Mathesis

[English version below]

In seinen Vorlesungen im Sommersemester 1925 schreibt Martin Heidegger im Hinblick auf Husserls bahnbrechende Logische Untersuchungen (1900/1901), die so wichtig für sein eigenes Verständnis und Lernen der phänomenologischen Methode waren:

"Ungewohnter und ganz gegen die übliche Art zu philosophieren, ist die Weise der Durchdringung und Aneignung, die das Werk fordert. Es hat einen durchgehenden untersuchenden Gang; es verlangt schrittweise, ausdrücklich anschauliche Vergegenwärtigung und kontrollierende Ausweisung dessen, wovon gehandelt wird. Man kann also nicht [...] einfach Resultate herausnehmen..." Gesamtausgabe Band 20 Prolegomena zur Geschichte des Zeitbegriffs GA20:32.

Nicht zufällig war Husserl zuerst ein Mathematiker, der unter dem entscheidenden Einfluß von Franz von Brentano zur Philosophie übergewechselt ist. Die mathematische Sprache selbst ist eine arbeitende Sprache, die verlangt, daß der Lernende jeden einzelnen Schritt in der Gedankenführung mitvollzieht. Sonst lernt man nichts, sondern bekommt höchstens einen äußerlichen Eindruck von dem, was der Gedankengang selbst zur Erscheinung bringt. So neigen auch die meisten philosophischen Gelehrten dazu, über die Phänomene oder gar bloß über Philosophennamen zu reden, statt von den Phänomenen selbst her zu denken.

Das Wort 'Mathematik' stammt vom altgriechischen _mathaesis_ 'Lernen' und ist also weiter als die Mathematik im engeren Sinn als Wissenschaft etwa von geometrischer Figur und Zahl. Für das philosophische Denken hat das zur Folge, daß auch die Philosophie die "schrittweise, ausdrücklich anschauliche Vergegenwärtigung und kontrollierende Ausweisung dessen, wovon gehandelt wird," verlangt. Das ist anstrengend, aber es sichert einen klaren Blick auf die Phänomene selbst. Die phänomenologische Methode ist Denkweg, der die "Anstrengung des Begriffs" (Hegel) fordert. Bekanntlich war auch Hegel Phänomenologe.

Umgekehrt bedeutet dies, daß diejenigen, die sich vor der "Anstrengung des Begriffs", d.h. der schrittweise arbeitenden, entbergenden Mathesis, scheuen, lediglich einer Selbsttäuschung unterliegen bloß meinend, daß sie philosophieren. Diese Selbsttäuschung ist die Regel unter den 'professionellen Philosophen', weshalb es nur äußerst selten einen Denker gibt. Denn jeder Denker, der echt lernend denkt, geht stets zurück in die tiefsten, noch ungeprüften Vorverständnisse bzw. —  stets stillschweigend verborgenen —  Voraussetzungen seiner philosophischen Vorgänger, um sie genauer zu prüfen und gegebenenfalls zu revidieren. Philosophisches Denken ist in erster Linie die schrittweise Arbeit des Abbaus von verdeckenden Vorurteilen. Die Philosophie befreit, indem der/die Philosophierende durch begriffliche Arbeit lernt, klarer zu sehen. Somit steht jede Philosophie auch stets der Kritik offen.

Vertiefende Lektüre: Martin Heidegger Gesamtausgabe Bd. 20 Prolegomena zur Geschichte des Zeitbegriffs.

English version:

In his lectures in the summer semester of 1925, Martin Heidegger writes with regard to Husserl's trail-blazing Logical Investigations (1900/1901) that were so important for his own understanding and learning of the phenomenological method:

"More unusual and completely contrary to the usual way of philosophizing is the mode of penetrating and appropriating demanded by the work. It has a thoroughgoing investigative path; it demands a step-wise, expressly clear bringing-to-presence and scrutinizing demonstration of the subject dealt with. Hence you cannot simply take out results..." Prolegomena to a History of the Concept of Time Gesamtausgabe Band 20.

It is no accident that Husserl was first a mathematician who, under the decisive influence of Franz von Brentano, switched over to philosophy. Mathematical language itself is a working language demanding that the one learning follows every single step in the train of thoughts. Otherwise you learn nothing, but at the most get only a superficial impression of what the path of thinking itself brings to manifestation. Thus, even most philosophical scholars tend to speak about phenomena or even merely about philosopher-names, instead of thinking from the phenomena themselves.

