Logical notes

In this post we place brief sketches of some ideas to be developed.  The criticism of the concept of 'possible world'. Our knowledge of the 'world' is approximative, incomplete, local and relative.  Thus it makes little sense to speak of an 'alternative world' or of a certainty that such is even 'possible'.  Rather there are local restricted domains and aspects of the world, coming from different spatio-temporal regions of the actual world, which we loosen and group together and inappropriately call 'worlds'.  For instance possible gardens are based on the collection of actual (present or historical) gardens in the actual world (which depend, in this case, on human agency and choice), and these may or not contain roses. It is absurd to speak of an alternative global world in which the red roses in this garden are white.  Possible worlds are an undue reification of aspects of imagination and consciousness. Criticism of statistical and probabilistic concepts: cannot judgments involving such concepts all be transformed into judgments without them, based on spatial-temporal events ? Is not the statistical and probabilistic inherently eliminable and reducible to mere arithmetic judgments regarding a collection of evidence from a set of spatio-temporal regions  ? And are not such concepts based on partial, artificial, approximative abstractions which totally ignore the underlying epistemically open-ended structure of reality ?  One cannot enter into a relation to something without entering into a relation with the relation and so forth. Logic is an a posteriori useful descriptive tool, not a foundation. There is a large amount of evidence that consciousness can subsist independently from the physical brain and that consciousness is not generated from the brain nor in particular are different psychological faculties determined by specialized functional regions of the brain. A philosophy which ignores this evidence is not philosophy but propaganda. Consciousness does not supervene on the brain or physical matter.  If linguistic utterances were a soup then Wittgenstein would hold that the meaning of 'soup' is reduced to the movements of the spoon (such movements could indeed serve as a non-verbal sign indicating 'soup').  One cannot abstract any symbol from meaning, nor use from mention (which is a misuse of the term 'mention' anyhow).  When attempting to grasp an empty purely syntactic meaning-free entity one is actually trying to grasp an ideal type and structure with an unlimited number of possible perceptual variants and instances, an extension which may indeed by vague (for instance in the case of poor sight when we are not sure of a certain letter). Thus 'the letter 'b'' is an abstract concept with an extension and hence with a meaning.  Frege and Husserl pointed out again and again that the meaning and reference  of terms or propositions certainly cannot be exhausted by the accompanying 'mental images' which need not coincide for different people and cannot provide thus a foundation for a so-called objectivity of meaning. True. Yet digging deeper  and applying the right introspective-descriptive method we may discover that intuitive mental content of a different order can be disclosed to consciousness which does indeed furnish a ground for inter-subjective, objective agreement. Yet this need not be naively taken to be some kind of identical extra-mental ghostly entity, and even less some kind of external sociological structure and dynamics,  rather it is a directly accessible aspect of consciousness which while sharing the same type for the same meaning across different minds also allows room for  individual variation. For instance if the common mental image is like the adornments that may adorn a statue (and there may be none at all), the statue representing a god, say for instance Athena, can be different one for different minds and yet be clearly isomorphic in a suitable sense across different minds for the same term or proposition. The fact that human beings must have hearts with the same structure does not imply that there is a common objective heart outside each body.  The objectivity of meaning can be understood in a way similar to the isomorphic structure of our bodies, rooted in what we are,  in the things themselves.  If incomplete and having errors, few western philosophers have ever probed consciousness like Hume and Kant and laid bare the deep forces underlying it, including the nature and constitutive role of 'ego' and the construction of 'naive realism'.  To these we add the powerful contributions of the fathers of introspective psychology (Brentano, the William James of 'The Principles of Psychology').  And see the work of K.N. Jayatilleke and the early Carnap (and also Rosado Haddock's on Carnap). Carnap uses the suggestive term : autopsychological.

After the autopsychological was chosen as basic domain, thus, the processes of consciousness or experiences of consciousness of the I, it must still be determined which formations of this region are going to serve as basic elements. One could, let us say, consider taking as basic elements the ultimate constituent parts obtained by means of psychological and phenomenological analysis of the experiences of consciousness, thus, let us say, the simplest sensory sensations (as Mach), or more generally: psychic elements of different sorts, from which the experiences of consciousness are formed. On a closer examination, however, we must acknowledge that in this case not the given itself, but abstractions from it, thus something epistemologically secondary, has been taken as basic elements…. Since we, however, wanted also to require from our constitutional system the consideration of the epistemological order of the objects, we shall, thus, start from what is epistemologically primary to everything else, from “[the] given”, and those are the experiences of consciousness themselves in their totality and closed unity…. To the chosen basic elements, those experiences of consciousness of the I as unities … we refer as “elementary experiences of consciousness. [Der logische Aufbau der Welt, pp. 91–2].

Is not the concept of vagueness itself rather vague ? Many natural language predicates admit more-and-less (in the terminology of Aristotle's Topics) but our adverbial resources are often clumsy or insufficient to express the underlying linear order of the corresponding 'semantic space'. Language is discrete but consciousness and the world are continuous.   Thus all difficulties involving vagueness and ambiguity can be resolved by introducing a fine enough (though finite) linear scale: this in practice is what is used in many sorts of questionnaires.  Baldness is a predicate capable of more-or-less hence with an underlying linearly graded semantic space.  It is absurd to believe that you can split a continuous linear segment into a binary classification. 

