Saturday, May 23, 2026

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).

Saturday, May 9, 2026

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.

Wednesday, May 6, 2026

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. 

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...