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).

Attention is all you need

Around 2017 I was thinking about the problem of automatic translation and how ambiguity and idioms could be dealt with. One idea was to tag every word $w$ with one of Roget's 1000 categories (represented by a set $C$). Thus we have map $\kappa: W \rightarrow P(C)$.  Roughly speaking an ambiguous word $w$ will have $\kappa(w)$ with cardinality at least 2. Given a context $T$ and a word $w$ occurring in $T$  my idea was to devise an algorithm which functioned a little bit like a Sudoku puzzle using a concept of 'semantic distance'.  We find a word $w$ such that based on the current words $v$ in the context with singleton $\kappa$ we can determine which $c \in \kappa(w)$ is 'closest' to the set of $c$'s inhabiting the singletons of such words. We then make the choice and this should lead to finding further words that can be resolved and so forth. Of course the problem is how to define such semantic distance as well as to guarantee that the process achieves its goal and does not get stuck (but we could introduce random choices). If we view Roget's 1000 categories as organized as leaves (or even nodes) of a binary tree then there is an obvious definition. For instance 'rotation' is semantically closed to 'motion' than it is to 'feeling'.

There is a problem with compositionality for idioms like 'raining cats and dogs' or for a term like 'white rhinocerous'. Thus composition of meanings is in general multi-valued. We have uploaded a small text about this on researchgate and other platforms.

The vector representations used in LLMs suggest the following speculation. Could it be that meaning can be coherently constructed out of complex entities which themselves have no intrinsic (or easily assignable) meaning ? Or like in quantum mechanics the wave function (proto-meaning) is essentially a superimposition of eigenstates corresponding to actual observables (meanings). 

See our paper on academia.edu about Text and Meaning for a more detailed discussion of these subjects. 

Dialectic of the combination of systems

Given two axiomatic-deductive systems S1 and S2, each is an island unto itself, each exists in the world of its own rules, the symbols of which are meaningful only relative to these rules and to the system as a whole. Thus S1 and S2 are neither mutually consistent nor non-consistent - and we can combine them into a new system in a free way.  To speak of consistency we must first identify symbols of both systems, we must somehow postulate a common language.  And we need a notion of contradiction. But all this only makes sense relative to a third system S3 which acts as an arbiter.  If S1 and S2 deduce contradictory things regarding a symbol A, how can we formalize this in S3 ? 

By introducing a symbol for S1 and S2 inside the combined system S1+S2, qualifying symbols representing 'from the perspective of S1' and 'from the perspective of S2'.  The introduction of subscripts or symbols for indexing by S1 and S2 is a projection of the system inside itself, a reflection-into-self.

But then S1 and S2 must be qualified by the arbiter system S3. Why is the perspective of S1 relating to A what it is ? (And the same for S2).  S1 and S2 share context S3 and the quality of S1 depends on that of S2 and vice-versa.  S1 and S2 have become parts of a whole, for-themselves so far as they are for-another. Communication is the outcome of contradiction. 

Hegel as symbolist poet of metaphysics

Hegel has three styles. Aphoristic (harking back to his school-teacher days), esoteric and exoteric (auto-hermeneutic).  The auto-hermeneutic texts (such as the Lessons on the History of Philosophy) are a kind of solution and key to the riddle of his aphorisms and esoteric texts.  

Another way to look at Hegel is to consider him to have been much like both a symbolist poet (where things are referred to never plainly and directly but by traces, associations, symbols and small details - as in Mallarmé) and a master craftsman of word puzzles (in the style of the charades of his day and even more in the manner of the later crossword). 

What Hegel (who had a pedantic and encylopedic knowledge of contemporary culture) did was take common places (topoi), ordinary 'platitudes', quite hum-drum  down-to-earth facts concerning philosophy, science, art, history, law,  and political science, and dress them up as enticing tantalizing riddles and puzzles with an oracular, abstract, convoluted but polished, idiosyncratic baroque literary style (already prevalent in Kant, Fichte and Schelling), at once suggestively illuminating and opaque.

There is something of a magician and showman in Hegel, in how he pulls one concept out of the hat of another seemingly unrelated concept. The secret to Hegel is the invariable platitude and down-to-earthness in his loftiest abstractions,  the familiarity and homeliness of the solution of his most daunting riddles.