The word 'mathematics' stems from ancient Greek _matheasis_, signifying 'learning', and is thus broader in meaning than mathematics in the narrower sense as, say, the science of geometrical figure and number. For philosophical thinking this has the consequence that philosophy, too, demands "a step-wise, expressly clear bringing-to-presence and scrutinizing demonstration of the subject dealt with". This is strenuous, but it secures a clear view of the phenomena themselves. The phenomenological method is a path of thinking demanding the "strenuousness of the concept" (Hegel). As is well-known, Hegel, too, was a phenomenologist.

This means conversely that those who avoid the "strenuousness of the concept", i.e.  step-wise working, revealing learning, only fall foul of self-deception, merely opining that they are philosophizing. This self-deception is the rule among the 'professional philosophers', for which reason genuine thinkers are extremely rare, for every thinker who thinks in a genuinely learning fashion always goes backwards into the deepest, as yet unexamined preconceptions and — invariably tacit, hidden — presuppositions of his or her philosophical predecessors in order to examine them more closely and, if necessary, to revise them. Philosophical thinking is primarily the step-wise work of demolishing prejudices that cover up. Philosophy is liberating in that, through conceptual work. the one philosophizing learns to see more clearly. Thus every philosophy is also always open to critique.

Further reading: Martin Heidegger History of the Concept of Time - Prolegomena

Gesamtausgabe Band 20, English translation T. Kisiel.

Gedankenlosigkeit empirisch erfahren

In Antwort auf meine beiden letzten Blogeinträge zum Positivismus, Russell und Heidegger hat sich ein angeblicher Freund des Denkens, der die philosophische Auseinandersetzung mit mir nicht fortsetzen will, mit einem Kommentar bei mir gemeldet, den man sich denkerisch auf der Zunge zergehen lassen sollte:

"Ich bringe den Text [in der eMail ME] auch als vage Reaktion auf Deine Positionen von zuletzt zum Messkircher und dem Positivismus. Dass Ersterer weder auf die konkrete Einschreibung von Isarkraftwerken noch von Atombomben je einging, macht ihn so irrelevant, urteilsunfähig. Die abstrakte Klage über den metaphysischen Niedergang hilft da gar nichts. Man muss schon für ein wenig mehr begehrensökonomische Einbindung sorgen, soll‘s nicht im Paralleluniversum verpuffen."

Diese Antwort hat meinen Widerspruch hervorgerufen, und zwar aus Gründen, die ich hier kurz angeben will:

Was beinhaltet der Vorwurf, daß der Meßkircher Heidegger "weder auf die konkrete Einschreibung von Isarkraftwerken noch von Atombomben je einging"? Lassen wir die "Isarkraftwerke" beiseite, im von mir zitierten Text Heideggers geht er gerade als Denker auf die "Wasserstoffbomben" ein. Was heißt "konkrete Einschreibung"? Heißt es: die Wasserstoffbomben ontisch in ihrer unermesslichen Zerstörungskraft genommen? Heidegger geht gerade darauf ein, um dann in einem zweiten Schritt auf eine noch größere Gefahr hinzuweisen, die jenseits des ontisch genommenen Seienden (etwa, einer Atombombe) in der Differenz zwischen dem Seienden und dem Sein, d.h. in der sogenannten ontologischen Differenz, liegt. Diese Gefahr kann nur gesehen werden, solange philosophisch diese ontologische Differenz — die seit Platon viele Namen getragen hat etwa: _idea_, _to on haei on_ ('das Seiende als Seiendes', Aristoteles), Spekulation (Hegel) — sichtbar bleibt. Und gerade die positivistisch-analytische Philosophie (neben der heutigen, immer noch Cartesisch-geprägten französischer Philosophie) ist es, die diese ontologische Differenz mit aller denkarmen Gewalt zum Verschwinden gebracht hat. 