A new philosophy of science and technology

What are vague monster concepts ? They might be described as having a huge comprehension which hinders them being grasped as an intelligible whole so that one is inevitably lead to form a subconcept of which important aspects are missing (we could call such concepts 'quantum' or even 'fractal' in the Baudrillardian sense). This allows a rhetoric of the concept which can pragmatically justify opposing statements according to circumstance (in the theory of Thom, it is almost if it were alive and had developed a sort of self-defense mechanism).  It also invites the questioning of whether the concept as a whole represents anything consistent and intelligible  beyond being merely a cloud, a manipulate veil for power and control.  Western culture abounds in monster concepts. We mentioned 'religion'. Another concept is 'intelligence' though this is also a the same time a pseudo-concept (as is the concept 'socio-economic class').  We do not of course mean here the sense of 'intelligence' which pertains to the essence, structure and dynamics of human reason, of the human mind, of consciousness...the subject of the philosophy of mind, cognitive science, etc.  Nor as in 'animal intelligence', etc.  No, what we address here is the pseudo-concept of 'intelligence' in which  in certain cultures individual A is said to be 'smarter', 'more intelligent', 'brighter', etc. than individual B. 'Intelligence' not as a common essence of a (biologically) normal human being, but as some kind  of alleged extra virtue or special attribute. There are universal valid concepts of being  'intelligent'  : i) knowledge of the moral law, or, knowledge of what should or should not be done,  knowledge of how one should treat other human beings and animals.  The organ of intelligence is empathy and compassion (durch Mitleid wissend...). Without empathy and compassion, without a firm knowledge of the absolute universality and inviolability of human and animal rights there is no way a human being could ever be considered 'intelligent', but rather  in this instance should be considered some kind of aberration and monster, a case of stunted development. ii) insight-wisdom in the practice of self-reflection into the nature of consciousness. iii) possession of skills which contribute to the common good and alleviation of suffering of human beings, animals and the environment.

We can say that genuine philosophy starts not so much with 'amazement' in itself but with compassion and horror at the malice and suffering of mankind and the desire to redress this state of affairs, and this includes understanding its causes. And the most important aspect of the philosophy of language is precisely that in which it is inseparably integrated into the science of consciousness.

 What we discuss in this post is the western monster concept of  'science'. 

In a nutshell: there are really only two species of authentic  'science': the science of consciousness, the philosophical psychology we have discussed previously,  and  the 'science'  (which we call welfare engineering, a primary example being medicine) whose primary goal is lessening the suffering and improving the lives not only of human beings but of all life (ethically guided medicine, engineering, history and other human sciences).   Human beings love to explore and travel and discover new worlds, and science can furnish the tools and vehicles for doing this but this tendency and activity in itself is not science, it is what science can serve.   Now purely theoretical and formal 'science' that abstracts from the conditions and needs of human beings and other living beings on this planet - and which is not concerned with the phenomenology of consciousness and psychotherapy -  has been vastly overrated, over-prized, overvalued as have the so-called abilities and achievements in it (the myth of the theoretical 'genius' who in reality is just an individual  payed and idolized by society to engage in games, hobbies and obsessions, often involving an amount of plagiarism,  with no true human, social or environmental value).  In ancient Greece beyond medicine and Thucydides welfare engineering was largely non-existent (before Archimedes and the Hellenistic era; however in an interesting passage Aristotle envisions the idea of tools which work by themselves).  And more importantly theoretical science,  the idea that man obtains fulfillment through an external knowledge which has no bearing on the welfare and life of living beings or any connection to the direct  phenomenological self-knowledge of consciousness aiming at personal liberation, clearly has its template in medieval scholasticism and the particular kind of historical, organized and revealed religion it served.  A whole new paradigm for the development of welfare engineering needs to be developed which emphasizes  collaboration and purges research from ulterior motives based on financial, social and personal gain as well as the poisonous ideology of competition and struggle or glorification of the  'entrepreneur'. There is also a vast new field of the archaeology of welfare engineering with regards to its presence in various historical cultures (even if not in a conscious conceptual form).

Perhaps welfare engineering is not the best term as we include under it also history and many of the human and social sciences. In fact historical analysis and research is the most important of all alongside medicine.  There are no 'sacred' or 'taboo' historical narratives, no narratives which cannot be questioned and concerning which documents, evidence and a rational reconstruction cannot and should not be demanded, no matter how much they are upheld and imposed by power and fear.  False narratives, myths in the service of power, domination, control and psychological oppression,  this is what Jung did not take into account.  Only through honest, objective and scientific historical research can human beings achieve psychological freedom and impartial justice be served.

Heidegger wrote much about truth and historicity yet according to Wolin's  'Heidegger in Ruins'  Heidegger engaged in deliberate falsification of his own manuscripts and uttered falsehoods regarding them. A liar and denialist of biographical history wrote about truth, human existence, historicity and forgetfulness !  We find the Heidegger-Husserl correspondence very depressing and the dreary pettiness of the corresponding academic milieu is striking ( itself a strong argument against academic philosophy), specially considering that these thinkers claimed to address huge transcendent questions about human history and existence.  Heidegger seems to have been rather duplicitous and ungrateful towards Husserl.  Heidegger was never a man to speak truth to power and defend the oppressed, rather for him power was truth and truth was power.  Someone has to say it: i) there is a lot of Nietzsche, Darwin and  racist pseudoscience in Heidegger, ii)  his philosophy is a secularized atheist variant of medieval scholasticism cloaked in the language of phenomenology. iii) it seems doubtful that there is any Heideggerian 'category' or 'analytics' that is not already found in Hegel's Phenomenology of Spirit and Science of Logic.  

The categories and analytics Heidegger sets up in Sein und Zeit in order to allegedly deconstruct metaphysics are precisely themselves those one learns to deconstruct in Buddhist philosophy and meditation.  Ontological pluralism and morality (compassion, non-harm, restraint) on the other hand cannot be deconstructed.  The way Heidegger approaches 'the question of being' is designed to invoke cosmic and existential anguish. But his 'question of being' is itself a  naturalistic opaque veil which can be viewed as hiding something else,  something  marvelous and wonderful. Even T.S. Eliot had a higher glimpse of this with his 'man cannot take too much reality'.  And: 'why is there something rather than nothing ?'  can be seen from a different perspective in light of the Mahâyâna doctrina of shûnyatâ. 

There is a structural analogy between philosophical psychology and welfare engineering; the Pali suttas abound with Indian medical terms and there is likewise a connection between ancient Greek medicine (where experimental and empirical methodology was present) and both Pyrrhonism and Stoicism.

