24 March 2014

Continuum and Time: Weyl after Heidegger

A new study is out:

Continuum and Time:
Weyl after Heidegger


The mathematician, Hermann Weyl, struggles in his 1918 book, Das Kontinuum, with the antinomies of the real number continuum, seeking a phenomenal basis in the subjective intuition of inner-time which, however, he ultimately rejects. Retrieving Aristotle on time and Heidegger on three-dimensional, ecstatic time offers an alternative path beyond Weyl. A bit of mathematics is required along the way.

1. Interest in Weyl's work on the continuum 

2. Attempt to break out from inside consciousness: intersubjectivity

 3. Time and continuum according to Aristotle 

  4. Dedekind's attempt at grounding the real number continuum

5. The mathematical continuum recast 

5.1 A recast real continuum R
5.2 Arithmetic operations on R
5.3 Continuity of functions on R
5.4 Differentiability of continuous functions on R

6. Indeterminacy of movement and time

7. Clock-time and three-dimensional, ecstatic time

8. References

9. Notes

19 March 2014

Elimination of time

It is very consistent on the part of those who believe absolutely in mathematics to eliminate time from the equations of motion to produce a so-called ‘block theory’ of the universe. However, does a mathematical trick to eliminate the variable, t, — as numerous physicists and philosophers of science (such as Julian Barbour, Huw Price et al.) propose — amount to convincingly eliminating the phenomenon of time as an illusion?
Or is it the other way round: Is the mathematical conception of time as real, linear variable a tendentious crudity made for the sake of calculating movement and change of all kinds? If the latter, then it is mathematics that is delusional about the phenomenon of time we all experience with every move we and anything else makes.
In my view, modern science and its appendant analytic philosophy are driven by an absolute will to efficient power over movement and change.
The now long-held absolute belief in mathematics as THE key to the secrets of the universe (cf. e.g. the Big Bang theory and the Large Hadron Collider) makes modern science blind. Against the foil of the recent publication of Heidegger's Black Notebooks and the outpourings of vitriol it has occasioned (see my blog entry: Heidegger Back in Black), I find it ironic that this absolute belief allows a founding forefather of analytic philosophy, Gottlob Frege, to pass as a great and creative thinker in the area of mathematical logic (which he doubtless was) without the least qualms with regard to his reactionary political views and deep anti-Semitism. It was Frege who introduced formalism to the foundations of mathematics, which amounts to asserting that logic and mathematics can be conceived as purely analytic truths, independently of any reference to intuitions of phenomena in the world, in particular, to the phenomenon of TIME.
It seems to me that philosophers of all ilks today are still incapable and unwilling to fathom the momentousness of mathematized linear time, including its elimination as a mere real variable in a set of equations.

17 March 2014

Heidegger Back in Black

In my 1996 study, Heidegger's Hölderlin and John Cage, published also in Italian in Rome in 2000, I pose several questions, including the following:
"Does the historical 'matchlessness' ('Einzigartigkeit',  Heidegger) of National Socialism consist in German being having destroyed itself in an orgy of self-annihilation? Was the attempted annihilation of the Jews the successful suicide of Germany, i.e. German being, as an independent historical magnitude?"
"Is it not, properly speaking, the German spirit that dissolved in the smoke of the stacks at Auschwitz? Is the genocide committed on the Jews at the same time the suicide of the Germans historically?"
Such questions concern not just Heidegger's thinking, but the historical German Geist itself. 


Apart from more thoughtful reflections from commentators such as Peter Trawny and Jonathan Rée, the comments posted in response to articles in The Guardian, Prospect Magazine and elsewhere show that Heidegger's Back in Black with the Schwarzen Heften is apparently a welcome opportunity for many to engage in renewed thoughtless bashing.

So what's new?

In 1941 Heidegger notes in his Black Notebook: "World Jewry, stirred up by the emigrants let out of Germany, is everywhere intangible and, despite all its expansion of power, does not need to participate in military actions anywhere, whereas we are left with having to sacrifice the best blood of the best of our own people." (my translation)

Disturbing, nationalistically ugly.


I share Jonathan Rée's critical attitude toward Heidegger's thinking. To be critical means to distinguish (from Gk. _krinein_), in this case, the philosophically invaluable from the untenable and worthless and even downright repugnant.

That so much affective vitriol is stimulated by the name 'Heidegger' in Pavlovian response indicates obliquely that something is at stake here.