Mein Freund des Denkens paraphrasiert diesen Aufruf zum Denken Heieggers als "abstrakte Klage über den metaphysischen Niedergang" und empfiehlt stattdessen, "begehrensökonomische Einbindung". Was aber besagt dies? Eine ontisch-soziologisch-politische Betrachtungsweise? Wohl ja, denn in einem längeren Teil seiner eMail geht es um "koloniale und postkoloniale" kapitalistische Ausbeutung in Afrika und der Karibik — also wird ein konkreter, linkskritischer Blick auf real-existierende Ausbeutungsverhältnisse eingefordert. Dagegen wird das, was Heidegger mit dem Vorwurf der Gedankenlosigkeit unserer Zeit einfordert, als "abstrakte Klage" abgetan, und zwar ohne sich darüber philosophische Gedanken zu machen, worin die Gefahr für die Menschheit besteht, daß sie nur noch fähig ist, die Welt ontisch, d.h. positivistisch, zu verstehen. Wie überall im heutigen Alltags- und Mediendiskurs reicht schon das vorurteilsbeladene Wort "abstrakt", um angeblich kritische Arbeit zu tun. Das heißt aber, daß dieser Freund des Denkens gerade jene Gedankenlosigkeit gedankenlos praktiziert, die von Heidegger angesprochen wird, um eben seine Zuhörer nachdenklich zu stimmen. 

Der Vorwurf einer bloß "abstrakten Klage" will auch sagen, daß man damit lediglich in einem "Paralleluniversum" landet. Somit wird beim uralten Vorurteil und der Fehleinschätzung stehengeblieben, daß das philosophische Denken fürs praktische Leben und für die Sorgen und Kämpfe der Menschen nichts bringt. Mir scheint, daß dieser Freund des Denkens nicht nur nicht weiß, was philosophisches Denken ist (es erfordert nämlich die "Anstrengung des Begriffs" (Hegel)), sondern noch schlimmer, daß er nicht bereit war noch ist, philosophisches Denken zu lernen. Mit dieser Haltung ist er keineswegs allein und er weiß auch nichts von seinem abgründigen Selbstbetrug. Stattdessen Abwehr auf sogenannt kritischem Feuilletonniveau.

Positivism & freedom's extinction

The rise and consolidation of positivism in the latter half of the 19th century signalled the death knell of philosophy and with it the extinction of human being AS such as a matter for thought. Encyclopaedia Brittanica provides a succinct definition: "The basic affirmations of positivism are (1) that all knowledge ... is based on the 'positive' data of experience and (2) that beyond the realm of fact is that of pure logic and pure mathematics. ... On the negative and critical side, the positivists became noted for their repudiation of metaphysics — i.e., of speculation regarding the nature of reality that radically goes beyond any possible evidence  that could either support or refute such 'transcendent' knowledge claims."

This positivist stance was associated initially with Auguste Comte, the founder of sociology, the social science that like no other serves as an Ersatz for philosophy today. It proceeded, via a detour resuscitating Kant as a mere epistemologist, to the logical positivism of the Vienna Circle and the early Wittgenstein who, in turn, served as the go-between enabling the merger between positivism and today's hegemonic analytic philosophy first announced by Russell and Whitehead at the turn of the twentieth century. Positivist-analytic philosophy is that mode of modern Western thinking which has capitulated to modern mathematico-empirical science. Facts (empirical data) are good. So are formal logic and mathematics. What's bad is metaphysical speculation. The very word, 'speculation', becomes with positivism a term of abuse for unfounded, and thus fanciful, ideas. Originally, however, 'speculatio' was the Latin rendering of Greek _theoria_ as practised by Aristotle in his Metaphysics: the inquiry into _to on haei on_, into beings AS beings. Both terms, 'speculatio' and _theoria_ derive from roots meaning 'to look'. Philosophically meant originally learning to look closely at the apparently most self-evident phenomena.

What positivist-analytic philosophy understands by metaphysics as "'transcendent' knowledge claims" is most often understood as speculation about a transcendent being beyond the physical called God. This speculation about the divine is what interested Christian theology from the outset in its appropriation and distorting adaptation of Aristotle's thinking. In turn, the transition from medieval philosophy, which is basically Christian theology, to the Modern Age, was a centuries-long philosophical struggle against theological thinking in favour of empirical evidence for knowledge gathered and mathematically processed by the modern human being cast AS the underlying subject of all knowledge. Philosophy becomes at core epistemology. With this shift in Western thinking, the original Greek meaning of 'subject', i.e. the _hypokeimenon_ that presents itself to view to be addressed AS such by humans, is turned upside down. The original Greek subject becomes the object of modern subjective experience in interior consciousness! Today this world-shaking inversion as such has long since been forgotten and suppressed.  All modern philosophy since Descartes via Kant to positivist analytic philosophy is philosophy of subjective consciousness vis-à-vis an external, objective world. The single exception is Heidegger's thinking which  — how could it be otherwise when power is at stake? — is vituperatively denounced and forcefully suppressed employing all contumelious means available. Consciousness replaces that which was known to Greek thinking as _psychae_ and _nous_, L.: 'anima' and 'mens'.

