Afrikan Spir (1837-1890) - Denken und Wirklichkeit (1873)

https://archive.org/details/penseetralit00spiruoft

This work is of considerable interest to the concerns of this blog. Spir belongs to that fascinating category of  'forgotten thinkers' who are only mentioned in the context of biographies of famous literary figures.

Spir (the name seems to be of Greek origin) was born in present Ukraine, but wrote in German. His father was a protestant military surgeon who was knighted.

Spir seems to have partially realized the goal of expressing the core philosophy of early buddhism within the tradition  of western philosophy with a particular emphasis on Hume (whom he calls 'the wisest of men') and the spirit (rather than the letter and specific content) of Kantian criticism.  Hume and epistemic relativism are placed on a consistent, coherent basis. However remarkably there is no specific mention of buddhism in the work above (though moral, humanitarian and spiritual concerns are central to his thought), but we note the equivalence between 'the norm' and dhamma/dharma.  Spir is certainly one of the most interesting 'Humeans' alongside Husserl and Meinong. Indeed his treatment of 'sensations' seems quite analogous to Brentano's and later Husserl's theory of intentionality.

A defect of much of phenomenological and empirical philosophy and psychology was not primarily considering 'impressions' and 'ideas'  as 'objects' of desire, attachment, obsession. And not considering the remarkable phenomenology of the process of overcoming such desires which is at once the most difficult of task and yet relatively easy if guided by the right insight - an insight that should be our key philosophical guide.

Poetry (such as Novalis and Hölderlin) should offer an alternative complementary mode and path to philosophical knowledge - giving equal importance to the scientific and to the literary/artistic.

Hegel's logic might be interpreted as extracting (in a kind of depth psychology) the schemata of thought, of consciousness. Hegel's logic in turn can be expressed, according to some, in category theory.  Hegel's absolute knowing is awareness of the multiplicity of structures of consciousness as well as their relativity and passing away into another - just as for Sextus spiritual peace involves awareness of the multiplicity of hypotheses and their equipollence without contradicting this awareness itself - this is itself similar to the Spirian-Humean process of enlightenment which finds the norm imitated by yet fundamentally incompatible with phenomena.

An interesting link to Hume is provided by the work of Sowa on conceptual structures (the percepts) - and more specifically the Humean-style work in cognitive psychology discussed in his book (and it is possible that some French philosophers and semioticians (Greimas) of the second half of the 20th century might be of interest as well) - and the connection to category theory might be provided by Goguen (initial algebras, institutions):

The lattice of theories of Sowa and the formal concept analysis of Wille each address certain formal aspects of concepts, though for different purposes and with different technical apparatus. Each is successful in part because it abstracts away from many difficulties of living human concepts. Among these difficulties are vagueness, ambiguity, flexibility, context dependence, and evolution. The purpose of this paper is first, to explore the nature of these difficulties, by drawing on ideas from contemporary cognitive science, sociology, computer science, and logic. Secondly, the paper suggests approaches for dealing with these difficulties, again drawing on diverse literatures, particularly ideas of Peirce and Latour. The main technical contribution is a unification of several formal theories of concepts, including the geometrical conceptual spaces of Gärdenfors, the symbolic conceptual spaces of Fauconnier, the information flow of Barwise and Seligman, the formal concept analysis of Wille, the lattice of theories of Sowa, and the conceptual integration of Fauconnier and Turner; this unification works over any formal logic at all, or even multiple logics. A number of examples are given illustrating the main new ideas. A final section draws implications for future research. One motivation is that better ways for computers to integrate and process concepts under various forms of heterogeneity, would help with many important applications, including database systems, search engines, ontologies, and making the web more semantic.

 https://link.springer.com/chapter/10.1007/11524564_4

Thus we wish for a theory of language and theory of mind based on concepts on a phenomenist-phenomenological (introspective-intuitive)  basis with roots in Hume, Kant, Mill, Brentano, Meinong and philosophical psychology (and cognitive psychology) possibly guided by  idealism, structuralism, computer science (in particular the relationship between assembly and high-level languages) and category theory (and categorical logic) - ultimately to result in a western elaboration of the philosophy of original buddhism.  We are radically opposed to  naturalism,  behaviourism and in general philosophies that reject the primordial foundational role of meaning and consciousness.  This philosophy is distinct from metaphysics or natural science.

And yet we do not even begin to have a clear solid idea of what self- introspection is or how it can be achieved in order to effect a systematic phenomenism and  philosophy of mind. That is, how does or can consciousness observe and know its own immanent process ? We can start by inquiring into belief. What beliefs do we hold ? And if so what does it mean for us to hold such a belief or rather what are the consciousness-contents which accompany or indeed constitute the state or act of believing something ?

Important figures: Brentano, Wundt (and other structuralists), Meinong, Lotze, Stumpf, Köhler,  Is the psychology of early Buddhism gestalt ? It is this work the constitutes the true 'phenomenology' or what we call 'philosophical introspective psychology'.

Prior's paradox and Plato's Sophist

We can show that for any propositional function $Q$ that there is a proposition $h$ such that

$$Qh\to h\mathrm{\&}\mathrm{\exists }p(Qp\mathrm{\&}\mathrm{\neg }p)$$

Having something which if asserted (when $Q$ is interpreted as assertion) is true is no big deal. For instance take the proposition $\mathrm{\exists }xQx$. The interesting twist is that we can also devise a proposition ($\mathrm{\exists }p(Qp\mathrm{\&}\mathrm{\neg }p)$ itself ) which if asserted not only is true but also implies that something else false is also asserted. This is related to the paradoxes of non-being and falsehood in the Sophist. 

In Bealer's logic consider also a relation $D(a,b)$ holding iff and only $a=[\varphi (x){]}_x$ for $x$ the only free variable in some $\varphi$ and $b=[\varphi ([\varphi (x){]}_x)]$. Then consider the sentence $G(x)$ given by $\mathrm{\forall }y.D(x,y)\to \mathrm{\neg }T(y)$ for some predicate such that $T([\varphi ])\to \varphi$. Then consider $G([\mathrm{\forall }y.D(x,y)\to \mathrm{\neg }T(y){]}_x)$ to derive an abstract version of Gödel's result. The relationship between first- and higher- order logic is still not entirely clear.  It seems more a question of convenience and level of abstraction relevant to a particular application.

