Quodlibet

 1. René Thom called quantum mechanics 'the greatest intellectual scandal of the 20th century'. Maybe this was too harsh, but quantum theory was meant originally just as to be crude very, provisional proto-theory to give place to something to better (which has not due to political, military, economic and industrial reasons ?). Consider the double-slit experiment. The 20th century was also the century of dynamical systems and chaos theory. It is clear to us that the random aspect of the double-slit experiment must be explained in light of chaos theory, thus of an underlying deterministic system. In a classical setting there will also be a pseudo-random aspect for particles traversing the two slits (but without the interference pattern). Nobody would think of interpreting this as a probabilistic collapse of a wave-function. In the non-classical situation it would occur to almost anyone to see the wave-function as real physical field associated to particles (a "pilot-wave"). If we rule out local hidden variables (but do we really need to ?), then we are lead no non-local yet deterministic non-linear systems which generate the pseudo-random phenomena of quantum theory in a standard way.

2. Quantum theory gave us the idea of introducing negative probabilities, i.e. signed measures. 

3. Category theory is intensional (non-extensionalist) mathematics based on minimal logic, thus hyper-constructive.  We ask about a natural number object (the concept of an 'element'  is not taken as a primitive; rather we have only generalized elements $1 \rightarrow A$) in a given category, that is, about its universal property;  we construct concrete generalized element 'numbers' through composition of primitive morphisms $z : 1 \rightarrow N$ and $s : N\rightarrow N$. Recall how the concept of primitive recursive function emerges naturally from this definition...

4.  Sights, sounds, etc. These are always sight-thoughts, sound-thoughts, formatted by the mind into objects integrated into a continuous semantic-temporal context. Sense-data are abstract results of conscious reflection.  Rupa is essentially a thought-constituted object modulo a sense-modality; only thus can it be an object of attachment and associated with feeling and consciousness. A raw abstracted sense-datum could never be the object of attachment or desire, except in rare pathological situations (the theory of the rupa-khanda is an ontology and general theory of categories for representations). Thus did the yogacarins refute the abhidhamma. We must investigate this carefully in the ancient texts. This must have been the original view which after becoming distorted  was then recovered in later sutras such as the Shurangama-sutra where a sky-flower object is given as an example of khanda-rupa.  Plotinus prefigured Kant.

What we know through sense perception is a simulacrum of the thing and perception does
not receive the thing itself. The later (the thing itself ) remains outside.  Enn. V, 5, 1.

De Anima 425a27: We already have (before actual perception) a common perception of the ”commons” (the categories of the sensus communis). Aristotle also wrote that it is impossible for time to exist without the mind (Physics 223a26).

Bhâvanâ cannot start with low-level abstractions. Husserl taught us to see the true categories at work in experience.

5. There have always been different notions of 'quantification' (and the corresponding determiners) which were conflated by extensionalist logicians.  This is clear in the distinction between intensional, conceptual universal quantification and extensional quantification. Also such distinctions are brought to light by the behaviour of quantifiers in propositional attitudes.  Constructivism tried to bridge the gap between extension and intension via a kind schematism (see previous post). We must bring all the different kinds of quantification to light again. 'Some' seem to be even richer in nuances than 'for all'. The distinction between the classical and intuitionistic/constructivist 'some' is deeply rooted in and reflected in cognition and natural language semantics. For instance, the intuitionistic interpretation fails for existential formulas in the scope of propositional attitudes. I may believe that the money in a book in the library without there being a specific book in which I believe the money is in.

Are set-theoretic extensions are atomistic structureless heaps, like the extreme abstract atomic alienated negativity in certain stages of Hegel's phenomenology of spirit ? This is not really so, they can have a very definite tree-like structure. Groupoids have more organic unity. We must investigate what it means to quantify over groupoids.

6. Some people are scared of homotopy type theory, higher category theory or of Coq and Agda. I respect that.  I feel the same about fractal calculus. But perhaps fractal calculus has something to do with the following important question. Numerical, discrete, computational methods are routinely used to find approximate solutions of differential (and integral-differential) equations. But we also need in a turn a theory of how differential and smooth systems can be seen as approximations of non-differential and non-smooth systems. Is this not what we do when we apply the Navier-Stokes equations to model real fluids ? Recall how continuous functions with compact support are dense in the $L^p$ spaces of integrable measurable functions (but see also Lusin' theorem).  Can all this be given a Kantian interpretation ?

