TPC, self and temporality

We have described TPC as being involved with the transcendental awareness of the total continuum or process of thought considered purely as such, as merely a process of thought.  But TPC has an important aspect: transcendental philosophical consciousness involves the transcendental awareness of those preconditions and structures upon which ordinary consciousness entirely depends and at the same time of which ordinary consciousness as a rule is oblivious of. It is almost as if ordinary consciousness only exists, can only exist, under the condition of it carrying a forgetfulness of its own transcendental preconditions and predetermining structures. Transcendental consciousness is thus also the consciousness of what non-transcendental consciousness must necessary forget.   If TPC in turns does not have full knowledge of such transcendental preconditions and structures, it falls back into a false dualism, limitation and illusory reification.  Two of the most important of such preconditions are selfhood and temporality.  That which claims to be a being which we carry along as a huge burden - all possible transcendental questioning, untangling and analysis being forgotten - and that which we must forget in the first place in order for the very being-ness of being to arise.  Only then we arise to the selfless liberated insight into the pure universal sphere and flux of pure thought processes: only thus is further progress of TPP possible. The ordinary self is the protoype of illusory unquestioned, posited, composite being. The original prototype of being in transcendental temporal oblivion. One task is to study the formative tendency which constructs this prototype employing among other things certain classes of conscious phenomena.This prototype is the the scaffold upon which world-positing and world-directedness and the mutual feedback of the identity construct takes place. Being-in-the world is not a transcendental condition or principle but a non-transcendental illusion conditioned by transcendental ignorance and forgetfulness. Following Plato a philosophical consciousness must include knowledge concerning the phenomenology of love and beauty.  This is a transcendental illusion which yet in its purest form  participates of the some of the modalities of TPP-liberated consciousness.  It paradoxically offers a glimpse of the bliss of beinglessness falsely conditioned and limited by being, by the illusory directed network of the self-prototype and its world. When we are born we are forced to build our identity and learn the world; when 'born into the spiritual life' our duty is to unbuild this identity and learn to see through the illusion and construct of the world. It is as if the first phase were like being plunged into the water, a downwards journey into illusion and forgetfulness. The second phase is when we begin to rise again and make our way back towards the surface and the air of light and truth. TPP is not about an 'individual' detaching itself from the 'world' and still less about an 'individual' transferring its feelings, desires, volitions and tendencies to alternative 'imaginary friends' or any kind of ontological construct - rather it is about seeing through both the 'individual' and the 'world' and their dependent interplay and mutual constitution. There is no contradiction between Yogacara and Madhyamaka. Two of the main tasks of TPC-based philosophy are: i) the untangling of all concepts and categories and the showing forth that they all exhibit the mark of the alleged being of the prototype (self), ii) exhibing the absoluteness of the moral law,  that the absolute can be characterized as morality (dharmakaya). The profound affinity between the consciousness and act of TPC and TPP and that of the essence of morality.  In all of the above the great interest of Kant is patent.  A model of the universal  flux of pure consciousness (Indra's net): neural nets, cellular automata, music theory, formal grammar, tessellations, Wang tiles, knots (and our own theory related to this) - unfolding of the concept of computation (paticcasamupada) and its concurrent parallel interconnected forms. And most importantly the theory of (meta) reflection and representation.  And the logical and mathematical theory of programs, specially the hierarchy of function definitions. The way forward in physics, the way to transcend and rectify quantum field theory, seems to us to involve a radical new foundation for physics based not on the formalism of functional analysis and operator algebras but rather on finitary combinatorics, theoretical computer science, graph theory and algebra. Maybe something following Birkhoff's lattice approach. 

A mathematical model of transcendental pure consciousness (which can only be a limited exterior projection, a partial mirroring...) will involve a spatialization of concepts (structures) wherein their interconnection and mutual (meta) reflection takes place - in a temporal dimension. A general theory of networks which generalizes neural nets, cellular automata, tessellations, crystallography, (higher)category theory and proof theory. This will include the spatial, topological aspects of music, and the architecture of a semantic universe (semantic space) or lexicology. But we can take also an atemporal space-time approach. Has the effects of special relativity on the physical realization of Turing machines been studied? Could special relativity be the key to how physical systems could compute beyond the Turing limit? Perhaps the quantum effects on physical computational systems can be studied in a way different from the current work in 'quantum computing'. In Hegel's  Logic we can discern a marked spatial, geometric way of thinking of concepts, their unfolding, mirroring and interaction.

The knot, the tangle, the projection, the multiplicity is not real, what is real is the formative energy which ties and then unties, tangles and then untangles, projects and then dissolves, multiplies and then unites. Is this not the ultimate meaning of the Hegelian Idea, the holomovement of skepsis which though necessarily dealing in formalism is not itself entirely formalizable ? Each thought (unit of consciousness) containing implicitly all other thoughts and each thought only existing through its relationship to them? That by trying to isolate a thought 'in itself' it inevitably looses the essence of what it really is.

Another approach is to view space-time as characterizing non-transcendental consciousness and being characterized by its algebraic and logical properties. Thus pure transcendental consciousness should be represented by a structure in which some of these logical or algebraic properties are different, the most famous being Heyting rather than Boolean (Brouwer), non-commutativity (Connes) or non-distributivity (Birkhoff).  Birkhoff's explaining away of the uncertainty principle as simply an expression of non-distributivity. However this approach does not go beyond the previous proposal, it is still a priori and phenomenologically a spatialized or space-time based 'collection' of components, parts, connected to each other by some kind of relation or network. And the essence of representation theory is bringing this spatial substrate further into the foreground.

The philosophical elephant in the living room is that we have not explored something which should occupy a fundamental place in TCP. That of symmetry, quasi-symmetry and analogy. Like temporality and the prototype of the self, it is so pervasive as to be habitually consigned to an implicit oblivion. Symmetry and its allied modes pervade biology, psychology, linguistics, chemistry, physics, mathematics, logic, computer science, engineering, the structure of philosophical systems, poetry, music,...so deeply, in such a far-reaching manner, that like temporality or the construction of self, we simply forget and cannot fathom its central, universal transcendental a priori role (symmetries abound in the architecture of Kant's and Hegel's systems, Linear logic brought forth the implicit symmetries and modalities in classical logic). We end with the following preliminary (Hegelian) descriptions: symmetry is the quality of a being which allows it to change and yet remain the same. Symmetry is also that by which a being may produce itself (notice than in symmetric tiling we can transport any tile to any other tile while preserving the identity of the whole). Symmetry is the foundation for reflection-into-another and reflection-into-self. Recall how spinors capture the 'memory' (homotopy class) of a rotation in SO(3), much like the dialectic in Hegel. And object may be brought back to itself and yet have gained something permanent.  Symmetry is that by which an inherently dynamic process can produce the illusion of stability and being. Symmetry allows us to fathom essentially interrelated holistic systems (illustration of 'maps of consciousness': dictionaries, grammars, thesauri, manuals of stylistics and translation, encyclopedias, biographies, novels).

A radical new look at science

Kantian question: what scientific and mathematical theories are strictly required for the design, engineering and effective implementation and production of modern technological and industrial artifacts (a computer, a drone, a car, a MRI machine, a satellite, a vaccine, a nuclear reactor). This is philosophically similar to the simpler question Aristotle posed about products of art (technê). It is seems plausible that there is a huge amount of published theoretical material which is neither necessary nor useful, strictly speaking.

A disturbing question: there are presently technological artifacts which are not fully understood (or even capable of being practically engineered) by a single human being. For instance current versions of the most common operating systems. Could technological artifacts come eventually to automate their own design, production and maintenance (and even security and defense) outside the possibility of human understanding, design and control ?

This approach favors the view that the differential mathematical apparatus in science is never meant to be nor should be read as a model strictly speaking but as a computational device synthesizing modelling information for concrete more realistic and complex models. In other words, the Navier-Stokes equations do not model fluids, we are in the presence of a mathematical device for compactly representing the potential computational information of actual approximate models of reality. Abstract devices which are used to extract finitary computational content (like the convenient fictions of Leibniz but without taking any philosophical position on mathematical platonism).

There are interesting arguments for the Lebesgue integral being useless and meaningless in the context of actual concrete engineering practice (limited by measurement and scale). 

Philosophical, historical and spiritual inquiries

There are many difficulties with the interpretation and practice of Buddhism as well as with trying to recover original Buddhism. This is well-known. It would be wonderful if we could find an ancient, prehistoric and living tradition which is identical to the highest essence and goal of philosophy - with TPC and TPP, that fully developed leads to the fulfillment of philosophy and vice-versa. It would allow one to consolidate and integrate different philosophical systems and perspectives and to disclose their highest meaning and value. And also it will furnish a basis to discern the scientific, psychological and ethical value of certain systems despite certain fundamental philosophical errors. It is Ariadne's thread that allows us to clarify, diagnose and resolve all confusions and errors in the history of Buddhism. But such a holy grail is not easy to find. What we have are a different distinct parallel ancient traditions and most importantly situations in which pure teachings are misappropriated and integrated into fundamentally antagonistic cultural life-forms. The Upanishads do not represent any kind of single spiritual-philosophical doctrine and practice but a heterogenous plurality of them (a thicket and jungle indeed). Moreover in the Upanishads we find what appears to be an adulteration and appropriation of pure TPC/TPP-oriented teaching in the direction of  proto-Hinduism with its caste system (a complex subject wherein we must be aware of British colonial influence in current perceptions; some argue that the caste system does not correspond to the fluid social division of labor based on qualities rather than birth said to have been present in the Vedic period), ritualism, the cult of procreation, family and material wealth, anthropomorphic and naturalistic religion and a spiritual legitimizing of warfare (notably in the Gîtâ - with parallels in the Kyoto school).  Nowhere is this more evident than in the doctrine of the four ashramas. However this does not rule out that there are ancient portions of both the Upanishads and the Gîtâ which furnish valuable material and information about ancient higher spiritual practices.  We must not overlook the extreme antiquity and importance of texts in Old Avestan.