The game Sokoban (which is NP and PSPACE hard) offers a very elegant computational illustration of the essence of mathematical proofs and axiomatic-deductive systems in general (though of course Sokoban  is decidable): the layout of the walls and initial position of the boxes are the hypotheses and the goal position of the boxes is the theorem to be proved. The possible movements of the figure and the boxes are the logical rules.  It would be nice if we could have an analogous illustration of the computational structure of debates or the Platonic and Aristotelian dialectic.

Philosophical and formal awareness of the concept of computability was one of the most outstanding advances in the history of western philosophy (Church, Turing).  We need to find a characterization of incomplete axiomatic-deductive systems - from a very abstract point of view.

It would be interesting to study C. S. Peirce's presentation of quantifier logic: that is, to devise an axiomatic-deductive system for first-order logic in which all formulas must appear in prenex form. Or investigate the deeper significance of Skolemization. 

It is fascinating how category theory, which on the surface level involves higher cardinalities and huge ontological redundancy(recall that there is a functor of Set into the effective topos), becomes united to finitary combinatorics and computer science.   The high cardinalities are perhaps reflections of our way of looking at things, at our own epistemic imperfection, incompleteness and ambiguity - they are convenient fictions from which we can derive real and optimal computational results as well as conceptual architecture. The true significance of the Löwenheim-Skolem theorem concerns the logical potential of countable infinity which is a direct heir to the traditional paradoxes of infinity.

Philosophy embraces the whole

Philosophy concerns the entirety of human experience and human existence.  Artificial, shallow, abstracted segregated collections of concepts and their 'puzzles'  (cut off from ethics, anthropology, or the theory of the Platonic dialectic) cannot be authentic philosophy or have very much value. This false abstraction is not the abstraction of  mathematics, logic or theoretical science which on the contrary is living - has an intrinsic open-horizon - and permeates, even if implicitly, all of experience.

The Platonic dialectic is closely connected to ethics.  But few have explored the deeper significance of the ethical thought found in the dialogues of Plato and other key thinkers of antiquity (both eastern and western).  Popper's view is well known. Simone Weil (sister of mathematician André Weil) sensed that there was something very significant in the ethical thought of Plato and tried to argue for its proximity to Christianity.  How could Popper and Weil come to such drastically incompatible and divergent views regarding Plato's ethics ? Few have noticed the irony, circumspection as well as blunt iconoclasm in the dialogues - or indeed how radically progressive and enlightened some parts were relative to the social-political conditions of the time. It difficult to judge how 'shocking' certain views expounded by Socrates were perceived to be (such as, in the Gorgias, that it is better to suffer injustice than to commit it).  Although Socrates praised the frankness of those that expounded Thrasymachus-type views, it is still difficult to gauge just how mainstream such views might have been contemporary Athenian society.

Platonic insights into ethics are perhaps what is missing in our project of reconciliation of Kant and Schopenhauer (as well as the tantalizing question of Hegel's ethics).  Our ethics is one of the timeless universality and absoluteness of human and animal rights (cf. Plutarch, Porphyry and the account of Pythagoras given by Ovid)  as well as the duty to uphold and defend them.

Platonism offers us key insights into the investigation of the concept of 'intelligence'.

Our conclusion (which is ancient and is expressed for instance in the Theaetetus) is that intelligence is before all else and essentially the possession of the knowledge of what is right and wrong, the knowledge of what should and should not be done, the knowledge of what ought to be done or not done. And this includes not only how we should treat other human beings and animals but also the knowledge of the duty of self-cultivation, the knowledge that it is a duty to develop certain mental habits and exercises which are a preparation for Platonic dialectic (cf. the passage in the Republic beginning with: . But when a man's pulse is healthy and temperate, and when before going to sleep he has awakened his rational powers, and fed them on noble thoughts and enquiries, collecting himself in meditation (...)). If we make an analogy of these to diet, then we have to distinguish between intellectual 'health food' (such as problems in pure mathematics, formal logic, theoretical science, poetry, classical music, the fine arts, games such as chess and go, etc. - these are anagogic, they build, clarify and refine higher concepts)  and pseudo-intellectual 'junk food' (word games and puzzles based on the arbitrariness, vagueness, homophony and ambiguity of a specific natural language, magic tricks,  riddles and puns, games of gambling and chance, puzzles based on perceptual illusions, legal equivocation,  games of psychological manipulation, etc.). These last can be seen as the exercises and the bag of tricks of the sophist (although at a basic level there can be general strategies). No question of relevance to intelligence can depend on being formulated in a specific language (i.e. its ambiguity or fluid contingent semantic/phonetic associations).

But, O my friend, you cannot easily convince mankind that they should pursue virtue or avoid vice, not merely in order that a man may seem to be good, which is the reason given by the world, and in my judgment is only a repetition of an old wives' fable. Whereas, the truth is that God is never in any way unrighteous—he is perfect righteousness; and he of us who is the most righteous is most like him. Herein is seen the true cleverness of a man, and also his nothingness and want of manhood. For to know this is true wisdom and virtue, and ignorance of this is manifest folly and vice. All other kinds of wisdom or cleverness, which seem only, such as the wisdom of politicians, or the wisdom of the arts, are coarse and vulgar. The unrighteous man, or the sayer and doer of unholy things, had far better not be encouraged in the illusion that his roguery is clever; for men glory in their shame(...) - Theaetetus.

Indeed, is there anything more monstrous and ignoble than dominating and harming others (or wanting to do so)  or the appropriation and accumulation of resources (beyond one's basic needs) ? Or calling 'intelligence' the ability or practice of doing so ? Or having a 'culture' based on valuing this ? 

If every just man that now pines with want
Had but a moderate and beseeming share
Of that which lewdly-pampered Luxury
Now heaps upon some few with vast excess,
Nature's full blessings would be well dispensed
In unsuperfluous even proportion, (Milton, Comus 768-773)  

We plan to analyze carefully Popper's criticisms of Plato (which are rather obvious points) and the role of Sparta in Plato's thought. Also how contemporary ideology and junk psychology can hinder the appreciation and practice of platonic dialectic (for instance by denying that 'analytic' and 'intuitive' thought are inseparable).

In the previous post we wrote 'overcoming the illusion of the ordinary self and consciousness'.   Hegel's Phenomenology of Spirit can be seem as the path leading from the illusion of ordinary consciousness and self to that of absolute consciousness and its self-knowledge as spirit. Plotinus on the other hand makes a strict connection between the Platonic dialectic and the anagogic process whereby the embodied and mixed soul is brought back to its essential unity with the nous and the One. 