If I had to boil down the message of Heidegger's 1927 opus magnum, 'Being and Time', I'd say, "Being means time" and "Time is the open clearing of absencing and presencing". Today's mainstream philosophical and scientific thinking is not up to speed on this, remaining content with the washing-line of linear time on which to hang its effective causality between beings, and viciously repudiating any philosophical attempt to rethink time after two-and-a-half millennia.

Heidegger's detractors like to make fun of him by mockingly citing, out of context, sentences such as, "The world worlds". To them I reply: 

What about the mathematically exact statement of the continuity of motion, namely:
"Motion is continuous at time t' if, for any positive epsilon, there is a positive delta such that for all t on the real time-line closer to t' than delta, position f(t) is closer to f(t') than epsilon."? 

Now, isn't that a fine joke and absurdity to mull over?

10 February 2014

Subject loses control, turns cannibal

The modern age, starting with Descartes, cast human being as subjectivity. Human beings were posited by Descartes' "cogito ergo sum" as the sub-ject of all that is and, in particular, of everything that moves, changes. The modern mathematized sciences, starting with physics, were and are out to predict and control all kinds of movement, both natural and social. All beings were cast as ob-jects 'thrown over against' the subject as the fundamentum inconcussum, the unshakeable foundation.

The subject has long since lost its under-lying status and its grip on the world's movements, but still suffers from the delusion that, at least in principle, it could keep everything under control. Its mind is still fixated on effectivity and on the effective, efficient control of movement, especially of the inexorable life-movement of mortals toward death..

Already in the mid-nineteenth century, Marx thinks through the movement of specifically capitalist society, uncovering that in the capitalist economy the subject becomes the object of the movement of reified value, demoted to player in the gainful game, each of whom strives for income, under the fascination of the fetishism of the game's universally desirable goal (cf. Capital and Technology: Marx and Heidegger Chap. 7).
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Max Weber investigates sociologically the rise of the nation state as the sovereign subject over a territory and its subjects. These subjected subjects become increasingly entangled in the ever-burgeoning bureaucratic web of regulations and in legal fights over mere words in documents through which the state attempts to rule its subjects more or less fairly and manage the affairs of society. The _logoi_ of the law and litigation become ever more complex and intransparent in the attempt to come to terms with and so regulate how people live their lives with one another. The legislative and the litigious _logos_ both fall short in world-understanding.

This impotency of the _logos_ in a social context is just one aspect of its limitations, which cannot be seen sociologically, but only by entering the realm of simple philosophical questions, i.e. the question concerning the locus of truth. Since Plato and Aristotle, and through to today's analytic philosophy, truth is located unquestioningly in the proposition, the statement, the apophantic _logos_, which can be either true or false, i.e. adequate or inadequate to what it is trying to say. The truth of the world, however, is its disclosure, which is seen, understood, intuited by existing in it. Situations can be interpreted appositely without their being put into words. Hence the distinction between the apophantic As and the hermeneutic As (cf. Sein und Zeit).

The shortfall of the logos in saying the world compared to looking at and sensing it interpretively is akin to the disjunction between the discrete and the continuous in mathematics, a disjunction not seamlessly papered over even to the present day (cf. e.g. the perplexing, unresolved Continuum Hypothesis). The _logoi_ are discrete and countable, like the natural and the rational numbers, whereas the world of movement and change is continuous and real, outstripping discrete, logical rationality, and thus irrational in the double sense of exceeding the power of the logos to gather and say, and exceeding also the power of rational, countable numbers to gather the irrational reals, that can be defined mathematically only as the unattainable limit of a rational, countable sequence that remains forever withheld from actual presence. The irrationality of the real numbers corresponds to the 'irrational' unsayability of an attunement with the world that can be resonated with and understood nevertheless (cf. 'Digital Being, the Real Continuum, the Rational and the Irrational').

In the context of politics and society, this implies that an ethics which relies solely on the rational logos necessarily will fall short, because it misses the atmosphere of an ethos that is sensed socially in the attunement with a situation. Above all, it is how people estimate and esteem each other in the manifold transactions of their daily lives that determines the resonating, 'musical' atmosphere of a given society's ethos.