Hegel has a lot to say about language and is relevant to the philosophy of language. He illustrates how the mind copes with reality by elaborating a kind of 'poem of the world', a mathesis universalis, a characteristica, but not based on mathematical logic. Hegel is about the shift of perspective of linguistic engagement, a perpetually self-conscious transcendence which refutes its own act of transcending. 

There is also irony (a Shakespearean one) in Hegel and a constant Alice-through-the-looking glass gibe at transcendence. Transcendence is (according to Hegel) the ignorant's maze, by attempting to escape you end up at the doorstep of what you meant to escape: the Heraclitean flux, the river of change persists by changing, that is by changing away from change. casting foam, a symbol, an illusion, a reflection (cf. the doctrine of Schein).  Hegel is scepticism laughing at itself (Nephelokokkugia). The absolute idea is just consciousness become at home with its own flux having laid the pretension of transcendence to rest (and the dualism between the theoretical and the practical).

Hegel is an encylopaedic parody of all human knowledge (cf. Jarry's pataphysics or even Hamann whom Hegel wrote about...).

The lesson Hegel's philosophy teaches us is that we do not possess a language adequate for a philosophy or science of consciousness and an attempt to use ordinary language cannot amount to much beyond  'language games' - and these can be fun, harmless,  even therapeutical or eye-opening,  but in other instances harmful. Another merit of Hegel is giving far more weighty and valid illustration of what a language game can amount to as compared to the Wittgensteinian account. Behaviorism and frenology both merit derision and scorn.

 

Preach away Hegel from thy wooden pulpit,
Let it squeak like the planks of a ship !
Preach away, catching the winds of Spirit,
Conveying meaning and motion
To an undulating adulating crowd.

Outside the armies march on,
Canons explode and laws are decreed.
What will be must be:
Minerva's cerebrations celebrate indifference
From an Olympian dais of unthought-of thoughts.

Philosophemes on Consciousness

Can there be consciousness without knowledge or knowledge without consciousness ? Does not all knowledge involve self-knowledge and the positing and definition of a self-subject ? All knowing involves a knowing of the knowing process itself. What can be known ? What should be known ? What is the highest knowledge and what is the highest knowledge about ?

What is ignorance ? An ambiguous term. It can mean erroneous thought or lack of the right cognition regarding something. But it can also mean simply non-knowing, that is, a consciousness which is not in the act of knowing. The ordinary conscious act of knowing is a relation, a flowing out, an entanglement, a diremption, limitation or even corruption of consciousness - accompanied by a positing of a subject-self and the awareness of the knowing process itself (the reflection into self via negation of the positing).

In another sense knowing is simply the state of any state of consciousness, a pure self-relatedness. Thus we have an absolute knowing which involves a non-knowing in the common sense, which is the fullness of the liberated mind that does not flow out relationally but has its self-positing in self-abrogation and self-reflection on its own freedom.

The highest knowledge is the effect of a self-referential, self-illuminating, self-enfolding (or self-unfolding) process of consciousness itself.

Know the structure and dynamics of the world to know the structure and dynamics of the mind : time, transience, impermanence, constant self-negation and self-production, self-implication, returning to immediacy and beholding its compositeness. Immediacy is actually result, relativity (reflection), mutual reference and dependence: past and future, memory and expectation.

Note the possibility of direct action of consciousness on consciousness, of expunging, and not being a passive spectator only - it cannot obtain detachment and freedom without breaking the cage.

The subtle body (or first-person experience of the body known from the inside) is an oasis were we can find a different mode of consciousness.

True philosophy cannot be academic philosophy, because it imposes and assumes an exterior a priori standard and reification - a certain enculturation, historization and socialization. This is what is so lacking in western philosophy, in Hume, the lack of orientation and insight capable of leading to personal transformation. Western philosophy is often just a shell.

Afferent vs. efferent nerves. The mind an internal feedback, a watermill, thoughts function both as input and as output (an internal loop driven by the main current - reflected in neural anatomy). A little like Barendregt's diagram. Thus we can have afferents we do not want or want afferents we don't have. We can be force to do efferents we do not want to do or want to do efferents we can't. The watermill feedback structure is built through this continuous current, an eddy. The prison of the mind.

