From phenomenology to a philosophy of consciousness to spiritual science

Alas there is no clear definition of what phenomenology is (which should not to be confused with the specific philosophical work of Edmund Husserl) or even what phenomenism, empiricism, positivism and the theory of knowledge exactly are.  There is no clear definition of what the philosophy of consciousness is or how it could differ from the philosophy of mind. And there is no clear idea of what a spiritual science could be or a science of consciousness. We are in possession however of the bodies of knowledge encompassed by the various branches of psychology and cognitive science - and there is surely much of value there.

In our writings we have emphasized a few important points relevant to the entire interwoven enterprise of all these subjects. The centrality of first-person experience, its descriptive insight and analysis and most importantly:  there can be no genuine progress without a radical and thorough form of personal transformation aimed at at self-transparency and self-transcendence of consciousness. We attach importance to the first-person experience of the body and the various feedback mechanisms involved, specially those related to sensory systems and the peripheral nervous system.

Is there any relevance or legitimacy in the idea of mathematical (or formal) models of consciousness? 

This question, which we will not attempt to give any definite answer for now, seems related to the circumstance of there being two distinct paths (but not necessarily non-complementary or non-convergent)  passing through all the subjects mentioned above, whose ultimate aim is not only spiritual science but the attaining of ultimate spiritual knowledge. We might characterize these two paths as pertaining to the Buddhist and the (neo)Platonic philosophical and spiritual sciences - it being understood that these terms should be read in a very universal sense encompassing in particular a huge range of philosophical literature from antiquity to the present, both from the east and the west. Both their differences and their common core (we have written on the connection between the Platonic-Socratic dialogues, Pyrrhonism, Damaskios and the Pseudo-Dionysian literature) are important.

The differences manifest in the kind of mathematical or formal model of consciousness we could associated with each one of them. The (neo)Platonic path would seem to point to geometric and topological models of consciousness (due to its synthetic, global, anagogic methods) while the Buddhist path (analytic and actively illuminating through insight) would prefer event and process-oriented computational models. Its western embodiment has great luminaries such as Sextus Empiricus, Hume, Kant and Brentano. Dialectics is found in both paths but with different modes of employment and emphasis. For both thorough psycho-somatic peace, calm and relaxation is a precondition for any progress.The dichotomy between the paths is not meant to be universal and disjoint as it is easy to find traditions that sit somewhere in the middle or incorporate core elements of both approaches (Yoga, Samkhya, various schools in the Upanishads and Bhagavad-Gita).

About the geometric-topological model of consciousness. This resolves around the ancient notion of topos (cf. Aristotle's Physics Book IV), the modern concepts of stratified space, and the granting legitimacy to traditional cartographical, architectural, horticultural and other metaphorical language regarding consciousness and the diverse faculties and regions of the soul (cf. the ars memoriae).  Its foundation is  the work of Plotinus (which integrates the best elements in the Platonic and Aristotelian texts). There are also interesting elements from neuroscience and psychology that can be integrated into such an account.

We can cautiously suggest that Plotinus' process of spiritual simplification, illumination and reversion (we would say rather 'involution' and 'inversion')  involves a radical shift in the self-perception of consciousness and at the same time a radical shift of perspective regarding what is perceived and conceived as spacetime and the laws of physics. We propose that this transformation, this shift of perspective, involves the Penrose transform of complexified (and compactified) Minkowski spacetime. The new reality is twistor space $\mathbb{P}^3$ and the previous Minkowski spacetime is something secondary and generated (its points correspond to lines in $\mathbb{P}^3$). As regard to the hyperboloid hypersurface which appears naturally in twistor theory (it corresponds to the image of real Minkowski space and stratifies twistor space), we can recall this verse by Alan Turing:

Hyperboloids of wondrous Light
Rolling for aye through Space and Time
Harbour those Waves which somehow might
Play out God's wondrous pantomime. 

 

The initial process of complexification and compactification can be likened to unveiling a more fundamental ontological domain, the intentions, meanings or processes of the world-soul at work in physics - which corrresponds to a parallel process in consciousness. Fiber bundles are perhaps a natural mode for the human mind to grasp high-dimensional spaces. The isomorphism of the fibers at different points represent their ubiquity and unity in the Plotinean sense.

 

Spiritual science will involve a geometry and cartography of  consciousness employing a stratification into spaces with their own dynamics and deformative processes which become aligned within a global anagogic process.  However we must begin with the most humble processes related to the psychosomatic domain and their geometry and dynamics. The geometry of biophysics furnishes the clues and can be transposed - through a process of variation, complexification and compactification -  into the domain of a geometry of consciousness. The branches of mathematics which offer a unification, fusion, of logic and geometry, are surely of great relevance here. 