7.  What are distributions ? They allow a mathematical treatment of the vague notion of particle. Indeed particles are just euphemisms for certain kinds of stable self-similar field-phenomena. The great geniuses in physics were those who helped build geometric physics (which is what is most developed and sophisticated in modern physics):  Leibniz, Lagrange, Euler, Hamilton, Gauss, Riemann, Poincaré, Minkowsky and many others.  But it is no use playing around with highly sophisticated geometric physics (which looses all connection to experiment)  if you haven't solved the problem of quantum theory first.

8. Study differential geometry as type theory; dispel all difficulties in a general understanding of mathematics as a language.

9. Many of our concepts have a tripartite nature $(A, A^\circ, \bar{A})$ expressing certain $A$, certain not $A$ and the grey neutral area $\bar{A}$. For instance: bald, not bald, sort of bald but not really bold. Each one in turn will depend on an individual and a possible situation of affairs. But this is not enough. In order to do any kind of 'logic' here we need some kind of quantified probability measure, for instance the ability to measure quantities of individuals and states of affairs. Then the sorites is resolved by presenting a tripartite distribution.  Thus it is interesting to have a logic which can express probability distributions.

10.  The goal is to pass from language-based philosophy to pure logic based philosophy. But this needs a mediator. The mediator can only be advanced, sophisticated, mathematical models, qualitative, essential, extending to all domains of reality (deformations, moduli are the right way to study possible worlds). All aspects of Kant and Husserl can be given their mathematical interpretation and from thence their logical-axiomatic interpretation. The same goes for naturphilosophie via René Thom and Stephen Smale. Theoretical platonism and idealism is not enough. We need this realized applied platonism. Mathematics furnishes a rigorous way of dealing with analogy and integrating analogy into philosophy. Also mathematics furnishes the deeper meaning and interpretation of Kant's theory of categories and schematism. Mathematics furnishes us with a way of studying concepts which is not divorced from the conceiving mind but at the same time is not psychologistic.

Kant and Computability Theory

It is strange that few have noticed that it can be strongly argued that the abstract concept of computability and its allied notions are a candidate for being part of the pure a priori necessary concepts for all our cognition and experience (Husserl seems to have anticipated some recursion theory in his Philosophy of Arithmetic).

We have the intimately connected triad of formal logic, arithmetic-combinatorics and computability theory.  To write and check a formal proof we already are deploying computability concepts. But to investigate computability notions we need formal logic and arithmetic. Computation, proof  and the sequence of the natural numbers share the ordered directed time-like quality (linear with branching possibilities). Note: we are not suggesting that computability exhausts human cognition. Also by computability we include all classes in the arithmetical and analytic hierarchies, etc. In a future post we will critique the denigratory use of the term  'mechanistic'  showing it does not hold water when confronted by a serious mathematical and philosophical analysis of the use of differential equations in science.  Computability theory seems very close to Kant's notion of rule and of an architectonic of reason. Church's thesis is a transcendental condition for the possibility of knowledge.

Computability has to do with prescriptive normativity (method) rather than mere general normativity (rules).

We wonder if Kant's realm of pure synthetic a priori intuition of space does not actually correspond to graph theory and combinatorics - and whether category theory, and specially higher category theory  are not best viewed from this perspective (cf. simplicial sets and cubical sets). Category theoretic diagrams have a a kind of dynamic nature - at least in the way they are commonly used and visualized - which recall Kant's schematism.

See also:

https://chryssipus.blogspot.com/2023/11/the-church-turing-thesis-kripke-and-kant.html

https://chryssipus.blogspot.com/2024/01/algorithms-and-numbers.html

Cognition and States of Consciousness

Husserl wanted us to develop a state of consciousness which also, of course, has a cognitive aspect - indeed the cognitive aspect might be seen as its raison d'être. But it is more than this. A state of consciousness implies a permanent habit, a transformation of character. Both Husserl and the oldest Buddhist texts dwell on (analytic) insight, disidentification, suspension and distancing (abgeschiedenheit).

If conscious experience is normally present in unreflected 'globs' , the goal of analytic insight is to unmask and be continuously aware of the ternary structure present in consciousness $\bullet \rightarrow \bullet$ and its subsequent higher-order unfoldings.

