversion is never total and perfect (for then the effect would disappear into its cause) but it happens parallel to the process of procession of the effect from
the cause prohodos. Hence the effect acquires a cyclic stabilizing nature .
34. The effect also remains monê in its cause by virtue of its similiarity.
35. Hence the universe is a hierarchy of levels of being in which each being of a given level is
the cause of a being of the closest inferior level which is its effect and the first being is in
turn the effect of a cause situated on a higher level called the proximate cause.
36. The prohodos is a flowing downwards and the epistrophê is a upwards against the current.
The stabilizing of the two maintains the being in its level.
37. We can follow both along chains or circuits in various degrees and in particular trace for
each being its procession from the Supreme One by descending various degrees until its
own specific level and then follow the same path in the opposite direction to revert again
to the One, the remote cause.
38. The Principle of reversion is desire or appetite oreksis for the One as the Supreme Good.
It is as a means to attain the Supreme Good that each effect reverts to its proximate
cause and desires it
39. There is a level of pure being, a level of life and a level of intellect.
40. There can be no degree of perfection without self-sufficiency.
41. An effect cannot be a cause in its own turn of effects on a lower level if it does not possess
within itself a certain degree of perfection, plenitude and good.
42. In higher levels of beings not only do effects revert to the cause but they can revert to
their cause insofar as this cause leaves an image in them: they find a vestige of good in
themselves and hence are self-constituted authupostata.
43. Everything self-constituted can revert to itself and is self-productive .
44. In the superior levels each being has an aspect of independence, self-sufficiency and selfconstitution when considered in itself independently of its cause.
45. The level of matter is not capable of self-constitution and hence is not a cause and is the
lowest level of the hierarchy of levels of being .
46. The capacity of self-constitution is parallel to the level of unification and proximity to
the One.
47. Each level of being has a multiplicity of beings. But the self-reversion of this level is only
possible through the existence of a monad corresponding to this level which unifies all
aspects of it.
48. After the Supreme One there is the level of intellect (including being, life and intellect)
which contains intellects and the intellectual monad (called simply intellect), then there
is the level of Soul containing souls and the monad of Soul, and then the material or
bodily level.
49. In the Intellect there is a multiplicity of intelligible forms and particular intellects, but
they are strongly unified. The Intellect transcends space and time.
50. In the Soul there is more multiplicity and there is the presence of inner discursive time.
But it is cyclic and unified and can manifest successively all the types of logoi.
51. Matter is the principle of space and extension - of corporality. Here multiplicity is maximum. If a form manifests itself in one place it excludes necessarily its manifestation in
another - one form can only occupy one space. Here differentiation and the capacity of
conflict and disharmony is maximum .
52. Everything capable of self-reversion is incorporeal - and matter cannot do so and is passive
and a source of indetermination
53. All form of this world is caused by superior levels.
54. The emanation issuing from Soul or souls on the level of matter is called nature, it is a
passive indefinite exterior flowing-forth-procession that does not revert to its source but
is lost in matter which is often an obstacle to psychically generated forms.
55. When the ineffable and transcendent One relates to an inferior level it relates through
the aspect of limit .
56. Procession corresponds to the active potency and to the unlimited. Remaining monê of
the effect in its cause corresponds to limit. Reversion corresponds to the mixture of the
limited and the unlimited. Everything that exists depends on these two principles.
57. Whilst in superior levels the unlimited is an active potency, matter is a passive potency .
58. However in the passive potency of matter we can distinguish an aptitude epitedeiotês of
a given matter for a given form which corresponds to a certain desire oreksis for this
form .
59. In all levels of being there is an active and a passive potency. The higher the level the
greater the active and lesser the passive potency .
60. Each effects proceeding from a superior proximate cause also proceeds directly from all
the successively superior causes to the proximate cause: the procession is not only hierarchically linear but a given level causes effects on all inferior levels without delegation
and these proceed and revert to them in different cycles .
61. The more superior a cause the more universal and potent it is in its effects along all levels.
The higher levels form the substrate of basis of lower levels whilst less higher levels cause
more specific principles .
62. Hence there is a double transmission: for example the Soul has in itself a layer that
corresponds to the direct effect of the One as well as an image of the Intellect. The body
not only participates in the One directly but also through the One present in the image
of the Soul that it receives .
63. Thus in the case of a human being we have a being that is not only an effect of the
immediately superior level, the Soul- which only furnishes specifically rationality - but an
effect of all the superior states of beings both directly and indirectly via the Soul - and
these give it for example organic unity and the sensitive and vegetative souls .
64. Matter only receives the influence of the One and its simplicity is as a mirror of the One.
65. All things are in all things, but each in its own appropriate way.
66. All causes contains all its effects (both proximate and remote) in potentiality according
to the excellency and super-eminence of its level.
67. Hence everything that exists exists either in potentiality in a cause, as an image in an
effect or as something self-subsisting.
68. At the level of intellect we can distinguish three levels: the higher level of being and the
intelligible noeton, then the level of life and finally the level of the intellective intellect
in the strict sense. For in our world in order for there to be intellection there but be life
and for life to be there must be being.
69. The level of life can be called the intelligible-intellective and be said to represent the
procession and potency of the intellection of the intelligibles of the intellect.