The exercises, the exercise of dialectic itself  transfigures, unveils and unmasks ordinary consciousness and the ordinary self (the Pali term vipassanâ) - this is what 19th-century philosophical psychology (cf. Brentano) struggled with, the inability to objectively observe the phenomena of consciousness (and Brentano is very frank about this). Understood in this light,  Sextus Empiricus and Hume can be given a consistent interpretation. There is some important literature on the relationship between Pyrrhonism and Buddhism  (Beckwith) as well as between Hume and Buddhism (sp. the Abdhidhamma). And of course there is the difficult matter of the evolution of the Platonic Academy and its convergence to something (apparently) similar to Pyrrhonism. 

The exercises discussed above obviously seem to involve 'concentration' -  but what exactly is this (how does the concept of concentration in Pali buddhism and Plotinus relate to intellectual concentration of study and problem-solving) and how does it relate to Platonic dialectic ? 

And do we need a critique of mathematics and a definition of what 'good' mathematics is (as opposed to mere addition to the repertoire of proofs and results and adding new definitions). Good mathematics depends on the ideal of axiomatic, formal, logical clarity and precision - but also of intuitive clarity and relevance to philosophy and science -  and on the ideal of elegance and simplicity of proof -  and on the possibility of an adequate explanation to others. There is nothing wrong with calling for a radical reformation of mathematics, for example via homotopy type theory or so-called 'formal mathematics' projects based on various proof assistants, or the reverse mathematics project, or a computable, constructive or finitary mathematics, etc.

A genuine mathematician must be half a philosopher, a genuine philosopher half a mathematician: examples Frege, Hilbert, Brouwer, Gödel.

Nothing is worse than aiming at proving certain results by whatever means, no matter how tortuous, artificial, obscure, convoluted, technical and lengthy.  This is not the mathematics of  interest to platonism. This is sledge-hammer mathematics, a huge rugged artificial contraption,  not the path of the philosopher.  We have also written between the difference between good (natural, logical, intuitive) and bad abstraction.

Just as for Plato we hope to show the profound connection between good (philosophical) mathematics and ethics.

The universality of computability, algorithms, combinatorics, graphs, core number theory and their inseparable 'logic' - this is what becomes manifest in mathematics seen in particular as a foundation for Platonic dialectic. 

We need a scientific philosophical linguistics which studies natural language seriously from a formal and mathematical perspective and at the same time is acutely conscious of and focused on the discrepancies and illusions of posing simplistic correspondences between the mathematical (i.e. grammatical) structure of a natural language and the actual conscious semantic content and intentions present in linguist utterance or internal discourse.  What does it even mean to use formal logic to analyze or express natural language ? Is it a translation in the same way we would translate into another natural language ? Or are we merely making more explicit certain aspects of the logical structure of an expression ? But what guarantee is there that even this logical structure of the natural language expression is reflected faithfully in the current systems of formal logic ? 

Maybe the psychologism opposed by Frege and Husserl was a strawman naturalized psychologism distinct from a pure psychologism which ironically has some similarity with what Husserl later espoused. Pyrrhonism and psychologism can be given a pure consistent foundation precisely if we abandon unproven naturalist assumptions or take positivism in its true sense as did Jayatilleke. And the Platonic dialectic is perhaps a kind of fluid general intelligence, the application of a universal method for solving any kind of problem and specially for psychological introspection: vipassana.

In original buddhism and its later development we find different perspectives: the abhidhamma, madhyamaka and yogacara - all of which have very close connections to their western counterparts, both ancient and modern: pyrrhonism (including the academy and sextus), stoicism and platonism (including middle and neoplatonism) and for the moderns specially: Hume, Kant (as read by Dennis Schulting), Hegel, Schopenhauer and Brentano. All this can be clarified and brought together into a consistent whole and nature and significance of the platonic dialectic be understood.

We don't know what meaning is

Gödel, criticizing a paper by Turing, remarked on how 'concepts'  are grasped by the mind in different ways, that certain concepts can become clearer, sharper and richer as time goes on. 'Concept' can be taken to mean one's conception of something (which can involve more than the 'psychological' as understood by Frege and Husserl)  or it can mean the thing (the ideal unity of all adequate conceptions of the concept) of which one has a (possiby imperfect) conception of.  Gödel's observation may not apply to all concepts, but only to some, for instance mathematical or metaphysical concepts.  The clarification, sharpening and enriching of one's concept of a concept has to be carried out through logical and intuitive exercise (which will involve interaction with other concepts). This exercise will have a spiral structure, for one will return to the concept again and again but now in a slightly different light.

We have no idea how concepts, meanings, intentions, references are related or even what these things are. We have no idea how their mereology works or the nature of this relation. 

Do we think of concepts or do we think through concepts ? And at a given moment can we be thinking of more than one concept or be thinking via more than one concept ? When I think of the concept of prime number am I also thinking of the concept of number ? (and is it not curious that we ask about the number of numbers satisfying a certain property ?).

What Frege got wrong was not knowing that the purity and objectivity he postulated in thought, meaning and reference is only an approximate ideal which depends on the exercise and training of the mind.  How can we understand (think of) this pure thought in its activity ?

In other words there is vagueness and there is clarity and objectivity - and there is a path and exercise leading from one to the other.   But ordinary conceptions and meanings of the ordinary mind - maybe these do not have any one definite clear objective counterpart.  These are simulacra, pseudo-conceptions, shadows.  

“Good Morning!” said Bilbo, and he meant it. The sun was shining, and the grass was very green. But Gandalf looked at him from under long bushy eyebrows that stuck out further than the brim of his shady hat.
“What do you mean?” he said. “Do you wish me a good morning, or mean that it is a good morning whether I want it or not; or that you feel good this morning; or that it is a morning to be good on?”
“All of them at once,” said Bilbo.