We mentioned before the archetypal structures and processes of consciousness. Here is an incomplete tentative list (with an implicitly Kantian basis):

Synthesis - gluing, covers, the sheaf-condition = extensibility on $j$-dense objects for a topos with a Joyal-Tierney topology.

               - different orders of wholes (higher groupoids)

Self-reflection - a system which can represent (partially at least) higher order aspects of itself within itself.  This is the original synthetic unity of apperception = I know that I am knowing. This is found in recursive definitions, inductive types, the successive powers of the $\lambda$-cube wherein external aspects of the system become internalized and internally represented, also the subobject classifier, truth-value object $\Omega$ in a topos. See also our post on the meaning of the logical connectives.

Return-to-self, that is, Kant's trinary structure in the CPR.  This is related to the negation of the negation, double negation as the third (synthesis).  In topos theory this relates to the dense topology and in particular to forcing.  The idea is simple. In rough terms it is as follows: consider $U\Vdash\phi$ as signifying that the sentence $\phi$ holds in region $U$. We define $U \Vdash \neg \phi$ if $\phi$ does not hold on any subregion $V\subset U$.  Then $U\Vdash \neg\neg \phi$ means that for any subregion $V\subset U$ we choose we must have that there exists a $W\subset V$ such that $W\Vdash \phi$.

Double-negation can also be connected to temporality: something must pass to reveal itself, ti to einai, quod quid erat.

But this is assuming a static consciousness, a fixed state of consciousness with its corresponding archetypal structures and processes. But what about the transformation into other states (such as found in Schopenhauer and Hegel) ? Do the archetypes change ? Or must we find further higher-level archetypes that govern and characterize this transformation ? To self-reflection we should add self-negation and self-transcendence whereby the correlative self of consciousness is abrogated and transposed to more universal and wide-encompassing modalities and states. 

Kant also had a Leibnizean dream, a complete axiomatic-deductive system of the pure a priori concepts and principles of the understanding. What is not clear is how he envisioned deduction and the interplay of the analytic and the synthetic.  Could the synthetic be exhausted in a finite set of axioms and all the rest be entirely analytic, Frege-style ? How could Kant explain that in mathematics there is often a convergence between intuition and formal deduction ? 

The history of transcendental idealism is yet to be written, specially as regards to the time between Kant and Husserl. Schopenhauer, Von Hartmann and Spir are far more important than Fichte or even Schelling. Tolstoy wrote of Spir: "reading Thought and Reality has been a great joy for me. I do not know a philosopher so profound and at the same time so precise, I mean scientific, accepting only what is strictly necessary and clear for everybody. I am sure that his doctrine will be understood and appreciated as it deserves and that the destiny of his work will be similar to that of Schopenhauer, who became known and admired only after his death". 

We can view Husserl' transcendental subjective idealism and Fregean-Leibnizean objective platonism as not mutually opposing by complementary or at least compatible. Also these two need not be considered exhaustive of reality,  as an important place should be given to ethics, to philosophy of art and to naturphilosophie and above all the practice and psychological basis of meditation (higher ethics).

Schopenhauer on the Content of Compassion

https://phil.washington.edu/research/publications/schopenhauer-content-compassion

Instead of simply saying that the compassionate person perceives no distinction between herself and the object of her compassion, we should say that she perceives them to not be distinct spatiotemporal individuals. That is, she perceives them to be distict only in the way that Platonic ideas are distinct. The latter distinctness is not sufficient for individuality in the normal sense, for Schopenhauer, since he calls space and time alone the principle of individuation (OBM 4:267, p. 250). The key difference is that, at the level of ideas, things metaphysically overlap with each other in ways that they do not at the spatiotemporal level. (p.7)

So we have here a holology which also suggests comparison with Plotinus' theory of how ideas are unified in the nous.

Hegel's phenomenology of spirit is the antithesis of both Kantian and Schopenhauerian ethics. It is essentially anti-transcendent, pragmatist, relativist, collectivist, deterministic and culminates in a totalitarian-statist mysticism (a fascism based on an esoteric Christianity which subsumes and buries the the possibility of the resurgence of the enlightenment).  This is seen in the treatment of the phase of practical reason and its transition into "spirit". Hegel turns Kant's noumenon into his secular pragmatic collectivist fatalistic thing itself Sache Selbst. From thenceforth it is no longer about the individual but only the drama of the collective. The individuality of the individual is allowed to manifest in its "negativity" only for the sake of, and in function of, the development of the power and self-transparency of the collective.  What corresponds to this 'spirit' is the third section of what is inappropriately called 'Begriff' in the Science of Logic, the weakest and most ad hoc part,  which appropriates the far deeper insights into the structure of consciousness found in Kant and Fichte. 

