Foundationalism and Logic

The point in question concerns the problems of foundationalism involving type theory or term-rewriting systems. In the final part of my Kantian-oriented paper "Analyticity, Computability and the A Priori" I attempt to tackle with this problem (as well as presenting in greater detail my analysis of term-rewriting systems, Turing completeness, the Curry-Howard correspondence and the limits of logic-like formal systems in representing all computable functions and extracts on Hilbert's philosophy taken from a paper by Claire Ortiz Hill). I propose in the end a methodology inspired Piaget's genetic epistemology in which one must effect a sort of regression to relive in a conscious way the stages since early childhood whereby one progressively gained computational competency - centered around the ability to understand, carry out and check the following of rules - and to compare the cognitive structures involved to formal systems and computational models at our disposal. While this cannot lead to the enthroning of any single formal system or model it can, I believe, nevertheless bring to light groups of specific systems and models which are "structurally akin" and "cognitively natural" to consciousness itself. While we cannot enthrone a single system, I believe we can use the language of a given system to express what are in the Kantian terms synthetic a priori principles of the human understanding. For instance when we find a finite derivation in one formal system (the metasystem) and conclude that this derivation "shows" that a certain goal cannot be derived in another system (the object system), which is something that we cannot directly show in the object system because it would require an infinite amount of time. Gödel's incompleteness theorem is (and has to be) formalizable and corresponds to a finite derivation in a system M. But it must be assumed that this finite derivation is sufficient epistemic grounds to conclude something about the infinite set of derivations in Peano Arithmetic, that the sentence G cannot be derived.  

A point about subjective idealism

Consider the opening sentence of Schopenhauer's famous book: "Die Welt ist meine Vorstellung/The world is my representation".  How can subjective idealism seem at once so utterly certain and so dubious? The answer is quite simple and lies in the definite article "Die/the" in Schopenhauer's dictum. The world in the sense of the world in which each one of us is acquainted with through first-hand experience - my world that I take immediately as the world - this cannot be in reality any more than a modification of the subject, of consciousness, a self-projection, self-occultation of consciousness inside itself. Even from neuro-reductionist physicalist assumptions there is no way of avoiding this conclusion without dogmatism (the ruse of invoking the objectivity or public nature of logic or language) or non-physicalist explanations and we can turn Benaceraff's overrated objection against Platonism against the physicalist who wishes to refute subjective idealism:  basic neuro-physiology and gestalt psychology show that a direct causal connection between nerve impulses and the "causality" of the phenomenal subjectively constituted world - is sheer nonsense. There are physical impacts on receptors which do not produce effects on consciousness and there are effects on consciousness which are not the direct result of impacts on receptors.

The world in the sense of that world with which I am acquainted with through first-person experience, is entirely phenomenal and exists in consciousness only, despite its objectifying externalizing intentions and pretenses.  However from this it does not follow in the least that a world, any world, is my representation. It does not follow that outside my world there is not another world. Nor can we rule out that there could be some sort of cognizable connection between our world and such a world, the world which is not our world.  In Kantian terms there does not follow that there is no thing-in-itself and it does not follow that we cannot know anything about this thing-in-itself (we already know that we know that it does not necessary not exist).  Despite Kant's own arguments, we may hold that such a world-in-itself is perhaps a grey, timeless, purely mathematically structured world but in which other world-creating consciousness subsist. We can even discern such a conception in Hume's Treatise. None of our causal scientific theories or explanation depend on the phenomenal intuition or concept of time, only on a vicarious geometric abstraction, a flattened timeless time.

Consider the stereographic projection of a sphere into a plane. The sphere is the subject,  the tangent bundle of the sphere is the modifications of consciousness,  the plane is the postulated world outside consciousness.  

But is this not logical dogmatism where we endow logic, a product (or condition?) of consciousness, with the right to judge that which is beyond consciousness? If logic corresponds to the ability to understand, carry out and check rules and to meta-interpret rule-systems,  where resource constraints can be taken into account,  then perhaps continuous processes - as infinitary rule systems - transcend logic. But logic functions through necessary principles of meta-logical agreement - thus it is reasonable to endow logic with transcendental epistemic scope. If a derivation in one formal system has to be considered sufficient for the cognition of a non-finitary property of non-derivability in another formal system, then surely the belief in the extensive epistemic range of formal systems - of logic - is reasonable.

