Projects

 1.  What is dialectics in classical (i.e. Plato, Aristotle's Topics, Megarians, Stoics, Pyrrho) and Hellenistic philosophy such as the late Academy, Sextus and Plotinus? And in Nagârjuna and other traditions such as Nyâya? And in Hegel? And in Hilbertian and Carnapian formalism and conventionalism? Continue and develop the paper of Analyticity, Computability and the A Priori.

2. How is formal logic (in particular the work of Chrysippus) essential to skeptical dialectics? Develop the work of Bobzien on Stoic Sequent Calculi.

3. How can dialectics be compared to a game and computation in light of our paper? Investigate the logical, computational and philosophical  aspects of the game of Go/Weiqi (Knuth, Conway?). 

4.  How is dialectics related to skepticism? And what was the essence of ancient skepticism and how did it differ from that of the Madhyamaka?  In what way was dialectical skepticism paradoxially a method for obtaining the absolute and the good?  

5- Develop how in Nâgârjuna skepticism and dialectics lead to the highest moral and spiritual precepts and show the agreement in this respect with Plato and Plotinus and present a novel interpretation of Pyrrho and the late Academy confirming Cicero's thesis.

6. How is dialectical skepticism related to phenomenology? Investigate Nâgârjuna, Cicero's Academica and Augustine. Also the relationship between phenomenology and the theory of knowledge in the sense that the former arises naturally from the latter.

7. Present a new interpretation of the sophists showing their relationship to the Madhyamaka,  Nyâya, Jain logic, Pyrrhonism, the Megarians and the late Academy.

8. Develop Shapshay's thesis regarding a systematic purely phenomenologically-based ethics of compassion in Schopenhauer's Two Fundamental Problems of Ethics. 

9. Elaborate an exhaustive study of opposition to slavery and the defense of animal rights in antiquity, both in the East and the West. 

10.  Develop a finistic and ultrafinitist constructivist (computational) and intentional logic of quantifiers. Quantification if not reduced to finite collections of propositions is simply the specification of a rule - like a Boolean circuit but intensionally and  structurally conceived. Reinterpret our work on Aristotle's second-order logic.

11. Develop a finitist and ultrafinitist foundations of mathematics which nevertheless incorporates Leibniz's theory of convenient fictions and the extraction of the computational content of proofs (Kohlenbach) of prima facie non-constructive and infinitary mathematics.

12. Show that in Plotinus (and Augustine) we can find the structural analogues (but with profound philosophical and spiritual differences) of Hegel's Science of Logic and Phenomenology of Spirit as well as of phenomenological-idealistic philosophy in the modern sense. 

13. Develop Plotinus' theory of dialectics and philosophy of consciousness and the precise role that mathematical and formal logic may play in his system. Show that Plotinus is a finitist.  In light of this transpose the mathematical illustrations of our paper "Hegel and Modern Topology" to  Plotinus.  

14. Can Plotinus' theory of the "holomorphic" omnipresent  souls and world-soul, the reason-principles (logoi spermatikoi) and indeterminate infinite dualistic matter provide insights into a new interpretation of quantum theory, in particular a strictly non-reductionist top-down theoretical physics?