70. By analogy and more generally the level of being corresponds to permanence monê, huparksis, the level of life to prohodos or dunamis and the intellect to epistrophê or energeia.
But they are different levels of being .
71. Hence by 66 and all that has been said about casues each level contains there others is
the corresponding way .
72. Matter only participates in the One, minerals in Being, plants also in Life, animals also
in Intellect and rational beings also in Soul. Hence the vegetative soul and sensitive souls
of man come from Life and Intellect mediated by their image in Soul. The Soul itself
furnishes rationality.
73. Another point of view on the relation of cause and effect is that of participation and this
is essential to describe the multiplicity of beings existent at a given level .
74. We can distinguish the being or form in itself when it is auto-sufficient and transcendent
- the imparticiple amethektos which is like the sun itself - the form when immanent in
the thing which participates in this form - the participle metechomenon which is as the
rays of the sun - and finally the thing which participates metekhon which is like the thing
illumined by the sun .
75. The participle only exists in function of the participant as an reflection only exists if there
is a mirror.
76. Each level of being has its principle in a monad and proceeds to a multiplicity coordinated
by this monad and all multiplicity on a given level can be traced back to a monad .
77. The monad is the universal or imparticiple essence of each elevel of being. The multiplicity
corresponds to the multiple aspects that a monad of an inferior level will participate in,
for it cannot participate in the higher monad itself but only in its multiple participle
aspects.
78. Only the monad of a given level can unify the multiplicity of participle aspects of this
level.
79. Hence a particular being participates in the higher level in two ways: either participating
in a particular being of the higher level or participating in the monad of its own level
which participates in the monad of the higher level and this is the only way of attaining
a synthetic and global vision of the higher level.
80. We can distinguish a whole anterior to parts, a whole made of parts and a whole in a
part .
81. The higher level monad is a whole anterior to parts, the lower monad as participating
simultaneously in a multiplicity of participle aspects of the superior monad is a whole
made up of parts. Finally the particular being is a whole in a part participating of a
particular participle aspect of the totality of the superior monad .
82. Each participle particular soul has a luminous and incorruptible body okhêma which first
participates in the soul, hence it is not the material body that individuates .
83. The is also a pneumatic body related to the vegetative and sensitive souls .
84. There are two kinds of participle beings corresponding to a monad: one kind are complete
in themselves and capable of reverting to themselves and are self-constituted, the other
kind are like radiations or illuminations .
85. A incorporeal being that is participle and capable of reverting to itself when it is participated in by other things participates in a separable way .
86. The higher participle depends on its participant for its existence only and has total control
of the participant and is not effected by it, but the radiation-participle depends of the
participant.
87. There are bodies participating in radiation-participles of the soul-level and there are participle souls that are yet self-subsisting and not affected by the body of the participating
vehicule. The participation in this case is achieved by another immanent illumination
ellampsis that is inseparable from the participant .
88. Hence in a human being we can distinguish: 1) the transcendent monadic Soul 2) the particular participle rational soul that is separable 3) the irrational soul that is an immanent
illumination of the participle soul 4) the body.
89. Hence just as the further a level of being is from the supreme One the more multiplicity
is present so at each level the self-subsisting participles are closest to the monad and less
numerous than the dependent participles .
90. Hence not all beings of a given level participate in beings of the next higher level. Hence
neither all intellects participate in a henad (and intellects that do are called divine) nor
all souls in an intellect nor all body in a soul .
