Showing posts with label Plotinus. Show all posts
Showing posts with label Plotinus. Show all posts

Friday, September 4, 2026

Yes, there are aspects of Plotinus which are problematic or unacceptable

Notwithstanding what we wrote previously, it is important to point out that there are aspects of Plotinus' philosophy that are not only inconsistent but profoundly mistaken and even potentially harmful.
Did Plotinus categorically condemn slavery? His socio-political connections (including a the Roman Emperor Gallienus) and Porphyry's account of the episode of the stolen necklace cast serious doubt that Plotinus (as disappointingly many other philosophers and the New Testament)  ever rejected the social institution of slavery. What is more serious is that  Plotinus appears to justify it based on his own metaphysics and theory of the soul. In III.2 we have perhaps the most disturbing and unacceptable passage in all the Enneads: It is not an accident that makes a man a slave; no one is a prisoner by chance; every bodily outrage has its due cause. The man once did what he now suffers. This passage can be construed as a profoundly spiritually, morally, sociologically, anthropologically and scientifically mistaken and unenlightened defense of caste systems and every form of political and socio-cultural injustice, cruelty, error, oppression and superstition. How could Plotinus explain the sublime philosophical and moral teachings of slave-born Epictetus in the 1st century CE (who ethically equals if not surpasses anything in neoplatonism or Christianity with the exception of Porphyry's defense of animal rights in De Abstinentia)

https://www.academia.edu/121293413/Philosophy_of_Epictetus

and on the other hand Roman Emperors such as Nero? There is perhaps not anything more injurious to morality, common humanity, reason and the facts of history and nature than the heinous opinion that being born into wealth and power has some relationship to spiritual merit in a past life. Clearly if a circumstance of birth were designed to be optimal for spiritual, intellectual and moral development then such a circumstance can only be one of modest means which avoids the extremes of wealth (and power) and poverty (and oppression) - "the middle station in life" according to Defoe (cf. also the introduction of Augustine's Contra Academicos).

And an analysis of the texts of Marcus Aurelius (2nd century CE) and Epictetus should lead us to question the official narratives concerning "Stoicism". No amount of sophistry or verbal gymnastics could make such "Stoics" into "materialists" or "empiricists" in the contemporary and vague sense of such terms. And this leads us to question if Plotinus was not unjust to the Stoics and misrepresented their positions.  We note that the wonderful thing about the Middle Academia was precisely the philosophical engagement between different schools. In the Enneads the Stoics are not given a chance to defend themselves.

The dismal defense of social injustice in Plotinus also reflects a fundamental inconsistency and uncertainty - the conflict between a pessimistic and optimistic outlook regarding the physical world - and this appears to have be a genuine concern for Plotinus (cf. his rather strange, not altogether fair and long-winded polemic treatise against the "gnostics"). Plotinus protests too much about the goodness and ultimate justice and harmony of the physical world (in particular with regard to the descent and ascent of souls and its providence and justice) and yet according to his biographer Porphyry he personally engaged in at type of asceticism (i.e. regarding hygiene or his attitude, according to Porphyry, of being ashamed to be in a body) which would have been condemned by the Buddhists. Also it is strange and inconsistent in this light that Plotinus refused to have his portrait taken or to say anything about his family. 

There are also problems with Plotinus' theory of consciousness and self-awareness (parakolouthêsis) regarding the soul's re-ascent into the intelligible realm.  It is safe to say that higher level of spiritual attainment always involve a higher consciousness of this attainment itself - and this agrees with Plotinus' theory of the nous and the noes of the individual souls.  In higher spiritual states (such as that of the jivan-mukti in the Vedanta or the Bodhi-citta)  individual and universal consciousness can co-exist. The idea of an unconscious, non-reflective or trance-like attainment of the intelligible realm is self-contradictory and absurd. In Pāli Buddhism, a person who is fully liberated (Pali: vimutta) explicitly knows and sees that their mind is liberated.The Pāli Canon frequently uses the phrase vimutti-ñāṇa-dassana (the knowledge and vision of liberation) to describe the final stage of awakening. We should examine critically the book  Pyrrhonism: How the Ancient Greeks Reinvented Buddhism by Kuzminski (2008).