Here is a recapitulation of what we wrote about Gödelian-Platonic dialectics which is central to the process of concept refinement and enrichment and the progressive clarity and objectivization of concepts:

We recommend this essay by Tragasser and van Atten on Gödel, Brouwer and the Common Core thesis. Gödel's theory, as recounted by the authors, is of utmost significance. Gödel was promoting the restoration of the authentic meaning of Plato's dialectics and the role of mathematics expounded in the Republic and other texts.  Perhaps Gödel has pointed out the best path (at once philosophical and self-developmental) to the absolute.  Here is a relevant quotation from the Tragasser and Van Atten chapter p. 179:

Rudy Rucker (1983, 182–183) has reported on his conversations on mysticism with Gödel. Gödel’s philosophy of mathematics is called Platonism. He held that mathematical objects are part of an objective reality, and that what the mathematician has to do is perceive and describe them. Gödel once published some very brief remarks on how we have a perception of the abstract objects of mathematics in a way that is analogous to our perception of concrete objects (Gödel 1964). Rucker, seeking elucidation of these remarks, asked Gödel ‘how best to perceive pure abstract possibility’. Gödel says that, first, you have to close off the other senses, for instance, by lying down in a quiet place, and, second, you have to seek actively. Finally, The ultimate goal of such thought, and of all philosophy, is the perception of the Absolute.  When Plato could fully perceive the Good, his philosophy ended. Therefore, according to Gödel, doing mathematics is one way to get into contact with that Absolute. Not so much studying mathematics as such, but studying it in a particular frame of mind. This is how we interpret Gödel’s remark about Plato. There is, then, no break between mathematical and mystical practice. The one is part of the other, and the good of mathematics is part of the Good. Gödel also talked about his interest in perceiving the Absolute with his Eckermann, Hao Wang.

And here is what is remarkable about the Platonic-Gödelian method: the confluence between pure mathematical thought and introspective transformative philosophical psychology.  But this project can be discerned in Husserl's Logical Investigations and Claire Ortiz Hill has written extensively about the objective, formal and logical aspect of this work, in particular the important connection to Hilbert's lesser known philosophical thought.  However the psychological and phenomenological aspect is just as important, just not in the way of the later Husserl, rather in the Platonic-Gödelian and transformative philosophical psychological way.

The epokhê as Husserl outlined (in the Ideen) is not possible (and even less is the Heideggerian alternative valid), rather such a clarity and 'transcendental experience'  is possible through the Platonic-Gödelian method. 

For a good summary of the role of mathematics in Plato see Sir Thomas Heath, A History of Greek Mathematics, Vol.1, Ch. IX.

The Socratic method of abstraction must not be confused with that of mere generalization or induction. Rather the examples are skillfully chosen so that the mind is (re)awakened to the cognition of a certain idea (the applicability of the idea to different situations comes afterwards). A geometric analogy for Socratic abstraction might be that the examples are like points and the ideas are like the lines, planes or other figures determined by those points.  

The Platonic idea is in itself the Fregean objective concept (the ideal pole) while its relational aspects are the conceptions, meanings and intensions that the mind has.

Platonic dialectic is like an ars inveniendi, a general method, a universal intelligence, capable of producing new results and solving problems in all subjects. Its interdisciplinary nature reflects it's being 'beyond hypotheses' yet 'using hypotheses as stepping-stones'.  Dialectic is like a universal strategy and practice that is applicable to a great variety of games (we use 'game' in a non-pejorative sense and rather in the spirit in which in the Platonic dialogues dialectics is seen as a form of intellectual athleticism).  It is also an exercise as well as a 'game'.  There is a similarity to the Pyrrhonian epekhein (abstaining from views), however: the practice of mathematics is an essential preparation for Platonic dialectic and its aim is to produce illumination and authentic knowledge (the vision of the good or the absolute).  Platonic dialectic also involves 'phenomenology' in the sense of including introspective psychology,  but phenomenology as such is only a preliminary part and phenomena are seen in an entirely different light (as part of the 'friction' and spiral of the cognition) and subordinated to an entirely different purpose (which is not a rationalization and becoming-at-home-in the world of the cave).

We need to clarify the false opposition set up by Tragasser and van Atten  in the Common Core Thesis.  For now we refer the reader to Plotinus Enneads I,3 (on Dialectic).  Continuing the metaphor and analogy, the role of mathematics for Platonic dialectic is analogous to exercises which are preliminary to artistic and athletic activities.  It would be a grave error to confuse the exercises with the actual art or to focus on the exercises rather than the art. Yet the exercises are not inessential and exterior, they are embedded immanently within the art. Thus mathematics can be seen as the immanent implicit 'joints' of dialectic. And yet dialectic (the procedure of leaving the cave, 'freeing the mind', overcoming the illusion of ordinary self and consciousness) is quite qualitatively distinct from both mathematics and philosophical psychology.

A note on formal philosophy

The following preliminary text needs to be corrected and the final considerations clarified and expanded in light of Platonic dialectics.

Is a philosophy a subject, an activity of authentic value, capable of genuine progress, worthy to stand alongside mathematics, the sciences and engineering ? This has been much discussed. One very few have proposed is that maybe mainly only ancient philosophy (both of the west and the east) is of value – is authentic philosophy – and that authentic philosophy in the western post-classical era has remained a very illusive, hidden tradition. The iconoclastic position is not so difficult to reconcile with our exposition of phenomenological metaphilosophy. But here we take a radically distinct point of view – a view which does not however discard the psycho-therapeutic and ethical value of phenomenology.

So then what is ‘good’ or ‘authentic’ philosophy (we refer to this metaphilosophical ideal as logical formalism LF) ? . Here are its essential characteristics:

1. it keeps mental habits, ill-defined concepts and prejudices from insinuating themselves into philosophy, in particular in a cloaked or transposed form.

2. it is deeply concerned with the question: What is an argument ? (in particular: What is a valid argument ?)

3. it is deeply concerned with the question: How does language work ?

4. it holds up pure mathematics as the canon of knowledge and it follows that philosophical concepts, theories and arguments (proofs) in order to be valid must be able to be presented, expounded and checked in exactly the same way as mathematics.

Furthermore we can divide 4 into

4a. acknowledging 4 as the canon and goal of philosophy

4b. actually realizing this goal in partial or full detail

A corollary of 4 is:

Authentic philosophy is not possible without an adequate formalization of a sufficiently rich fragment of natural language.

We see also that ‘linguistics’ (in the post-Saussurean and contemporary sense) is a major part of philosophy.

Here we wish to present the antiquity thesis:

By and large we find a larger presence of LF in pre-modern philosophy than in modern philosophy (with several very important exceptions).

To show this we can study the 4 characteristics in the Peripatetic, Stoic, P latonic/Academic/Neoplatonic and Pyrrhonian schools. To show this is the case for Aristotle is the ultimate motivation for our paper ‘Aristotle’s Second-Order Logic’.

