We present here very briefly some aspects of our larger philosophical project (in continuation of our previous posts). Here are the main points:
1. Finitism and constructivism are not modern developments but represent the main current of the ancient philosophy of mathematics. And in the modern age its fathers should be considered to be Leibniz, Kant, Krause, Schopenhauer and Gauss (among others). Proclus' philosophy of mathematics as expounded in his commentary on the first book of Euclid (and its accompanying epistemology and philosophy of mind) are by and large not original but a transmission of much older material in the finitist and constructivist tradition, for instance Iamblichus, Porphyry and much earlier, Geminus and Eudemus.
2. Proclus and 5th-century neoplatonism represent a fundamental corruption and distortion not only of the original school of Ammonius Saccas, Plotinus and Porphyry (and to a certain extent Jamblichus) but the original teachings of Platonism, the Peripatetics and the Stoics. Proclus's dogmas ontologically and epistemically downgrade the human soul, imprison it to deny it access to higher modes of being and knowledge and thus betray the fundamental truth regarding the ultimate essence and possibility of the human soul, clearly articulated in Plato and the Enneads. The flawed destiny of neoplatonism is plausible linked to its failure to take up and incorporate the higher developments in ancient logic which were indubitably attested in Chrysippus, Galen and Boethius. Proclus was trained as a lawyer and rhetorician, not a logician. The Elements of Theology are, with regards to their pretense of exhibiting a logical-deductive form, are a farce, much like the Ethics of Spinoza.
3. Our most radical and doubtlessly disturbing claim - which nevertheless finds a definite echo in Plato, Plotinus, Kant, Hegel and to a larger degree in Schopenhauer - involves the inseparability of theoretical and practical reason. We question if the term "intelligence" denotes anything precise and objective and if much that is encompassed by this term should not really be considered humanly worthless and even contemptible. That is to say, human so-called "rational" activity based on claims of being independent or abstracted from a moral and spiritual dimension and goal should be considered as lacking any value whatsoever. In particular its very epistemic, semantic and ontological claims should be radically challenged. And this is precisely the highest function of philosophical logic, finitism and constructivism and one of the key interests of the philosophy of Schopenhauer.
4. A child that grows up in a war-torn area, experiences abuse, imprisonment, hunger, famine, sickness, the death of parents, friends, relatives and animals, is a million times more "intelligent", a million times a greater knower of what the reality of life-experience is, a million times nobler and a greater partaker of being, a million times more capable of compassion and of directly knowing the fundamental aspects of reality, than an arrogant, heartless, shallow, selfish, insignificant, humanly ignorant, "professor", grown up in the lap of material, luxury, self-delusion, flattery and conceit, that monkeys around without any metaphysical understanding with language and symbol games. One cannot divorce true intelligence, true knowledge, from morality, moral knowledge and spiritual transformation. Profane immoral reason is a deception and delusion which believes in nonsense like completed infinities or non-constructive and non-intuitively verifiable entities and inferences. Language is a social engineering tool riddled with vague, ambiguous terms. Brouwer and a certain linguistic circle to which he belonged were keenly aware of the immoral and socially manipulate aspects of language. This is our reading of Kant and Schopenhauer: intelligence and morality are one. Or in the ancient Pali texts: by one's deeds is one a Brahmin.
5. Legitimate reason, good reason, inseparable from morality and illumined by the higher light of transcendental knowledge, has two aspects. That which leads to progress in engineering and medicine and is thus an incarnation of compassion, and the sword of philosophical logic - effecting a universal ultrafinitist and constructivist critique of all mathematics, science and language. It is in this way that we should trace Pyrrhonism (and possibly Hume if we believe Gopnik) to their Buddhist roots. But philosophical logic also has a complementary positive philosophical role in unveiling the genetic constitution of logic, computation and legitimate finitary constsructive mathematics as well as Platonically unveiling their connection to inner and higher levels of being and cognition.
Regarding the first aspect there is a question which nobody wants to answer: what is the minimal essential mathematical apparatus strictly required for all the positive beneficient achievements in the world in engineering and medicine? In other words, can we give numerical analysis a finitist computationalist foundation?
Regards the second aspect it is important to point out that this universal critique is based on the possibility of a finitist and computational interpretation or transformation of the mathematics in question (as in the work of Kohlenbach), not a superficial rejection in the style of Kronecker.
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