The problem of human existence is to convert the suffering deluded ordinary individualized somatic consciousness into transcendent universal super-individual luminous blissful super-consciousness. Such a super-consciousness does not need to cancel individual consciousness, it only renders it transparent (one could say, "child-like") and reconnected to its source.  And to obtain this goal one can use analytic dialectics and analytic phenomenology - which we argue are found developed in the Enneads. As recognized by Schopenhauer, a fundamental principle and insight allowing the reintegration of individual consciousness into super-consciousness is provided by the foundation of morality - compassion - which is transcendent knowledge regarding the oneness, value and interconnection of all living sentient beings. 

In the future we plan to develop the interesting insight found in Shapshay's book : Reconstructing Schopenhauer Ethics. Shapshay argues that Schopenhauer's work The Two Fundamental Problems of Ethics offers a self-contained strictly phenomenological system of ethics which is logically independent from Schopenhauer's particular form of Kantian-inspired transcendental idealism.

And supremely important is the clarification of Pyrrhonist ethics afforded by Nâgârjuna. In the Madhyamaka Pure dialectics lead directly to the ethics of compassion and the Bodhisattva ideal.

Spiritual consciousness and knowledge (such as attested in the Pali scriptures) must lead to the complete rejection and condemnation of slavery and all caste-systems based on birth and wealth. We also note the echo in the Platonic Socrates' best discourses in the Theaetetus. 

Now in the Hellenistic world and in Alexandria and the early Neoplatonic school in particular there was a substantial cosmopolitanism and culture exchange - including with India. Even if Plotinus's historical-cultural outlook is explicitly strictly Greek (with some passing reference to ancient Egyptian hieroglyphics) it was recorded that he wished to enter into contact with certain philosophical-spiritual schools in Persia and India. With Porphyry and Iamblichus the awareness and connection to other cultures becomes much stronger. This was also the case for ancient Greece and we can ask why the philosophical and spiritual sources and influences of Egypt, Phoenicia, Syria, Chaldea, Persia and India (cf. Pyrrho) as well as other places in south-eastern Europe, were systematically erased and downplayed. If we can prove that Vedantic, Mahayana and Theravâda schools were well-established in Alexandria and other places during the Hellenistic Era, then much of the above problems regarding Plotinus could be solved: the teachings and spiritual practices of Ammonius Saccas (we reject the fantastical claim that Ammonius Saccas was just a pun on Pali Sakya-muni, even if the clan's namesake god Sakya, i.e. Indra, could well correspond to the Egyptian Amun) and his student Plotinus were Hellenic adaptations of only-partially understood (or which became compromised with the Roman Empire) Vedantic and Buddhist spiritual-philosophical teachings and practices (just as Aristotle derived his Categories and Syllogistic from the Nyâya and Pyrrho his philosophy from a prototype of the Madhyamaka).

The Megarian and Skeptic orientation of the later Academy could well corroborate Cicero's thesis to a certain extent. The Madhyamaka and Nyâya elements were deployed in the same spirit as they were in Mahayana Buddhism and the Vedanta. As we argued before, this is another fundamental weakness of Neoplatonism: the disregard for the sophisticated formal logic of antiquity and the practice of the (proto-Madhyamaka) dialectic of the later Academy and Pyrrhonism, and the possibility of a more thorough development of proto-phenomenology (proto-yogâcâra) - a possibility attested in Augustine. Note that Plotinus' dialectic can be construed as the inverse of Hegel's logic in that the most exterior categories are derived (proceed) from the higher interior ones in the intelligible realm - even if the inverse anagogic process also plays a certain role.  Hegel's logic also maintains a strong connection to Madhyamaka, Pyrrhonism and to the Megarianism and dialectics of the later Academy. Plotinus has no interest in formal logic or the critique and deconstruction of concepts as such.