There can be no doubt that in original Pali Buddhism as well its flowering into the great philosophical Mahâyâna systems of the Yocara and Madhyamaka, represents, together with the parallel traditions of the Samkhya (Burley has vigorously argued for its close affinity to Kant and Husserl and not to naive realist cosmology),  the sister schools of Nyâya and the Kanada's original Vaisheshika,  Râja-Yoga and Jainism, the most pure, profound and beautiful root and fountain that arose in Indian soil and its supreme expression of TPC and TPP. The best aspects of the Vedanta are completely indebted to it, though Advaita Vedanta represents an orthodox Hindu appropriation  of Buddhism (an artificially idealized version of the Vedanta has been presented to Western audiences). Just compare the Pali suttas concerned with caste with what over a thousand years later Shankara writes in his commentary on the Brahmasutras.

These supreme flowering of TPC and TPP  provide the clue to understand what is best in the Western spiritual and philosophical tradition, for instance the Platonic, Pyrrhonic and Plotinean schools, the texts of the Corpus Hermeticum, the ultimate meaning of Hume, Kant, Schopenhauer and Hegel.

It also presents us with a significant challenge and project: the enigmatic gnostics and gnostic texts, for instance the Pistis Sophia and the Nag Hammadi library. One view is that the gnostics and the gnostic texts represent a rare and fortunate survival of very ancient traditions cast in a 'Christian' form. This is the view of G.R.S. Mead in the introduction to his translation of the Pistis Sophia: gnostic texts represent a rare and unique survival of very ancient higher spiritual traditions pertaining to Egypt, Syria (and Phoenicia) as well as Persia and Babylonia. It is also important to study the 'Chaldean Oracles' and their commentaries. A very important place must be occupied by the study of Manicheism and Mandaeism.  Also the investigation of how far the medieval Sufi texts (including those of the Iranian esoteric traditions) represent a a transmission or more-or-less veiled continuation of much earlier neoplatonic, hermetic, manichean, mandaean, zoroastrian, gnostic traditions (the gnostic traditions seen in turn as Egyptian, Syrian, Phoenician and Chaldean). It would also seem that certain more philosophical Sufi texts contain already all the essential ideas of Leibniz and Spinoza (a fact which is historically not that surprising if we consider the possible influences on both these philosophers). It seems plausible that Sufism had a huge overlooked role and influence on all other medieval spiritual traditions (not only Christian but also the medieval Zohar).

However it is also possible that we might arrive at the conclusion that at least some 'gnosticism' does not represent a TCP/TPP directed spiritual-philosophical traditions or its reflection in the higher currents of western philosophy (recall Plotinus's critique of the gnostics). It could be that so-called gnosticism is un-philosophical and does not align with the spiritual orientation and goals of TCP and TPP. Rather so-called 'gnosticism' may represeny an essentially ritual-magical tradition, like certain aspect of later neoplatonism and very much akin to the Tantric schools of India and Tibet. Perhaps there is a kind of myth-making, magic and ritualism - for instance the presence of astrology - that is not only a perversion of science and mathematics but also of art. Maybe this is why TCP and TPP oriented India and philosophical Greece - both guided by TPC and TPP - produced such works of genius in logic, linguistics, mathematics, science and art. Does this assessment apply to Manicheism gnosis (which is of interest for its link to Buddhism) ? Perhaps such texts as the Pistis Sophia heavily indebted to Manicheism (the 'Virgin of Light' is the Manichean Kanig Roshn).

TPC unveils, skeptically analyzes and circulates among fundamental principles and structures of consciousness in absolute pristine given-ness and TPP is concerned with the path of liberation.  There could not be a greater opposition and contrast between TPC and TPP on one  hand and religious anthropomorphic mythologies and cosmologies on the other - like those of the gnostics and Manicheans. It is as if someone took the concepts, categories and principles in Kant's Critique of Pure Reason and turned them into a cosmic mythology of anthroporphic eons and archons mixed with astrology and magic.  It is as if we took Kant's transcendental critical subjective idealism and turned it into the most crude dogmatic realistic anthropomorphic naturalism: for instance associating the twelve categories of the understanding with the twelve signs of the Zodiac.  It seems as if Mani did precisely this with the TPC-doctrines of  Samkhya and Buddhism and the gnostics did this with the Hermetic texts and Plato. This represents a dangerous and unfortunate human cultural-spiritual tendency and in light of this we can appreciate even better the original teaching of the Buddha as well as Pyrrho.  We add: would it be possible to take certain theories of pure mathematics and convert them into a gnostic-like mythology ? 

But we note that certain texts in the Nag Hammadi like the Gospel of Thomas, Gospel of Phillip and the Gospel of Truth do appear to have a certain affinity to TPC and TPP and little in common with typical gnostic cosmologies and mythologies. Or at least they have a more philosophical, critical even Socratic-ironic bent that recalls the Zen koans.  Also we do not know how precisely the gnostic texts were read and interpreted, or who wrote them.

One of the greatest enigma of history is the relationship between such texts and Judaism and the  Old Testament.  Nothing could be more different, unrelated and even directly antagonistic.  What could the Gospel of Thomas have in common with the Pentateuch and book of Joshua ? A vegetarian, animal-rights upholding pacifist community that took the Exodus and Leviticus as holy texts ?  The same absurdities are patent in those who would wish to make the Therapeutae described by Philo  some kind of Buddhists. It seems clear what we have here is the historically pattern of borrowing (in fact plagiarism because the sources are not acknowledged) and (mis)appropriation of certain higher spiritual traditions and materials (probably taking place in Alexandria, but also among the Jewish Stoics who wrote the Pirkei Avot). The world of the Nag Hammadi scriptures is a kind of alternative reality where the only cultural-historical context is the mythology of the Old Testament: the rest of the world and history is almost entirely ignored and cancelled. What about the countless other Middle Eastern peoples (Chaldeans, Syrians, Phoenicians, etc) and Egyptians (whose traditions the Pistis Sophia appropriates) ? We must never loose sight of the pre-eminence and antiquity of the Egyptian tradition and the Graeco-Egyptian gnosis. This is what McBride writes in his book The Egyptian Foundations of Gnostic Thought:

It is in the area of Hellenistic Gnosis that the Egyptian foundations of Gnostic thought attained their greatest synthesis with the diverse strata of metaphysical thought in Hellenistic and Roman times. Here we have the beguiling and obscure phenomenon of literate Jews who were no longer Jews in any real sense of the term, Greeks who were no longer Greeks in their religious affiliations and bloodlines, Egyptians who were no longer “pure” Egyptians, and proto-Gnostic magicians and priests in the period from 100 B.C.E. to 100 C.E., all of who contributed to the evolution of Gnostic thought. Above all, there remains the essential enigma of the literate and bilingual, if not multi-lingual, “Graeco-Egyptian”. In a sense, this group represents both and neither of the scholastic categories of “Greek” and “Egyptian”, so removed were they from traditional modes of thought and even clear ethnic divisions.

 A somewhat similar situation is found in the Pali suttas where other ancient Indian philosophical and spiritual practices is are strangely ignored (except the Jains). It seems pretty clear that the authors of the Nag Hammadi library are supposed to be Jews (or descendents of Jews) who converted to a radically 'heretical' (allegorical, gnostic) form of Judaism.  

Already in the 1st century CE Epictetus was preaching a philosophical, spiritual and ethical doctrine which equals if not far surpasses anything we find in the Bible or the Gospel of Thomas. Along with the strong presence of Pythagorean, Middle Platonic, Hermetic,  Neoplatonic, Stoic and Pyrrhonic schools there are strong arguments for a pervasive transmission of the Buddhist, Jain, Samkhyan and Yogic doctrines in the ancient world. TPC and TPP were both ancient and widespread. Thus there is no spiritual, philosophical or cultural-historical excuse or justification for the Old Testament centric world-view implicit in the New Testament or part of the Nag Hammadi scriptures. Other parts of the Nag Hammadi library furnish radically distinct 'evil demiurge' interpretations of the Old Testament which are even more bizarre (the Old Testament remains central but now for a different reason: offering unique intel into the doings of a bad deity). Docetic Christology (such as found in Manicheism, Marcion, the Acts of John) is also bizarre. It would be interesting the compare this with mythicist views regarding the historical Jesus (which for some reason, which has nothing to do with new evidence, have fallen out of favor). In the Docetic-Manichean view Jesus is a cosmic being and principle (much like the Mahâyâna Bodhisattva) who manifested via a spiritual body in ancient Palestine. It us curious that many aspects of Manichean Christology were adopted by Wagner in the libretto of Parsifal. 

The Aramaic dialects: one of the oldest and most important of the languages (both spoken and written) of ancient Palestine (including Syria).This ancient language was adopted by the inhabitants of Palestine (and Syria) before and during the Roman era (one might call it the semitic counterpart of koinê Greek). A common word for God was Alaha ܐܲܠܵܗܵܐ .  A version of the (cursive) Syriac script was used by the Nestorians and is very similar to the Arabic script. Ancient authors sometimes referred to Aramaic as 'Syrian'. The term derives from the place-name 'Aram' (supposedly in Northern Syria). A common view is that the Aramaic square script, also called Ktav Ashuri (i.e. Assyrian writing), basically the modern Hebrew alphabet, was adopted by Jews after the Babylonian exile (c. 6th century BCE) from Imperial Aramaic, a cursive script used during the Achaemenid Empire.There followed a decline of Aramaic as the spoken language of the Jews which parallels the subsequent domination of Arabic in Egypt and Palestine.There were many important Aramaic speaking currents of early Christianity and the Pesshita is widely used in NT studies. It is possible that some of the neoplatonist philosophers like Porphyry spoke Aramaic. Some Manichean scriptures are in Aramaic.