Nevertheless, the democratic subject-citizens clamour to be cared for more and more by the 'advanced' social-welfare state, thus relegating responsibility for their own lives to the democratic state's power plays, in particular, between left and right. In this relegation, the ethical atmosphere becomes especially strifeful and wordy, supplanting an ethos of everyday worldsharing. The democratic We is more or less successful in setting the world up so that it is cared for by caring institutions that rule it. Since democratic politics is driven by mass egoism of the 'people' wanting more and more, and democratic political representatives as politicians necessarily strive for election and re-election, promises to care-for become inflationary, and this is regarded as social progress. Not only does the democratic subject's dependency on the (now: social welfare) state grow, but sovereign debt balloons to the detriment of yet unborn generations (cf. my Social Ontology).

Heidegger's retrieval of the implicitly productive, efficient nature of the key concepts of metaphysical thinking, starting with Plato and Aristotle, has opened deep insights into the tunnel vision of Western thinking through to today's modern science. Science and technology today become the agents through which the world is kept moving and controlled according to criteria of effectivity. In this constellation of how the world opens up to the mind, the subject becomes ultimately mere functionary in the functioning, efficient set-up. The set-up and the gainful game intermesh in an endless striving to enhance productivity and efficiency, thus minimizing costs for the sake of gain. And this inexorable drive is celebrated as enabling more and more people to enjoy the fruits of modern technology, all the way through to, and including especially, increasing longevity.

The modern mathematized sciences result from a wedding between the _logos_ and the _arithmos_ (number), both of which are countably discrete. In the Cartesian cast of the being of beings, the mathematical _arithmos_ is prescribed as the mode of access to the world, whose movement, however, is continuous. The marriage of _logos_ and _arithmos_ is consummated in discrete, countable digitization. The logos becomes 'nothing other than' a number, i.e. a digital bit-string. Moreover, as Turing discovered, such digital _logoi_ can copulate with each other, thus producing step by step, i.e. algorithmically, further bit-strings that in turn have cybernetic effects in the world (cf. 'Turing's cyberworld of timelessly copulating bit-strings'). Human understanding of a given situation can now be translated from words into the bit-strings of an algorithm that can be outsourced to a computer (i.e. a universal Turing machine) which then processes data (further bit-strings) to produce digital results that serve in some fashion to control the world's movement (cf. The Digital Cast of Being).

The outsourcing of the algorithmic arithmologos into computing systems of all kinds for the sake of the enormous productive convenience of users, however, turns on the human subjects, who thus become increasingly entangled in that digitized web of Turing machines emerging today ever more conspicuously as the cyberworld (cf. Digital Whoness: Identity, Privacy and Freedom in the Cyberworld). Henceforth, the subjects' cybernetic servants confront the subjects more and more as their dictatorial masters, demanding conformity with their algorithms and conditions of operation.

The end-game in the scientific mathematization of the world, along with a narrowing of the mind's horizons, is its culmination in neuroscience. Arrived at this apex, the subject cannibalizes itself. Human being is well underway toward obliterating its mind as exposure to the three-dimensional time-clearing. The subject no longer thinks and perceives, but rather its brain does, so that cogito ergo sum becomes meaningless. 'I am' = 'I think' or 'I perceive' comes to mean 'the brain's neurons inside my skull are processing, computing informational sense data'.  What you sense, feel and think is then 'nothing other than' the neuronal activity of some specific region of your brain. Who I am, who you are becomes a queer illusion unmasked by neuroscience. Ditto for human freedom. Through the brain's being conceived, or rather cast, as some kind of complicated computer based on neuronal firing, there is no longer any barrier to intermeshing the brain (i.e. the cogitating subject) with the cyberworld. As a first approximation, the subject is cast as some kind of as yet imperfectly understood, boggling, universal Turing machine. What doesn't fit with this scientific model is discarded as ineffective.

Mind blind going forward = unfreedom.

07 February 2014

Ereignis and the issue of freedom

I suppose even Ereignis can become a flogged dead horse, although we haven't gone quite that far yet. You can look at historico-political events -- say, of the 1930s -- from the perspective of Ereignis, by which I mean, from the perspective of the "step back" from metaphysics, but Ereignis itself cannot be thought from these events because it has to be thought first of all in its own right as a stage in grappling with the deepest issues in Western thought itself. So, on the one hand, Nazism can be viewed through the metaphysics of Nietzschean will to power but, on the other hand, will to power characterizes the entire epoch of subjectivist metaphysics starting with Descartes (its seed lying already in Aristotle's ontology of 'powerful', 'efficient' movement/change). The will comes more and more to the fore in the metaphysics of Descartes, Leibniz, Schelling, Schopenhauer, and finally Nietzsche.