At the basis of ethics must be a consciousness which does not make a distinction between self and others or between today, yesterday and tomorrow. Ethics concerns the timeless individually directly cognizable universal ought which is completely independent from any hypothetical necessary developmental law or process just as it has nothing to do relativistically with arbitrary convention. At a social-cultural level there can indeed be ethical progress, but this should never be seen as the working of some kind of natural law or the result of necessity. Confusing the ideal of human ethical progress with speculation about evolution in natural science has been a very serious error.  Human ethical progress is a normative ideal never a law or natural necessity. A normative ideal that remains invariant throughout recorded historical humanity, even if tragically it seems to be less and less realized in the world today. There are non-human sentient beings which cannot be subject to the normativity of the moral law. But we could explore how there is an implicit, albeit imperfect, morality already at work in nature. What we must reject are arbitrary speculations attempting to link non-human and human beings whereby such a link serves as a foundation or explanation of morality.

The correct theory of ethics is much like Frege's  philosophy of logic. Or, to paraphrase Husserl:

Whatever is a moral duty, is absolutely, intrinsically a moral duty: the moral law is one and the same for men or non-men, angels or gods. Moral laws speak of the ought in this ideal unity, set over against the real multiplicity of races, individuals and experiences, and it is of this ideal unity that we all speak when we are not confused by relativism.

The moral law implies that we should strengthen our historical organizations dedicated to the universal unconditional upholding of human rights and international law.

Theory of theories revisited

Given a theory, a systematic theory, we can analyze i) its intrinsic logical-conceptual structure, ii) the process by which a person comes to learn and understand the theory, and iii) the historical or personal biographical genesis of the theory (which of course can involve i) and ii) at previous times).

Regarding approach i) we can ask to what extent is the organization of the theory drawn by necessity and each logical step or 'development' (in an asynchronic sense) guided by implicitness or inner necessity ? (These considerations seem to have played an important role for Fichte and Schelling).

Speculation: can ii) and iii) somehow shed light on this question regarding i) ?  What is the relationship of this to Aristotle's distinction between things clear to us and things clear in themselves and his methodology of starting with the former ?

Speculation: can the study of biological organization or general systems theoretic concepts help with i) ?  What are the most important metatheoretic concepts we need to consider (for instance the idea of something external and ad hoc becoming internalized, the discussions in our post about reflection-into-self, etc.) . Category theory and categorical logic offer a very important paradigm and key. The bare concept of category (and higher category) functions like a supreme genus. As more properties are added these are mirrored in the nature of the internal logic. They way successive relevant properties emerge is certainly not arbitrary but seems to conform to basic meta-theoretic archetypes, if we are careful to unfold them in a gradual and ordered way. 

But let us look at the processes and archetypes of consciousness (such as unification, return-to-self, negation, intentionality, etc.). How are they reflected in or determine theories ? Does the logical-conceptual structure of theories reveal the structure and processes of the mind and vice-versa ? The formula for Aufhebung $A \rightarrow \neg\neg A$. However this process stops after the first iteration. Subpresheaves (subfunctors) of a presheaf over a category $C$ form a Heyting algebra. It is interesting to look at $\neg\neg A$. This is related to density (the dense or double negation Grothendieck topology).  Given a subset $A$ of a set $X$ we can look for the smallest set $B$ for which $A$ is dense in $B$, that is $B$ is the closure or completion of $A$. 

Sheaf theory recalls Kantian schematism: it is the synthetic realization (in particular topological) of an abstract category. The sheaf axioms express Kantian synthesis.

Of particular importance are theories of wholes, of different kinds of wholes, in particular non-distributive (mass-noun-like) and constructive/computational wholes.  All quantifiers (in dependent type theory) are intensions related to wholes and it is important to know what kind of whole is under consideration.