Wednesday, September 2, 2026

Formal models of consciousness and other matters

From the previous considerations are we able to answer the question: can there be a formal model of consciousness?  This depends on how we understand "consciousness" and how we understand "formal model".  Ordinary human consciousness is just a segment of a vast multi-tiered system of spiritual consciousness of which it is but a small part and emanation - and yet to which it is potentially and essentially identical. Thus if by consciousness we mean the intelligible realm then there can be no direct formal model as we have demonstrated previously.  There can however be a symbolic illustrative mathematical model of the intelligible realm. And also a formal logic and computation based formal model of dialectics which models reversion and the procession of the logoi whereby the human soul reverts and ascends to a higher state.  We do grant that it is conceivable that strictly at the level of soul and its logoi as they unfold and project into the imagination or act upon extension in nature there could indeed be a direct (rather than merely symbolic) mathematical model. Here that our ultrafinitist philosophy of mathematics and theory of analyticity and computability would enter the stage.

We propose the beautiful notion of finitary Turing completeness. Rather than attempt to give a complete formal definition we can give the following preliminary definition for board-games. A board-game is finitary Turing complete if its canonical, most natural or free extension to an infinite (to us indefinite, indeterminate) version of the board is Turing complete. In this sense it has been shown that Chess and Go are finitary Turing complete. Finitary Turing complete systems capture the essence of certain stages of dialectic and the structures and processes of the logical-discursive cognition of the soul. We note that the game of Go has been used traditionally (specially in the Ch'an and Zen tradition) to illustrate profound psychological and philosophical principles. 

If some of the previous considerations were focused on the schema of Hegel's Science and Logic in relationship to the Enneads,  no less important (and indeed more foundational) is the first-person introspective of the phenomenology of consciousness, not only as deployed in Hegel's Phenomenology of Spirit (but in an inverted and distorted way, to be sure), but in the entire first-person, introspective, spiritualist, idealist,  phenomenological and epistemological tradition of philosophy which only achieves its complete validity and goal through spiritual development and transformation (cf. chapters X and XI of Augustine's Confessions and the introduction to Ennead IV.3). 

ζητεῖν τε τὰ ἄλλα καὶ εὑρεῖν βουλόμενοι δικαίως ἂν τὸ ζητοῦν τί ποτ̓ ἐστὶ τοῦτο ζητοῖμεν, τό τε ἐραστὸν ποθοῦν λαβεῖν θεαμάτων. 

Our goal is thus to develop the correct neoplatonic phenomenology of consciousness which expresses the souls' self-knowledge and concomitant re-ascent to the intelligible realm and beyond, and to engage critically with the posterior western phenomenological and proto-phenomenological thought. Mathematics and formal logic can also play an important role here but from an essentially different perspective than in the previous goals. Here we are interested in genesis and constitution, with ultimate foundations and philosophical logic and with the act and effect of logical-dialectical practice.

Note that we must distinguish how intelligible categories unfold and originate sensible categories as it happens in itself and as discursive reason grasps it as a reflection.  But this reflection at the level of the logoi is also part of the dialectical process which leads to the soul's illumination and re-ascent. 