 

There are several interrelated geometries of the mind. The geometry of the architecture of our cognitive-semantic spaces. The geometry of our personal narrative (our biography) and of narratives in general, specially the initiatic journey. The geometric physiology of the soul's powers and functions. An important aspect of such geometries is not only their stratification, multidimensionality, dynamic nature, relation to projective space,  but also their foliated nature, all forms manifest as a simultaneous united continuum of many different levels. An opposing view would see all this as a cultural inheritance of forms of illusion (prolongations of a standard naive pre-biochemical understanding of biology), of aggregation and identification and put in its stead Hume's sublime concurrent process vision of consciousness. We distinguish between objects and beliefs constituted by function (mistaken for essence) and true essence revealed in the reality of the underlying concurrent processes which do not reveal themselves necessarily as they are when they construct belief-objects subordinate to function.

 

But perhaps indeed the vision between the two paths is not so significant in comparison to what they have in common - the science of the subtle and spiritual bodies. Also recall also how Hegel and Husserl would hold that, as strange as it may seem, Plato, Sextus Empiricus and Hume  present complementary aspects of the one truth and are capable of unification at a higher level. But also postulating unity can be harmful at the level of spiritual paths, contrary to a common trend. Rather one must be lucky to find a path that is 'beautiful in the beginning, beautiful in the middle and beautiful in the end'.

 

Before the question "how can we gain higher knowledge of consciousness itself?" we should ask "what is the best knowledge for consciousness?"  It is the knowledge that lets it see through itself and liberate itself from itself. A central object of the best knowledge is the difference and unity between perception, feeling, volition, thought and the sense of self and awareness. Also of temporality and temporal intentions and the construction of objects and concepts. And is not logic the science of consciousness par excellence? And even more importantly: the best knowledge is not just knowledge of the highest object but the best knowledge is the knowledge of the best knowledge itself in its illuminating and transcending function. Consciousness must be unbounded light and its knowledge be knowledge of its own knowledge and of its own knowledge's illumination. Recursion and reflection-into-self permeate the Pali Canon and its path of spiritual development. Consciousness lives usually passively immersed in and hypnotized by its own self, forgetting its own power not only of freeing insight but its ability to act directly upon itself, dissolving the mistaken belief in the necessity of certain mental content.

 

And we can give a symbolic-anagogic formalization of consciousness properly understood, or at least partially mirror its self-clarifying, self-transcending, self-subsuming process. We have sketched some of this in our "Hegel and Modern Topology".  We could add thereto some considerations on monoidal categories (which furnish a common ground for linear logic,  concurrent processes, algebraic geometry, PDEs and quantum theory). What is important here is the internalization of their own "boxes" into wires (input and output) allowing the modelling of dynamic rewiring (closed monoidal categories).

 

About the coherence conditions in monoidal categories. The coherence condition can be viewed as the necessary amnesia which forgets the history of a process to look only at the final state and  conditions the connection isomorphism only on the final result (cf. Kant's example of surveying a house in the CPR). This is what allows objectivity to emerge: objectivity is the postulated forgetfulness of the plurality of different presentations and the postulate of their essential equivalence. As Aristotle wrote: the road from Athens to Thebes is the same road as that from Thebes to Athens. Coherence expresses the emergence of objectivity (hence order) by a voluntary forgetfulness of a system's memory via focusing only on the final state. The condition of (shallow) objectivity is that something is what it is independently of its process of coming to be.  If you start with a certain composition of $\otimes$-products X and switch them around using tensorings of ids and associators to obtain a new composition of $\otimes$-products Y then the resulting composed isomorphism linking X and Y will always be the same, no matter the intermediate route. Without a partial repulsion of memory one will be constantly becoming something different - this act is also that of the Understanding in Hegel's Logic that forgets, attempts to cancel,  its own process of coming to be.

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.

Yet more short considerations on AI

The philosophical significance of LLMs and a potentially powerful philosophically based critique of LLMs have not yet been developed and perhaps their importance has not even been recognized yet.

Could LLMs be tied to a certain philosophical view regarding the mind, language and the world? And if such a view is manifestly erroneous could not this furnish a sound basis for acknowledging - alongside numerous other reasons - the social and cultural harm of LLMs?