Finally we address the fundamental question: what criterion do we have that allows us to judge whether a given person, spiritual practice, spiritual school, etc.  has attained TPC and genuine spiritual realization? The answer is simple: we have one perfect criterion which is perfect in the negative sense, it allows us to eliminate false claims of enlightenment. This perfect criterion involves testing the alignment of the person with universal moral principles applicable unconditionally to all human beings (human rights) as well as universal moral principles regarding the treatment of animals and indeed all life forms. For example any philosopher and spiritual teacher who accepted or tolerated things like a caste system, slavery, torture, the mistreatment of animals, cannot categorically be considered as having achieved complete or a higher TPC-enlightenment. The universal moral law is a revelation of the absolute and a path to the absolute. Another infallible criterion is that TPC is inseparable from the scientific spirit and the spirit of criticism and free inquiry.

Elementary Combinatorics

 

Consider the ordered sequence $(1,2,3,4,5,6,7,8)$ organized as in the figure above. We are interested in potential generators of the permutation group $S_8$.  The generators in question are the following (which also explains the diagram):

$F = (1 2 3 4),  B = (5 6 7 8),  L = (1 4 8 5),  R = ( 2 6 7 3), U = (1 5 6 2), D = (3 7 8 4)$.

These generators shift the numbers on their corresponding boundaries  in a clock-wise direction.  These generators $4$-cycles and thus of order 4 and $F^{-1} = F^3$ and so forth for the other generators. For convenience we list the inverses:

$F^{-1} = (1 4 3 2),  B^{-1} = (5 8 7 6),  L^{-1} = (1 5 8 4),  R^{-1} = ( 2 3 7 6), U^{-1} = (1 2 6 5), D^{-1} = (3 4 8 7)$.

We have the following elementary facts about permutations and transpositions:  $(a b c) = (a c) (a b)$ and  $(c d) = (a c b) (a b c d)$ (for $a,b,c,d$ distinct).  We use the notation $[X,Y] =     X^{-1}Y^{-1}XY$. Note that $[X,Y]^{-1} = [Y,X]$ and that if $[X,Y]$ can be written as a composition of disjoint transpositions then $[X,Y]^2 = I$ and $[X,Y] = [Y,X]$.

Let us calculate:

$[D^{-1},F^{-1}] = (14)(37)    \quad [D,R^{-1}]= (37)(42)$

Hence  $T = [D^{-1},F^{-1}][D,R^{-1}] = (14)(37)(37)(42) = (4 2 1)$.

Then $TF = DFD^{-1}F^{-1}D^{-1}RDR^{-1}F =  (4 2 1)(1 2 3 4) = (2 3)$.

It is now easy to see that $F,B,L,R,U,D$ generate $S_{8}$. 

Let $\Sigma = \{id,\sigma,\sigma^2\}$ be the cyclic permutation group on $(1,2,3)$ (of order 3).  

Consider 8 copies of $\Sigma$ denoted by $\Sigma_1,...,\Sigma_8$ and let $W = \Pi^8_{i =1} \Sigma_i$.

Suppose  we had a map $S^i$ acting on $W$ which for $i = (1,2,3)$ multiplies components $1$,$2$ and $3$ of $W$ by $\sigma$. And likewise we have $S^i$ for $i = (2,3,4), (3,4,1),(4,1,2)$ and also $i = (1,2,5)$, etc.

Then $Y = (S^{(2,3,4)})^2 S^{(1,2,3)}$ is equivalent to applying $\sigma$ to the first component and $\sigma^2$ to the fourth component. For instance for $w = (id,id,id,id,id,id,id,id) \in W$ we have $Y(w) = (\sigma,id,id,\sigma^2,id,id,id,id)$. 

 

We now consider the subgroup (of $S_{12}$) generated by certain permutations, where the ordered set $(1,2,3,4,5,6,7,8,9,10,11,12)$ is organized as in the figure above.

The generators are:

$f = (2 \,7\, 3\, 6), b = (1\, 8 \,4\, 5), u =(1 \,10\, 2\, 9), d = (3\, 11\, 4\, 12), l = (5\, 9\, 6 \,12)$ and $r = (7 \,10\, 8 \,11)$ together with

$X = (5\,6\,7\,8), Y = (1\,2\,3\,4)$ and $Z = (9\,10\,11\,12)$

Then $Y^{-1} = (4\,3\,2\,1)$ and $f^2 = (2 3)(67)$. Therefore

$f^2Y^{-1}f^2Y =  (1\,3\,2)$ and hence $f^2Y^{-1}f^2Y^2 = ( 34)$. Now it is easy to see that our generators generate $S_{12}$.

We will define a group morphism via a correspondence of our generators for $S_{12}$ to the generators for $S_{8}$ defined above: $f \longrightarrow F$, etc. 

(to be continued...)

Note on TPC and TPP

Yoga citta vritti nirodhah

. How can we speak of the thought of being, the thought of existence and forget that before all else thought itself is, thought is there, for us, in us, in its convoluted unceasing stream and primordial being. But to be aware of, conscious of, thought as thought, that thought is itself the great a priori screen and window wherein plays out the play of the world, this is already a path to TPC. How does this transcendental awareness of the totality of the thought-process work ? How can thought then think itself and be beyond itself ? How does TPC work ? How can being be a thought and yet thought be a being? How is thought related to language ? How is thought related to the impression or structure of 'self'? How is thought tinctured by sense-images and other psychological material ? How does temporality work in the diverse modes of thought, memory, recollection, anticipation, habit ? We should be very careful about dissections of thought: for instance Brentano's intentionality, Husserl's noesis vs. noema, the concept of 'content', etc. And it is astounding that those who disparage conceptual realism accept at the same time completely arbitrary, dogmatic, unproven and implausible functionalist theories. Neuroreductionism, eliminationism, functionalism and neothomist theories of embodied consciousness should be considered dogmatism and philosophical naivety par excellence. What is the transcendental meaning of the construction or bringing to light of formal systems which are supposed to act as masks, or exterior projections, doubles, of thought ? How does translation and multilingual consciousness work, what do we mean when we say that we think in a given language ? Sextus, Hume and Kant can be read as an absolute untangling and allaying of thought by thought itself transcendentally aware of itself. The true self, pure consciousness (bodhicitta), is revealed to itself and at the same time the deep producer and controller of thought is unveiled.

So TPC and TPP aim at lifting and untangling thought or rather consciousness-thought into a super-consciousness and super-thought.  But ordinary consciousness does not consist of thought alone, it includes feelings, volition, desire, longing,  beauty, love, eros, intimacy, habits and dispositions like pride and humility and so forth. In ordinary consciousness these spheres stand apparently apart from pure thought (to a certain extent). But Kant wrote more than one Critique and the author of the Parmenides and Theaetetus was also the author of the Phaedrus and the Banquet.  Our description of TPC and TPP must be completed and perfected with a philosophical and practical account of how these sister spheres are also untangled and rise above themselves and become united to super-consciousness and super-thought.

The constituted constructed self stands at the center of the division of these two regions and is a common hindrance, obstacle, to the untying and transcending of both.

The significance of temporality and in particular of one's own concrete temporality, memory and identity is immense for TPC and TPP.  We cannot go into here the immense meaning and power of abgeschiedenheit, of 'letting go', of the process whereby we let the past go, let of memory-attachment-persons, intuiting that the past was the present of its own past and turn,  and  learn to embrace a new and better past and identity. We understand the process of coming to be and passing away and gain transcendental acceptance and freedom (freedom from guilt, ought, destiny).

We could also discuss the relationship between TPC/ TPP and the scientific spirit, the scientific method, the engagement in a serious, patient, philosophically aware, critical, detailed study of the sciences.

TCP/TPP is a priori radically incompatible with any form of religion while capable of recognizing positive ethical, philosophical and scientific elements in different spiritual traditions. TCP/TPP is also ideally an effective psychotherapy against the delusions and pathological effects of religion and its misguided spiritual practices. 

The central philosophical theory of TCP/TPP is the exhibition of its essential unity with universal morality. 

Mathematical projections or representations of consciousness. They can have a field-like spatial-like aspect $\phi: S \rightarrow U$ ($S$ expressing certain concomitant psychological material) and a non-local aspect akin to distributions $\Phi(S,U) \rightarrow V$. Distributions can be interpreted in a way similar to the collapse of the wave-function in quantum theory. In quantum theory we derive a probability relative to each eigenvector, for distributions we a have a real or complex value for each test function. Because of freedom all temporal transition $\phi_t$ must be described probabilistically.  There is no reason to suppose that a thought at a given moment has a single 'content' (noema). The extraction of the content can be likened to evaluation at a test function or quantum measurement. The evolution of thought generalizes computations and proofs (arguments). Denotational semantics and content: the (teleological) question what is the program computing ? 

The great project: uniting theoretical computer science and theoretical physics (and the general theory of dynamical systems, differential equations, etc.).  How can we compare the executing of a program and a physical process satisfying a given law ? Put another way: what is a running program, specifically a concurrency of different systems, from the point of view of dynamical systems and theoretical physics ? For a given solution of a partial differential equation we can say that the process represented by the solution is virtually and approximately computing the numerical integration algorithms which could approximately derive that very solution.

Question: are PDEs Turing complete ? That is, given a Turing machine M can we write a partial differential equation having a numerical integration algorithm A such that M can be simulated by the running of A ? 