Plotinus starts his investigations in the difficulties related to souls in IV.3-5 with a very non-solipsistic question indeed, regarding the relationship of each soul to others souls and with the world-soul. IV.3.5-6 is of great interest in that the text points to a plurality of noes inseparably united in the total nous. Souls are called the logoi of the nous which represent a stage of evolution/unfolding. Thus each soul has its own particular nous within itself  (IV.3.6 17). Individual souls (note also the remarkable passage in IV.7.14 on the souls of animals) proceed from the world soul at the same time as their proceed from their individual nous while the world soul proceeds from the global nous and is its logos. In order to illustrate unity-and-multiplicity (the soul is the body like light in the air) and the relationship between individual souls and the world-soul, Plotinus states that the same thing can be at different places at once: just as one indivisible soul can be simultaneous present and acting in different parts of the body in different ways so too the world-soul is one and yet completely present in different ways in each individual soul (cf. IV.9). One can use holomorphic functions to symbolize or illustrate Plotinus' theory of how the soul relates to spatial extension or the world-soul to individual souls. If $f$ is holomorphic in a region $U$ then the germ of $f$ at any point $p$ of $U$ completely determines the whole function on $U$ (through the uniqueness of analytic continuation). Thus we can say that f itself (the formative aspect of soul) is virtually entirely present at each point $p$ of $U$ (the body) and at the same time f is spread out through $U$, unfolded into $U$, by taking germs.

In IV.3.9-11 we read that the world-soul is the author of life and mediator of the intelligible realm from which proceeds matter, space and extension and which has received the  logoi spermatikoi from above which she transmits to nature and gives life to all beings and mediates also the soul's re-ascent to the intelligible realm. Later on in the same Ennead the concept of kosmos as a complete and harmonious whole and providence are discussed. The world-soul is also called universal life.  The etheric/astral bodies (called okhêma or vehicle) are mentioned showing that this was not  theory specific to later neoplatonism.

But Plotinus' phenomenological psychology (about sensation, kinds of memory, reflection, reason) can be found for instance in IV.3.25-32 and the following part of IV.4 and IV.6 as well as the key treatise I.1. There in internal textual evidence (in IV.3.25 Plotinus states that memory has been deal with elsewhere and extensively discussed, using the verb θρυλέω)  - as noted by A. H Armstrong in the Loeb Edition of the Enneads, that Plotinus wrote a now lost extensive treatise on memory or perhaps this represented a strictly oral teaching. IV.3.26 30-55 is an important passage wherein Plotinus expounds the purely spiritual active nature of memory and self-consciousness (contrasting to a being in the state of flux), making use of key terms: sunaithesis, parakolouthesis, sunthesis and sunesin. Without negating external sensible objects we can nevertheless consider that Plotinus attains a transcendental phenomenological consciousness in this passage in which consciousness reflects on itself and perceives itself as an independent, free, self-acting, self-representing, self-reflecting, self-conscious being. There follows a discussion on the phantastikon and  antilêpsis and their relation to noesis and memory. In the remarkable section IV.6.3 is developed the refutation of the theory of perceptions and memories as the result of passive imprints and the establishment of the theory that they result from the essentially active role of the soul, the deployment and training of attention (epibolê, prosbolê): directedness, aboutness or intentionality.

Sunday, August 30, 2026

The Logic of the Enneads and its mathematical reflections - preliminaries

Plotinus was also a consummate logician in the sense of universal logic, ontological logic or logical ontology.  Buried deep and intricately interwoven within the Enneads we find a sophisticated Science of Logic in the sense of Hegel but expressing a radically different spiritual and philosophical framework and outlook. We will not discuss here the interesting question of a direct influence on Hegel or of Hegel having directly and extensively appropriated neoplatonic doctrines in his own system (we have already given some references concerning this topic). Nor will we discuss the radical rupture in the philosophy and spiritual practices of the neoplatonic school  that occurred after Iamblichus.  We can only stress again the importance of expounding systematically a non-Proclean and indeed anti-Proclean neoplatonism.  

 The project we sketched in our paper "Hegel and Modern Topology" was to given a Hegelian interpretation of key aspects of modern mathematics, logic and computer science and to in turn use these to furnish an interpretation of Hegel (the hermeneutic virtuous circle). We find that most of the insights contained in what we sketched of this project can be transposed from Hegel's Logic to Plotinus's Logic where they seem to find a even more adequate and natural setting. But it must be understood that, as we explained before, in this framework mathematics and formal structures function essentially as an elaborate system of symbolism and hierarchical reflection rather than as candidates for a direct and complete formalization.  The other aspect of mathematics and logic, culminating in dialects to be used as a tool for direct spiritual ascent, has to be considered separately.  