Now there are two objections that easily present themselves:

i) cannot engineering and even medical research be used equally for immoral ends and for great harm ? How about advances in medicine which involve experimentation of animals ?  Or in general what about the misuse of engineering for the power and profit of a human group causing great harm to other human beings, animals and the environment ? So  why use the term 'welfare engineering' ?  

ii) does not progress in applied science, in engineering and medicine depend crucially on theoretical science and even on mathematics ?

iii) are you not espousing a kind of pragmatism for natural science which contradicts what Aristotle wrote in the beginning of the Metaphysics: all men have by nature the desire to know ? 

We will address i) in a future post (the pragmatism of engineering makes manifest its essential link to ethics and human consciousness, contrary to the cold hypocrisy of purely theoretical science).  We can also observe that there is a connection to the theory of magic and sacrifice in antiquity where, according to some, the gods were originally conceived as impersonal forces (either of nature, of consciousness, of both) which are governed likewise by fixed impersonal laws.  The magician or shaman or medicine man would then apply a corresponding technique in order to harness and direct these powers to obtain a certain goal.  The huge problem is when such techniques (ceremonial magic) were believed (in the most degenerate and barbaric cultures) to have to involve causing suffering or death to living beings (sacrifice) - something which can drastically contrast to the 'path of power'  found in the Pali texts, wherein  'magic'  powers are a direct result of personal spiritual attainment and have nothing do so with causing suffering to other beings.  We can certainly draw a parallel between the heinous presence of experimentation on animals in modern science  (whose justification often verges on sacrificial rhetoric) and such sacrificial magic.

   ii) is easy to answer. The fact of the matter is that the extent and depth of the purely theoretical and mathematical underpinnings of much of medicine and engineering have been grossly and drastically exaggerated.  Rather the legitimate and modest theoretical and formal apparatuses emerge naturally through the context of experimental feedback. It is as if somehow nature needed to say something and she somehow manages to say it in the most succinct and practical form, contrary to the shadowy, artificial and sickly proliferations of the theoreticians. The legitimate theoretical should be a tool for a tool, or rather a tool that should be designed to best operate on the tools of engineering.  As for iii) this ideal of pure knowledge is found in philosophical psychology. And Aristotle can be considered (despite the presence in his work of material of a different nature such as the De Anima) the founder of the monster of a purely theoretical and formal science divorced from engineering and welfare and divorced from a science of consciousness and phenomenology.  His theoretical science held back progress in applied and experimental science for centuries and helped justify misogyny, racism and colonialism. 

We have seen how core logic, arithmetic, computability, games and combinatorics form a closed interdependent circle (thus there is no reason to postulate the primacy of the 'logic' component, i.e. the one based on language) and how authentic logics come in families, the members of which mirror each other.  We have also seen how philosophical psychology espouses ontological pluralism and thus, without sacrificing the deep truths of phenomenism, phenomenology and the self-reflection and self-introspection of consciousness,  freely postulates the existence of a physical universe as well as a multitude of poles of conscious experience. Thus we can speak of an implicit 'order of the world' which encompasses both domains of consciousness experience and domains of physical existence as well as their relationship.  Logic is about bringing to light  the implicit unconscious order (which is also the order of the world and thus linked to praxis) of aspects of conscious thought, and as thus its task is always incomplete, its achievements partial. Logic in an extended sense is revealed in the structure and dynamics of the living activity of authentic science, there is no a priori armchair logic (a comparison might be made with some aspects of Adorno. Also we can address the issues Habermas raised regarding the focus on consciousness and the subject.).

Our philosophical methodology

It is a tendency for a structure which has found some partial practical use in a given context and situation to be extrapolated and applied to other situations and regions as well. In fact such a structure can become a preconceived category and part of a projected ontological system with claims of furnishing a more general  understanding of reality.  Contrary to what we have suggested previously it is extremely dubious that  common formal systems can have much direct relevance to our project of a philosophical psychology, that is, the project of recovering the first-person introspective science that had many remarkable developments in the 19th century (many of which appear in Husserl's Logical Investigations) and which later was tragically and wrongfully rejected or neglected (including by a hugely pretentious and destructive current of philosophy whose sole novelty was repeating obvious facts about language found in Saussure). We have discussed some important aspect of the project in previous posts, for instance how it should not be confused with subjective idealism and also the view adopted on the subject, the body and the physical world. The method pertaining to formal abstract research is completely distinct from that of such a philosophical psychology and indeed is antagonistic to it. The method required actually has more similarity with that of experimental science (cf. Hume's 'experimental method of reasoning') though obviously should not be confused with it.  Abstract formal concepts and methods should only come in after substantial progress has been made in philosophical psychology.  After pure introspective insight and knowledge has been gained (as explained before, it involves the detached awareness of the stream of inner verbal discourse and imagination, divided into its sensual species and their web,  perceived in its conceptual dimension as well and as proceeding from a fundamental process of identification), then through reminiscence the philosopher may be able to return and attempt to articulate this knowledge in the language of abstract formal computable systems (maybe the systems of consciousness has some similarity to the design of operating systems, themselves based on human social structure). Until then, natural language remains an imperfect but still amazingly flexible and serviceable tool. An analogy might be used from software development: first we must have a global systems theoretic intuition and idea of how the program is to be structured and work and then can be begin its concrete coding in a given language and platform. Or rather: first we must explore and view and know the mind first-hand and only afterwards can we use  known concrete systems  as tools or language to present an approximative model of the mind.  