Some of Our Recent Philosophical Papers (all available as preprints)

1. Quantifier Reasoning and Multiple Generality in Aristotle and Ancient Logic

2. Aristotle's Second-Order Logic and Natural Deduction (to be published)

3. On Analyticity and the A Priori 

4. Natural Term Logic (in preparation)

5. On the Nature of Logic in Kant’s Critique of Pure Reason (to be published)

6. Ancient Definition and Modern Definition

7. Hegel and Modern Topology

8. Computability, Differentiability and Beyond

Papers 1, 2 and 6 are of an historical nature and they argue for the sophistication and scientific adequacy of ancient logic as well as proposing novel hermeneutic tools based on modern logical and mathematical theories.

Paper 5 is an application of the conclusions of the above papers to the interpretation of Kant defending that Kant was not formally limited in his table of judgements to monadic logic.

Paper 4 (which is work in progress) involves developing a new formal-mathematical approach to the logical-syntactic structure of natural language.

Paper 3 is the most important and philosophical of the papers and is complemented by 8.   Paper 7 needs no introduction. 

In addition there is our extensive monograph 'Philosophical Monologues' (not yet available) which is based on material previously published on this blog. 

We mention also a much older paper:

9. Aristotle's Analysis of Consciousness and Pali Buddhism 

Prehistoric philosophy and spiritual culture in Europe

 

The close connection of the grammatical structure of Old Church Slavonic to Sanskrit (and Indo-European in general) is fascinating. The Glagolithic alphabet is curious and more interesting are pre-Christian Slavic scripts such as the Alekanovo inscription.  There is nothing 'crude' or non-sophisticated about having a writing system of the Ogham type (Hrabar's чръты и рѣзы, črŭty i rězy).  On the the contrary, it indicates a high level of arithmetical symbolic (or cryptograhic) thinking, which Hrabar probably was not even able to understand.  Take a really good look at the 'Sun ship' from Bronze-age Poland.

 The  Byzantine historical attestation of the Bandura (Ukrainian: бандура) among ancient Bulgarians  points to a survival of an ancient musical tradition (the counterpart of the Celtic Bards).

We entertain the idea that certain peoples among the ancient Slavs may have possessed a form of Buddhism (we see, as attested in the Pali suttas themselves,  Gotama's doctrine and practice as a restoration of something even more ancient) or a similar system of yoga or spiritual cultivation. A common view would be that ancient Scythians and Sarmatians may have played a role (also with later manichean connections: consider the Bogomils and the story of Barlam and Josaphat, this last name being an adaptation of a middle Persian rendition of Bodhisattva). However we obviouly reject arbitrary occultist fantasies (without any serious scientific basis) about Slavic prehistory - which are often unfortunately aligned to questionable political ideologies. But we note also that much of 'mainstream' theories of history and prehistory are equally tainted by ideological agendas and prejudice (just as the account of the pre-Christian Slavs by early Christian writers is not reliable).  Can we find a correlation between the elegance and sophistication of a language (its closeness to Sanskrit or some other measure) and the cultural and spiritual level of its speakers ? And by cultural and spiritual level, we mean consciousness and implementation of universal ethical principles regarding human beings and animals, philosophical consciousness (that is to say, TPC and TPC) and spiritual cultivation based on it, the development of formal logic and analysis, the template of the scientific method, the refined development of the arts, etc. 

From an historical and archaeological perspective we argue strongly against and completely reject the opposition between so-called 'polytheism' and 'monotheism' and all the ideologies and connotation such an opposition or distinction implies. The theological doctrines (cf. kathenotheism, henotheism, etc.)  of Proclus' Elements of Theology are the same as that of the Vedas and the Avesta. Christianity in most of its historical manifestations was never  quite 'monotheistic' in the crude sense and the same goes for the esoteric teachings and practices in Iran.  For indeed the absolute (the good) is that which is beyond all gods which are in the highest sense are its emanations (angels) and mediators (henads). And the absolute as well as the highest gods are essentially to be sought within.

Historically we find high levels of idolatry, anthropomorphism, materialism, violence and barbarism among so-called 'monotheistic' cultures. This so-called monotheism is just a cultural expression of political supremacist ambitions of certain peoples wherein a tribal deity is given traditional attributes of a military conqueror and emperor.

What is far more important is how the concept of divinity is essentially united to that of universal moral principles and philosophically to that of TPC and TPP. 

Returning to the Slavs (the so-called Slavic deities alignment to the natural cycle of the seasons and to the experience of love and beauty  may have been a sign of an elevated philosophical spirituality akin to the Vedic one),  we note that the ancient Slavic woodcraft was quite sophisticated and must have made use of considerable knowledge of geometry and physical engineering. The archaeological site at Biskupin in Poland (c. 8th century BCE) could be proposed as an example, but of course we cannot know how precise and sophisticated this structure originally was. The artifacts related to this site are of exquisite beauty. 

We discussed briefly the prehistory of the Slavs (the Slavic or proto-Slavic speakers) and the thesis of the existence of a higher spiritual literate culture akin to Vedic culture which included a complete system of spiritual realization as well as certain types of science (like Paninian grammar). Furthermore we have hinted elsewhere that the western Slavic  (and Baltic) substrate in the territories of what is now Germany played a central role in higher philosophical and cultural manifestations (for instance Bach, Leibniz and Kant and Frege, mother's name Bialloblotzky). Bach (like Eckhart) was born in Thuringia. 

Thuringia has significant historical Slavic influence, primarily from the Sorbs (Wends) who settled the region in the Early Middle Ages. This influence is most evident in place names and the genetic ancestry of modern inhabitants

A similar and very strong argument could be carried out for a certain substratum of Celtic-speakers, specially in Ireland, Wales and the regions of what now are Belgium and France. This substratum expresses both the persistence of an original higher spiritual culture (and here we cannot go into the question of how proto-Celtic relates to proto-Slavonic) and specially a propensity and affinity for TPC. The testimony of classical authors leaves no doubt as to the high and central place that was given to philosophy (Druids), science (Ovates) and art (Bards). Also a high place accorded to women (cf. the Druidesses Veleda and Aurinia).

Just consider the extraordinary TPC luminaries that arose from northern Celtic soil: 9th-century neoplatonist Scotus Erigena, Berkeley and above all Hume - who can be considered a kind of Celtic Vasubandhu or Nagarjuna. William James' grandfather was from County Cavan, Ireland. British neo-Hegelian McTaggart had (as evidenced by the family name) Scottish roots.

For Celtic France (including the territories of what now is Belgium) we have of course the spiritual culture of  the Troubadours/Trovères, the Cathars (and Gleizes may be a distant heir), the Grail literature of which much could be said regarding its expressing a continuation of an older traditions (Manichean, Buddhist, Hermetic, Avestan, Druidic, etc.). Noteworthy are the philosophical-spiritual writings of Marguerite Porete (a 13th-century Beguine from Hainault, now Belgium) who may have been a source for her more famous contemporary Eckhart.

Beyond Ireland and Scotland, in England there has always been a tension and duality between opposing tendencies, a great number of things high, noble and beautiful flowing forth from the Welsh-Brythonic substrate. And much could be said about the history of the Welsh Quakers.

As for France (whose first great philosopher was Jean Buridan),  there is an evident presence of TPC in the schools of Descartes and Malebranche with a strong connection to Leibniz. Of particular interest is the later merging with the Kantian tradition in such figures as Maine de Biran, Renouvier and Lachelier, showing the essential affinity of the French philosophical genius for TPC-oriented philosophy. Indeed if Husserl's phenomenology certainly has some affinity to TPC then nowhere has this philosophy been expounded with such meticulous care as by Gaston Berger or René Schérer. Whether French existentialism, phenomenology and psychoanalysis had some positive and valuable elements from the perspective of TPC and TPP - following the suggestion of Paul Demiéville in a preface to a book by Walpola Rahula - is something to be investigated.

There were also TPP-oriented poets like Mallarmé. Very noteworthy were the Belgian scholars Louis de La Vallée Poussin and Étienne Lamotte  who were the first to study and expound the Madhyamaka based on the original sources (and already in 1849 H. Chavée produced an indo-european lexicology). While Belgian philosophy (which does not compare to Belgian mathematics and linguistics), beyond the unfortunate influence of neothomism (even Maréchal's more interesting Kantian version),  has been dominated by ad hoc anglo-american neuro-reductionist/functionalist and  'analytic'  influences (Gochet, Devaux, Barzin), the poet François Jacqmin (Le Livre de la Neige) represented a pure and unique expression of the wedding of absolute philosophical insight (TPC) and personal spiritual realization (TPP). Jacqmin was likely a reader of de Waelhens' books on Heideggerian phenomenology (Husserlian phenomenology is represented rather by Marc Richir). 

This 1960 paper by Jean Ladrière is interesting (formal systems as 'doubles' or projections of thought).

We could also investigate the existence of a prehistoric higher spiritual culture among certain branches of Germanic-speakers in certain regions (for instance Frisia, Brabant, the study of the Beguine mystics like Beatrice of Nazareth and what might be authentic in the Oera Linda boek - or certain traditions in Scandinavia related to Baldur). This is a complex topic that we cannot enter into here. 

Hegel and Metaphysics

We can trace much of Hegel back to Spinoza, Leibniz and Kant. But what if Spinoza and Leibniz themselves represented but an adaptation or even simplification of little known medieval philosophical  texts (much earlier than Böhme) ? And that such texts gave a firm foundation for the synthesis of Hegel with Schopenhauer? What if the unfolding of Hegel's Logic or Phenomenology of Spirit can be interpreted as representing the process of spiritual liberation, totalization  and harmonization of all states of being?