But there were those heroes of early modernity that had this metaphilosophical ideal, philosophers, logicians, linguists/lexicographers (like Wilkins)– however lacking they were in the actual realization of this philosophy (if not falsely presenting their work as being more geometrico when it is not even close). It is unnecessary to go through the luminaries of the much maligned “rationalist” tradition of early modern Europe. We wish however to make the following points:

1. The alleged failure of characteristic 1. The religious influence in rationalism is in fact far less (and less specifically Christian rather than Hellenic) than in all the powerful concealed or transposed forms which it took in subsequent philosophy.

2. The genial insight and far-ranging influence of Descartes is not appreciated enough (and the same goes for medieval philosopher Jean Buridan).

3. The rival “empiricist” tradition is also surprisingly aligned to the ideal and rigor of LF.

Paradoxically there is far more religious influence in the specifically 19th and 20th century evolutionary kinds of naturalism (as well as Heidegger) than in 17th century rationalism.

It is trendy to blame Descartes for introducing so-called “mechanism”, “mathematization of nature” and much of what is bad in western civilization: we reply with the challenge to define what exactly they mean by “mechanism” and refer the reader to the discussion on determinism, computability and differential models of nature. Descartes’ low point is his abhorrent view on animals (found also in Malebranche) which would seem to proceed not from logical argument but from inherited scholastic dogma. In fact Descartes’ (comparative) physiology might be easily interpreted as furnishing powerful arguments for animal rights (cf. the improved views of Leibniz) which already found a 17th century voice in Shakespeare.

We can question whether German idealism be not actually very far from this metaphilosophical ideal and if we do not find also a frequent conceptual and naturalistic transposition of Christianity into this philosophy order to make it more palatable and apparently compatible with the perceived progress of science and social changes (as well as the tastes of Romantic art). The conceptual and argumentative aspects of its texts do not seem, at first glance, very close to the ideal of mathematics: sometimes this is explicitly acknowledged, taken as a virtue (as in several passages in Hegel). We find alleged ‘deductions’ (in Kant and Fichte) which are difficult to see as proofs in the logical or mathematical sense.

Jules Vuillemin wrote a book about Kant’s intuitionism. While it is certainly reasonable to allow for a relation between primitive concepts (and axioms) and intuition, Kant’s use of intuition in the form of the synthetic a priori is very different. Schopenhauer has pointed out the inconsistent definitions of many key terms in the Critique of Pure Reason.

It would be impossible to discuss Bolzano, Cantor, Frege, Peirce, Peano and other important figures in the second half of the 19th century as well as 20th century philosophy without going into detail about points 2,3 and 4, something which would go far beyond the scope of this short note. If Frege represents a revival of Leibniz’s characteristica project (another aspect was developed in Roget’s Thesaurus, an underrated work with strong philosophical roots) he also represents (according to Bobzien) a conscious re-emergence of some of the core elements of Stoic philosophy. We argue in “Aristotle’s Second-Order Logic” that Frege’s second-order logic is simply the logic and metalogic of Aristotle’s Organon (although we need an alternative way of presenting natural deduction closer to natural language reasoning).

We must make the important observation that so-called formal and symbolic logic became part of the education and interest of certain philosophical schools, but as a rule in a very deceptive and misleading way if we are looking for the kind of metaphilosophical ideal in question (Wittgenstein does not seem to have much in common with it). It is very important to study certain non-mainstream philosophical currents in French philosophy of 19th century and the first half of the 20th century (among both the “spiritualist” and ontologist schools but also among such noted thinkers as Brunschvicg, Rougier, Vuillemin, Cavaillès, etc.). Neokantianism however fails because of its defective logic inherited from Kant, its confused account of intuition and its typical Kantian dogmatic assumptions about the limits of reason.

After so-called ‘early analytic philosophy’ (Frege, the early Russell, Carnap but also lesser known contributions by Hilbert, Mally, the Polish school of mereology, etc.) anything approximating LF was lost sight of in the analytic philosophy mainstream and has to be careful looked for and investigated. The project of formalizing natural language has been carried out in ways less interested in logic and in the definition of philosophically relevant concepts. LF -relevant work is found outside official academic philosophy among linguists and researchers in artificial intelligence and knowledge representation (like John Sowa) – and most specially in mathematical general systems theory – a mathematical model theory encompassing consciousness, living systems, social organization and every kind of scientific and engineering domain.

It is worthwhile to examine in detail the re-emergence of metaphysics in analytic philosophy since the 1980s (specially the work of Timothy Williamson and Edward Zalta).

We must find a reconciliation between LF and universal phenomenology (UP). Notice how Descartes is a key figure for both and how both share the same high regard for ancient philosophy. They both esteem Hume. They both are opposed to inferentialism and meaning-as-use theories. If Husserl has an obvious connection to UP, the work of Claire Ortiz Hill has shown that LF-related concerns run deep as well in Husserl with a close connection to Hilbert. A similar situation is found Gödel (see J. Kennedy and Mark van Atten: Gödel’s Philosophical Development). Gödel was not only enthusiastic about the phenomenological method but considered also the quest for the primitive terms and their axioms to be a viable alternative. Even Kant never ceased to dream of a kind of Leibnizean project.

To effect this synthesis or reconciliation we can take inspiration from how there is a mutually helping and corrective feedback loop between insight and formal deduction in actual mathematical practice. Descartes called deduction the intuition of the relation between intuitions.

It would seem however that LF cannot itself furnish the higher or ultimate foundations for logic or mathematics itself, specifically with regards to combinatorics, number theory and recursion theory – thus it would seem that LF already assumes that a large portion of logical and linguistic issues have been settled and thus it serves more as a tool for second philosophy. It would appear thus that LF cannot in itself completely solve the problems in the philosophy of logic, philosophy of language, theory of knowledge and metaphysics.

We are led to the difficult problems of the self-reflection of formal systems and the self-foundation of LF. The idea of self-foundation and self-positing. Category theory seems to be relevant here as a conceptually rich and multidimensional formal system which yet differs in its structure and use from classical logico-deductive systems. In Category theory concepts can be co-implicit in each other; there is a facility of passing to the meta-level inside the system, proofs are more analytic in the sense of involving generally an unpacking of concepts employing only minimal logic. Category theory’s ascent into abstraction bears a similar relation to ordinary mathematics as Descartes’ analytic geometry did to Euclidean geometry.