It might be a very good thing to dissipate misunderstandings and distortions which would confuse this first-personal introspective methodology with that of psychoanalysis (i.e. Jung's analytic psychology), its theory of the unconscious and its proposed methods of exploration of the latter,  or with the method of the later of Husserl (we have in fact already discussed this in previous posts).  The problem with Jung revolves around the term 'religion'.  This is a large 'monster' vague concept which is incapable of definition and many partial, idealized and artificial aspects have been historically abstracted (or sanitized) to suit particular scientific, historical and philosophical theories. A question is: do we find in Jung the strange idea that religious beliefs, practices and narratives should be regarded as potentially psychological beneficial and therapeutic regardless of their objective historical, scientific, ethical and even social value and consequence ? Can we say that Jung diagnosed the modern age with 'lack of religion' and that he proposed a suitably adapted 'religion' as a cure  ? (the problem with Noll's famous book is that is mixes important factual material with more-or-less obvious intrusions of their author's own anthropological and historical ideology).  Or is the concept of 'religion' used by Jung a rather artificial idealized one that would lump together fundamentally heterogeneous things ? If the lover, the poet and all art involving creative imagination are interpreted as 'religious'  then this is clearly a very different sense of the term than the usual 'theological' and 'ecclesiastic' one (even if we take into account Hegel's lucubrations about the  'religion of art' of the Greeks and the similar Hellenism in the writings of Heidegger).  And what about 'initiatic' societies like Freemasonry ? And Jung's practice of analytic psychology itself ? For now we will pull out from the huge vague term 'religion' a single negative aspect (which links it strongly to the term 'cult') : that of passivity, surrender and dependence on a leader or group - in which is involved passivity with regards to aspects and manifestations of one's own psyche which cause lack of cognitive clarity and calm.  Passivity is of course a very difficult and complex term when applied to consciousness and in Pali buddhism 'passive' (in the sense usually translated as 'letting go' or 'detachment')  and 'active' aspects are combined in subtle and powerful ways.  Jung is  wrong in making an analogy between an alleged western 'extrovert' tendency to dominate the world and an eastern 'introvert'  tendency to dominate the psyche.  There is very little analogy between western material domination and the goal of original Buddhism which is ultimately not any kind of  'control' and 'domination': rather its mottos are know thyself and cure thyself.  An obvious enormous difference between our philosophical psychology and Jung is that imagination, dreams, symbols. images, myths etc. play a central role for Jung (and note the absurd importance allocated to 'gender' in  Jungian myths,  why cannot the sun be considered feminine as in ancient Japan, ancient Germanic and many other cultures ? ).  And such things are indeed found both in the original Pali texts and in Platonism - but what is really important is their function and attitude that is displayed towards them therein - and such function and attitude is quite different in Tibetan Buddhism (Jung was a keen reader of the Bardö Thodöl, though his personal library also included the editions of the Pali text society). Jung's interesting remarks on the salvation of the gods in Buddhism applies to Tibetan Buddhism. 

A very disturbing aspect of Jung (and Noll certainly identified this)  is that his ideas appear bound up with a kind of religious, cultural and even 'racial' conservatism, traditionalism which Noll amply elaborates on in function of  'völkisch'  blood-and-soil ideologies.  We find this aspect of Jung shallow, completely mistaken and  harmful, as is the theory of 'psychological types' applied to individuals and a fortiori to human groups such as the division between East and West or the imbecile pseudo-scientific theory of  races or cultures that could be 'aryan' and 'semitic',  terms only having meaning as linguistic classifications. Was Jung somehow ignorant that the ancestors of the most of the population of the Germany of his times consisted in a great portion of speakers of  Latin, Baltic, West Slavonic and Celtic alongside Germanic languages ?

Contrary to Jung we claim that cultural material that is factually erroneous, immoral and which causes psychological harm to oneself and to others,  does not deserve the slightest reverence or respect just for being 'tradition'  or being associated with one's ancestors or country. And that this certainly cannot be a positive basis for psychological and spiritual progress or self-knowledge. At worst it can be represent a kind of generational trauma - the 'collective unconscious' should be viewed as containing very negative things as well, things that were imprinted through the ages by religious authorities and their brainwashing .  Even on the historical plane so-called 'traditions' reveal themselves not to be continuous traditions at all, but materially triumphing aspects of a rugged process of bloody and ideological conflict with other equally historically legitimate 'traditions' which happen to have lost through many disparate circumstances and factors.

 What is truly rooted in our essence and represents our spiritual continuity, is the spirit of questioning, criticism, evaluation and potential liberation from all 'tradition', both the social-cultural structure of  the waking world and from all contingent  negative unconscious influence (which Jung would essentialize). Foucault, Guattari and Deleuze correctly hold that the true revolutionary spirit is as much about self-transformation as social transformation, but fall into error in not acknowledging that this spirit is itself a continuous and ancient tradition.

Maybe the 'collective unconscious'   of a given social group does not emerge according some dubious speculation about man's prehistory,  but is rather largely the product of the conscious creative power of special individuals.  Jung himself made a curious remark that India was not up to what the Buddha wanted to reveal and teach. 

Jung spent his life surrounded by the love and devotion of numerous women, from which he likely found a source of great spiritual and psychological energy.  Maybe we could say that he exploited the profound spiritual energies of these women in such a way as to deceive himself that he was a kind of  'solar hero' when in reality he was more like a moon surrounded by a constellation of suns. Not only does Jung seem to have a completely shallow, mistaken and uncritical account of gender and  the gendering of imaginary, mythical and religious figures but we question if in Jung we find a good theory of the numinous object of consciousness at all, and in particular in the context of the whole process of the experience of eros and beauty.  Does Jung offer us a phenomenology of the modes of presentation and functions of an 'object-person' of imaginative consciousness which yet is perceived to 'be'  a known real being  or else a person of religious narratives - and the phenomenology of why particular object-image-persons are chosen, preferred, come to dominate consciousness in a numinous revelatory manner, and how these can become (including through certain spiritual practices) the initiatic vehicles for achieving higher states of consciousness and spiritual realization ?