In the Zusätze to 573 of the Encyclopedia, we read:

If we want to see the consciousness of the One (...) in its finest purity and sublimity, we must consult the Mohammedans. If, e.g., in the excellent Jelaleddin−Rumi in particular, we find the unity of the soul with the One set forth, and that unity described as love, this spiritual unity is an exaltation above the finite and vulgar, a transfiguration of the natural and the spiritual, in which the externalism and transitoriness of immediate nature, and of empirical secular spirit, is discarded and absorbed.

Essence becoming actuality in the Science of Logic: beyond different models for a theory, different frames of reference for physics, representations for an algebraic structure, etc. Do we not here have the phenomenological reflection which neither attempts to have empty thought grasp directly its own structure nor is thought loosing itself in the objectified engagement in its action, but rather is the self-reflected awareness of thought in its thinking, a shift of perspective which knows itself in its process?  This goes beyond causality, computation and formal logic to inner and infinite spiritual knowledge. Spiritual knowledge is knowledge that what is in consciousness is taken and proceed from its inmost center, a revelation, veiling-unveiling, which must pass to reveal the process: the revelation is re-velation.

Hegel's treatment of modality in the section of Actuality is very relevant to contemporary discussions on possible worlds and arguments against the world being a sum of independent contingent facts. There are also connections that could be made to modal logic (i.e. the connection between possibility, actuality and necessity and the axiom $\lozenge P \rightarrow \square \lozenge P$). 

The considerations on necessity and substance (and indeed the long digressions on Newtonian forces already suggest this) can be interpreted in terms of the solutions of differential equations (or in general smooth vector fields on a manifold). The local existence and uniqueness of a solution for a given initial conditions expresses determinism which extends to a global determinism. 

The first part of Schopenhauer's World as Will and Representation is divided into four books. It would be interesting to establish a correspondence with the Science of Logic.  Clearly books 1 and 2 correspond to Being and Essence while books 3 and 4 correspond to Concept. However books 1 and 2 are written from the perspective 'for us', from the point of view of transcendental reflection. From this perspective books 1 and 2 belong to Essence and their philosophical knowledge expresses with great rigor and detail Hegel's theory of appearance, existence, substance, necessity, causality and actuality.  Or maybe Hegelian substance is much like the spontaneous production and manifestation of the will in Schopenhauer. It goes beyond phenomena and appearance because the will is immanent in its manifestation, totally in each one and beyond any particular one. The will has to manifest. Transcendental reflection, artistic contemplation and spiritual development represent the will's progressive self-knowledge, return to self, the Hegelian Spirit in the form of the concept.

Category Theory: a category expresses essence. Each object is a different mode whose determination is inseparable from its relations (morphisms) to the whole (all possible determinations). An object is an expression of the category and yet not the category (for there are other objects). At the same time this circumstance of the object not being the category is itself internalized and expressed as the object being itself the sum-total of its relations (morphisms) with all other objects (i.e. with the totality of the category). This expressed also that the object is the category. 

The Concept can  be seen as arising when we have the cyclic transcendental consciousness of metatheory. That is to say: we realize that transcendental presuppositions are in cyclic dependency: to do logic we need computation, to do computation we need arithmetic and combinatorics, to these we in turn we need computation and logic. The germ of this in the reciprocal causality at the end of Essence (which we have also associated with higher groupoids). And also, as we have discussed in more detail everywhere, the partial (meta)reflection of one formal system by another (or the formal system by itself) is clearly relevant here: it is the idea of the whole being implicit to some extent in the part. For instance in ZF set theory itself we can prove that there are non-equivalent models of ZF.

Logic, Computability and Grammar

Given a natural language, we can ask what the logical and computational prerequisites for generating and checking and analyzing valid expressions of that language ? And can we define the minimal, optimal way in which expressions are generated and checked and analyzed ? We are looking here at meta-grammar,  the formal language of grammar itself.  How rich are formal languages in themselves compared to standard algebraic systems ! How much remains to be said about the relationship between (specially imperative) programing languages and logic, between logic and recursion theory, between recursion theory and combinatorics and formal languages. These are all topics of our Analyticity and the A Priori.

We view a descriptive grammar as a function which takes a series of choices, semantic categories, and generates the corresponding expression. We should formalize grammar using functional programming. 

Take the rules of Sandhi in Sanskrit. To express them we need the same logical framework as in Aristotle's Topics, in particular as Galen's Relational Syllogism. 

But we can also think of an abstract mathematical framework for Sandhi.  Suppose we have for instance finite sets $A,B,...,G$ and let $P \subset A \times B \times...\times G$.  Then we can define an operation $\otimes: P \times P \rightarrow P \times P$ such that for instance a certain component is right-dominant:

if for $p \in P$ we have $p_C = c_1$ then $q\otimes p = (q', p)$ with $q'_C = c_1$ and $q'_X = q_X$ for $X \neq C$.

For binary sets $A = \{a,b\}$ we can define transposition $p^A$ as $(p^A)_A = a$ if $p_A = b$ and $(p^A)_A = b$ if $p_A = a$.  Then the above example becomes $q \otimes p = (q,p)$ if $q_C = p_C$ and $q \otimes p = (q^C, p)$ otherwise.

In order to represent Sanskrit sounds more precisely we can include in each finite set a 'null' element $0$ expressing that the classification of this set does not apply. For instance $p_N \neq 0$ means $p$ is a nasal and then $p_A = 0$ means for instance that the aspiration  Boolean does not apply.

The algebraic aspect of Sandhi can be illustrated by the existence of left and right (quasi-) absorbing elements or identity elements. $\dot{n}$ is a left identity element. 

While external Sandhi can be given relatively simple well-defined rules, even Max Müller shies away from giving a complete list of rules and exceptions for internal Sandhi.

We will also give  representation of external Sandhi using permutation groups (inspired by the Rubik cube). 

Pâninian Linguistics

https://web.stanford.edu/class/linguist289/encyclopaedia001.pdf

Is Pânini's formal system (which appears to be in the form of a term-rewriting system and is the true source of generative grammar) Turing complete ?  That is to say, could the same formal mechanism Pânini used to specify the structure of Sanskrit be used to generate the expressions of any recursive set of strings ?

Here is a paper addressing this question:

https://aclanthology.org/C12-2092.pdf

This would make Pânini of supreme logical and philosophical interest. There might be a connection to Vedic rituals: the development of a formal language (a programing language) to codify rituals.

https://ijirt.org/publishedpaper/IJIRT187010_PAPER.pdf

We note that the syntactic transformation of our natural term logic can be expressed more easily as a term-rewriting system than standard quantifier logics.

In fact Pânini is of immense interest to our positions expounded in our paper on Analyticity and the A Priori (and also our paper on Ancient Quantifier Logic).   One view is that true logic (let us say in the form of second-order logic) comprises only universal quantification and implication and their natural deduction rules (cf. Prawitz, Natural Deduction, p.67, Dover edition). This is the logic which can be transcendentally examined to be the pre-condition to understand, check and apply rules, formal term-rewriting systems (or similar systems), such as that of Pânini. We must also examine Pânini as a logic of relations.

But derivations in formal languages are like proofs and are instantiations of rules (a derivation is called a prakriyâ in Pânini's system).  So even the introduction of the universal quantifier is itself the application of the rule of the elimination of the universal quantifier. Pânini's system is a sophisticated system of formal rule-based proofs which is close to the sequent calculus in that memory of past rule applications carries conditions the application of rules later on in the derivation (as in control structures or focusing).

Classical Arabic is also quite interesting and has a formal perfection similar to Sanskrit, the so-called irregular verbs are formally determined by phonetic rules similar to Sandhi rules. Furthermore the roots are also interesting as are theories which would associate an idea to each letter, much in the style of Leibniz's characteristica. All this is highly relevant to the study of other ancient Semitic languages (like Aramaic) as well as the reconstruction of Proto-Semitic.

Claire Ortiz Hill (1951-2025)

https://www.riverafamilyfuneralhome.com/obituaries/claire-ortizhill

Claire Ortiz Hill was an American philosopher (who spent the later part of her life in France) who in the last quarter of the 20th-century authored some lucid and meticulously written books on Frege, Husserl and intensionality as well as offering a cogent critique of some central trends of 20th-century analytic philosophy. In recent years she dedicated herself to Cantor and little known aspects of Hilbert's role in philosophy. Her magnificent article Hilbert's Fight for Philosophy (2021) has many important connections to our paper on Analyticity and the A Priori.

The unknown Dharma of the West

Can we trace a continuous tradition from original Buddhism to Socrates to Plato and the Megarian school to Pyrrho to Sextus to Plotinus to Damascius to Pseudo-Dionysius ? As strange as this may seem to some, there are some striking arguments that can be made to support many links in this chain. In fact we are pleased to note that Sara Ahbel-Rappe in her edition of Damascius' Problems and Solutions concerning First Principles, makes a direct reference to Sextus. The Buddhism-Pyrrho link has been studied for instance by C.I. Beckwith's Greek Buddha (2015). It has also been argued (by C.M. Mazzucchi)  that the author of Pseudo-Dionysius was in fact Damascius who managed to inject core doctrines into the heart of the 'mystical'  tradition of Christianity (which has nothing to do with the literal sense of dogmas): and here we mean its better (predominantly medieval) manifestations such as Hadewijch, Porete, Eckhart, the author of the Cloud of Unknowing, the Viae Sion of Hugh of Balma (which we dedicated a small note to).  It is in this light that we would reinterpret Plato and the close connection to Socrates, Pyrrho and the Megarians.

'Spiritual realization' (we use this term temporarily) is not the same thing as psychotherapy (etymology aside). Psychotherapy aims at helping people adjust and balance personality traits so as to be at peace with themselves and the world around them.  It is about the constitution of an individual 'personality' and 'ego', often seen as the result of an integration of different tendencies or the product of past development and adaptation strategies.  Spiritual realization such as we outlined in our previous account of TPC and TPP more or less presupposes physical and mental health as a condition and its aim involves shining a light through self-hood and overcoming its underlying impulse, motives, determinations and limitations. But this does not rule out that it can also be highly beneficial in a psychotherapeutic context.