If the above considerations do not seem convincing, we can point out that the validity and transcendental scope of logic (the highest a priori condition) is an essential assumption in Hume (as we discussed in detail before), Kant, Schopenhauer and Husserl.  We can always ask Kant: what gives reason the right to judge itself and its own limits? Does not transcendental logic have to follow the rules of general logic as well (even if it includes important differences)?  And another important approach involves the formal verification principle: challenge the meaning-as-use ordinary language philosophers and neoscholastic dogmatists  to set up their theory of knowledge and mind in a formal system and then proceed to critique those systems using their own rules. The weak conclusion remains the same: either physicalism is false or (qualified) subjective idealism is true. The stronger conclusion is that if consciousness is essentially non-physical and non-local (or even trans-temporal) then this fact tends to strengthen rather than weaken the case for qualified subjective idealism. And if the dogmatists invoke a direct intuitive "given" or direct intuitive acquaintance with allegedly real exterior things then they have no right to discard the direct intuitions of consciousness being the fundamental reality that can be experienced during spiritual development and altered states of consciousness.

If we are certain that there are universal moral laws known a priori then it would seem to follow that we should treat phenomena which appear to us as being sentient beings as if they really were sentient beings (treat them according to the moral law),  regardless of the non-reality of their first-person phenomenal presentations. This is because we do not have nor could ever have certain knowledge that they do not exist (either entirely or in part) and secondarily because regardless of the situation the practice of moral deeds can only strengthen character and morality itself.  If a child is nice to its toys it will probably be nice to people and animals as well. The similarity of this argument to Pascal's wager is noted.

But subjective idealism is a misleading term because it suggest than an individual ego-subject, finite personality or self-in-the-world is at the same time some kind of substrate of the world. But in reality cosmo-ontology and egology are illusions to be dissolved together. This is the task of transcendental dissolving and liberating insight,  true philosophical phenomenism/positivism/empiricism and skeptical dialectics.

Also considerations on temporality, finitism, mereology, the mysterious nature of concepts and meaning - and in general intrinsic intentionality, synthesis, constitution and constructivity - applied to both the self and experience  - are quite sufficient to establish the above liberating insight with regard to the egological and cosmo-ontological illusion.

How do we interpret quantification from a finitist perspective? How can we develop intentionalist finitism? What does alleged arithmetic knowledge mean from a finitist perspective? Was Hilbert really defeated? Was Leibniz actually a finitist?  Can finitism offer new perspectives on the theory of knowledge? Can we solve the problem of the stubborn non-finitism of category theory? Do we need a new interpretation of Carnap and Russell?

Can statements about numbers involve an infinite number of relations to actual numbers? What is the significance of Ockham here? Can psychologism be revindicated?

The new synthetic a priori principle: finite derivations must ratify and represent an indefinite but bounded set of truths. This is applied also to specification and verification of programs.

And yet, what are logical, semantic, phenomenal, physical atoms? What could they be? Can paraconsistent and infinitary logic be justified in the framework of our "Analyticity, Computability and the A Priori"?

Very short note on formal concepts in science

From whence do we get the impression that some mathematical models are closer to physical and spatio-temporal intuition,  more down to earth and intimately tied to concrete applications, while others hover close to the heights of allegedly less useful  'abstract-nonsense' ? The real numbers and differential equations, these are seen as tied to dynamic-geometric intuition and of vast applicability and interest in engineering and science.  But abstract algebra and category theory appear to have no direct relevance to applicable mathematical models or to their kind of concrete geometric-dynamic intuition. We present here a few short speculations.

Perhaps the abstract models do capture fundamental levels of reality (maybe even more fundamental than the so-called concrete spatio-temporal ones) and what is required is first of all the methodic development of a special kind of intuition or cognition to grasp the planes of reality which they model (maybe something like Goethe's method is called for?). And then further models are required which can effect a mediation or transfer between these two levels, or at least allow a continuity or gradual deformation between concrete spatio-temporal reality and higher levels of reality.

A beautiful illustration of such a meditation and construction is furnished by the double fibration in Penrose's twistor theory which allows a mediation and transfer between physically significant objects on Minkowski space and abstract cohomological objects on the complex algebraic variety $\mathbb{P}^3$.This operation allows solutions to conformally invariant differential equations on spacetime (e.g., Maxwell's equations, Yang-Mills, or linearized gravity) to be identified exactly with Cech or Dolbeault cohomology classes on specific regions of twistor space. This appears to have been Penrose's attempt to give a geometric (topological) interpretation of quantum non-locality. 