In order to embark on this project we should list the fundamental categories, concepts and processes of Plotinus' Logic which we can organized somewhat along the lines of Hegel's Science of Logic but with fundamental differences which are often the complete inversion of Hegelian conceptions or which collapse what Hegel separated or separate what Hegel joined. Bearing in mind Hegel's Logic of Being we can remark that Plotinus has an elaborate and deeply interesting theory of quantity, extension, number, quality, essence, determination and measure (i.e. the interaction between quantity and quality found in VI.1-3, VI.6 and II. 6) which permeates in the Enneads (and justifies our classification of Plotinus as a finitist) - together with a remarkable theory of relation which when deployed at the intelligible realm fits exactly our considerations of groupoids as models for essential relationality and interconnectedness.  The theory of a self-moving number and relationality of the nous fits well with our previous considerations on Galois groups and Galois extensions. Also the intelligible realm can be symbolized or illustrated as the category of relations.

We note that Proclus's theory of Henads is found in VI.6 but with the difference that for Plotinus they are a proto-determination in Being (as an infinite ouflow) which preceed the intelligibles rather than the One. For a form to exist as a distinct entity it must be bounded, structured, and distinct from other forms. Substantial number is the internal articulation that establishes this multiplicity within unity. In Plotinus’ view, number precedes being: intellect must possess the principle of number to differentiate being into distinct forms. Thus Proclus got his theory of henads from Plotinus' theory of essential number.

 And also a highly developed and articulated theory of infinity (outflow, power) and limit (reversion, theoria)  and a theory of "matter" (both physical and intelligible) which amounts in the physical level to the poorest and emptiest determinations of being (strongly echoing the initial stages in the Logic of Being). Indeed in II.4.9-10 (cf. also VI.6.2-3) Plotinus invites us to perform an abstraction of the quantity and all qualities of a body to arrive a the concept of indetermination. Matter has existence and a disposition to become other things. Intelligible matter is equated to being and intelligible apeiron (the infinity of the One) and physical matter to non-being and to physical apeiron.

Plotinus states explicitly that indeterminate matter will display contradictory dualities - a striking possible interpretation of quantum theory which becomes less paradoxical once we abandon a foundationalist reductionist framework for a top-down emanationist one. 

Plotinus' theory of quantity and quality agrees admirably with the framework of modern topology (he recognizes geometry as a kind of quality in quantity) and differential geometry specially as applied in field theory and differential equations. Indeterminate matter first must receive extension and it is only upon extension that quality can be received. This corresponds exactly to the primordiality of a base space (space-time manifold) relative to its fiber-bundle or sheaf which expresses the local physical-phenomenological properties of the field (Plotinus considers intensive quantities like temperature to be qualities). This lower kind of qualitative structure in turn is only the product of a higher structure and power. For Plotinus space (extension) itself is a product and emanation of higher structure just as a non-commutative $C^\star$-algebra may have within itself various commutative (maximal) subalgebras.  

Thus sensible non-essential quality corresponds closely to Hegel's concept of measure, as quantity determined by something from without and as qualified quantity. The first section on Quality in the Science of Logic corresponds rather to the genesis of quantity in the intelligible realm and soul, where we deal with united multitudes, intelligible forms and their relations and overflow and limit (and we can include indefinite quantity here). Hegel's subsequent treatment of quantity and measure corresponds to sensible quantity and quality in Plotinus and is quite adequate for the mathematical illustrations in Hegel and Modern Topology.