Maybe we need an entirely new self-reflective concept of formal systems and the role of formal systems. Maybe the activity itself of doing LF can manifest or show something higher though this can never be expressed or deduced in a formal system of LF. This again is an instance of the feedback loop aforementioned, which echoes the famous letter of Plato.

Beyond phenomenology

The text (text 1) that follows expressed an attempt to find a universal characterization of phenomenology which can be applied both to antiquity and modernity, to the west and the east (there is of course already a substantial literature comparing for instance, German idealism or Husserlian phenomenology with Buddhism philosophy or with Advaita Vedanta).

The description given here is of course very crude (and to some it might recall both Hume and the Abhidhamma). This kind of phenomenology (of 'inner sense elements') is lost in the realm of shadows and in fact deals with artificial abstractions. The basic impetus if of course correct, but the ordinary shadow-immersed and shadow-watching mind does not have the force to free itself from this realm in order to be able to know the shadow realm from a point of view beyond this lowest realm. This is discussed in (text 2). The required force is given by Platonic dialectics and this reveals the truth that the stream of ordinary consciousness is actually first and foremost a stream of (immanent) concepts.

(text 1)

The most basic idea is that of a methodology based on a pure, calm, detached awareness and observation of consciousness as it is in itself, as it presents itself to itself without being colored or altered by any presuppositions or modifications.

Instead of perceiving consciousness as a part of the world, the world is perceived as a part of consciousness, as immanent in consciousness. And it seems that what is involved in hindering this shift of perspective is forgetfulness and non-awareness of certain fundamental constitutive elements of consciousness (and the world): temporality and the active subjective nature of recollection and imagination which dominates ordinary experience. The world with its persons and objects that we are normally so completely entangled with and engaged with reveals itself to be upon careful analysis a temporal flux of subjectively constituted structures based on combinations of imagined and recollected inner sense elements. And we have the tendency to perceive and make use of 'wholes' forgetting that they are wholes and not perceiving the parthood of their parts or the way these parts are brought or bring themselves together. It would be interesting to develop a theory of forgetfulness and remembrance and of the different degrees and modes in which things can be brought to mind and be persistently present (not immediate but yet ‘at hand’, a kind of threshold awareness) in connection to the study of the terms sati and sampajañña in Pali buddhism. We can adduce evidence that this methodology is clearly set out in ancient eastern and western texts as well as in modern times (specially the tradition the runs through Descartes, Hume, Kant and Brentano). Of special importance is the concept of sâksin in Advaita Vedanta (see the book by Bina Gupta on this subject). Also buried within the Pali suttas we find injunctions to develop a special type of neutral awareness and analytic attention to experience. We encounter expressions such as diṭṭhe diṭṭhamattaṃ bhavissati, sute sutamattaṃ bhavissati, mute mutamattaṃ bhavissati, viññāte viññātamattaṃ bhavissati, Samyutta Nikâya 35.95 (and in the Bāhiyasuttaṃ of the Udâna), 'in the seen there will be merely what is seen, in the heard merely what is heard, in the sensed there will be merely what is sensed, in the cognized there will be only what is cognized'. This same sutta also contains passages involving past, present and future modes of presentation of the contents of consciousness.

(end of text) 

The text that follows can be considered as a preliminary motivation for the necessity of the Platonic dialectics for anything resembling the goals of this 'phenomenology'. The Platonic dialectic furnishes also a crucial distinction between immanent concept (which is more than just the 'psychological component' which was the object of a certain scorn by both Husserl and Frege) and a pure and transcendent 'concept' which is not readily available to ordinary consciousness.

(text 2)

Many would object that ordinary consciousness can only effect this self-transparency and self-reflection imperfectly and to a very limited extent – and by this we do not mean only a Kantian-type postulation of epistemic limitations but also the difficulty of first-person self-transparency in a more ordinary psychological sense (further ahead it will become clear why we consider the kind of limitation postulated by neuroreductionism to be invalid). And hence a kind of cultivation of consciousness is required in which, so to speak, consciousness goes out beyond itself without abolishing its ordinary processes so that these processes can be seen in the most perfectly objective way. The guiding idea is the possibility of consciousness stepping outside itself and becoming integrally and clearly aware of itself: transcendental self-transparency. There is a connection to deeper significance of the arguments of 19th century anti-psychologism (such as Frege's) although we note that the basis of the aforementioned anti-psychologism can already be found in Kant.

One aspect of this transcendental self-transparency is a state of consciousness in which we are directly and primarily aware of the stream or current of our thoughts seen as thoughts (i.e. the totality of the world and experience is seen as derived, dependent, constituted and immanent in the current of our thoughts). But the most fundamental aspect is understanding the whole of consciousness as a process which unfolds (from a unified to a more fragmentary state like the growth of a tree) directed by root causal forces; transcendental self-transparency hinges on the ability to obtain contact and seize control of the above root causal forces and thereby obtain the ability to freely invert, revert and reintegrate the whole out-folding process of consciousness. Phenomenology is not mere detached gazing at the shadows on the wall, it must have an anagogic dialectical component.

This stepping outside oneself has applications to psychotherapy and self-development. This is tragically lacking in modern western philosophy: a 'practical reason' acting not on the world but on consciousness itself and specially on certain aspects which are not afforded an adequate role in most modern theorizing. Ancient philosophy involved psychotherapy. A further topic to be explored would be that of the philosophy of lucid dreaming and the role of dreams in many historical philosophers. Also we mention that meditation has always been a deeply appealing and yet rather elusive endeavor. The reason for lack of solid progress seems to be unawareness that meditation is not an activity or study like others for which a scheduled time is set aside for, thereby hoping that progress will be directly related to the intensity and time of practice. Rather the precondition for progress involves a total reformation and overhaul of one's everyday life habits and mental patterns. Once this global reform has become established and solid, which can likened to diffuse light, meditation can then take place as a kind of focus or diffraction of this energy. But this local active engagement in meditation can also in turn serve as a tool for such a global reform. There is another problem: if meditation can be likened to the escape from the Cave, then what is the role of phenomenology here ? It is certainly not focusing on the shadows qua shadows. Rather it is a vertical phenomenology that pertains to effecting a fundamental insight leading to conversion and an impetus to escape.

(end of text)

The following text is not really interesting except as pointing out some important facts about certain forms of meditation and the body. The kind of atomism found in Hume and the abhidhamma is radically false.

