Logical notes III (Mathesis Universalis)

Many of the problems which concerned western philosophy are just consequences of an a priori rejection (and this rejection also reflects a spiritual, cultural and intellectual regression) of the platonic philosophy (and its sophisticated form found in Plotinus and Proclus and the Proclean philosophy of mathematics).  And indeed it seems that we can do justice all at once to the geniuses of Frege, Gödel, Hilbert,  Russell, Church, Turing, Brouwer, Skolem, Gentzen, Girard, Lawvere, Martin-Löf and to Meinong and his school and to Hegelian phenomenology and dialectics (which has a striking correspondence with Proclus' theory of eternity, time, dianoia, dialectics, the logoi and their projection and the process of reversion to the nous). 

There is nothing wrong with thinking of consciousness as a spiritual substance and as a place wherein are 'located' a system of pure concepts which are independent of and not derived from sensation or imagination.  Our access to these pure concepts is purely objective and yet they are 'subjective' in the sense that they are part of the substance of consciousness and not (directly) outside it.

They are also involved in the morphogenesis and activity of the body.

This system of pure concepts in human consciousnesses is one and the same because it has one and the same cause beyond ordinary human consciousness and this cause is also involved in the explanation of how the system of pure concepts adequately relates to the knowledge of nature (thus the universe is permeated by reflection and analogy). In our ordinary knowledge these pure concepts come into play, there is also a lower rank involved in abstraction from sensation.

Hegel's science of logic gives us an illustration of the Proclean account of dialectics. Furthermore Hegel's science of logic has some deep connections to modern mathematics and mathematical logic and foundations of mathematics (in particular category theory).  Hegel allows one to reconcile  Frege and Brouwer within a larger and more thorough framework (which is to be an typed, intensional, computational-algorithmic-oriented logic and mathematical foundations - which rejects completed infinite cardinalities in the extensional sense).

Modern mathematics (as well as modern physics) needs very much a clarification, improvement and radical reformation of its foundations.  Voevodsky opened up a promising approach. Category theory is not to be seen as universal theory but rather a specialized and partial one suited for the particular turn modern mathematics took in the 20th century.  It is to be replaced with a structure related to dependent type theory or a more universal theory of higher-order relations.

Plotinus and Proclus offer an integral solution to the problems of the theory of knowledge (which in antiquity are associated to the Academics, Pyrrhonism and the debates with the middle Platonists and Stoics - but also found in Augustine).

Neoplatonism also offered a consistent and insightful theory of spiritual yoga within a coherent philosophical and scientific context. And indeed the theory of dialectics gives the genuine  clarification and possible higher meaning of madhyamaka and Pyrrhonism. Also, the apparent discrepancy between Proclus and Plotinus can be explained by a better understanding of procession and emanation  as a kind of instantaneous continuous current between levels: thus there is no difference between the attainment of nous or henosis by the soul and the metaphor of a drop of water merging into the ocean without loosing its individuality.  Or rather, reversion and return is not to be seen as a lower level reflection but as a direct 'plugging in' to a higher current connecting the levels in eternal continuous simultaneity.