Positivist-analytic philosophy is oblivious to the ambiguity inherent in Aristotle's Metaphysics, whose latter part deals with _epistaemae theologikae_, i.e. theological knowledge. The former, major part of Metaphysics investigates _physei onta_, i.e. physical beings themselves, not any 'transcendent' beings at all! As an inquiry into the being of beings AS such, the former books of the Metaphysics deal with the simplest, most inconspicuous phenomena associated with ordinary, everyday beings (_pragmata_) which are preconceived in multiple ways AS beings prior to any empirically-based science getting under way. Such ontological preconceptions are the tacit presuppositions for any empirical science whatsoever. In particular, the phenomena of movement are brought to crucial concepts in an ontology of movement that represents the apex of Aristotle's thinking that brought to culmination ancient Greek thinking on the perplexing phenomena of movement AS such.

Of the three fundamental ontological concepts of movement (_dynamis, energeia, entelecheia_) studied in depth in the Metaphysics, two have been borrowed in an excruciatingly superficial manner by modern science without thinking twice about this thoughtless misappropriation. Nevertheless, without this appropriation of metaphysical (or better: ontological) concepts of movement AS such, there would be no modern science as all! Positivist-analytical philosophy thoroughly confuses ontology and theology.  For it, ontology is the philosophy of existence, i.e. that things exist. It never poses the question as to the meaning of existence itself, i.e. what being means, but takes existence as a self-evident fact, like any empirical fact. At most, analytic ontology undertakes a taxonomy of beings, becoming thus a dry and empty enterprise. Completely lost is the depth of Aristotle's deepest thinking that struggled to philosophically, i.e. ontologically, comprehend the being of _kinoumena_, that is, of beings that can move and change which comprise all physical beings. The ontological difference between beings and their being AS such is fundamentally denied as if it were just one more unfounded "transcendent speculation" like 'speculating' about the 'existence' of a Supreme Being. But the ontological difference concerns those subtle preconceptions that enable the human mind to understand beings AS beings. Hence, not 'transcendent' but prior.

The ontological difference is the site where human freedom itself resides. Why? For it enables the world in its fundamental ontological structure to be seen AS such, and this AS as an historical cast of being is what enables each of us to act from his or her own individual starting-point proceeding from a guiding understanding of the world. By denying the ontological difference, analytic philosophy extinguishes the possibility of human freedom. Today, it takes a distinguished mathematician like Sir Roger Penrose to salvage a final hope for human freedom through the back door by proposing that a conjectured quantum indeterminacy of neural processes in the brain could provide some wiggle-room for free will to move outside the ambit of rigorous efficient linear causality. Since philosophy has abdicated and capitulated, advanced science, which has the pants on anyway, steps into the breach.

The insistence on empirical fact leads positivist-analytic philosophy to narrow the view of the world to what the conscious subject can garner temporally one-dimensionally from the world via the media of its senses in the present, with or without the aid of sophisticated technical apparatuses. The gathering of empirical data provides the bedrock material that skilful, mathematically adept consciousness works up into theoretical models of the world which, in turn, have to be verified or refuted by referring back to empirical data.

Modern science in whatever form is intent, nay, hell-bent, on developing empirically based, mathematically mediated, models for effectively controlling or predicting movements and changes of all conceivable kinds. Enter the cyberworld, with whose advent the logical _logos_ becomes self-active as algorithms controlling all sorts of movements. In particular, with so-called artificial neural networks and their learning algorithms, the mathematical means are at hand for predictively bringing all kinds of movement and change in the world algorithmically under control. Hence the insatiable hunger for Big Data on every front to feed all those learning algorithms out there, poised to pounce on any data you might divulge. Today, humanity is willingly, blindly, thoughtlessly plunging into and allowing itself to be devoured by this ever-encroaching cyberworld. Positivist-analytic philosophy aids and abets this fateful movement of our time; it is no help whatever for learning to see our predicament. 'Learning to see' phenomenologically is replaced by artificial intelligence's learning algorithms. If this centuries-old historical trend is not to be inexorable, it will be redirected only by our learning a kind of thinking that does not block the view of the simplest phenomena themselves by dogmatic prohibitions on seeing.