91. The human souls are the first beings that are submitted to temporality and susceptible to
change and to lose the illumination of the superior intellect. From this comes the source
of evil .
92. We call henads the participle aspects of the imparticiple monadic One and they can be
seen as different modes or individuations of the Supreme One .
93. The totality of henads has the character of unity to the intelectual monad where there is
a unified synthesis of plural participle aspects of the One.
94. But the henads in themselves in their own mode are in an extreme degree a Unity. They
are only plural considered as causes.
95. All henad is in all other henads but they all have a pure individuality and distinction.
They do not need to be unified .
96. All hypostases are unified groups henomenon but are not unitary heniaioi. Only the
henads that are superior to being (super-essential), to life (super-vital) and to intellect
(super-intellectual), are unitary, that is, have the source of unity in themselves .
97. The henads, which are also called gods, are primordially and supremely simple and totally
self-subsisting .
98. There are four different types of relation between beings: identity, difference, part and
whole and whole and part. But the absolute immaculate purity amigeis of the gods is
bereft of any relation.
99. The only distinctive characteristic of the gods is their individuality idiotes, which is a
primordial determination of the One.
100. But they are ineffable, unknowable - only knowable as unifyers of their causes .
101. All gods together cannot be compared to the One which inconceivably surpasses the divine
multitude .
102. Each level of being must have a highest layer corresponding to the One and which can
also participate in the One through the corresponding monad. Hence just as only some
souls participate in an intellect so too only some souls participate in a god and are divine
souls and only some intellects are divine intellects .
103. But all the hierarchy of levels of being must pre-exist in the gods as in their cause. Hence
there are intelligible, vital, intellective, hypercosmic (corresponding to the soul-level),
hypercosmic-encosmic and encosmic (corresponding to nature, the corporeal world and
intermediate level) henads63 .
104. The henads in which the higher levels participate are closer to the One, are more universal
and potent in their causes, but the ones that the lower levels participate in are further
away, less universal and less potent .
105. Only the level of being can directly participate in the gods. All the level of being must
participate not only in the corresponding god but also in all subsequent gods so as to be
able to transmit their participation on down to lower levels .
106. Hence all monad is divine and metaphysics coincides with theology. All multiplicity
proceeding from a monad has in first place a divine order according to the level of the
monad, call the summit of the level.
107. All the order of the gods derives from the principles of Limit and Unlimited .
108. The gods in which Limit predominates are the patrikoi , paternal gods and are the highest
level. The gods in which the Unlimited prevails are called genetikoi and occupy the lowest
rank. The ones in which these two principles are in balance occupy the middle rank and
are called telesiourgos, or workers-of-perfection, and they preside over the reversion of
being .
109. There is also a fourth order of gods called the phrouretikoi, protectors, or achratoi, the
immaculates, that preserve each being in its own level and prevent it from falling into
lower levels .
110. The influence of the gods extends to the lowest level of our world .
111. Every being is connected to a corresponding divine order which extends in a chain culminating in the supreme One .
112. Hence there is the order of divine souls, then the order of souls that always follow these.
Many times they fall into generative temporality. However they remain part of that divine
order .
113. Even in the material world all being is connected to a order of encosmic gods through
the correspondence with beings that represent a divine encosmic being. For example the
Lotus flower and the Heliotropos which have a solar connection and represent a certain
order of encosmic gods belonging to a vertical chain leading to the supreme One.
114. Hence all being is a symbol sumbolon and a sign sunthema connected to a divine chain.
The human soul has the symbols and vestiges of the gods and the plenitude of all the
logoi.

