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.

Principia Logico-Mathematica

https://mally.stanford.edu/principia.pdf

Zalta uses second-order logic extended with what might be called 'third-order' predicates which express the encoding relation between $n$ first-order objects and $n$-ary predicates. These he calls the 'encoding' relation (inspired by Meinong and Mally). To us the great interest of the work of Zalta and his collaborators is that it offers a solid example of 'formal philosophy', philosophy carried out in entirely in a formal language standing in for natural language. But the real significance of Zalta's work is not so much a setting up a particular metaphysical-philosophical system or giving plausible charitable (re)interpretations of Plato, Leibniz and Frege but rather furnishing a framework for purely formal dialectics, argumentation and debate. The challenge is to formalize and express in this context the process of debate (we could take for instance the formal game outlined in Aristotle's Topics). This will involve a certain theory $T$ which both players must accept (which will include the core axiomatic-deductive system), a sequence of choices of assumptions which one player or both players must be forced either to accept or reject.  Perhaps the resulting logic is like temporal logic? We have given an example of the formalization of philosophical dialectic (debate) in our preprint "A formalization of a fragment of Plato's Lysis".

Another interesting example of formal philosophy is given by R. M. Martin' first-order formalization of Whitehead's philosophy. 

Hegel and Metaphysics

We can trace much of Hegel back to Spinoza, Leibniz and Kant. But what if Spinoza and Leibniz themselves represented but an adaptation or even simplification of little known medieval philosophical  texts (much earlier than Böhme) ? And that such texts gave a firm foundation for the synthesis of Hegel with Schopenhauer? What if the unfolding of Hegel's Logic or Phenomenology of Spirit can be interpreted as representing the process of spiritual liberation, totalization  and harmonization of all states of being?

In the Zusätze to 573 of the Encyclopedia, we read:

If we want to see the consciousness of the One (...) in its finest purity and sublimity, we must consult the Mohammedans. If, e.g., in the excellent Jelaleddin−Rumi in particular, we find the unity of the soul with the One set forth, and that unity described as love, this spiritual unity is an exaltation above the finite and vulgar, a transfiguration of the natural and the spiritual, in which the externalism and transitoriness of immediate nature, and of empirical secular spirit, is discarded and absorbed.

Essence becoming actuality in the Science of Logic: beyond different models for a theory, different frames of reference for physics, representations for an algebraic structure, etc. Do we not here have the phenomenological reflection which neither attempts to have empty thought grasp directly its own structure nor is thought loosing itself in the objectified engagement in its action, but rather is the self-reflected awareness of thought in its thinking, a shift of perspective which knows itself in its process?  This goes beyond causality, computation and formal logic to inner and infinite spiritual knowledge. Spiritual knowledge is knowledge that what is in consciousness is taken and proceed from its inmost center, a revelation, veiling-unveiling, which must pass to reveal the process: the revelation is re-velation.

Hegel's treatment of modality in the section of Actuality is very relevant to contemporary discussions on possible worlds and arguments against the world being a sum of independent contingent facts. There are also connections that could be made to modal logic (i.e. the connection between possibility, actuality and necessity and the axiom $\lozenge P \rightarrow \square \lozenge P$). 

The considerations on necessity and substance (and indeed the long digressions on Newtonian forces already suggest this) can be interpreted in terms of the solutions of differential equations (or in general smooth vector fields on a manifold). The local existence and uniqueness of a solution for a given initial conditions expresses determinism which extends to a global determinism. 

The first part of Schopenhauer's World as Will and Representation is divided into four books. It would be interesting to establish a correspondence with the Science of Logic.  Clearly books 1 and 2 correspond to Being and Essence while books 3 and 4 correspond to Concept. However books 1 and 2 are written from the perspective 'for us', from the point of view of transcendental reflection. From this perspective books 1 and 2 belong to Essence and their philosophical knowledge expresses with great rigor and detail Hegel's theory of appearance, existence, substance, necessity, causality and actuality.  Or maybe Hegelian substance is much like the spontaneous production and manifestation of the will in Schopenhauer. It goes beyond phenomena and appearance because the will is immanent in its manifestation, totally in each one and beyond any particular one. The will has to manifest. Transcendental reflection, artistic contemplation and spiritual development represent the will's progressive self-knowledge, return to self, the Hegelian Spirit in the form of the concept.

Category Theory: a category expresses essence. Each object is a different mode whose determination is inseparable from its relations (morphisms) to the whole (all possible determinations). An object is an expression of the category and yet not the category (for there are other objects). At the same time this circumstance of the object not being the category is itself internalized and expressed as the object being itself the sum-total of its relations (morphisms) with all other objects (i.e. with the totality of the category). This expressed also that the object is the category. 

The Concept can  be seen as arising when we have the cyclic transcendental consciousness of metatheory. That is to say: we realize that transcendental presuppositions are in cyclic dependency: to do logic we need computation, to do computation we need arithmetic and combinatorics, to these we in turn we need computation and logic. The germ of this in the reciprocal causality at the end of Essence (which we have also associated with higher groupoids). And also, as we have discussed in more detail everywhere, the partial (meta)reflection of one formal system by another (or the formal system by itself) is clearly relevant here: it is the idea of the whole being implicit to some extent in the part. For instance in ZF set theory itself we can prove that there are non-equivalent models of ZF.