Watchfulness must be centered on a turning inwards, not only looking on exterior spheres of common experience, but encroaching on and discovering and centering itself on previously hidden, inwards domains, the abode of forces that act behind the scenes, which wield power if unseen, but weaken under the sunlight of clearly conscious watchfulness, turned inward, casting a steady light wherein they are caught, found out. Ordinary consciousness is a kind of exteriorization and out-flow of itself, a self-nescience, self-passivity and self-marginalization.

Parallel to watchfulness progressively consolidating itself inwards we must also develop the practice of considering the total sphere of experience, of consciousness, as a whole, considered in its entirety, in a balanced way radiating, as it were, out from the innermost center, so that there is attained a balance of the inner and the outer and the exterior sphere is re-integrated into the unity of the center.

Thought is a product, a proliferation, the leaves, the buds, the result of inner forces, energies, organizations and productions - all stemming from a central source. Watchfulness and its sphere must regain the usurped throne, wherein sits the original producer, controller of all thought. 

If the self is an illusion, a fuzzy concept, a false concept - how can there be a theory of self ? Can there be a theory of illusions or of false, vague, fuzzy, ill-defined inconsistent, mutable concepts ? How does Hume explain - according to his theory - a fake impression which cannot be traced genetically to a complex of sense impressions or feelings ? Few modern western philosophers (for the ancients it is a different matter) have attempted a theory of illusion. Schopenhauer's theory of the negation of the will is noteworthy, a real attempt at a theory of the illusion of self (and finite individuality).

Logic is an attempt at the psychoanalysis of language. Language acts in different ways and at different levels on the mind, ways and levels beyond the most immediate abstract level.

There is so much more to be said about 'meaning' (beyond both surface representation and mere social dynamics). Wittgenstein took a wrong a theory of meaning and replaced it with an even worse one. The deeper levels of meaning and action are related to a kind of rhythm and music in language (both metaphorically and non-metaphorically). Hence the importance and irreplaceability of direct reading, hearing, recitation of certain kinds of texts.

There is a lot to be said about the heart and how it relates to spiritual development and in particular to consciousness, to the breath, to impression and illusion of 'self' , to Schopenhauer's negation of the will, to the irradiant contemplations, the little known significance of 'poverty', 'simplicity' and a certain spiritual act related to unification and anagogic intent, certainly found in Plotinus and of course in the Yoga and Vedanta.

It is not a question of replacing the false sophistry with a single true philosophy. Rather true philosophy must mean a collection of possible perspectives (darshanas) with an anagogic dimension - as well as powerful rebuttals of false philosophies. Thus different vectors can point at the same center, but there are also vectors which categorically do not point at this center. While there are false philosophies such as Wittgenstein, Ryle, Dennett, Parfit, Rorty and Brandom there are a plurality of truth-pointing perspectives.

Truth is relational: one formal system representing another divides sentences into provably true, provable false, neither provable or not provable but anagogic and self-referential (true in a higher plane) and neither provable nor not provable but not anagogic or self-referential. Two systems can be mutually inconsistent and yet metaconsistent in the sense of there being a canonical higher-level encompassing system which integrates them both at a higher level.

Know the texture, the symptoms of the mind, if the defilements are there. To inspect objectively, in an unfiltered way, the totality of one's consciousness, but to inspect diagnostically, reviewing the symptoms. Thus we must look, inspect, distantly, objectively, in a neutral way, but in order to interpret, diagnose, reveal symptoms.

Introspection must be total, all-encompassing, neutral, balanced and include the body-sensation (pressure, temperature), proprio-perception, the breath, feeling just as much as thought, the fields of sense-perception, inner speach, imagination etc. Find the center, progressively deeper layers, turn inwards. But also act, transfigure, integrate, calm, expunge the mind.

