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 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).