Contrary to Jung, we have argued extensively for the profound affinity - even almost identity - between the philosophy and spirit of original Pali Buddhism and that of ancient Greek philosophy, and this correspondence and affinity certainly extends to later Buddhist philosophy and later modern Western philosophy as well. Thus we can say that original Pali Buddhism represents to lost soul, essence and root of what is best in Western humanity, provided we pay special attention to its knowledge of the universality and unconditionality of the duty of compassion and non-harm with regards to all human beings and animals. The collective unconscious of Western humanity itself needs to be healed and regenerated in the pure life-giving waters of the critical and revolutionary spirit at once new and ancient.  A very important aspect involves the study and investigations of ancient Europe (and its links to Druidism, ancient Greece and the regions in which original Buddhism developed) and the dispelling once and for all of the harmful myths or partial truths regarding our ancestors which are patent in Jung . The furor Teutonicus, the cult of *Wōðanaz  are unoriginal foreign elements borrowed from the warlike tribal gods of the Eurasian steppe nomads as patent from Beckwith's extensive book on the Silk Road; on the other hand the seeresses and prophetesses of some Germanic tribes as recounted by Roman historians were actually Druidic. Without going into this subject, we remark that the Old Turkic script and the Futhark are strikingly similar.  We attach great importance to the proof of the historical, cultural and philosophical affinity and continuity between Greco-Roman antiquity and ancient Celtic speakers (and perhaps even the culture of the Megalithic monuments). Many of the Germanic speaking tribes seem to have been at the cross-roads between the Buddhist-Greco-Roman-Celtic light of humanity and civilization and the shamanic war-god and war-retinue culture of the Eurasian steppes (which is associated to Mongolian and Turkic speaking peoples and is not in any way a specifically  'Indo-European'  religion). In the territory of what is now Germany there is a powerful substrate of Western Slavs and Balts alongside the older Celtic component which may be associated to manifestations of higher philosophy and spirituality in Germany (and similar considerations can be made for Great Britain).   The Celtic genetic and cultural influence in Iceland is very large and we can speculate that likewise the genetic and cultural influence of the Sámi on historical Scandinavia has been extensive, though in what can be reconstructed of  'Viking culture' (the object of ridiculous distortions and fantasies in popular culture) we find a strong presence of the Nietzschean war-and-conquest-based values and culture of the Eurasian Mongolian and Turkic  steppe nomads (cf. the ancient mingling of the Goths and the Huns).

The reason we focused on original Buddhism is because of its profoundly philosophical nature (it is not a 'religion' in the common sense of this term)  and its close correspondence to much of what is best in ancient and modern western philosophy and philosophical psychology (thus refuting again and again the idea of an essential distinction between east and west).  Nor do we wish to suggest that original Buddhism exhausts ancient wisdom and valid spiritual practices (one need but glance at the Yoga-Sutra of Patanjali, the works of Plato or Plotinus to see their variety and complementarity). Also note that the speculations above on ancient peoples (a topic which deserves many books) should be taken as based primarily on ethical, religious, cultural and linguistic divisions without implying any kind of genetic or 'racial'  reductionism or essentialism.  In a future post we will address all the standard criticism concerning 'cultural appropriation' and allegedly taking the artificial restricted secular view of western scholarship regarding the Pali texts, ignoring the actual living traditions of the Theravada, etc.

We need not only a typology but a systematic pathology of spiritual traditions, religions and cultures.  Not simply a linear scale between the poles of purity, spirituality, interiority, morality, universality,  'philosophicality', humanism and all their opposites, but an understanding of how pathological religions and cultures branch into many different and apparently distinct forms while preserving the same underlying negative essence.  Thus we need to understand better what a tribalist, sacrifice-based, violent, colonialist, genocidal,  fear-based culture and religion is and not be mislead by classifications like patriarchal and matriarchal or confuse  corrupted forms of certain cultures and religions with traces of or naturalistic disfigurements of something more ancient and pure.  Pure religion pertains to the science of consciousness (either solitary or through the transfiguring/manifesting path of spiritual love and communion) and morality and not to the natural world other than as an object of love and compassion and aesthetic numinous transfiguration. It is inconceivable that concepts like 'caste' or 'race'  should have any validity or role therein. 

In other words,  any 'higher' or 'pure' religion (if we can even use this term)  is essentially and solely about i) the science of consciousness, about self-analysis and self-awareness of consciousness ultimately achieving  a liberated super-consciousness, and ii) the transcendental unfolding of the possibility of human love.  Its foundation is intelligence of the moral law and empathy and compassion.  It has absolutely nothing to do with 'gods' (beyond an imaginative-symbolic function or as representing possible states of human consciousness).   Although we can certainly conceive of other beings analogous to humans or even in some sense 'superior' beings existing in other worlds or planes of existence,  attaching a religious significance to a relationship (worship, faith, sacrifice, prayer, rites, etc) to such beings (the number being immaterial, though having a single tyrant god is worse) is a serious aberration. 

We hope to prove that the history of cultures and religions does not exhibit anything like a linear progress from so-called 'primitive' (animistic, naturalistic, war and fertility based,  etc.) to so-called 'advanced' religions (as if any religion that can justify cruelty to human beings and animals, bloodshed and genocide could ever deserve the designation 'advanced'....) but rather a complex multi-cyclic decay from higher to lower followed by partial restorations of the higher. 

Evidence can be adduced from the history of India in which many traditions which exhibit certain key 'higher' non-theistic traits are very ancient - Yoga (to a certain extent), Nyâya, Vaisheshika, Samkhya, Pali Buddhism, Jainism,....  Note that in ancient Greece we have already have as far back as  the 5th century Leucippus and the ethics of  Democritus (said to have traveled extensively and learnt from various now lost traditions) and Plato's critique of religion in books 2 and 3 of the Republic and concept of the transcendent good, which surely is just a transmission of Pythagorean philosophy which, according to Ovid, completely rejected animal sacrifice. And of extraordinary interest is Confucionism and the amazing literature of Ch'an and Zen as well as the earlier highly sophisticated Mahâyâna philosophical texts: all these appears to contain powerful and complex articulations of a pure science of consciousness and well as a more-or-less explicit rejection of religion (cf. Hui Hai: the sage seeks the Mind not the Buddha, etc.). Maybe some mysterious ancient people, with some connection to Manicheism and Zoroasterianism, is behind both Mahâyâna and ancient Chinese culture.  