Analytic metaphilosophy

By analytic metaphilosophy we mean a methodology which aims to apply mathematical and formal logical rigor and the full force of linguistic analysis to philosophical texts in order to assess their argumentative and epistemic value. Analytic metaphilosophy has a strong affinity and connection to early classical analytic philosophy (though it has many brilliant precursors before that time) but no connection to subsequent post-classical analytic philosophy - indeed it can be conceived as the ultimate tool to thoroughly refute and show the nonsense and vacuity of its various currents as well as some of those that claim to break with it.  A novel aspect is that it attaches an enormous importance to the style of philosophical texts and aims to be far more wary and careful about the pitfalls, delusions and psychological foibles of the whole process of literary creation. It never forgets that the philosophical writer is never far from the precipice of literary fantasy often exhibiting egocentric and sycophantic qualities geared to socio-economic advantages rather than epistemic and ethical goals.  Analytic metaphilosophy studies in particular the sociology and psychology of sophistry and literary delusion. More Platonico we shamelessly proclaim that it is impossible to engage in analytic metaphilosophy without either a solid undergraduate background in mathematics and mathematical logic or at least a couple of years of experience working on a formal mathematics project employing a proof assistant.  In a nutshell: analytic metaphilosophy applies mathematical standards of logic and rigour to philosophical texts and refuses to be impressed by the mirages and artifices of language (though an ideal philosophical text can have also beauty, elegance and clarity of style as in the writings of Frege and Claire Ortiz Hill). Jargon-laden and convoluted texts rarely betray deep, complex, rigorous or valid thoughts. Such pseudo-difficulty is of an entirely different nature from the 'difficulty' of mathematical texts. Analytic metaphilosophy can also be seen as a kind of prolegomena and justification for the formal philosophy project we described in previous posts.

In that most rigorous, clear and certain of the sciences, mathematics,  mistakes and confusions still arise, there are gaps in proofs, there are unjustified assumptions, careless generalizations, confusions in terminology, silly oversights, circular reasoning, etc. As the length of the proof increases so does the probability of error, even for the best mathematicians and Fields Medalists like Vladimir Voevodsky. Careful checking by several experts is absolutely necessary. In some areas the length of the proofs become almost too long for this to be feasible, so proofs are formalized and run through specialized proof checking software.

Now consider philosophy, the least rigorous, clear and certain of human epistemic enterprises. Once a philosophical 'argument' becomes long, convoluted and (on the surface level) complex one can be almost certain that it is wrong or inconclusive. The same goes for texts with an elevated number of technical terms or  'jargon density', so to speak. 

Mathematicians have an artist's liberty to use and invent symbols for their primitive and defined notions and variables.  The philosopher, shackled by natural language and lack of mathematical training, is in a very dire situation, terms are pathologically and enormously semantically overloaded and the resulting terminology is opaque, ambiguous and stylistically repugnant. Perhaps this can be partially overcome by the construction of an artificial language for philosophical terms.

The majority of philosophical texts have nothing to do with the logical standards and rigour of mathematics or even the exact sciences. What reason is there to attribute to them any meaning or epistemic value at all ? Or even social value ?  And many of their authors are aware of this, don't care, or consider it a virtue.  They have their communities with their founding narratives and (non-reflectively) received doctrines and they happily engage in their 'language-games'  and strictly controlled boxed (bottled ?) 'innovations'. They have their own 'logic' and 'rules' and 'criteria' for parsing and deciding the value or legitimacy of textual-output - and this output is a torrent, an endless deluge and logorrhoea that seemingly might be generated by large language models. Ex falso quodlibet. 

Analytic metaphilosophy (which favours Martin-Löf type theory as an adequate intensional and modal logic) is entirely immune from objections culled from mathematical logic itself such as all-too-common misunderstandings and misappropriations of Gödel's incompleteness theorems.  Although mathematics can be conceived as a subset  of logic (by assuming special axioms such as univalence), logic can also be conceived as an application of mathematics. There is no concept of computability without involving arithmetic and no concept of arithmetic which does not involve some notion of computability.

Recall that we hold that logic is embodied in a closely unified (organic) family of formal systems which are related to each other by gradation or (mutual) embeddability and reflection. There is no trace of convention or arbitrariness.

And in nowise does our metaphilosophy claim to be philosophy itself or a substitute for it. However knowledge of applied mathematics at an advanced theoretical level has huge conceptual advantages for thinking about possible worlds, possibility, causality, identity and states of being which far surpass the crude models used in analytic philosophy.