With cogito ergo sum Descartes posits human being AS subjectivity. Henceforth the human being under-lies all movement/change, and strives to master all movement/change through modern (mathematized) scientific means. On THAT score, National Socialism and the caring welfare state are the same. To differentiate between the two, as a thinker, you cannot simply proceed self-evidently from your own 'liberal' or 'progressive' political convictions, criticizing Heidegger's anti-modern anti-liberalism along the way. Rather, the issue of FREEDOM is posed philosophically and it has to be penetratingly asked wherein free human being lies as a (possible, future) historical mode of worldsharing. That freedom and democracy are usually treated as synonyms these days is a scandalously complacent thoughtlessness, in my view. If human being 'gets over' ('verwindet' rather than 'überwindet', 'overcomes') being the under-lying subject of all presencing and absencing in stepping back from the metaphysical will to effective power in linear time, what could freedom look like in the open, three-dimensional free play of the time-clearing?

First version posted on the An und für sich blog.

The issue of freedom in worldsharing is dealt with in more detail in my Social Ontology.

05 February 2014

Niall Ferguson "Wir löschen unseren Erfolg"

Der Abdruck von Niall Fergusons Vortrag 'Wir löschen unseren Erfolg' in Die Zeit. vom 08.05.2013 ist lesenswert. Der Historiker zeigt auf sechs Schlüsselphänomene in der Entwicklung des Westens, die er auf "bestimmte Ideen, vor allem aber die Institutionen, die diese Ideen vorantrieben", zurückführt. Aus philosophischer Perspektive gebe auch ich "bestimmten Ideen" den Vorzug, die aber von viel weiter als dem 16. Jh. herkommen. Sie sind nämlich griechischen Ursprungs.

Die Idee der Freiheit (_eleutheria_) überhaupt ist mit den Griechen und ihren internen und externen (vor allem mit den Persern) Freiheitskämpfen entstanden. So wurde zum ersten Mal auch mit einer Herrschaftsform wie Demokratie experimentiert, worin die freien Bürger mit- und gegeneinander streben, ihre öffentlichen Angelegenheiten (res publica) zu regeln und zwar auf der Agora, die zugleich Marktplatz und Versammlungsplatz der Bürger war. Dort wurde also gehandelt und verhandelt in zweierlei Sinn und so sowohl Dinge als auch Menschen bezüglich ihres Werts in einem 
laufenden Wertschätzspiel eingeschätzt.

Die andere Idee entstammt der Bemühung in der von den Griechen 'erfundenen' Philosophie über Jahrhunderte -- angefangen mit Parmenides und Herakleitos -- mit dem Phänomen der Bewegung bzw. der Veränderung klar zu kommen. Diese vielfachen Bemühungen kulminierten schließlich in Aristoteles' Bestimmung der ontologischen Struktur der Bewegung als herstellender, produktiver, effizienter Bewegung durch die Kernbegriffe _dynamis_, _energeia_ und _entelecheia_. Es war gerade dieses Verständnis von Bewegung bzw. Veränderung, das 
dann im 17. Jh. vor allem von Descartes und Newton mathematisiert wurde, und so die Entstehung der modernen mathematischen Wissenschaften -- angefangen mit der Physik -- ermöglichte. Dieses Wissen -- in Technologie übersetzt -- hat geführt und führt heute immer noch sowohl in den Naturwissenschaften aber auch in den Sozialwissenschaften zur Explosion der Wirksamkeit, der Produktivität, der Herrschaft über Bewegungen jedweder Art.

Diese beiden Grundideen des Westens entfalteten in zwei 'Konstellationen' bzw. hermeneutische Weltentwürfe, einerseits in das von Heidegger genannte Gestell und andererseits in das von mir genannte Gewinnst. Diese beiden
Konstellationen verschränken sich wiederum in dem, was ich das Gegriff nenne (siehe mein Kapital und Technik: Marx und Heidegger, Kap. 7).

Heute freilich ist der ganze Erdball im Griff des Gegriffs. Ob die Chinesen den Westen an Wirksamkeit überholen, ist eine wichtige Frage im Zusammenhang mit der Überlegung, ob die Europäer mittlerweile viel zu sehr selbstzufrieden mit ihren Institutionen -- vor allem mit dem fürsorgenden, inzwischen schuldenbeladenen Sozialstaat -- geworden sind. 