For instance, could we not explore the relationship between LLMs and Quinean extensionalism and meaning-as-use theories? Are not LLMs based on the rejection of the irreducible intensionality of human symbolic activity? Behind every symbol there is an intension. And a formal theory of intensionality must itself acknowledge the intensions of its meta-symbols.  But there is no intensionality in LLMs beyond that of the humans involved in their creation. Searle's Chinese Room ignores the deeper philosophical meaning of computation - or a potential associated geometric theory of meaning - but may be of interest for a critique of LLMs.

Do LLMs compute? Computation is a primordial intensional human activity (see our paper Analyticity, Computability and the A Priori). 

Perhaps there are other machine learning models of language of a more geometric or even combinatorial-algebraic nature which would have interested Riemann who wanted to relate meaning to a kind of cognitive geometry.   Perhaps statistical regularities should be traced back to geometry.

What are LLMs really, formally? Can we formalize the critical values wherein they become 'adequate' for their proposed task? What exactly in 'large'? How can this be formalized rigorously? Can LLM techniques be used for formal axiomatic-deductive systems and automated theorem proving? Or can we prove certain fundamental limiting theorems about the powers of LLMs akin to the unsolvability of the halting problem and Gödel's incompleteness theorems?

LLMs only exist because of the Internet. The Internet and LLMs are part of the same historical-cultural-technical process.  This ontological process might be described as the datafication of humanity. Language ceases to be a tool of human thought, communication and culture-building but rather a tool for the reduction, degrading, emptying, perversion and commodification of humanity itself. The Internet and LLMs are the anti-Gutenberg. Man has become text, sound, image, data, statistics. LLMs are a counterfeit reality, a monstrosity, the world becomes one big corporate controlled screen.

 If we compare the training data and the resulting LLMs is there or not a loss of information? Would it not be more worthwhile to develop sophisticated search algorithms and querying language to access the training data directly?

 LLM culture is the culture superficiality, atomization, banality, cosmetics and deception (a LLM is almost a trained deceiver in the biological sense - it detects and mimics human patterns). There is a loss of the multiple layers of meaning behind every symbol which cannot be reduced to statistical correlations with other symbols. Meaning is replaced with arbitrary social-statistical emergent correlative patterns.

The realm of pure mathematics - and that of pure logic, combinatorics and computability - is a pure realm which LLMs cannot touch or corrupt.  So the formal mathematics and formal philosophy projects, contrary to popular misconception likely resulting from deliberate propaganda and deception - are the antithesis of and antidote for LLM culture. There is a pure universal computational-mathematics-akin language (far beyond the natural language or the audio-visual data  that can be perverted and imitated by LLMs) and a pure logic and a pure thought and mankind may indeed hope to attain them. 

LLMs are not intelligent and statistics cannot solve formal computational problems nor can they encompass the pure a priori synthetic principles of formal computational systems (i.e. the cognitive certainly of the foundational principles for metatheoretic knowledge) as detailed in our paper mentioned above.

No statistical pattern analysis of the shadows are sufficient to lead to knowledge of the object. Pixel injection in image recognizers demonstrates this fact, and similarly for formal reasoning.  Besides lacking intensionality, LLMs lack reference and context (despite the misleading terminology of context windows). 

And most important of all since the true intellect is inseparable from morality, empathy and compassion, completely beyond the reach of LLMs. LLMs do not have the bondage to an illusion of a self.

A major task of philosophy is to destroy the evil empire of LLMs and a good starting point is deconstructing and refuting the worldviews (extensionalism, meaning-as-use) which LLMs embody. 

Is a lawyer someone trained in a specific system of laws or someone who has developed the skill to study, interpret and apply any given system of laws or perhaps be able to cope with significance changes in present laws?  Such a metalawyer is the analogue of a universal Turing Machine. A LLM could never be a judge or a metalawyer - it could not grasp the spirit of legal institutions or the deeper meaning of a given legal context.

Billions use light-bulbs without understanding the underlying physics. Billions could use LLMs thinking they are conscious.

LLMs will become more interesting in the measure in which the multilayer perceptrons models are replaced by geometrically and mathematically more sophisticated models (KANs are a step in the right direction).

Short philosophical considerations on AI

Hegel and Heidegger were thinkers about their own time, thinkers about historical events and happenings. Few have the insight and courage to fathom the full depth of the meaning of an historical event, the coming to be (coming of age?) of an historical process. Tragically,  it is only some time after the event (the time of monsters?) has hit humanity with full force that Hegel's famous owl can spread her wings. Is it not true that some of what the prophetic author of Sein und Zeit wrote about technology only makes full sense at the present?