Intelligible quantity exists as pure number and structural order (the archetype of limit and harmony. Intelligible quality exists as the specific power and form (eidos) of an Ideal entity.  At the higher intelligible level, quality and quantity do not conflict or merely sit side-by-side; they are unified aspects of the divine Forms. When projected down into the physical world, they split into extended magnitudes (sensible quantity) and superficial properties (sensible quality). In II.4 we have that pure matter has no magnitude or spatial extension of its own. Extension (megethos) is a form or quality superimposed onto matter. In VI.4-5 dealing with omnipresence we read that the Soul is not spatially spread out or extended. Instead, physical extension is a limitation, whereas incorporeal reality possesses a unified, non-particulate presence that contains spatial extension without becoming spatial itself. In III.7 we read further that just as time is an unrolling or diastasis of the eternal life of intellect into succession, physical extension (megethos) is a dispersion or unfolding of unity into divisible parts.

A fundamental mathematical symbolism or reflection will be that of the limit (let us say, in the category theoretic sense) of a sequence or diagrams expressing an indeterminate outflow or process. This limit is a reversion, completion, perfection and theoria in the Plotinean sense and an aufhebung and being-in-and-for-itself in the Hegelian sense.  We can think of this process as dynamic and limit and reversion as a fixed point (cf. Lawvere's account of Gödel's incompleteness theorems and diagonalization arguments).

The reversion of the physical word and the human soul to the level of Soul and Nous parallels to a certain extent to Hegelian levels of Essence of Concept (for instance the supreme genera in the intelligible realm include identity, difference and in VI.3 rejects that essence or ousia could apply to the physical world) but with many radical differences and fundamental corrections from a neoplatonic point of view. The physical plane can be considered in itself or as it is the result of the activity, influence and emanation of the the plane of soul taking account its act of reversion (i.e. Objective Concept, the theory of life) - and the same goes for the the plane of soul itself. Thus Subjective Concept can correspond to the theory of the soul's logoi, to the theory of the world soul or to such as it relates to the intelligible realm and to the intelligible realm in the aspect of knowledge. Hegel's progression from outwards qualities to essential qualities in Subjective Concept finds its parallel in VI.1.15–22 which distinguishing true intelligible qualities (forms or reason-principles - logoi) from mere sensible qualities (passions, colors, surface shapes).  For Plotinus universal Being (i.e. the Absolute as the perfect emanation of the One) is Being, Intelligence and Life and the perfection of energy/act/power.

When using mathematical structures as neoplatonic symbols and reflections we find that it is best for formulate them and think of them in a strictly constructivist way.  Thus the number of objects in a category must be conceived as being indefinite and defined as one would do in a dependent-type based proof assistant - considering it to be the object object in the definition of an internal category.  The finitist can consider intentionally the sequence $\frac{1}{n}$ as computable process without having to admit the finished extended set of such numbers. And then the finitist can consider $0$ as being its limit.

The considerations presented above are very sketchy and highly insufficient. We point out the the deep exposition of Plotinus' logic can be found in VI.2 and VI.6. The five supreme genera suggest the fundamental importance of the equality type and transformations which preserve structures and express coherence and relational unity or interconnectivity.

Identity is related to stability, difference to movement. Consider the two possible orientations of a vector space. They are indistinguishable, intrinsically identical yet different. Their difference is expressed by a non-trivial automorphism of the underlying vector space which transforms one into the other.  

Plotinus states that number is produces by a combination of movement and rest (as supreme genera) and that extension is posterior to number and is the result of a movement produced by infinity which is halted and limited by rest. In VI.6 we have the theory of multitudes as outflowings and divisions of being. In VI.6.1 we read that if the parts maintain some connection then we have extension which have lost perfection must receive the form of beauty. The negation of negation is the reversion of the outflow through limit.  Negation is related to set-theoretic complementation (for instance it is the interior of the complement for the Heyting algebra of regular open sets of a topology). Thus the dyad, the unlimited, indeterminate outflow, considered in itself independently of its source can be characterized as negation. The negation of negation (a reversion of the outflow) corresponds to a closure operator which encompasses in a limited determined way the object which was initially negated. If negation corresponds to the sun's unlimited rays then double negation corresponds to a halo around the sun's disk.