(text 3)

We can attach great phenomenological importance to the body, feeling and the senses. But this in a way distinct from mainstream body-centered phenomenology which involves naturalist assumptions. Indeed the ultimate goal is the very opposite: we study and acknowledge the embodiment of consciousness in order, so to speak, to ultimately disembody and denaturalize phenomenology. And by 'body' we mean the internal first-person experience of the body including the analysis of elements of consciousness according to the different sense-fields and their associated neurological systems. It will be seen that the inner experience and concept of the body is related to the constitution of personal identity and the self-in-the-world. Also that the body can play a central feedback role in the previous methodology of transcendental self-transparency. There is also much that could be said about the methodological value of the more general contemplation of the composite structure and processes of the natural world.

We could compare physical (Democritus, etc.) and psychological atomism (abhidhamma, Hume). Atomism fails to give an account of space and time both in its subjective and allegedly objective modes and of why these two aspects could coexist. It gives no account of gravity or electromagnetic fields, of the nature of 'atoms' themselves, why and how they causally influence each other from any distance, how they can be substances bearing properties and relations, how they can exist 'in' space, how they can change and yet be indivisible, have individual identity, why they should follow a priori mathematical laws, etc. Atomism offers no account of mathematics or intentionality or meaning. It cannot account for the body of experimental evidence supporting the claim that fundamental physics is essentially a theory of fields rather than particles (which are abstractions and epiphenomena without fixed identities). The relations between the atoms is just as important if not more than the atoms themselves. It is anthropomorphic to think of atoms as free independent individuals. The equations that determine the relations show that atoms are just nodes inseparable and existing only as a part of holistic structure (like a tapestry). Atomism does not explain space, time or change and that it is plausible that timeless space-time is what actually exists (and hence atoms are space-time tubes or curves each one determining and determined by every other one) and that instantaneous present time exists relative only to a particular consciousness. However atomism remains (once it discards its absolutist claims) an important paradigm of rationality.


The following text is a study of the relationship between phenomenology, ancient skepticism and Hegel. These consideration are just preliminary and far from being correct. It is important to study in depth the relationship between Platonic dialectics and ancient skepticism and Hegel. Our previous note on Analyticity and the A Priori is relevant from skepticism. Hegelian dialectics can only become a part of Platonic dialectics through a careful study of the logical and mathematical core present therein. The goal of Hegelian dialectics (just as the goal of phenomenology) is quite illusory outside the central theory and practice of Platonic dialectics and specially its mathematical component.


(text 4)

Following phenomenological methodology we hope that we can obtain direct global insight into higher primordial constitutive structures and processes of consciousness, notably with regards to the complex domains commonly labeled under the terms 'self', 'agent', 'knower', personal identity and specially the domain of concepts and the process of reason itself. Key formal aspects are self-reference, self-modification, self-positing, self-othering, return-to-self, self-transcendence. We also propose to elucidate the subtleties of the doctrine of non-self (anattâ) in the oldest most authentic subtrate of the Pali canon, the part concerned with purely philosophical, moral and yogic elements. See C.I. Beckwith's Greek Buddha for argumentation for a purely philosophical and yogic (in the sense at aiming at the liberation of the mind) form of original Buddhism virtually identical in content to Pyrrhonism - a thesis which is strengthened by Hegel's interpretation of Sextus in his Lessons on the History of Philosophy. Bina Gupta has shown that the Vedanta and the other main darshanas can be approached from a purely philosophical point of view.

An important goal is to obtain not merely a theoretical understanding but direct intuition of the radically different nature of what was previously apprehended and taken to be our ordinary 'self' and personal identity. Also to show how cognition of objects is tied to self-consciousness (as Dennis Schulting argues in Kant's Radical Subjectivism).

It is interesting to present the following passages from Hegel. In the Encyclopedia Logic:

In other words, every man, when he thinks and considers his thoughts, will discover by the experience of his consciousness that they possess the character of universality as well as the other aspects of thought to be afterwards enumerated. We assume of course that his powers of attention and abstraction have undergone a previous training, enabling him to observe correctly the evidence of his consciousness and his conceptions.

And in the Lessons in the History of Philosophy:

The two formal moments in this sceptical culture are firstly the power of consciousness to go back from itself, and to take as its object the whole that is present, itself and its operation included. The second moment is to grasp the form in which a proposition, with whose content our consciousness is in any way occupied, exists. An undeveloped consciousness, on the other hand, usually knows nothing of what is present in addition to the content.

Phenomenology can contribute to a philosophical corrective reconciliation and synthesis between disparate philosophical views, both ancient and modern, eastern and western (but without implying any teleological progress). One key to this endeavor will attaching importance to a radical new interpretations and evaluations of the influence and significance of Pyrrhonism, Stoicism and the phenomenism of David Hume. Also to show that Plotinus has much to offer in the form of rigorous philosophy. Porphyry in his Life of Plotinus states that both the Stoic and Peripatetic doctrines are sunk in the work of his teacher. Preliminary work towards this goal will involve bringing to light neglected agreements and correspondences between different philosophical schools. For example: the dialectics of the middle Platonic dialogues is quite close to the argument structure of Sextus. So too is later neoplatonism's preoccupation with the ineffability of the Good. The connection of Pyrrhonism to the Sophists needs to be explored. Aristotle's De Anima has a striking agreement with eastern systems such as Yoga and Samkhya and the ideal sage of the Nichomachean Ethics (as well as the ethics of Democritus) differs little from the Stoic sage or eastern Yogi.

Plotinus indirectly engages with the sceptical later Academy through Saint Augustine's Contra Academicos (in this work we find the remarkable definition: I call world whatever appears to me.) but such an engagement is already found in middle Platonism, for instance in Nummenius as well as among the Stoics (as reported by Cicero's Academica). It is illuminating to compare the psychology and epistemology found in the Stoics and Academics to their counterparts in the Pali suttas. There are some surprising Plotinean anticipations of Kant, some of which seem to correspond even in the very phrasing (see our paper Aristotle’s Analysis of Consciousness). Hume's system (which has close affinities to the scepticism of the later Academy) is very illuminating despite its errors and shortcomings: a careful unveiling of these last that leads directly towards progress in phenomenology. Also Hegel's reading of Sextus (in the Lessons in the History of Philosophy) provides a powerful corroboration to the thesis defended in C.I. Beckwith's book Greek Buddha.

