Update: work-in-progress on new papers

New papers:

1. Transcendental Subjective Idealism

2. Category Theory and Philosophy

3. Computability, Logic and Mind

(We have removed many important posts as their material in now being incorporated in the above papers)

4. Inquiry into Kant's logic (this is related to 3)

5. Formal metaphysics. As far as the project of a formal axiomatic-deductive philosophy we have been investigating the role category theory might play in this endeavor which at the same time is fully aligned with Kant's critical idealism and Husserl's transcendental phenomenology. But there are other possible approaches and perspectives which preserve this alignment. One that takes dependent type theory to be more fundamental, universal and fine-grained than category theory. Another is based on the philosophy of computability and second-order monadic logic. One problem is that we still do not a have a completely clear understanding of quantifiers or connectives or intensionality.

Topos theory (as is well known) is the natural environment for higher-order logic. My idea is that if we consider the type of possible worlds endowed with a kind of 'topology' (this could be an abstract Grothendieck topology defined by a Joyal-Tierney topology) then it seems natural to consider the environment for object logic to be not a general elementary topos but a Grothendieck topos, a topos of sheaves over the 'space' of possible worlds. The objects of this topos are sheaves, that is, they are types parametrized over possible worlds. The great challenge is to seem how core notions of Zalta's object logic, specially the encoding relation, can be expressed in this context and whether they have natural categorical descriptions...

6. Expand S. Shapshay's work on the compatibility of Kantian and Schopenhauerian ethics. In particular by the drastic constrast with Hegel's implicit or explicit historico-evolutionary relativism and pragmatism. Also address the pertinent questions raised by Shapshay regarding Schopenhauer's theory of the 'denial of the will' and show how the internal tensions in Schopenhauer's thought can be resolved through understanding the process of personal development in original Buddhism and its counterparts in ancient philosophy.

 The first project involves understanding the famous enmity between Schopenhauer and Hegel. My thesis is that this antagonism was not rooted merely in personal animosity but rather in irreconcilable ethical positions. So it is important to bring to light the ethics implicit in Hegel's Phenomenology of Spirit and show how they constitute the greatest contrast both with Schopenhauer's and Kant's ethics. My tentative position is that, very roughly, Hegel is basically a kind of pragmatist, evolutionist and historical relativist while for Schopenhauer and Kant ethics must be universal, valid for all people at all times. For example, for Hegel slavery was 'good' for its time and indeed a 'necessary' phase of the historical-development of human consciousness while for Kant and Schopenhauer it is intrinsically and universally 'bad' - a violation of basic human rights.
My second project involves addressing the internal tensions and contradictions you discussed involving the theory of the 'negation of the will' and world-rejecting asceticism which you contrast with the more hopeful aspect of Schopenhauer anchored in compassionate reason-guided morality and aesthetic contemplation. My thesis is that this internal tension is due primarily to Schopenhauer's idea of 'negation of the will' and 'asceticism' being almost entirely derived from the Christian mystics, his understanding of oriental traditions and practices being colored and distorted by this preconceived idea. I wish to put forward that original Buddhism (for example) offers an entirely distinct concept and practice of 'bhavana' (which can be translated as personal development or asceticism) which is radically incompatible with Christian mysticism and asceticism. This radical incompatibility is centered on divergent attitudes towards and role of suffering, specially with regards to the points you so brilliantly analysed in your book. The conclusion is that if we take this concept of bhavana then the internal contradictions and inner tensions largely disappear.

7. Deployment of a theory of knowledge, philosophy of language and philosophy of logic within the framework of 1-3. In particular continuing the work of Ortiz Hill, Rosado Haddock and several others...showing the superiority of Kant and Husserl over Russell, Carnap, Quine and Rorty.  The Frege-Husserl relationship and divergence can be greatly illuminated by a true understanding of Kant. That is, Frege's anti-psychologism (quite distinct from Husserl's)  which became the original impetus for so much of subsequent analytic philosophy is seen to be questionable and based on serious confusions. This is one of our fundamental problems: reconciling epistemic absolutism and objectivism (with regards to fundamental philosophical and scientific domains, including ethics) with full transcendental subjective idealism. Kant and Husserl offered solutions (and we should consider Brouwer as well). Frege just could not see any.  The other problem involves the historical consciousness of logic, the nature of transcendental logic,  multiple generality, intensionality and a rigorous theory of symbolism and analogy. We can reframe this historically as the problem of reconciling neoplatonic philosophy (understood as a synthesis of Plato, Aristotle and the Stoics) and Kantian and post-Kantian subjective idealism.  In the East such a reconciliation seems to have been as the basis of both the Vedânta and certain schools of Mahâyâna Buddhism.  Also in the west there are certain esoteric writers.

We are planning to write a series of notes and commentaries on Word and Object and Rethinking Identity (perhaps as blog posts). The  discussion of the Frege-Husserl relationship is very inspiring and thought provoking.  There is a perfect consistency between the early 'objective' Husserl and the later 'subjective idealist' Husserl - and it is Kant (in particular as read in the light of subsequent philosophy) that furnishes important clues. This all hinges on the different varieties and nuances of psychologism and anti psychologism...The book by Robert Hanna, Kant and the origins of Analytic Philosophy, is an interesting read, specially as it argues that there was already a strong anti-psychologism in Kant. We continue to investigate some central problems in the philosophy and history of logic, but right now focused on multiple generality and quantifier logic. With regards to intensionality we have come up with a new idea about the set of possible worlds. We think that just considering a set of possible worlds is wrong; rather there must also be a concept of nearness between worlds, based on the possibility (are we being circular here ?) of continuous deformation and variation. This can be justifies both on Husserlian grounds and by ordinary linguistic usage: our counterfactuals are usually based on more or less small variations (deformations) of the actual world or state-of-affairs.

 

8. Critical study of the Neoplatonic school both from a philosophical perspective and from an historical and archaeological perspective, that is, studying the views of the Neoplatonists themselves regarding the nature of ancient cultures and traditions: Chaldean, Egyptian, Greek, Syrian, Phoenician, etc.

 

https://antiqualux.blogspot.com/

 

9. The meaning of the Abhidhamma literature which, independently of the particular views held, is a logical, epistemological and psychological monument of enormous importance. By 'atomism' we can understand a theory of a given domain of reality which is logically based on primitive conceptual units and their relations, in particular the causal relation for temporal processes. It represents the dawn of authentic relational, non-monadic logic and systematic evidence-based rationality. Study also the relationship to Hume.