The remarkable sections  VI.2.4-12, which deduce the supreme categories through an anagogic process of turning inwards, the key concepts being soul, the logoi. one, ousia, life, intellection, reversion, movement and stability, identity and difference, are important for comparison with the Logic of Essence and Logic of Concept and well as for pointing out the radical difference with Hegel. At the same time Plotinus' henological ontology and the deduction of the other genera from the supreme pentad in VI.2.13-21 should be compared to the processes and structures of Hegel's Logic of Being. We note the remarkable fact that VI.2 (which employs many argumentative structures interesting from the point of view of formal logic) can be seen as realizing the idea of dialectic which Plotinus sketched in I.3.  In VI.6.10 we read that Being became Number when it became a multitude, having  had a pre-formation, previous representation,or  allocation for the beings it produced. We note that Augustine copied VI.6.12-13 almost directly. A section in VI.6.3 should be compared to Hegel's absolute negativity in the beginning of the section on Essence: τὸ δὲ μὴ ἀποδρᾶναι ἔχειν, εἴργεσθαι δὲ ἔξωθεν καὶ κύκλῳ καὶ μὴ ἐξεῖναι προχωρεῖν, στάσις ἂν εἴη: ὥστε μὴ μόνον ἐξεῖναι κινεῖσθαι λέγειν.

We note that a fundamental mathematical illustration of the genesis of sensible quality will be that of the unfolding of a singularity (or deformation of a structure). We must bear in the mind that intelligible extension is expressed as the intensive power of a intelligible form which then unfolds and expands spatio-temporally in the world-soul. Or the forms can be symbolized by infinitesimals as we developed in "Hegel in Modern Topology" - and indeed in V.9.6 Plotinus gives us an interesting illustration involving the logoi and a seed.

Note the Hegelian categories of ground and appearance, phenomena, etc. find their treatment in Plotinus theory of sensible substance which is a shadow produced by the Soul casting form onto receptive, featureless matter. Physical substance is a composite (synolon) of matter (hyle) and dynamic immanent form (logos or reason-principle). Physical motion is the life and process of change inherent in time and physical nature. It is the physical shadow of the eternal activity (energia) of Intellect.

Consider an object $A$ in a category. Then $A$ may have internal symmetries in the sense that $hom(A,A)$ may contain more than just $id_A$. Given $f \in hom(A,A)$ we can ask if there exists $g : A \rightarrow B$ and $h : B \rightarrow A$ where $B$ is not isomorphic to $A$ such that $f =   h \circ g$.  This offers an illustration of $B$ being an emanation of $A$ (flowing out in $g$ and reverting by $h$) and proceeding from $A$'s internal structure.

Friday, August 14, 2026

Hegel and Neoplatonism

Platonismus und Idealismus by Werner Beierwaltes

Hegel und der spätantike Neuplatonismus by Jens Halfwassen (2005)

Hegel's Hermeneutics by Paul Redding (2007) / Continental Idealism: Leibniz to Nietzsche

"Hegel’s Programmatic Recourse to the Ancient Philosophy of Intellect" by Jens Halfwassen

"Thinking the One: Studies in Neoplatonic Philosophy and its Reception" by Werner Beierwaltes

"Hegel on Neoplatonism and Proclus" (Lectures on the History of Philosophy) 

Hegel the Consummate Neoplatonist (Philip Stanfield, Marxist orientation)

We can also remark that Proclus plausibly got most of his philosophy of mathematics from Iamblichus, Porphyry, Geminus and Eudemus and provides us with a fascinating glimpse of much more ancient material that has not come down to us.