Another illustration is the theory of $\mathcal{D}$-modules which presents a mediation between derived categories (and monoidal categories) and concrete models of systems of partial differential equations.

The idea of Kant's schematism of the pure concepts of the understanding can be interpreted as finding the mediation between logic and geometry (including mathematical physics). This is of immense contemporary significance as we find versions of Kantian schematism in topos theory, homotopy type theory and in areas involving monoidal categories in algebra, geometry and physics and in linear logic and computer science. 

There is also apparently a mediation and transition between the theory of bifurcations of smooth vector fields, fundamental  and ubiquitous in concrete applied mathematics,  and monoidal category and operad theory. See also Physics, Topology, Logic and Computation: A Rosetta Stone by John C. Baez and Mike Stay.

An objection can be raised that our concrete allegedly intuitive mathematical models are themselves quite abstract but are only perceived as immediate and intuitive in our present cultural context by a deliberate forgetting of the complexity of their cognitive-historical past and genesis. For instance real numbers are constructed from the rationals by quite abstract, cardinality increasing, procedures involving equivalence classes and identification. And the same goes for the concepts of continuity, differentiability and so forth. Surely the ancient Greeks had other forms of intuitive perception and concreteness in their geometry, physics and engineering. We answer this objection by our arguments that the fundamental dynamic and geometric-topological intuitions of modern science were in fact identical to those of ancient Greece. It is the modern foundations in terms of Dedekind cuts and $\epsilon$s and $\delta$s that can be critiqued from a philosophical and logical point of view and alternative foundations (locales, realizability topoi, synthetic differential geometry, homotopy type theory) can be defended which are also more aligned to the theory of space and change found for instance in Aristotle's Physics.

Short note on philosophical methodology

Cultivating what we should call not transcendental consciousness, but transcended consciousness, the true epokhê in the school of Pyrrho and Hume, we realize the following.

That the formal mathematics and formal philosophy projects and the philosophy developed in our paper Analyticity, Computability and the A Priori are themselves perfectly legitimate forms of transcendental philosophy and neutral superpositivism.

That the purpose of life is to die well, finis vitae bene mori. 

Transcended consciousness is not only the power of being beyond time and its manifold constructions, but to have the liberty and freedom to concretely imagine and to virtually live consequences and alternative possibilities and to change perspective regarding a given contingent time.

Thus desire is dissolved by the simple transcendental consideration of: what if I had that which I am now desiring? Thus the taking-for-granted, the masking, of the good and blessings we have in the present and the twisted mirage of having a better past are dissolved by the recognizing that we will almost always live in our past, in the golden age, relative to the total temporality of our life. 

Thus we may long to live again in the world before the advent of LLMs.  But if we had the total perspective of how the world will change in our lifetime, we would have greater appreciation of living in the precise present that is present to us.

Anatta

Anatta was indeed the central philosophy of early, authentic buddhism. But is was not fully understood and rapidly compromised and corrupted. Its recovery, preservation and further exposition and development is found nevertheless in various schools of the East and West, both ancient (and even pre-buddhist) and modern.

Our working hypothesis is that original Buddhism was strictly based on ethics, philosophical insight and meditation (bhavana) and had no religious component whatsoever. Metaphysical questions and questions regarding the afterlife were treated exactly as in Pyrrho or Kant's transcendental dialectics. The concepts of karma and rebirth were originally philosophical teachings whose meaning was lost, being corrupted into literal religious beliefs (wherein the bhikkhu ultimately replaced the brahmin). The original teaching on karma (which involves impersonal polarized psychological energies) did not depend in the least on a literal mythological understanding of rebirth. 

Thus for example we can think of human beings as receptors, generators and transmitters of certain psychological energies, and as being immersed in an environment in which such energies can also exist in a free form.  Negative energies and deeds not only rebound with unfortunate consequences in the life of the individual but also, conceivably, during the process of death the sum-total of such an individual's habitual and accumulated energies may be explosively released into the world and thus influence other beings in a positive, neutral or negative way (there might be an analogy with a supernova in astrophysics). Also during the process of death the individual may experience a kind of final dream in which that individual's life-history and sum-total of energies and habits is lived out in a final synthetic way. 

We hold that Anatta is the essence and culmination of TPC and TPP.  We have discussed and highlighted the importance of Pyrrho, Hume, Nagarjuna - and a certain approach to Hegel.