We are conscious of the present and the past in the form of recollected or anticipated mental content in the present. Past and future are mediated by the present and are indeed in the present. TPC involves awareness of the presentness of past and future directed or colored mental content. The theory of the 'present moment' and 'letting go of the past and future' and finding 'the timeless present moment' taught in many approaches to Buddhist meditation conceals something of huge psychological and philosophical depth and importance. Temporality is linked to the conditioning of the mind by thought, the constitution of the world by thought, and the falling away from TPC. Time is the magical stage of thought, the impermanence which is made permanent mixing perception and forgetfulness. We might say that this proper philosophical consciousness of psychological (inner) temporality is at the heart of TPC and TPP.  The same goes for self-identification, self-projection,  craving, repulsion.  But the aforementioned practices require the good fortune of being able to retreat to a secluded, quiet, safe and solitary place, the best option  being the countryside.

If we leave this world to attain another state of being we can at least control what we bring along to the next plane.  Let us not bring with us the least trace of anger, hatred, resentment, desire, attachment, clinging - or ignorance and delusion, specially delusion regarding identity and identification or the magic show of our own consciousness.

It is important to note that by 'buddhism' we mean the philosophy, psychology, ethics and spiritual practices that we interpret to be arguably and quite patently present in old Pali and Sanskrit texts (independently of the presence of elements of a different nature, textual history and corruption, etc.). Our meaning of this term does not depend in any way on any particular historical or cultural embodiment of buddhism and as such is not open to the common criticism that we are ignoring its cultural roots or merely picking certain elements which fit a pre-conceived agenda (we are not claiming to represent or interpret any concrete cultural buddhist tradition).  Also we are well aware that modern distorted abstractions and (mis)applications of buddhism can from a psychiatric point of view have harmful effects (cf. negative experiences with so-called 'mindfulness', vipassana and Goenka retreats, experiences which according to our interpretation have nothing to do with the buddhist spiritual path).

We would be quite happy to debate anyone on this topic. Also the focus on buddhism does not imply that we attach less value to the parallel traditions of the Upanishads, Yoga, Samkhya, Vedanta and so forth. 

It is quite possible that the philosophy of Schopenhauer (the philosophy of the principium rationis, the principium individuationis, the central role of voluntas, the theory of representatio, the theory of  supra-individual timeless, ubiquitous cognition,  etc.) offers some of the deepest and most important components of TPC and TPP. Schopenhauer claimed as ultimate source the Upanishads. In Schopenhauer all the sphere of manifest consciousness, individuality, identity, spatial and temporal limitation, conditioned by the Kantian intuitive and conceptual categories, is the product of a primordial impulse and energy.  The only way out of this prison is through a total reversal and repolarization of this fundamental impulse and energy which results in the 'involution' of all the modes, conditions and determinations of individualized consciousness and the consciousness-immanent world.

Also Schopenhauer might help us understand better what we wrote about the inner, first-person, experience of the body. 

One might entertain the idea that there is a far greater unity and affinity between Kant, Hegel and Schopenhauer than is generally believed.  Shapshay has argued this with regards to the ethics of Kant and Schopenhauer. And beyond the personal animosity between Hegel and Schopenhauer it is quite possible that Hegel might furnish some valuable structural and interpretative enrichment of Schopenhauer and that Schopenhauer could provide the essential clarification, correction, deeper meaning and completion so lacking in Hegel.

Philosophy of Awakening

 We mentioned before that the is a difference between a true spiritual path (leading beyond anguish and suffering) and a false spiritual path. A true spiritual path involves essentially a habit and state of mind which  we call philosophical awareness or consciousness. The false spiritual path completely lacks it. This state of mind we could attempt to describe as transcendental philosophical consciousness (i.e. awareness, analysis, inquiry)  of the totality of consciousness itself (the immanent world). We use the abbreviation TPC.  One of its oldest and most magnificent attestations is found in the Pali nikayas (with the Socratic dialogues and Pyrrho) and more recently to a certain degree in Hume and Kant (and there was an influence of the late Academy and Pyrrhonism via Augustine and Descartes). This is what Schopenhauer said concerning Kant's Critique of Pure Reason (the analogies of experience): never has the world been looked at from a greater distance. At the present we have a scholar, by name of Dennis Schulting, who has written several books dedicated to defending and expounding the true meaning and spirit of first edition of Kant's Critique, that is, to bringing out the centrality of a form of TPC in the entire deductive and argumentative scheme of the aforesaid work.   Our project is not only to say something about what TPC involves but also to discuss its epistemic and logical aspects, a subject of uttermost difficulty. And of central concern is of course its close relationship to introspective psychology and so-called psychologism (as well as the ambiguous hydra of the term 'idealism'). And discussing the often subtle yet ultimately radical difference with Hegel and Husserl.  There is always a danger that TPC may lapse back into the modes of non-TPC consciousness. That is, a false objectification of TPC insight and knowledge. Such an objectification involves forgetfulness (of constitution, condition and presupposition) and loss of insight and transcendental progress.   TPC crucially involves a way of seeing and questioning (bracketing, suspending) the totality of (conceptual, intuitive, affective, volitional, egological, spatial-temporal, somatic, etc) experience. The total awareness of the total sphere and process of thought and what is beyond all thought and what thought is actually behind and the fact that it is behind it. TPC is a gradual affair,  an ideal which is worked towards by practice and training. TPC traces back and unveils the unified common source of all branches of philosophy. Poetical language achieves its highest function in the expression of TPC. All this we have written about in our compiled Philosophical Monologues collection.

There are no mathematical models of consciousness, and a fortiori for the boundless sphere of TPC,  and no formal axiomatic-deductive systems either. Rather these all proceed from the knowledge and insight offered by TPC. But there could by mini-models, projections, symbols and for every false philosophy or false scientific theory  a certain and valid formal refutation. TPC itself cannot be part of academia (but more concrete, specialized subjects, guided by TPC, can) and it is something that one must find for oneself. TPC can be compared to the state in which when dreaming one knows one is dreaming, or at least, seriously questioning if the totality of one's experience be not in this situation a mere dream. And also importantly, asking: what is a dream?

It is TPC that is about 'saving the phenomena' and involves noticing how there is a vast domain of phenomena, of 'realities' as real as anything else, which includes all forms of sensation, perception, feeling, volition, thought, cognition, meta-cognition, memory, imagination, learning, habit, attachment, sense of self, sense of identity  and so forth which is a central and important part of  the 'world', as important if not much more than anything other alleged aspects (specially those pertaining to so-called 'natural' science). This truth is powerfully present in the Pali suttas which predate Socrates and, as argued by Mikel Burley (2007), in the ancient system of Samkhya.  The terms 'consciousness' and 'the psychological sphere'  are often used in a deflated, trivialized, distorted and illegitimate way. Understanding, such as it is and presents itself, the vast and central role of consciousness and meta-consciousness in all that is, in all the 'world',  is a first step from waking up from  the dream, and it follows the shining wake of Socrates and Pyrrho and there is much to be said about certain aspects of Democritus (atomism is in itself a formal template of logical analysis, as in the abhidharma, and not an hypothesis in natural science or positing of a reductionism between different ontological domains), Carneades, Sextus and Augustine's Contra Academicos: 'I call whatever appears to me the world'. Another powerful force leading to this direction is the theory of knowledge (the earliest known text being the Theaetetus), the questioning of how we come to know things, of how we know that we know (the criterion of truth),  of what knowledge is. The theory of knowledge draws us inevitably back towards the great forgotten pristinely primordial sphere of consciousness. Becoming aware of consciousness as consciousness (and experience as essentially consciousness) and its true position in the scheme of things is truly waking up from a dream and drawing close to TPC.

How does TPC relate to our other distinct considerations on the computable axiomatic-deductive condition and ideal of knowledge (which evidently does not involve any claim to exclusivity or to exhaust valid cognition) which we expounded in our paper on analyticity and the a priori ? The conclusions of that paper can be seen as flowing directly from TPC. Our formal verification principle is epistemically modest. To come to this conclusion relative to formal axiomatic-deductive systems,  TPC must be presupposed. Hence formal axiomatic-deductive systems cannot in themselves be sufficient to unveil their own transcendental determinations and conditions. And formalized transcendental deduction itself cannot subsume TPC but again presupposes it. TPC must be self-deducing, self-illuminating, self-sufficient, self-founding, self-justifying (somewhat like for Kant the 'I think' is the condition and source of the categories and hence of logic itself). And yet does it make sense to speak of a 'deduction' here without circularity ? TPC cannot depend on logic anymore than anything in a dream can in itself awaken one from the dream. And yet this does not decrease the value and importance of the formal verification principle. If a philosopher or anyone else engages in linguistic activity, linguistic expression, then it is legitimate to subject the output to the formal verification principle, to the ideal of a formal game. All logos is bound to logic, including philosophy and any discourse about logic and reason. Philosophical logic is like two mirrors reflecting each other. Yet via TPC one plays the game knowing it is a game (dreams the dream knowing it is a dream) but without trivializing it for being a game. The game is much like a children's game with the purpose of teaching.  Logic is a crutch to help us learn to see (i.e. to develop TPC). But TPC is not deduced or justified from logic anymore than swimming is justified or deduced from water wings. But there is another aspect beyond the simile of a helping crutch. Logic is the laws of thought but not the justification of thought itself. We think, or rather, we are thought, but we seldom see thought itself as it is, from a distance. The ability to see through the game, not only to see the game as a game, but to see immediately non-discursively the game, the playing of the game, the player of the game,  as something that is not necessary and yet at the same time the direct cause of many unpleasant things. Exactly like Alice's final attitude to a 'pack of cards' or Schopenhauer's metaphor about the chessboard after the game is over.  This is related to transcendental philosophical praxis (TPP). TPP involves the coming to awareness that the things that bother us are not really things in themselves and but only images in our own minds. And that we have actually the capacity to exert an enormous power over the entire content of our own mind, conditioned by habit and practice. And the most importance practice and habit is that of viraga, nirodha and patinissagga. Thus TPP (the sister of TPC) gives the true philosophical meaning to the often abused or trivialized assertion: we create our own reality. 