Analytic metaphilosophy can be integrated seamlessly into the Gödelian and Husserlian frameworks as complementing and helping the metaphilosophy and methodology of ultimate evidences and intuitions as well as ethical metaphilosophy*. It works alongside it and provides powerful aid by refuting anti-idealist arguments.

Schopenhauer's detailed criticism of Kant in the WWR and T. H. Green's long introduction to Hume's Treatise are  good examples of pre-Fregean analytic metaphilosophy. The investigation of the expression of multiple generality and its associated reasoning in ancient philosophy is clearly a cornerstone to analytic metaphilosophy's  approach to ancient and early modern philosophy.

*ethical metaphilosophy focuses on the explicit and implicit content relating to human and animal rights, in particular the status, dignity and consciousness of animals,  in historical philosophy - and thereby comes to general conclusion about the value and merit of different philosophical systems.  Leaving aside ancient eastern philosophy, the cases of Porphyry, Schopenhauer and Husserl are enough to de-fang ethics-based anti-idealist arguments whilst arch-anti-idealist Nietzsche's raving praise of Descartes' view of animals delivers a fatal counter-blow.

Medieval philosophy has been criticized for being the handmaiden of theology and merely a tool for the apologetics of the dogma of organized religion.  If this is justified then philosophy also cannot be allowed to be the handmaiden for para-scientific ideology and dogma either, which is what we find predominantly in the so-called 'philosophy of mind'. Is there anything more silly than  a priori arguments for speculations  based on incomplete or faulty experimental science ? Image the money it saves on equipment and resources for the materialist neuroscientist.

Nevertheless Kant's language is often indistinct, indefinite, inadequate, and sometimes obscure. Its obscurity, certainly, is partly excusable on account of the difficulty of the subject and the depth of the thought; but he who is himself clear to the bottom, and knows with perfect distinctness what he thinks and wishes, will never write indistinctly, will never set up wavering and indefinite conceptions, compose most difficult and complicated expressions from foreign languages to denote them, and use these expressions constantly afterwards, as Kant took words and formulas from earlier philosophy, especially Scholasticism, which he combined with each other to suit his purposes; as, for example, "transcendental synthetic unity of apperception," and in general "unity of synthesis" (_Einheit der Synthesis_), always used where "union" (_Vereinigung_) would be quite sufficient by itself. Moreover, a man who is himself quite clear will not be always explaining anew what has once been explained, as Kant does, for example, in the case of the understanding, the categories, experience, and other leading conceptions. In general, such a man will not incessantly repeat himself, and yet in every new exposition of the thought already expressed a hundred times leave it in just the same obscure condition, but he will express his meaning once distinctly, thoroughly, and exhaustively, and then let it alone. "_Quo enim melius rem aliquam concipimus eo magis determinati sumus ad eam unico modo exprimendam_," says Descartes in his fifth letter. But the most injurious result of Kant's occasionally obscure language is, that it acted as _exemplar vitiis imitabile_; indeed, it was misconstrued as a pernicious authorisation. The public was compelled to see that what is obscure is not always without significance; consequently, what was without significance took refuge behind obscure language. - Schopenhauer, WWR (II).

Updated Project

We authored papers on ancient logic and on Aristotle's theory of the continuum.

1. Investigate Ortiz Hill's theories on identity, equality, intensionality and extensionality in the light of dependent type theory and homotopy type theory.

a) intensions and modalities are irreducible parts of logic and the structure of reality

b) we must never confuse identity with equality which is better to call equivalence, there being several notions of equivalence

c) extensions (and completed infinities) can be problematic and do not have logical or ontological priority 

d) type theory was a step in the right direction  which became perfected by Martin-Löf

2. Investigate embeddings of formalizations of philosophical systems (specially modal type theories) into dependent type theory.

3. Defend Husserl's philosophy of logic and theory of knowledge against its opponents.

3a. Continue Gödel's philosophy based on a unique interpretation and reconciliation of Leibniz and Husserl.

4. Continue the project of a virtuous hermeneutic circle between higher category theory and Hegel's logic.

5. Give a detailed philosophical intepretation of Pali Buddhism in terms of ancient and modern western philosophy (Skeptics, Stoics, Plato, Aristotle, Plotinus, Kant, Schopenhauer and Husserl) and show how popular accounts of original Buddhism are mistaken.  This involves in particular

5a. Develop a synthesis between Kantian and Schopenhauerian ethics.