In Sextus the transcendental subject abstains (epikhein) from positing finite determinations either sensuous or rational as the truth - while at the same time considering how consciounsess 'goes back from itself', considering its very operation in addition to the content. 

(end of text)

The following text is more interesting and can be reinterpreted as a justification for Platonic dialectics (as a vertical phenomenology although the use of this term is perhaps not at all appropriate) - although of course there is much that needs to be corrected and clarified. Indeed the problems raised at there end can be solved by Platonic dialectics. The text very correctly points out the essential role of pure reason, specially pure mathematical reason for the feasibility of the attainment of the goals of phenomenology.

(text 5) Let us make the distinction between horizontal and vertical phenomenology more clear. The distinction is based foremost on the nature of the goal that is to be achieved, something what is in turn reflected in the methodology. Horizontal phenomenology’s goal is to reach back to the grounds of consciousness itself in order to explain and find the ultimate foundations of the world and ordinary consciousness. The goal is not to transcend the world or even to overcome ordinary consciousness (as if this could be a goal in itself) but rather to find an ultimate justification and source of meaning for the world. It is as if the prisoners in Plato’s Cave were interested in the objects behind them only for the sake of guaranteeing that the shadowy spectacle in from of them could be given a certain consistency and meaning, and thus their whole life as prisoners be in some sense consolidated and less rather more likely to be questioned. The prisoner-philosophers would be very interested in and focused on the shadows as shadows and study all their forms and variations and attempt to reconstruct the source-object as a kind of invariant. Vertical phenomenology on the other hand is concerned primarily with the escape from the Cave. The awareness of the shadows qua shadows is inseparable from the awareness of the chains and knowledge of the light-source. Its methodology is all about chain-breaking, light-seeking and truth-seeing and the shadows are studied both in their unreality and as factors of limitation and conditioning (horizontal phenomenology is incorporated but never as an end in itself). Vertical phenomenology is at once epistemic, ontological and ethical. It can be found most clearly in the systems of Yoga, Samkhya and Advaita Vedanta as well as in Plotinus.

As already mentioned the Pali texts are complex, heterogenous and difficult to interpret though there are grounds for postulating on oldest purely philosophical, yogic and ethical substrate. What is curious is that a kind of horizontal phenomenology seems to play an important role in the form of the well-known practice of satipatthana, although there can be little doubt that this takes place in the context of the aims of vertical phenomenology. However satipatthana can taken out of context and appropriated in the form a horizontal phenomenological psychology or psychotherapy and we can ask if certain ‘mindfulness’ or ‘living in the present moment’ practices are not really hindering the prisoners’ propensities to break free and seek the Truth.

The concept we wish to put forth in this section is that horizontal phenomenology is a vital element of a valid vertical phenomenology. This is because ordinary consciousness has a dual nature consisting of those more properly conscious elements and those that form a kind of complex substrate acting “behind” our more conscious experience. Thus the awareness of ordinary awareness needs to increase its range, its rays need to shine upon all the hidden obscure corners and recesses of our habits, conditioning and buried memories. The cultivation of a horizontal phenomenology as outlined in the first sections of this note appears thus as an important even necessary step along the path to self-transparency. Without this preparation the prisoner cannot hope to escape from Cave, rather she will only meet with more shadows.

Language permeates consciousness and our representation of the world yet just as the primordial constituting factors we discussed above are normally forgotten so too do we usually lack the transcendental awareness of the manifestation of language qua language (in particular inner verbal discourse) in our conscious experience. We find the idea of the philosophy of language as phenomenology well worth exploring (and there appears to be some significant connection to Zen/Ch'an).

How can we apply logic and language to determine the relationship between logic and language themselves and something which is beyond logic or language ? The philosophy of logic and the philosophy of language can be seen as part of phenomenology for logic and language are key parts of the structure and dynamics of consciousness. While standard attempts to theorize a foundation of logic itself will evidently depend on logic, there is away out of the predicament once we move to consciousness.

How are we to understand the theory that logic and language are precisely aspects of the structure and dynamics of consciousness (but not ordinary consciousness in the sense of psychologism) when to understand any process we must presuppose logic and language ? Hegel offers this solution in his Introduction to the Science of Logic:

Die Logik dagegen kann keine dieser Formen der Reflexion oder Regeln und Gesetze des Denkens voraussetzen, denn sie machen einen Theil ihres Inhalts selbst aus und haben erst innerhalb ihrer begründet zu werden. Nicht nur aber die Angabe der wissenschaftlichen Methode, sondern auch der Begriff selbst der Wissenschaft überhaupt gehört zu ihrem Inhalte, und zwar macht er ihr letztes Resultat aus; was sie ist, kann sie daher nicht voraussagen, sondern ihre ganze Abhandlung bringt dieß Wissen von ihr selbst erst als ihr Letztes und als ihre Vollendung hervor.

Logic, on the contrary, cannot presuppose any of these forms of reflection, these rules and laws of thinking, for they are part of its content and they first have to be established within it. And it is not just the declaration of scientific method but the concept itself of science as such that belongs to its content and even makes up its final result. Logic, therefore, cannot say what it is in advance, rather does this knowledge of itself only emerge as the final result and completion of its whole treatment. (Di Giovanni tr.)

To understand this more fully we would need to understand more fully how the Phenomenology of Spirit is articulated with the Science of Logic.

But let us consider another point. What is the relationship between pure rational activity (such as pure mathematics) and phenomenology ? And how are we to understand the anagogic role of the Platonic dialectic (which was also accepted by Plotinus), if we take this dialectic in the sense of the anagogic use of pure reason (as in Gödel) ? Also, how does Hegel’s concept of Logic compare to that of the Plotinean self-knowledge of the nous or the lower form intellection of the soul’s logoi as conceived by Proclus ?

An alternative to the horizontal vs. vertical distinction might be simply that phenomenology itself represents an early less advanced stage of the anagogic path (concerned more with appearances, images, opinions and the relations of ordinary consciousness – a mere antechamber of Truth) which must ultimately give place to something else.

Addendum: Brentano and the Nikayas: We saw that the inner consciousness which accompanies every mental phenomenon includes a presentation, a cognition and a feeling, all directed toward that phenomenon. It is obvious that each of these elements corresponds to one of the three classes of mental activities which have now emerged (Psy. from the emp. standpoint).

inner consciousness = viññana,  cognition = samskara, presentation = sañña, feeling = vedana, the phenomenon = rupa.