There are also some special 'divinities' which express something higher, older and non-theistic, the union between the science of consciousness and the moral and cosmic order of the world: such are certain ancient luminous feminine figures incarnating divine wisdom, light, life, compassion and cosmic order (which also feature prominently in Mahâyâna and Vajrayâna): for instance the ancient figured of Aredvi Sura Anahita and Daena for the Persians,  Nut for the ancient Egyptians,  Athena for the ancient Greeks and  to a certain extent Sophia and Barbelo of the so-called 'gnostic literature (the origin of the Hag Nammadi library is completely obscure, but it very likely includes  transmissions of now lost later Egyptian, Phoenician, Syrian and Chaldean traditions alongside other type of material).

It can furthermore be speculated  that many ancient 'theogonies'  (as well as perhaps emanationist and gnostic-type cosmologies) were initially symbolic-mythic expressions of pure philosophical and scientific theories of consciousness (like the paticcasamupadda and the system of samkhya, specially as interpreted by the excellent book by Mikel Burley, 2007) which in themselves had no more 'religious' significance than the categories of Kant. It is tragic that so much of the science and philosophy of the ancient world has been lost (Thracians, Chaldeans, Syrians, Phoenicians, Egyptians, Berbers, Druids,...or lost civilizations like Tartessos.).

All this again shows a most profound difference from Jung. It is laughable and displays a blind colonialist hubris to say that modern western man is on the average more 'rational' or 'logical' than other parts of humanity (historical and present). The machines modern man uses are products of controlled 'rational' thought, but modern western man per se ,  with all his capitalist fetishes and commodities,  is likely far less 'rational' and 'logical' (forgetting for a moment the problem of clarification of such monster concepts) than the average for this planet (historical and present). The smartphone is a product of the  'rational', the mental life of the personal buying and using it,  mostly not. Also there is not the slightest evidence that human beings at any period in time did not have naturally a form of consciousness containing what Jung calls the 'ego'. Another profound difference regards  Jung's theory of the 'libido' which is a grotesque distortion of the platonic and neoplatonic theory of the erôs, a primordial substance and power (prior and infinitely more vast than biological sexuality)  which allows spiritual realization through a mediating and transfiguring spiritual communion with another person - that erôs and its pure independent religion and creative imagination (the love story as the the pleroma and cycle of archetypes)  has  been degraded (naturalized, biologized and sexualized), concealed,  slandered, appropriated, inappropriately gendered,  imprisoned by historical power structures and their myths and narratives.  

Following Hegel we can see the development of art, literature and drama in ancient Greece as having (through the self-discovery of the freedom of the creative imagination dissolving religion and prefiguring the science of consciousness, which Jung did not seem to understand )  a parallel significance to that of the spiritual culture of philosophy.  This is what inspired Shelley to write Prometheus Unbound.  Indeed this development in ancient Greek literature manifests the spiritual interpretation and transfiguration of nature  which is irreconcilable with corrupt religious cults.

The modern and post-modern world seems heavily based on 'false forks', pairs of linked vague concepts which function like twin semantic whirlpools forcing the mind into two of equally false and harmful options. Forked concepts contain two components which appear opposed and even unconnected while in reality sharing the same life-blood, function and essence.  Forked concepts are 'false flag concepts' and correspond to 'every accusation is a confession',  one side accuses the other of the exact same thing that that side in reality is guilty of. Each side presents the other side as being the only possible alternative.  It is a strawmanning of the negation.  Forked concepts are standard parts of the apologetic arsenal of organized religions and cults. 

The considerations set forth in this post did not succeed in slaying the slimy multi-headed hydra of the monster concept 'religion'.  Why can't we just use the sense of 'religion' in which 'religion' is clearly essentially false and evil (historically, socially, culturally, scientifically, philosophically, psychologically, spiritually) and in the sense in which 'religion' totally perverts, appropriates and hijacks ethics and morality.  The most evil kinds of religions, the ones steeped in bloodshed, cruelty, ignorance, racism and deceit,  are ones based on a supreme fetish: a collection of texts, a 'race', a narrative, a rite, an organization or a caste,  and in making pacts for worldly ends through blood and sacrifice to one or more capricious immoral beings (whose activity is limited to war, sex,  quarreling, food and enjoying sacrifices) allegedly controlling the natural world and subsisting independently from human consciousness. And in cultures unfortunately dominated by such 'religions',   often a kind of semi-science of consciousness develops (which in some cultures and historical epochs is designated by the (universal) religion of love, the science of love, science of the heart)   -  although compromised by the enveloping religion and its harmful psychological conditioning.  The leaders of these religions as a rule make the ridiculous claim that such struggling science of consciousness its rooted in their 'religion' and does not make sense independently of it - when the science of consciousness and morality are more ancient than religion and not only independent from it but radically incompatible with it ! And today this is the great danger and error of parapsychology (the study of NDEs, OBEs and other phenomena) and so-called 'transpersonal' psychology: falsely presenting such data as lending credence to 'religions' (in particular the religion of the person undergoing such experiences) when the reality is exactly the opposite.  Note that we have discussed the science of consciousness both in its pure solid form and in a more problematic  'relational' form based on a platonic theory of love (the first form is far superior because for instance it does not depend on external contingent circumstances).  And is this not what Jung is all about, reviving and lending credibility to religion ?

Human law must be founded on human rights, the universal moral law.  It is a monstrosity to found law on religion.

The fork: religion is a human cultural construction, the product of the worst instincts, impulses and ideas mankind has to offer (or in which one small social group has used to control, terrorize and exploit others).  But exactly the same instincts, impulses and ideas can be given apparently non-religious and equally bad materialistic and pseudo-scientific form. This is the key to understanding the history of the last three hundred years.

