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.
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