Let us just say that an entity or structure can be inherently not only fragmentary and incomplete but also inconsistent. A fragmented inconsistent being does not have within itself a representation of its own negation, non-being, of a state where it is not. That is to say, there is no true being without self-transcendence. The best that can happen for an entity is to see clearly the circularity of its own inescapable inner contradiction.

The core of TPP is the development of intentional habits and fundamental energies and forces, virtues of consciousness which counteract from a central source and in all dimensions  the limitations, delusions, inconsistencies and self-postulation and self-proliferation of the fragmentary being.

The categories of consciousness (including space, time, locality) are to be transcended.

We must find strong evidence for the presence and practice of this same TPC and TPP among the most diverse places and people in prehistoric, classical antiquity and subsequent history, all in complete agreement with regards to the only necessary central essential core (which in itself as virtually infinite inexhaustible content).

The primordial tradition is not some kind of primitive human culture, rather it is the ubiquitous and timeless presence of the power of complete transcendence of humanity.

 There is not great difference between logic and argumentation and games. These are the factors involved. One accepts a game  G as a game and holds that the game is interpersonally objective and follows publically agreed upon rules.  One fixes a side, a starting point, a choice X in G. Then X is processed by G (in a way which may involve deliberate choice and participation, or not) and eventually yields an element U from a predefined set of possible outcomes. Logic and argumentation involves furthermore that acceptance of a translation-representation between intentional mental-cognitive content and a choice X as well as the reverse translation from U back to meaningful mental content. Furthermore it is often the case that we postulate a principle of continuity in that the processing steps of G are transparent in their mental interpretability though such do not play any role in the processing itself.

The interpretation of Gödel's dialectica translation in terms of games is one of the most interesting developments in logic in the recent decades (a formula is turned into a game-like formula and proofs become winning strategies codified by closed terms in system T) - and should be compared not only with our reconstruction of the debate game in Aristotle's Topics but also with modern proposals for a logic of dialogue.

We observe that in original Buddhism we meet with many suttas which share a logical-argumentation template and dialectical method which is itself far more important than the contingent details. This method involves a combinatoric bringing to light and articulation of possibilities aiming a bringing about a catharsis and detachment (like the Pyrrhonic epokhe).

Thus Buddhist dialectics and Buddhist phenomenology rest both on a subtle hermeneutics of language, that is, language considered as the vehicle and dwelling place of the proliferation and self-reinforcement of the fragmentary entity. Hermeneutics asks the most fundamental questions which lead to the appearance of cracks and tears in the fabric of constructed reality.

Philosophical Psychology

Na kiñci loke upâdiyati. Total disinterestedness cannot be the disinterestedness of any finite self. Letting go of all, detachment. Short expressions, easy to apprehend superficially. But in their deep meaning they hold the keys to the heart of the world. To let go of the past, of all persons, to let be, let pass. This means relinquishing all desire and identity. This means freedom. It is utterly foolish to make relinquishment something external and physical. It is a transcendental act in the secret depths of the heart. We come to be, come to be what we are, through what we are attached to and desire. And every person is radically different people throughout the stream of life - where lies this identification of different masks ?

The royal road to TPC is i) through the perception of the universal a priori condition of temporality and transience. This reveals alleged objectified being as but a (modalized) moment in the flux of consciousness - and ii) through the perception that the self is determined through the delusion of the sense of mine, through appropriation and identification. A process and tendency, not a substance - and iii) that thought is often like a screen that consciousness uses to hide from its own nature - the world is born when consciousness wraps itself in the veil of its own thought.

Seeing through thoughts and thought. Analyzing posited 'units' of thought and showing their inner contradictions, essential dependencies and implicit containment of other thoughts.  Like characters in a story that only really have meaning relative to the story as a whole. The excitations of a self-interacting quantum field.

How to transcend the world. There is another aspect of TPC based on an intellectual analysis of the ordinary world, ordinary human life and psychology, which nevertheless has a transcendental philosophical goal of great import. This is ability to clearly see and virtually live various possibilities (for self and others, empathetically taking the perspective of others) and to extrapolate and accelerate a given life-possibility in time. In this way all delusional desires and attachments dissolve once the heap of inevitable sufferings, limitations and anguish entailed by what was taken to be their desired fulfillment are clearly understood. The feeling of possession of something desired is in reality you being possessed by it, its allure, its delusion and its desintegration and downfall.

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, also in the Pali suttas, and 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. An 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).

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.