Tossing Algebraic Flowers down the Great Divide (contains extensive bibliography of the papers of Joseph Goguen)

 https://cseweb.ucsd.edu/~goguen/pps/tcs97.pdf

We are working on a github repo with the collected papers of Goguen (just as has already been done for Lawvere).

In the 21st century among the 'algebraic flowers'  (in Goguen's sense of post-structuralist structuralism embodied in the applications of category theoretic and algebraic models in computer science to cognitive science, concept analysis,  cognitive linguistics  and other human sciences) we can include also  topos theory (see Olivia Caramello, Ontologies, knowledge representations and Grothendieck toposes, joint talk with Laurent Lafforgue) , homotopy theory (and higher category theory in general) and homotopy type theory.  Voevodsky constructed a model for dependent type theory based on simplicial sets. William Troiani wrote a master's thesis about 'Simplicial Sets are Algorithms'.

We took a look at the slides of Olivia Caramello's talk Ontologies, knowledge representations and Grothendieck toposes. The very interesting philosophical interpretation given to classifying toposes is good reason to investigate her work more closely. Along the way there occurred some research ideas:

i) Does the correspondence between geometric theories and classifying toposes form an institution (in the sense of Joseph Goguen) ?
ii) Can the concept of the classifying topos of a theory be extended to theories with models in non-grothendieck toposes such as the realizability topos ?
iii) Can we characterize theories whose syntactic toposes have a (non-trivial) structure of a triangulated category and more generally can we say more about the relevance of cohomology to logic ?

On the philosophical side: Consider our paper on the concept of continuity in Aristotle. Aristotle does not view space as being constituted by points, rather his notion is closer to that of a locale or a site. In an unpublished note we suggested that Aristotle's theory of the dependence between space, time and motion could be modeled with functors between sites and that the 'continuity' of motion is expressed by these functors preserving covers. We think it is fascinating that cover preserving functors appear also in the treatment of categorical logic.

On the mutual interpretation between category theory and Hegel's science of logic (which is inspired by, but also distinct from, that of Lawvere and the material available on this subject on nlab).   For the section on Essence (Wesen) we have some considerations on modern physics, specially relativity and gauge transformations,  but we find that this philosophy of classifying toposes as bridges provides to be the best interpretation of Essence vs. Appearance and the idea of a unifying conceptual system.

From cognitive science through category theory to philosophy and psychotherapy

We seek a satisfactory philosophy of mind based fundamentally on first-person introspection (on consciousness itself) which includes likewise a theory of concepts and language based on meaning and consciousness (but which nevertheless is an open ontological pluralism, rather than a strict subjective idealism).  The organization of semantic memory will play an important role.  We find that there is much valuable material found for this project to be found in the selection from work in cognitive psychology (with an important component of Gestalt psychology) expounded by John Sowa in his book Conceptual Structures. This work extends and consolidates many important past philosophical traditions.

However such a philosophy of mind has much to gain (methodologically) from the framework of general systems theory and specially from its embodiment in computer science - all this without emplying per se any kind of (neuro)physicalist reductionism/parallelism/functionalism.  But category theoretic methods should play a central role in a truly scientific and philosophical general systems theory and computer science based approach to cognitive psychology and specially a theory of concepts and language.  Foundational to this project is the work of Joseph Goguen and William Lawvere. Thus for example we attach great importance to categorical approaches to type theory, to institutions and Goguen's systems theoretic applications of sheaf theory (and hence topos theory).  It is also interesting to explore the applicability of higher category theory and monoidal categories (which has an elegant application to quantum security protocols).  Higher category theory and homotopy theory emerge naturally from ordinary category theory (cf. there is a canonical model structure on the category of small categories: the homotopy category makes equivalences of categories actual category theoretic isomorphisms, that is, we are considering the category of structures).  A vital aspect of category theory is that it allows to capture simultaneously the bottom up and top down aspects of complex concurrent systems - important both in the study of consciousness and in computer systems (machine code vs. high-level languages). A problem with category theory is its dependency on the category of sets, something that is not really overcome in enriched category theory, higher category theory, internal category theory, etc.

But this categorical systems theoretic approach based on cognitive science is essentially a first-person intuitive introspective approach to psychology and the philosophy of mind and a continuation of a rich philosophical heritage.  Its ultimate aim is soteriological (or psychotherapeutical)  and identical in spirit and goal to original Buddhism:  it is by direct scientific knowledge of consciousness that we are led to be able to let go and be free.  However the psychology which can be found in the earliest substrate of the Pali canon which has been meticulously studied by Sue Hamilton in her 1995 book Identity and Experience is difficult to grasp due to its laconic incompleteness and many fundamental terms are used in different ways depending on context.  It is clear that it is the spirit and meaning which was essential and that a more complete and thorough first-person based psychology was achieved  by practitioners of the various buddhist traditions throughout the centuries and by the best insights and work of the western tradition of philosophy and psychology. 

Raga and dvesha are grouped together in the Pali texts according to the profoundest insight: the greatest danger involves engaging in ardent detachment from things attached to, loved, which cause suffering - and not being equally careful to avoid the subtle cultivation of hate, aversion, resentment, anger, etc. towards the same object (cf. eros and thanatos linked together in a circle). Both desire and aversion must be overcome at once in regards to the object and replaced with equanimity and joyful pure detachment.

The expressions 'living in the moment', 'mindfulness' and those involving the 'now' have made their way into popular discourse. However these are very superficial and distorted ways of looking at some profound philosophical and scientific truths regarding consciousness: that the flow of consciousness includes the concurrency and interrelated streams of inner verbal discourse and inner visual imagination together with associated feelings and desire, all in complex feedback. This flow of consciousness is at the same time a kind of directed dynamic deployment of the storehouse of our network of concepts. Becoming progressively aware of this flux as it is nakedly in itself and observing it in a progressively detached manner - leads to its eventual cessation or transfiguration (inner silence, inner emptyness) into a timeless beautiful present.  This awareness extends to a deeper level, to the fundamental structure and dynamics behind the whole process of consciousness - and it is this that is to be the primary object (this shows the subtle but profound difference from standard phenomenology).  The whole process and field of consciousness is perceived to be the result of a certain direction and distortion at this fundamental level - something which is also reversible by focused attention and practice.

