Nihilism Now! Monsters of Energy by Keith Ansell Pearson and Diane Morgan

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Blurb: Have we had enough? But enough of what exactly? Of our mourning and melancholia? Of postmodern narcissism? Of our depressive illness and anxieties of not ‘being there’ any longer? Enough of enough! We now ask: what of the future of the human and of the future of the future? Is it now possible to produce revitalised ways of thinking and modes of existing that have digested the demand for transhuman overcomings and so are able to navi- gate new horizons of virtual becoming? Is it possible to save thought from its current degenerative and vegetative state at the hands of a smug and cosy postmodern academicism? Can we still invent new concepts?

If one follows certain influential contemporary accounts, it would appear as if the experience and question of nihilism have become passé. Is not the urgency informing the question of the `now’ of nihilism redundant and otiose? For Jean Baudrillard, for example, there is now only the simulation of a realised nihilism and little remains of a possible nihilism (a nihilism of the possible) in theory. In relation to previous forms of nihilism ± romanticism, surrealism and dadaism ± we find ourselves in an ‘insoluble position’. Our nihilism today is neither aesthetic nor political. The apocalypse is over, its time has gone and lies behind us:

The apocalypse is finished, today it is the precession of the neutral, of the forms of the neutral and of indifference. (Baudrillard)

Baudrillard goes on to make the claim, terrifying in its full import, that all that remains is a ‘fascination’ for these indifferent forms and for the operation of the system that annihilates us.

Surely, Baudrillard is being ironic when he claims that this mode of nihilism is our current ‘passion’? How can one be passionate about indifference and one’s own annihilation? As Baudrillard acknowledges, this is the nihilism of the observer and accepter. It is the nihilism of the passive nihilist who no longer aspires towards a transcendence or overcoming of the human (condition), but who simply announces and enjoys its disappearance, the spectator watching the spectacle of his own demise. History, politics, metaphysics, have all reached their terminal point, and willing nothingness appears to be the only desire of the will available to the post-modern mind:

The dialectic stage, the critical stage is empty. There is no more stage . . . The masses themselves are caught up in a gigantic process of inertia through acceleration. They are this excrescent, devouring, process that annihilates all growth and all surplus meaning. They are this circuit short- circuited by a monstrous finality. (Baudrillard)

Diane Morgan and Keith Ansell Pearson Nihilism Now Monsters of Energy

Categorial Logic – Paracompleteness versus Paraconsistency. Thought of the Day 46.2

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The fact that logic is content-dependent opens a new horizon concerning the relationship of logic to ontology (or objectology). Although the classical concepts of a priori and a posteriori propositions (or judgments) has lately become rather blurred, there is an undeniable fact: it is certain that the far origin of mathematics is based on empirical practical knowledge, but nobody can claim that higher mathematics is empirical.

Thanks to category theory, it is an established fact that some sort of very important logical systems: the classical and the intuitionistic (with all its axiomatically enriched subsystems), can be interpreted through topoi. And these possibility permits to consider topoi, be it in a Noneist or in a Platonist way, as universes, that is, as ontologies or as objectologies. Now, the association of a topos with its correspondent ontology (or objectology) is quite different from the association of theoretical terms with empirical concepts. Within the frame of a physical theory, if a new fact is discovered in the laboratory, it must be explained through logical deduction (with the due initial conditions and some other details). If a logical conclusion is inferred from the fundamental hypotheses, it must be corroborated through empirical observation. And if the corroboration fails, the theory must be readjusted or even rejected.

In the case of categorial logic, the situation has some similarity with the former case; but we must be careful not to be influenced by apparent coincidences. If we add, as an axiom, the tertium non datur to the formalized intuitionistic logic we obtain classical logic. That is, we can formally pass from the one to the other, just by adding or suppressing the tertium. This fact could induce us to think that, just as in physics, if a logical theory, let’s say, intuitionistic logic, cannot include a true proposition, then its axioms must be readjusted, to make it possible to include it among its theorems. But there is a radical difference: in the semantics of intuitionistic logic, and of any logic, the point of departure is not a set of hypothetical propositions that must be corroborated through experiment; it is a set of propositions that are true under some interpretation. This set can be axiomatic or it can consist in rules of inference, but the theorems of the system are not submitted to verification. The derived propositions are just true, and nothing more. The logician surely tries to find new true propositions but, when they are found (through some effective method, that can be intuitive, as it is in Gödel’s theorem) there are only three possible cases: they can be formally derivable, they can be formally underivable, they can be formally neither derivable nor underivable, that is, undecidable. But undecidability does not induce the logician to readjust or to reject the theory. Nobody tries to add axioms or to diminish them. In physics, when we are handling a theory T, and a new describable phenomenon is found that cannot be deduced from the axioms (plus initial or some other conditions), T must be readjusted or even rejected. A classical logician will never think of changing the axioms or rules of inference of classical logic because it is undecidable. And an intuitionist logician would not care at all to add the tertium to the axioms of Heyting’s system because it cannot be derived within it.