Eine andere Frage allerdings ist, ob wir durch philosophische Theorie (Gk. _theorein_ heißt 'anschauen, betrachten') erst mal sehen lernen, wie es dazu kommen konnte, daß die Wirksamkeit und der "Erfolg" so eindimensional in der heutigen Welt, und zwar global, als die Kriterien schlechthin gelten. Dann ergäben sich vielleicht andere Möglichkeiten, die Welt zu entwerfen.  

Agamben's (mis-)interpretation of Ereignis

In Giorgio Agamben's Homo Sacer there is the following passage:

“This is the direction in which the late Heidegger seems to move, if still insufficiently, with the idea of a final event or appropriation (Ereignis) in which what is appropriated is Being itself, that is, the principle that had until then determined beings in different epochs and historical figures. This means that with the Ereignis (as with the Hegelian Absolute in Kojève’s reading), the 'history of Being comes to an end' (Heidegger Zur Sache des Denkens p. 44), and the relation between Being and being consequently finds its 'absolution'. This is why Heidegger can write that with the Ereignis he is trying to think 'Being without regard to the being,' which amounts to nothing less than attempting to think the ontological difference no longer as a relation, and Being and being beyond every form of a connection.”


It's right to point out the risk of relapsing into old metaphysical habits of thought. But there's no danger of this if you keep your wits about you. I don't find anything about "absolution" on p.44 of Zur Sache des Denkens, but there is mention there of the history of being coming to an end. This must be so once the step back from being thought as the beingness of beings is taken to the giving of being itself. The step back is a matter of learning to see something new that metaphysics was unable to see explicitly. It did not see the intimate connection between being and time, and had recourse instead to an _idea tou agathou_, a summum ens or the like conceived as Ur-Sache, i.e. as primal thing. Hence the fatal ambiguity of Metaphysics from the start as ontology (the investigation of _to on haei on_), on the one hand, and as _epistaemae theologikae_ (theological knowledge), on the other.

 In any case, Agamben muddies the waters by characterizing Ereignis as a "final event or appropriation (Ereignis) in which what is appropriated is Being itself". The propriation that eventuates is that of being itself and human being to each other. Since being itself is Anwesen (presencing), which unfolds as the three-dimensional time-clearing of the Da, it's equivalent to say that the Da and Dasein are enpropriated to each other; they belong to and need each other. This is the retrieval (Wieder-Holung) and re-sending of Parmenides' message: "For minding and presencing are the same." (Frag. III) (Cf. my 'Out of your mind?  Parmenides' message'.)

Ereignis is the abyssal (groundless), hidden (_laethae_) It that gives. Its giving is twofold. Firstly it "reaches" the three-dimensional interplay of the ecstasies of time to each other through to human being itself. The Da as the interplay of presencing and absencing impacts, affects human beings, rendering them as Dasein. Secondly, It gives the respective hermeneutic As of each historical epoch which defines AS what or who presents present themselves in the Da (time-clearing).

Is Heidegger "attempting to think the ontological difference no longer as a relation, and Being and being beyond every form of a connection," as Agamben claims? No. Why not? Because the ontological difference is now thought as the sending of the historical casts (the hermeneutic As in the plural) of the presencing of presents, and hence still as a "relation", but seen differently. This sending can only eventuate within the open time-clearing of the Da to which Dasein belongs and which in turn needs Dasein.

Agamben is off on a wild goose chase insofar as he wants to 'explain' the thinking of Ereignis from the ontic political situation of the 1930s. Such explanations are worth nothing for issues of phenomenological thinking which is grappling with those simplest thoughts through which history is shaped decisively, definitively. Phenomenological thinking is thus a 're-vising', a 're-seeing' of these sendings of historical casts, a learning to see what we already see unthinkingly, in order to re-cast a more appropriate hermeneutic As into the future that may arrive one day. Any attempt to 'explain' phenomenological  thinking politically is misguided, since the political itself as an historical way of worldsharing is itself a phenomenological-hermeneutic question. Therefore, you have to enter this hermeneutical circle to gain clarity about the political. In the West, this question concerns the historical issue of (the possibility of) FREEDOM in worldsharing.