The nature of this detached and happy consciousness is not necessarily either that of a 'subject'  or a 'soul' in the rationalist and scholastic sense (which, be it noted, is quite a distinct conception from neoplatonic and even original aristotelian theory). The power over one's own mind is completely heterodox and is incommensurable with social power dynamics, in fact, this power is precisely the renunciation of all will of domination over others.

Our project employs a methodological neutrality or epokhê (cf. the ontological pluralism) and aims to be essentially a science of consciousness as  it appears and is in itself and not a form of subjective or absolute idealism, philosophy of nature, metaphysics or theology.  However we are radically opposed to and dedicated to the refutation of any form of psychology or philosophy of mind that rejects the foundational role of first-person conscious experience and any linguistic theory or philosophy of language which rejects the fundamental role of consciously apprehended meaning and its connection to concepts (see A. Wierzbicka's Semantic Primes and Universals for an account of the situation of much of 20th century linguistics); like Sowa we understand that there can be complex conceptual yet non-linguistic thought. It is precisely the rejection of consciousness or its essential nature or innate dimensions which is the true foundation of historical oppression, domination and totalitarianism.

Later on we will discuss the deep connection to ethics and how our approach involves a knowledge of the unity of consciousness and thus of physically separated /individuated consciousnesses.

We will discuss later how are approach relates to theories of symbolism and dream interpretation. 

And the unethical and deceptive character of those who write mathematics books which are not dedicated to clarity, precision and respect for the reader.

There are Mahâyâna sutras which suggest a higher 'physics' of consciousness analogous to modern 'unified theories' such as quantum gravity, supersymmetry, string theory, etc. but we are unable to say more about this at the moment. And indeed the natural (non-conscious) universe may be analogous to the conscious experience of some 'cosmic mind'  which in turn may be associated to some unknown super-natural universe. The kind of idealism this involves might be thought of the 'greater mysteries' and we are not concerned with it in this blog.

The truth of phenomenism and subjective idealism does not contradict the existence of a physical realm, only that this realm, the more it is considered in its pure objectivity, as it is in itself independent and distinct from our psychological (mis)representations, the less it can be considered a cause of suffering: what causes suffering is the naive realism of the projections and ontology of our own mental life (its fabrications and drama it stirs up  and constructs out of impersonal mathematically discrete non-sensual sense data). Likewise the existence of other poles of psychological experience outside ourselves is not rejected. Though consciousness and the physical can influence each other, each is what it is in itself and no other, the alleged physical in and by and of the mental is really just the mental, nothing more: the mental is in reality just the mental, not a world, and the physical is just the physical, not what the mental takes it to be (later on we shall touch upon how this relates to the problem of truth, certainty and a priori knowledge).

In desire there is both the constituted desiring subject as well as the constituted desired object. It is a great mistake to only concentrate on the constitution of the object and thereby to falsely hypostatize the desiring subject as a kind of substrate. Rather the two are bound up and raveled together; to entangle oneself from one means entangling oneself from the other.

Let us recapitulate on some important points:

i) We do not have direct access to things of the world but only to presentations of and in the mind. This is an unconscious illusion.

ii) Point i) does not however entail in any way that extra-mental beings do not exist.

iii) Mental contents are also imbued with a sense of self and of being mine when in reality they are just as self-less and impersonal as our conception of the natural world.

List of my papers and writings (published or available online)

Category Theory  

M. Clarence Protin, Pedro Resende, Quantales of open groupoids. J. Noncommut. Geom. 6 (2012), no. 2, pp. 199–247

Logic and Type Theory

M. Clarence Protin, Type inhabitation of atomic polymorphism is undecidable, Journal of Logic and Computation, Volume 31, Issue 2, March 2021, Pages 416–425, https://doi.org/10.1093/logcom/exaa090

M. Clarence Protin ; Gilda Ferreira - Typability and Type Inference in Atomic Polymorphism, lmcs:7417 - Logical Methods in Computer Science, August 12, 2022, Volume 18, Issue 3 - https://doi.org/10.46298/lmcs-18(3:22)2022

Combinatory Intensional Logic: Formal foundations

 
On the Various Translations between Classical, Intuitionistic and Linear Logic (with P. Oliva e G. Ferreira), Ann. Pure and App. Logic (2025)

Introduction to Pylog

 

Philosophy of Logic and Language

 (This is one of my main interests: see most posts in the present blog Philosophical Monologues)

On proper names, sense and self-reference. Constructivist Foundations 20(2): 82–84. https://constructivist.info/20/2/082

On Analyticity and the A Priori

Inquiry into the nature of Kant's Logic in the CPR

Aristotle's Organon 

Protin, C. L. (2022). A Logic for Aristotle’s Modal Syllogistic. History and Philosophy of Logic, 44(3), 225–246. https://doi.org/10.1080/01445340.2022.2107382

Modern Definition and Ancient Definition

Aristotle's Second-Order Logic


History and Philosophy of Topology


Clarence Lewis Protin, Modern incarnations of the Aristotelian concepts of Continuum and Topos, in Intentio Nº 4 (2024), ISSN : 2679–4462, ISBN : 978–2–494988–03–3.

Hegel and Modern Topology


Stoicism


Commentary on Bobzien and Shogry's Stoic Logic and Multiple Generality

Stoic Logic and Dependent Type Theory

Philosophy of Epictetus 

Pali Buddhism and Western philosophy


Aristotle's Analysis of Consciousness and Pali Buddhism

Hegel

Commentary on the section on Verstellung in Hegel's Phenomenology of Spirit

Philosophical General Systems Theory

What is a System ?

Systems Theory

Some topics in the philosophy of nature (draft for the article below)

Differential models, computability and beyond

Ethics, political philosophy, history and anthropology

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.