Proclus' Elements of Theology as Holology and Aetiology

 https://chryssipus.blogspot.com/2024/04/proclus-elements-of-theology-as.html

Eunapius - About Plotinus, Porphyry and Iamblichus

https://via-hygeia.art/eunapius-about-plotinus-porphyry-and-iamblichus/

Ovid on Pythagoras (from Met. XV)

Here lived a man, by birth a Samian.
He had fled from Samos and the ruling class,
a voluntary exile, for his hate
against all tyranny. He had the gift
of holding mental converse with the gods,
who live far distant in the highth of heaven;
and all that Nature has denied to man
and human vision, he reviewed with eyes
of his enlightened soul. And, when he had
examined all things in his careful mind
with watchful study, he released his thoughts
to knowledge of the public.

He would speak
to crowds of people, silent and amazed,
while he revealed to them the origin
of this vast universe, the cause of things,
what is nature, what a god, whence came the snow,
the cause of lightning—was it Jupiter
or did the winds, that thundered when the cloud
was rent asunder, cause the lightning flash?
What shook the earth, what laws controlled the stars
as they were moved—and every hidden thing
he was the first man to forbid the use
of any animal's flesh as human food,
he was the first to speak with learned lips,
though not believed in this, exhorting them.—

“No, mortals,” he would say, “Do not permit
pollution of your bodies with such food,
for there are grain and good fruits which bear down
the branches by their weight, and ripened grapes
upon the vines, and herbs—those sweet by nature
and those which will grow tender and mellow with
a fire, and flowing milk is not denied,
nor honey, redolent of blossoming thyme.

“The lavish Earth yields rich and healthful food
affording dainties without slaughter, death,
and bloodshed. Dull beasts delight to satisfy
their hunger with torn flesh; and yet not all:
horses and sheep and cattle live on grass.
But all the savage animals—the fierce
Armenian tigers and ferocious lions,
and bears, together with the roving wolves—
delight in viands reeking with warm blood.

“Oh, ponder a moment such a monstrous crime—
vitals in vitals gorged, one greedy body
fattening with plunder of another's flesh,
a living being fed on another's life!
In that abundance, which our Earth, the best
of mothers, will afford have you no joy,
unless your savage teeth can gnaw
the piteous flesh of some flayed animal
to reenact the Cyclopean crime?
And can you not appease the hungry void—
the perverted craving of a stomach's greed,
unless you first destroy another life?

“That age of old time which is given the name
of ‘Golden,’ was so blest in fruit of trees,
and in the good herbs which the earth produced
that it never would pollute the mouth with blood.
The birds then safely moved their wings in air,
the timid hares would wander in the fields
with no fear, and their own credulity
had not suspended fishes from the hook.
All life was safe from treacherous wiles,
fearing no injury, a peaceful world.

“After that time some one of ill advice
(it does not matter who it might have been)
envied the ways of lions and gulped into
his greedy paunch stuff from a carcass vile.
He opened the foul paths of wickedness.
It may be that in killing beasts of prey
our steel was for the first time warmed with blood.
And that could be defended, for I hold
that predatory creatures which attempt
destruction of mankind, are put to death
without evasion of the sacred laws:
but, though with justice they are put to death,
that cannot be a cause for eating them.

“This wickedness went further; and the sow
was thought to have deserved death as the first
of victims, for with her long turned-up snout
she spoiled the good hope of a harvest year.
The ravenous goat, that gnawed a sprouting vine,
was led for slaughter to the altar fires
of angry Bacchus. It was their own fault
that surely caused the ruin of those two.

“But why have sheep deserved sad destiny,
harmless and useful for the good of man
with nectar in full udders? Their soft wool
affords the warmest coverings for our use,
their life and not their death would help us more.
Why have the oxen of the field deserved
a sad end—innocent, without deceit,
and harmless, without guile, born to endure
hard labor? Without gratitude is he,
unworthy of the gift of harvest fields,
who, after he relieved his worker from
weight of the curving plow could butcher him,
could sever with an axe that toil worn neck,
by which so often with hard work the ground
had been turned up, so many harvests reared.
For some, even crimes like these are not enough,
they have imputed to the gods themselves
abomination—they believe a god
in heaven above, rejoices at the death
of a laborious ox.