There are models of consciousness inspired by physics: consciousness a self-subsisting field spread out across space-time as well as beyond space-time. The body represents a kind of fragmentation and limitation of this field (a Faraday cage). Like a receiver and transmitter. The limited and trapped consciousness must energize and expand and regain its unity with the total field of consciousness. These kinds of models that objectify consciousness are problematic. Also not all merging of ordinary consciousness into another enveloping 'larger' consciousness is necessarily good (i.e. consider collectivism and cults) or represents a higher state of enlightenment and freedom. The contrary could well be the case. What is of interest is consciousness in and for itself, the consciousness of consciousness which is absolute and free. Consciousness by folding in on itself finds the secret to unfolding itself and thus attains freedom.

There can be no science or philosophy of consciousness yet (only that of the products or reflections that pass through consciousness, logical and linguistic and other artistic-semiotic artifacts) - because we to do not possess immediately any proper means or language to analyze it or to express things about it. The only thing that can be given is a practical guide to gradually develop the sight required to see and know what should be seen and known. Regarding consciousness, language is practical, methodological, never purely scientific or philosophical. That must come much later. Consciousness must transform itself first in order to become an object unto itself and to be able to talk about itself. Consciousness is not so much a given as that which may and should come to be.

What is our philosophy ?

The following account needs to be greatly expanded, revised and clarified in the light of transcendental philosophical consciousness. 

A theory of truth that argues that although we can say categorically that certain philosophical systems or propositions are false, we cannot say that any philosophical system is absolutely true or definite.  Only that a plurality of philosophical systems - satisfying certain conditions -  are legitimate in the sense of being anagogic to truth.  Though manifesting incompleteness they have yet an intrinsic virtue of pointing beyond themselves to truth.  The anagogic theory of truth must not be confused with relativism nor in particular Pyrrhonism in its most superficial reading. 

A theory of meaning which depends upon a philosophy of mind.  We argue that all meaning-bearing objects possess multiple layers of meaning which are apprehended by or act upon the mind simultaneously at many different layers.  That modern western philosophy largely focused only on the mere shell of the meaning process and the most exterior aspect of meaning as a mental phenomenon.  This tendency went into an even worse extreme with meaning-as-use theories, though paradoxically this tendency also presents a kind of distorted echo of hitherto deeper neglected aspects of meaning.

A theory of mind and and theory of knowledge which integrates fundamental insights of such thinkers as Aristotle, Plotinus, Locke, Hume, Kant, Schopenhauer, Brentano, James and Wundt. It is a theory based on a multi-tiered, multi-leveled concept of the mind known progressively through a special methodology of insight and introspection which itself evolves and becomes more refined during this process. The core idea is that the ordinary mind is something folded in on itself and solidified by a self-reinforcing illusion. 

We can say that the problem with cartesian dualism is not that it was not physicalist but that it was not non-physicalist enough. On the other hand the history of science and the analysis of the concept of matter reveals it to be a fundamentally unclear and flawed concept.  We freely acknowledge that great advances in physics may lead to a radical new view of the physical and chemical aspects of living beings.

A theory of analyticity and the a priori based on computability and Turing-completeness which categorically refutes mainstream philosophical logic while acknowledging the central role of a plurality of perspectives,  incompleteness, mutual interpretation between formal systems and formal metatheory.

A philosophical logic based on an alternative graph-theoretic and combinatoric-computational abstraction of the logical mechanisms of natural language.

A philosophy of science which offers new perspectives on determinism, computability and the role of continuity and differentiability in science. We also point out the relevance of Hegel's Science of Logic to the recent history of mathematics and theoretical physics as well as to general systems theory.

In ethics a moral sense realism akin to Shapshay's interpretation of Schopenhauer: that Schopenhauer's ethics can be seen to be based directly on the facts of consciousness and is not incompatible with Kantian ethics, free will and the hope for social progress. We would also add that Hume offers many valuable insights as well as well as various ancient authors who defended animal rights.  We also criticize current misreadings of Stoicism and strive to show the affinity between the self-cultivation promoted in the Pali canon and that of several schools of ancient philosophy.

In cultural and political theory we offer a critique of supremacy and superiority concepts and beliefs - the mismeasure of man -  and take particular aim at faulty concepts of  'intelligence', 'race', values and institutions based on the accumulation wealth,  and all ideological justifications of violence.