Notes

The embedding matrices used for instance in ChatGPT-3 are a vector space representation of co-occurrence frequency matrices for a given context-window size. This matrix can also be seen as a complete graph with edges labelled by probability values (we can assign values also to polyhedra).  It is important to study the properties of these matrices.

Locally integrable functions (fundamental to distributions and weak solutions to PDEs) are a kind of sheaf-theoretic completion of the $L^p$ spaces. On the other hand from a finitist point of view simple functions are the basic kind of function and these are 'dense' in many fundamental spaces in an appropriate sense. What is the meaning of a PDE in a scientific context ? A positing of certain recursive numerical algorithms and approximation ideals.  How curious that numerical conditions for stability involve the pairing of space and time.  And fascinating is that smooth initial conditions for PDEs as simple as $u_t - g(u)u_x = 0$ may generate shock waves. And what is, from a computational finitist point of view, a weak solution ? A good philosophical goal: to gain a deeper understanding of distributions (cf. Sato's hyperfunctions). Distributions arise from the practical situation of measurement. We do not measure a field at a point but only an integral average weighted with the peculiarity of the instrument employed.

Some of the most interesting concepts in mathematics and applied mathematics: absolutely continuous functions and functions of bounded variation. What does a finitist and computationalist perspective say ? Both the Weierstrass and Cantor step functions are constructed step-by-step. There must be a property expressable in terms of re-scaling.

How could we prove that a physical system is computing beyond the Turing limit ? We could of course produce experimental evidence to the contrary, producing a certain algorithm that agrees with know observations. There are irrational numbers whose sequence of digits are not computable. How are we to view scientific theories about such numbers (which could represent measurements of some fundamental physical constant), calculations and approximations of such numbers, and confrontation with experimental evidence ? Obviously such a question is only interesting from a non-finitist perspective.

The interest in solving the P=NP problem hinges on the complexity of the algorithm for transforming a NP-machine into a P-machine. 

Uncountable infinities (must check Bolzano regarding this subject) are highly questionable (they express a false objectivism). They imply indiscernibles which should be rejected in the light of subjectivism (in terms of computationalism or more generally definability). There is also the problem of the identity and determination of mathematical objects (Benacerraf, etc.).  A foundation for calculus like Lawvere is called for (in which intervals are primitive). The standard definition is that a set A has cardinality greater than a set B if there is no injective function from A to B. But once we restrict the possible functions on philosophical grounds to being recursive or some more general type, then this situation can happen without increase in 'Cantorian' cardinality. Indeed 'infinity' is always present in the concept of recursively enumerable but not recursive and the same goes for the rest of the arithmetical hierarchy (the true hierarchy of 'infinities') ? This makes perfect sense also for ordering. What is the point of ordering something if it is not in a computable way ? In sheaf models (a partial improvement and clarification of the forcing techniques) there is an acknowledgment of the essential relativity of the whole Cantorian framework of monos and cardinalities (already patent in the Löwenheim-Skolem theorems).

A problem, given an inconsistent set of sentence in some language L  is there a canonical disambiguifying language L' (which associates to certain symbols s of L a set of possible clarifications s1,s2,...) such that with a choice of assignment for occurrences of symbols of L to symbols of L' the set becomes consistent ?

Non-classical logic vs. classical logic. What is important is the question: what is the logic required to be able to understand, carry out and check any system of rules ? Kant's rule-based philosophy is a precursor of our computational a priorism. 

Heirs of Poincaré

It is difficult to evaluate the quality of mathematical work or the particular destiny of mathematics in the 20th century. We have already given some criteria: logical, conceptual and didactic clarity and rigor, clarity of intuition (which, contrary to common myths, is not incompatible with logical rigor),  an orientation towards synthesis and simplification, an orientation towards applications to the sciences embodying novel unifying ideas,  awareness of the deep problems regarding  mathematical models of reality,  awareness and interest in fundamental philosophical problems.

Logicism is irrefutable. Mathematics is in its purest essence is the deployment of computability (and hence logic), but this game cognitively involves intuition (just as chess strategies) as its develops towards perfection. It is a 'game' in the noblest sense: not 'to calculate' in the sense of mere application, but 'to calculate' as in 'be able to calculate' through finding a strategy and sequence of right moves in a formal game. The very conventionalism is not conventionalist in its a priori logical and computational cognitive presuppositions (see our paper On Analyticity and the A Priori). Moreover, beyond the genius of Frege, Turing and Church (and Brouwer's intuitionism is just computationalism), there is a presupposition in mathematics of a certain objective-intuitive correspondence and specially a claim to enter into the objective truth of the world in the form of science. Kant saw the tip of this iceberg: "Thoughts without intuitions are empty, intuitions without concepts are blind" .  The problem of the intuitive correlation of mathematics is similar to that of the efficacy of mathematical models of nature.

We can ask if ancient philosophy was not simply ancient science and mathematics (and its politics and ethics but applied mathematics)  or if there is any real difference between the ideals of philosophy, mathematics and science ?  Experiment and observations influence the setting up or modification of axiomatic-deductive systems but their computability and logic is ideally the same as that of mathematics and allegedly rigorous philosophy (the appeal to intuition is part of what renders certain arguments plausible).

Mathematics, the science of sciences, occupies a special central elevated region in the geography of the sciences (and the arts and humanities).  It could be argued that only mathematics surveys and illumines and contributes to and interprets all the other sciences. And that the other sciences reach their perfection only insofar as they adopt and conform to the language and concepts of mathematics. But mathematics' claim to the throne can be challenged by (philosophical) logic and computation theory, (philosophical) linguistics, (philosophical) psychology and even some other disciplines (recall how we completely lack a formal logic or mathematics of consciousness).

The universalist point of view, the state of mind, corresponding to differential equations and dynamical systems and the direct intuitive awareness of their omnipresence and all permeating nature, is an elevated state of consciousness indeed. 

In the 20th century (if the number of mathematical publications increased exponentially)  we saw a drastic decrease in logical-conceptual synthesis and clarity and a great lack of philosophical intelligence and awareness, specially regarding the relationship between mathematics and science, regarding the essence and scope of mathematical models themselves (cf. my paper Differential Models, Computability and Beyond).

We saw a proliferation of a kind of junk philosophy and junk science allegedly based on mathematics, specially in the consciousness of the general public, something which can be traced to the reigning ideology of the times (reflected in popular media personalities) and to  questionable core elements of 'general systems theory' and 'game theory'.  We can name a few of these fads: 'chaos', 'fractals', philosophies of vagueness, randomness and uncertainty, 'bifurcations', certain usages of the terms 'emergent', 'self-organization',  'self-referential' (later we shall discuss the  agenda implicit in Smullyan and Martin Gardner as well as Hofstadter's appropriation and distortion of the legacy of Gödel, Escher and Bach - the same concepts the book focused on are deployed with far greater sophistication and artistry in Gaarder's Sophie's World) , 'neural',  'non-linear',  'evolutionary' or 'quantum' beyond its narrow legitimate technical sense and at the same time offering no clear and cogent logical and philosophical account of them.

There are not that many people who could be considered the genuine heirs of Poincaré (in differential geometry, topology and differential equations). These stand out as philosophical-scientific-mathematical giants, towering above others. We have already discussed the problems with the history of algebraic topology and its loss of its geometric and combinatorial essence elsewhere. We name first of all philosopher-mathematician René Thom (and his collaborators and followers) and Stephen Smale (and the Brazilian school of dynamical systems). For Celestial Mechanics Siegel stands out. Jack Hale has written  some excellent textbooks. For geometers we have people like Élie Cartan,  Georges de Rham, Teichmüller, Leray (father of sheaf theory), Whitney, Morse, Shing-tung Yau, Milnor, Thurston, Roger Penrose, Pierre Deligne,  Stanisław Łojasiewicz, Coxeter and John Horton Conway.  Ergodic theory (which embodies Lebesgue's measure theory in the mathematical modelling of nature) , originated by Birkhoff,  is also important (as is Boltzmann and Shannon). And we attach great importance of fluid dynamics (cf. David Ruelle's theory of turbulence - a distant heir to da Vinci). And also Lyapunov, Pontryagin,  A.N. Kolmogorov, A. Fomenko. It may be well that the pioneering contribution of Polish mathematicians  like Kuratowski and Sierpiński to topology has been downplayed or ignored (for instance Zorn's lemma was actually proven by Kuratowski and the Hausdorff property was already formulated by him in the 1920s; so-called 'fractals' were already studied by Sierpiński. The Cantor set was discovered previously by Henry Smith in 1874. Indeed the Weierstrass function is a perfect example of a fractal curve. Gauss certainly knew the p-adic numbers and called them congruentia infinita). This list is obviously tentative and incomplete. We also have to show that if Thom does engage in slightly vague discourse at times, at a fundamental level Catastrophe Theory is both mathematical rigorous and philosophically cogent and more generally represents the correct approach to using the methods of differential topology and singularity theory in differential equations and differential mathematical models of nature and linguistics. For profound work in the mathematical philosophy of continuous and smooth structures and their application to physics, Lawvere stands out.