The foregoing considerations sufficiently show that in logic and mathematics there is something that, with full right, can be called “a priori“. And although, as we have said, we must acknowledge that the concepts of a priori and a posteriori are not clear-cut, in some cases, we can rightly speak of synthetical a priori knowledge. For instance, the Gödel’s proposition that affirms its own underivabilty is synthetical and a priori. But there are other propositions, for instance, mathematical induction, that can also be considered as synthetical and a priori. And a great deal of mathematical definitions, that are not abbreviations, are synthetical. For instance, the definition of a monoid action is synthetical (and, of course, a priori) because the concept of a monoid does not have among its characterizing traits the concept of an action, and vice versa.

Categorial logic is, the deepest knowledge of logic that has ever been achieved. But its scope does not encompass the whole field of logic. There are other kinds of logic that are also important and, if we intend to know, as much as possible, what logic is and how it is related to mathematics and ontology (or objectology), we must pay attention to them. From a mathematical and a philosophical point of view, the most important logical non-paracomplete systems are the paraconsistent ones. These systems are something like a dual to paracomplete logics. They are employed in inconsistent theories without producing triviality (in this sense also relevant logics are paraconsistent). In intuitionist logic there are interpretations that, with respect to some topoi, include two false contradictory propositions; whereas in paraconsistent systems we can find interpretations in which there are two contradictory true propositions.

There is, though, a difference between paracompleteness and paraconsistency. Insofar as mathematics is concerned, paracomplete systems had to be coined to cope with very deep problems. The paraconsistent ones, on the other hand, although they have been applied with success to mathematical theories, were conceived for purely philosophical and, in some cases, even for political and ideological motivations. The common point of them all was the need to construe a logical system able to cope with contradictions. That means: to have at one’s disposal a deductive method which offered the possibility of deducing consistent conclusions from inconsistent premisses. Of course, the inconsistency of the premisses had to comply with some (although very wide) conditions to avoid triviality. But these conditions made it possible to cope with paradoxes or antinomies with precision and mathematical sense.

But, philosophically, paraconsistent logic has another very important property: it is used in a spontaneous way to formalize the naive set theory, that is, the kind of theory that pre-Zermelian mathematicians had always employed. And it is, no doubt, important to try to develop mathematics within the frame of naive, spontaneous, mathematical thought, without falling into the artificiality of modern set theory. The formalization of the naive way of mathematical thinking, although every formalization is unavoidably artificial, has opened the possibility of coping with dialectical thought.

Chinese Philosophical Pythagoreanism. Thought of the Day 14.0

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The universe is just like a right-angled triangle of standard unit. The two right-angle sides oppose each other and yet also complement each other like quantum entanglement. They superpose and counterbalance each other in a system. They grow and decline, but identically equal to “1”. From this perspective, the Traditional Yin-and-Yang Double Fish Diagram and the core idea behind it is counterbalance and unity of opposites, a geometric expression of “being of beings” and an illustration of the ground of “being”, or the “being” in “being of beings”, the “one” in “one is all”. It roots in the Pythagorean Theorem and goes beyond the Pythagorean Theorem. It illustrates the idea in the Euler Equation:

e·e−iθ =(cosθ + isinθ (cosθ − isinθ) = cos2θ + sin2θ = 1),

and has opened the door of relativity, expressing the key idea of Fuzzy Set in modern mathematics developed in contemporary and modern times. “If each right-angled side multiple itself, the sum will be the square of hypotenuse. The extracted root is hypotenuse”. Thus, the xian (in Chinese meaning either “hypotenuse” or “profound”) is “profound” because we don’t understand the principle and add too much mysterious explanations to it.

This reminds us of the “Needham question”, why didn’t science rise in China? And the emotional sigh of Mr. Liang Shumin, “The Chinese culture is a pre-matured one of mankind.” In a material desire-pursuing physical world, metaphysics is so lonely and with- ering. As Heidegger pointed out, truth is hardly acceptable just because it’s too simple. Facing the rapidly-changing advancement of science, we need inquire with earnestness and reflect with self-practice, and ask ourselves whether we need “lead people to perfection” and “having known where to reset at the end, one will be able to determine the object of pursuit”, and try our best to “return to things themselves”; Facing the cultural flourishing, whether we should keep to the original intention of “speech” and come back to the original point of language.

Facing the complicated world, human beings need another renaissance to search, keep and return to the “1” to create “a community of common destiny”. The philosophical element of traditional Chinese culture and the dialectical unity of Marxism could make continuing contributions to the aim since whether ancient or modern, Chinese or foreign, arts or sciences, they must be “unified” in basic principle of the universe.