This seems to us particularly true of the emergence of the age of the Internet and the age of generative AI which is its logical development.

And yet nothing could be further from our own philosophizing than any form of historicism or historical philosophy. As such both Hegel and Heidegger, for all their interest and insight, must be considered as having crafted systems based on an incorrigible error. 

Social progress is not a law of nature but a legitimate hope - even if at present it seems a distant one - and it is our moral duty to work towards it in the midst of uncertain outcomes.

The advent of the internet was the advent of connection between people. This connection carried rhetorically moral undertones and echoed enlightenment ideals about the desirability of sharing and making knowledge available.  In the present age of the generative AI based Internet powered and controlled by corporations and governments aligned to anti-enlightenment ideals, it may be that it is morally called upon us to practice instead the process of disconnection and the purification and preservation of knowledge(not obviously in the sense of the 'great simplification' of the Canticle of Leibowitz).   

The most basic step is ensuring locality of core information. That is, to be in possession of machines onto which have been downloaded significant portions of Internet Encyclopedias (despite their serious shortcomings) as well as some decently performing LLM. To this we add, it needs not be said, massive of digital preservation of human cultural artifacts, notably libraries.

One can use Kiwix and download for offline viewing the most recent English Wikipedia (50GB text-only 150GB with pictures).  With a AMD Ryzen 7 5825U processor with 16GB RAM and 2GB Radeon Graphics one can use Ollama and download and use some decently performing LLMs (gemma4 comes in E2B, E4B, 31B and 26B A4B). 

Most living beings alternative between states of being awake and of sleep. Can would we design a dynamic LLM which similarly alternates between states of user interaction and re-training based on this interaction? The most important being the correction and/or updating of knowledge or perhaps the removal of harmful and biased content and "thought patterns". If LLMs can improve then it is not only  a question of having the number of parameters equal to the number of neurons of the human brain.

Computers can enhance and aid human cognition as well as hinder and destroy it (there is a growing body of evidence concerning the disastrous effect of excessive or inappropriate generative AI use for individual mental health and cognitive development, not to mention for society as a whole). 

But the harms of generative AI have little to do with lesser-known extremely powerful and beneficial aspects of the computer for human cognition. We cannot go into this in detail here. Let it just be said that it involves using adequate software for the rigorous formalization of human scientific theories and concepts (specially logic and mathematics and formal methods in the sciences) and the vital feedback-loop between human thought and the software interface (IDE) which results in the simultaneous enhancement of human understanding and production and the quality of the software-based formalization and implementation. 

The software in question includes not only Rocq (formerly Coq), Agda and functional programming language but such languages as Python, Javascript and C/C++. Python is a multi-paradigm and highly versatile language with an elegant syntax. Python comes close to achieving the ideal of a universal language in the Leibnizian sense and is a wonderful tool for formalization, implementation,  verification and exploration in a variety of areas in mathematical logic and finite mathematics. 

We note also the importance of minimalism (using as few dependencies as possible) and building things from the ground up - this goes for scientific and philosophical projects, not of course for commercial and industrial ones.  We will address in the future the question of the possible role of machine learning in this process.

The geometry of cognitive biases and fallacies

 

Categorizations of objects are certainly a useful, even necessary, part of human cognitive development. We cannot underestimate the interest of so-called Venn diagrams which while going back to Leibniz arguably are strongly yet somewhat implicitly present in Aristotle's Organon. Venn diagrams can describe human categorical-cognitive architecture but with the caveat that we should be aware of the extreme geometric complexity of the sets involved as well as how a vast array of psychological tendencies and schemata are at work in shaping our perception and reasoning about such sets. 

Here is one example of cognitive fallacy (linked to geometric inadequacy) which doubtlessly occurs in political propaganda and statistically flavored pseudoscience. We have two categories of human beings A and B (the universe U can represent a given human population). A can be a desirable or desirable trait while B can represent a self-identified human group. The situation in the diagram above represents a situation in which for a standard notion of probability we can say both that 'most As are Bs' and yet  'most B's are not A's. A typical fallacy (perhaps linked to a tendency for the mind to generate a symmetrical geometric scenario) is to assume that if  'most As are Bs' then most 'Bs are As'.   We can however say that B is over-represented in category A and seek a sociological explanation. In some instance a category may appear to be defined precisely by its intersection geometry with other categories.

The above considerations show that while categories are useful cognitive constructs one must be aware of  fallacies and biases - some linked to a poor grasp of geometry - and never lose sight of what is cognitively of far greater importance: the individual.