From Wagner's Religion and Art (1880) - W. A. Ellis tr.

ONE might say that where Religion becomes artificial, it is reserved for Art to save the spirit of religion by recognising the figurative value of the mythic symbols which the former would have us believe in their literal sense, and revealing their deep and hidden truth through an ideal presentation. Whilst the priest stakes everything on the religious allegories being accepted as matters of fact, the artist has no concern at all with such a thing, since he freely and openly gives out his work as his own invention. But Religion has sunk into an artificial life, when she finds herself compelled to keep on adding to the edifice of her dogmatic symbols, and thus conceals the one divinely True in her beneath an ever growing heap of incredibilities commended to belief. Feeling this, she has always sought the aid of Art; who on her side has remained incapable of higher evolution so long as she must present that alleged reality of the symbol to the senses of the worshipper in form of fetishes and idols,— whereas she could only fulfil her true vocation when, by an ideal presentment of the allegoric figure, she led to apprehension of its inner kernel, the truth ineffably divine.

Poetry and states and structures of consciousness

How can we make clear and rigorous the idea that consciousness is characterize by being in certain 'states' or having a certain structure and dynamics ? And very importantly what is means for consciousness to change state and structure, either voluntarily or involuntarily. 

How does or can the state and structure of consciousness change with ageing and education and habit ?  

Parallel to this question of how differences in state and structure determine how consciousnesses interact with each other and their environment. 

Can certain states and structures of consciousness be more cognitively competent or possess a greater and more powerful array of cognitive faculties than other states and structures of the same consciousness ?

How does the perception of time and place and identity change ? 

What does intimacy and union means for consciousness (specially the experience of beauty and love) ? To what extent can consciousnesses communicate and merge ? 

And how are we to understand the relationship between consciousness and the individual body and how is identity determined or defined ? And can there be a consciousness which is not limited by its association to a single living body but rather to a plurality of living bodies or other entities or perhaps even existing in a state independent from any physical body (non-locality) ?  

And how are different states and structures of consciousness related to language, to the use of language and its correlative cognition and experience ?

This brings us to poetry.  We propose the following. In its highest and truest form and potential poetry (and its mode of linguistic-cognitive deployment)  is simply the spontaneous expression of the possession of a higher state and structure of consciousness which at the same time has the virtue of assisting such a transformation in other consciousnesses and most specially leading other consciousnesses to dedicating themselves to composing poetry as a form of cultivation leading to higher states and structures of consciousness, or in particular, regaining such states and structures of consciousness which may have been possessed long ago but have subsequently been lost.

As Hans Sachs sings in Wagner's Meistersinger:

Mein Freund, in holder Jugendzeit,
wenn uns von mächt'gen Trieben
zum sel'gen ersten Lieben
die Brust sich schwellet hoch und weit,
ein schönes Lied zu singen
mocht vielen da gelingen:
der Lenz, der sang für sie.
Kam Sommer, Herbst und Winterszeit
viel Not und Sorg im Leben,
manch ehlich Glück daneben:
Kindtauf, Geschäfte, Zwist und Streit: -
denen's dann noch will gelingen
ein schönes Lied zu singen,
seht: Meister nennt man die!

Now there is great and harmful error involving such higher states and structures of consciousness. This involves its erroneous association with 'religion' (a extremely vague, ambiguous and context-dependent term, to be sure) or more vaguely with 'spirituality' and 'the sacred'.  In itself the attaining of higher states and structures of consciousness not only has absolutely nothing to do with religion but is in most cases radically antagonistic and opposed to it.  We will only point out two aspects here. First of all higher states and structures of consciousness have nothing to do with collectivism or integration into a group - the latter may well lead to an inferior state and structure of consciousness which has nothing to do with super-individuality and non-locality.  Secondly the term 'god' (Greek theos) can only be meaningful as referring to a consciousness in a higher state and structure (local or non-local, associated to a body or not). Communion with a god (either in waking life, in dreams or in other modes) means essentially a profound experience of love, intimacy and beauty (which transfigures the whole of experience and perception of the world) - and this is the only true 'divine revelation', 'sacrament' or 'mystical prayer'. Lucid dreams are particularly important and have a special relationship to poetical creativity. 

Love is a secret seed that only germinates, grows and blossoms in garden of innermost peace and silence. 

However the above considerations need to be reconciled and integrated with the theory and practice of the nimittas and jhanas.  Indeed, not everything out of the ordinary in consciousness is necessarily good or beneficial. Great discernment is needed.

Poetry shows forth the correct relationship of humanity with nature, one based on kindness, compassion, openness to artistic vision and inspiration, theoretical and philosophical contemplation - and we can include also an obviously practical aspect, but one that does not involve harming animals (as in the ancient tradition of Pythagoras, Plutarch and Porphyry, and those of Buddhism, Jainism and the ancient Epics).  This purest most marvelous relationship with nature - one in which nature is transfigured and united to a higher state of consciousness (and this is the original significance of 'gods' being involved in nature - manifestations of truth, more like the concept of 'angel', sp. in ancient Iranian traditions) - has again nothing to do with 'religion' : with fear, priestcraft, collectivism, immoral and false doctrines about gender and eros,  blind obedience, self-torment,  submission to authority, exclusivity, supremacy, pseudo-historical dogma,  rites, propitiation, or with the heinous doctrine and practice of blood sacrifice (i.e. sacrificing the innocent).

The above considerations have immense consequences for the philosophy of language and philosophy of mind. Poetry is to be seen as the queen of linguistic competence and language is to be seen as belonging to a feedback loop for the transformation and elevation of consciousness. Furthermore poetry must reveal its profoundly scientific and philosophical dimension, for instance semantic categories and associations, the theories of irony and metaphor which figures so prominently in Shakespeare and profound psychological aspects. Finally we must address the question of developing a correct theory surrounding the terms 'subconscious' and 'unconscious'.  Poetry is a higher form of logic and deduction and analysis just as much as a form of unfolding intuition and creativity.

In the transfiguration of the state and structure of consciousness the shift of perspective regarding nature and the entire spatial-temporal-historical framework as well as regarding personal identity is so drastic and far-reaching that it is all but impossible to reconcile the two in any simplistic scheme. A fatal flaw of religion is that it cannot admit this and hence betrays its incompatibility both with authentic philosophy and with the  gnosis. Also the deep psychological and spiritual aspects of love and eros is a  complex matter: but we can say from the point of view of 'depth psychology', of the deeper states and structures of consciousness.

The original higher meaning of 'virtue' has been lost. Originally a virtue was a certain fundamental practice, habit, orientation, dynamic quality of consciousness - whose effects operate at radically deep levels - which had its essence and goal precisely in  the achieving of higher states and structures of consciousness (inseparable with its moral consequences relating to how other people and animals are treated).  The common metaphor is that consciousness is entangled, chained and corrupted and that virtues correspond to cutting the chains and fetters, to cleansing and purifying corruptions - also the fetters can be seen as certain forces and intentions which need to be radically inverted. So in this sense the practice of poetry is also one of the greatest virtue which nourishes consciousness and opened its eye to its lost higher primordial state, helps develop the 'wings' of Plato's Phaedrus.  Virtues are a series of secret keys which unlock secret gates.  Virtues that are commonly associated to Christianity,  like faith, hope,  humility, forgiveness, charity, compassion, surrender, spiritual poverty, etc. have in fact an original very deep esoteric meaning and value.

If we take the text of the New Testament, despite all its inconsistencies, serious errors,  interpolations and corruptions, then it is quite possible to read it as a purely neoplatonic (or even Mâhayana buddhist) text (curiously enough Augustine makes a similar claim) in which the theory and practice of anagogic virtues is expounded not through the elaboration of a philosophical system but through the fables and myths of the Gospels and the more poetical utterances attributed to Paul and other epistolary writers:  we are in presence of a kind of prosopopoeia of sophia or divine wisdom (a very important part, for instance, of ancient Hellenic, Egyptian and Iranian traditions, but also found in middle eastern traditions and in several passages of the Old Testament). In the myths and fables of the Christian gnostics we often find more developed and varied feminine embodiments of divine wisdom.

Another aspect of love and eros is that it can be seen (let us say we are taking a semi-non-local view here) as involving 'channels' which link different consciousness together so that one consciousness can be tethered to another or be in a kind of 'circuit' or feed-back loop (thus participating of the same divine energies and illuminations). Thinking of this in topological terms or even in terms of physics can be illuminating. And so-called 'sacred art' might be interpreted as having as its principal goal the creation of a kind of 'portal' or 'channel' whereby one is brought into communion with beings from a higher world.

The attainment of higher states and structures of consciousness has the following paradoxical aspect. There is a part which involves active striving, it is the part that is done 'manually' or 'on foot'. But the real process only starts once the right 'vehicle' has been 'caught' or 'boarded' (discernment is required for this). One has to be 'embraced' and 'carried upwards'.  And what is the Latin root of the word 'rapture'  ?  Then it is proper to say that 'spiritual attainment is realized in me' or 'I am being realized' rather than 'I am attaining' or 'I am realizing'. 

However it needs to be said that contemporary society is in general ill suited for certain ideals relating to spiritual practices (those involving spiritual communion with living persons). It is better to concentrate and focus on persons from other places, times and states of being.

Or better, understand that  there is a fundamental distinction regarding spiritual paths. There are pure solitary paths (full of philosophical insight, dedicated to overcoming the fundamental illusions and energies of consciousness) and those paths which depend crucially on the communion with others (we might call these paths of  mystical 'eros' and divine union).  On another occasion we will show that it is this last type can be perverted and used as a instrument of power and harm (such as for what happens with the 'mystics' of organized religions).