Wednesday, April 15, 2026

The method of meditation and the philosophical method

There is something to be said about books presenting a "basic method of meditation" such Ajahn Brahm's "Mindfulness, Bliss and Beyond". Such books are part of marketing ploy to sell retreats organized by religious institutions (which serve ultimately as recruiting grounds for new monks and nuns). As such the methods described - which may have unquestionable value - are only suited to the specific conditions of the retreat. Such conditions are inaccessible to the vast majority of us. This includes those who have the luck of having access to the seclusion and peace of nature for some limited amount of time, but certainly not for weeks - the time needed for such methods to be effective. These methods count on philosophical insight about consciousness manifesting on its own during the long periods of seclusion and silence, or they count on the guidance of a teacher. These methods in themselves fall under the category of  "samatha" rather than "vipassana", even if there are also "vipassana" -themed retreats. 

We note that Ajahn Brahm himself probably became aware of the Herculean task of detaching oneself from the world (abandoning past and future to abide in the eternal present) and so introduced an alternative method which amounts to calming the body and mind through body-scanning, a sweeping focus built on psycho-somatic feedback (this method can also be traced to the earliest suttas). Rather than trying to tear the stubborn agitated child from his toys or tearing the toys from the child one engages in calming and lulling the child to sleep.  What is involved here is a doctrine concerning the fundamental importance of the first-person experience of the body and concerning the fundamental unity and cyclic dependency between this first-person experience of the body and all aspects of consciousness. The first-person experience of the body involves localized 'feeling'  and the cultivation of consciousness of such feeling can open up vast domains of very subtle and significant experience. The doctrine is that such domains of subtle feeling in first-person body experience are the key to total mastery of all domains of consciousness (cf. how the flux of consciousness is woven with sense impressions and sense impressions are intimately psycho-somatically related to sense organs, receptors and their neural pathways). The doctrine appears to be present in a more-or-less veiled way for instance in the sutta MN 119. We can think of the psycho-somatic feedback as creating a kind of field, container (cf. the simile of the soap and bath in MN 119) in which the rest of consciousness is then immersed to become pacified and purified (cf. again the similes in MN 119). One can say that the initial process of both local and global psycho-somatic feedback prepares a thoroughly purified and pacified 'container',  'field' or  'body' (there are many meanings of khaya in the suttas).  Once this is thoroughly achieved then piti and sukha will 'dawn' and 'well up'.  We then interpret the similes in MN 119 as involving the further purification, 'drenching',  'irrigation' and total 'covering' of this 'container-field-body' with piti and sukha. There are interesting connections that could be made with Plotinus as well.

Hence the necessity of a "method of meditation"  which is still powerful and effective in the context of ordinary life in the world.  Such a method must be based - alongside the considerations above -  on introspective-philosophical psychology founded on phenomenological insight. A method of philosophical psychological analysis, introspection and insight which aims at liberation from both the "world" and the "self" whose starting point is the positivist neutral consideration of consciousness, the facts of consciousness, as they are in themselves, as manifest in their manifestation, without the screen of metaphysical reification or the habitual oblivion of their fundamental co-conditioning factors such as temporality or the underlying mental directedness in recollection and anticipation. A powerful tool for this method is hearing or reading the original suttas of the Pali Canon or foundational philosophical texts of the Mahâyâna tradition. It is in this spirit that much of what we have written should be read.

Another point concerns the difference between Western and Eastern art. It does seem to us indeed that in some schools and works of Eastern Art (specially traditional Japanese art inspired by Zen) have a very strong connection to the pure neutral phenomenological-philosophical insight discussed above. In some sense, there are schools of Eastern Art which manifest anatta and the holistic flux of a neutral phenomenological consciousness (for instance the traditional Shakuhachi)  which is rarely found in classical Western art (but we do find such for instance in more contemporary compositions such as Brian Eno or the Polish ambient band How to Disappear Completely). 

Saturday, November 8, 2025

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.

Remark on proof-assistants and formalizing mathematics

 There seems to be a kind of Heisenberg uncertainty relation type constraint: the tradeoff between intelligibility and certainty. Writing a...