“A victim free
of blemish and most beautiful in form
(perfection brings destruction) is adorned
with garlands and with gilded horns before
the altar. In his ignorance he hears
one praying, and he sees the very grain
he labored to produce, fixed on his head
between the horns, and felled, he stains with blood
the knife which just before he may have seen
reflected in clear water. Instantly
they snatch out entrails from his throbbing form,
and seek in them intentions of the gods.
Then, in your lust for a forbidden food
you will presume to batten on his flesh,
O race of mortals! Do not eat such food!
Give your attention to my serious words;
and, when you next present the slaughtered flesh
of oxen to your palates, know and feel
that you gnaw your fellow tillers of the soil.

Proclus' Elements Prop. 1

A nice edition of Proclus' Elements of Theology.

There would seem to be a problem with Proclus' proof from the point of view of modern set theory. If we take the natural numbers N then the even numbers E are a 'part' of N and yet have the same cardinality as N. So in this case in what sense is the whole N 'greater' than the part E ?

We could  do an idealist and phenomenological reading of this proposition, specially in light of Husserl's Philosophy of Arithmetic which is actually a treatise on some of the highest categories and operations of the understanding, in particular the act of combination or synthesis. So let us take Proclus' plêthos to be any object of consciousness which can be called an aggregate.

We begin with the psychological characterization of that abstraction which leads to the (authentic) concept of the multiplicity, and subsequently to the number concepts. We have already indicated the concreta on which the abstracting activity is based. They are totalities of determinate objects. We now add: "completely arbitrary" objects. For the formation of concrete totalities there actually are no restrictions at all with respect to the particular contents to be embraced. Any imaginable object, whether physical or psychical, abstract or concrete, whether given through sensation or phantasy, can be united with any and arbitrarily many others to form a totality, and accordingly can also be counted. For example, certain trees, the Sun, the Moon, Earth and Mars; or a feeling, an angel, the Moon, and Italy, etc. In these examples we can always speak of a totality, a multiplicity, and of a determinate number. The nature of the particular contents therefore makes no difference at all. (Husserl, PA, p. 17 Dillard tr.)

Thus we must distinguish between concrete multiplicities and abstract multiplicities.  Husserl explores the the aspects of combination and synthesis involved, including syntheses of syntheses and so forth. Proclus' conclusion would then seem to be follow from the limitations of such syntheses operations for human consciousness. The problem is that this is relative to the human mind only.

However perhaps we can glean some insights into neoplatonic epistemology and psychology from the interesting work by Gregory MacIsaac, The Soul and Discursive Reason in the Philosophy of Proclus, 2001.

Proclus' proof (his assumption that there is nothing greater than the apeiron) seems to suggest the axiom of foundation of ZFC.  If we view a set as a tree ordered by the membership relation then all paths starting at the root (the original set) must eventually end.

Introduction

This blog has the following objectives:

1. To study neoplatonism as bona fide philosophy, taking it at face value in a contemporary context. Thus our analyses and discussions will not shy away from a hermeneutics and dialogue with contemporary philosophy and the technical apparatus of modern mathematical logic.

1a. What was the relationship between neoplatonism and so-called middle platonism (which seems to have been philosophically very rich and thorough) and how original was the former with regards to the latter ?  Why was not middle platonism preserved but suffered the same fate as the numerous works Chryssipus and other Stoics ? It seems Numenius only survived in fragments mainly because these suited the apologetic aims of Eusebius.

We must study the evidence and traces of the most elevated and advanced philosophical, ethical and socio-political thought in antiquity.  Genuine philosophy and philosophical vitality were doubtlessly to be found in the ancient Stoics (Chryssipus) and certainly in many successors of Aristotle (like Theophrastus and later commentators) and the Academy (in its many forms). And certainly in Xenophanes, the Eleatics, an alternative interpretation of the Sophists such as Protagoras, Democritus and Leucippus,  Pyrrhonism (Sextus Empiricus) and in Galen. We just do not have enough evidence to judge the philosophical vitality and purity of middle platonism, though there were clearly ethically advanced neo-plythagoreans like Plutarch. Perhaps the most interesting elements in Plotinus where precisely those derived from Ammonius Saccas ?

