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.
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