Genuine philosophy and the philosophical spirit are inseparable from profound ethical and socio-political implications (and Popper saw this).  Genuine skepticism and the development of the most refined and sophisticated logic are closely related. We must look for the pure, uncompromised spirit of logic, ethics and mathematical science in antiquity.

After the first centuries of the Common Era philosophical and ethical vitality and progress seem to have become somewhat extinguished. Neoplatonism and even middle platonism might be seen as reactionary (religious, occultist and socially and politically conservative) manifesting a considerable similarity to many later western 'traditionalist' movements.

2. To study neoplatonism from the point of view of practical philosophy, ethics (in particular vegetarianism and animal rights) and a path of spiritual cultivation quite analogous to the practices of eastern traditions. And to answer the question: what was theurgy for the neoplatonists ?

A major problem is that after the enlightened animal rights elements in  Porphyry's De Abstinentia - which includes the rejection of animal sacrifice for the philosopher  - with Jamblichus animal sacrifice is again promoted as an essential part of theurgy. For Plotinus and Porphyry the pure activity of pure thought, philosophical and probably mathematical thought, seems to have been the essence of theurgy together with, it seems, a kind of poetry. It seems that neoplatonism drifted further and further from its original Pythagorean (see Ovid's account in book XV of the metamorphoses and also works by Plutarch) and Buddhist (?) roots. In Plato we certainly can discern powerful reasons for the rejection of animal sacrifice.

See the interesting study Blood Sacrifice and Bloodless Sacrifice in Porphyry and Iamblichus by Eleanora Zeper.

Thus we must understand the theurgical dimension of certain ethical habits and pure logical thought; the same goes for certain experiences of love and beauty depicted in the Phaedrus.

Our major interest is finding evidence for ancient cultures, cultures of remote antiquity which did not practice slavery or animal sacrifice or glorify warfare and hunting or reduce women to a subordinate role.

Plotinus seems to have accepted both slavery and the flogging  of slaves as attested in the episode of the stolen necklace in Porphyry's biography of Plotinus (section 11 in the Loeb edition).

3. To study and evaluate the historical and archaeological theories of the neoplatonist philosophers concerning  the ancient cultures and traditions of Chaldea, Phoenicia, Syria and Egypt (a great number of the neoplatonists were also born in those regions) and of course ancient Greece itself. This is what Thomas Taylor wrote on Jamblichus' De Mysteriis:

It appears to me that there are two descriptions of persons by whom the present work must be considered to be of inestimable worth, the lovers of antiquity and the lovers of ancient philosophy and religion. To the former of these it must be invaluable, because it is replete with information derived from the wise men of the Chaldeans, the prophets of the Egyptians, the dogmas of the Assyrians, and the ancient pillars of Hermes; and to the latter, because of the doctrines contained in it, some of which originated from the Hermaic pillars, were known by Pythagoras and Plato, and were the sources of their philosophy; and others are profoundly theological, and unfold the mysteries of ancient religion with an admirable conciseness of diction, and an inimitable vigour and elegance of conception. To which also may be added, as the colophon of excellence, that it is the most copious, the clearest, and the most satisfactory defence extant of genuine ancient theology.

4. Investigate if the revival of neoplatonism could play a positive role in addressing the political, social and religious problems of the modern world. In particular investigate in what way have Zoroastrian, Chaldean, Phoenician, Syrian, Egyptian and Hellenic traditions been incorporated and preserved (faithfully or distorted) in Judaism, Christianity and Islam (specially in Iran) ? What are we to make of theories which take this transmission to have been carried out only in a highly veiled and cryptic way (though of course there are countless examples of very obvious continuation in the Nag Hammadi texts, in the Marian cultus and theological doctrines as well as the extensive explicit presence of neoplatonism in Christianity and Islam) ? Notice also the great difference between the limited role of the Devas in the Pali Canon and the role of the bodhisattvas in the Mahâyâna which clearly have a theurgical role (Jamblichus' anagogic Gods).

5. It what sense was the so-called 'neoplatonism' of the Renaissance (Ficino, Pico della Mirandola, etc.) a faithful continuation of the original neoplatonic school ? Perhaps it was an appropriation or compromising of genuine neoplatonism to suit  certain political, religious or magical-occult agendas ?