Further reading: Martin Heidegger History of the Concept of Time - Prolegomena; original German in Gesamtausgabe Bd. 20 Prolegomena zur Geschichte des Zeitbegriffs. Summer Semester lectures 1925; see Michael Zimmerman's review. Raul Rojas Neural Networks. See also my The Digital Cast of Being and A Question of Time.

Russell & Heidegger

 Bertrand Russell is universally admired as a philosopher who also had political guts and commitment, such as when he engaged in the Ban the Bomb movement in 1950s' Britain, protesting against the H-bomb in demonstrations, &c. to prevent nuclear annihilation of humankind on Earth. By contrast, Martin Heidegger never took part in an anti-bomb demo, nor perhaps in any street protest, nor even had the imminent threat of nuclear war at the top of his list of dangers confronting humankind. More on this below.

Russell commented on Heidegger, echoing the sentiments of many a twentieth-century logical positivist or analytic philosopher:
"Martin Heidegger's philosophy is extremely obscure and highly eccentric in its terminology. One cannot help suspecting that language is here running riot. An interesting point in his speculations is the insistence that nothingness is something positive. As with much else in Existentialism, this is a psychological observation made to pass for logic." Bertrand Russell Wisdom of the West 1989, p. 303.

 According to Russell, Heidegger's philosophy does not come up to scratch when measured against the yardstick of logic. This may even be correct, because Heidegger's thinking puts even logic into question, not by spinning off into so-called irrationality but by returning to, revising and resetting the roots of Western thinking.

With his co-author Whitehead, Russell is famous for his ground-breaking work on the logical foundations of mathematics, Principia Mathematica, which furthered the work of the deeply anti-Semitic, arch-conservative German logician, Gottlob Frege and is still hailed as one of the founding texts of analytic philosophy. Is Principia Mathematica any easier to learn to read and understand than, say, Heidegger's Being and Time? Is the former work's language obscure? As both a mathematician and philosopher, I can vouch for both works placing strenuous demands on the reader, but neither is incomprehensible. Both can be appropriated by close study and both make sense. Each requires a different kind of thinking, the one logical-mathematical, the other phenomenological-hermeneutic.

It is well-known that around 1930 the logical positivist, Carnap, pronounced Heidegger's thinking on nothingness to consist of meaningless statements, much the same as Russell's verdict. The criterion for possessing meaning in logical positivism is that the statement must be scientifically verifiable; otherwise the statement must be rejected as utterly nonsensical. Analytic philosophy's criterion for meaningful statements is hardly less rigorous. Both kinds of philosophy have placed unconditional bets on science, with its experimental scientific method, being unquestionably the arbiter of the truth of the world. Heidegger's thinking, being more radical by questioning even the modern scientific mode of access to the world as one-eyed, must fail the criterion of truth posited by Carnap or Russell. Scientificity and logicality, however, are both posited dogmatically, as if they were the final word of a modern philosophy that had finally become truly rational.

In 1955, at a time when the Ban the Bomb movement was still active, Martin Heidegger gave a talk in his hometown of Meßkirch in which he said, among other things, that 

"Denn gerade wenn die Wasserstoffbomben nicht explodieren und das Leben des Menschen auf der Erde erhalten bleibt, zieht mit dem Atomzeitalter eine unheimliche Veränderung der Welt herauf." (M. Heidegger Gelassenheit Neske, Pfullingen 1959/1985 p.20)
"For, precisely if the hydrogen bombs do not explode and human life on Earth is preserved, with the atomic age an eery change in the world is approaching."

This eeriness concerns humankind's "not being prepared for this change in the world" (ibid.). Why? Because "modern man is fleeing from thinking" (p.12), and "thoughtlessness is an eery guest who today comes and goes everywhere" (p. 11).

These seem to be highly quotable dicta that can be dropped casually like bombs in any dinner-party conversation. But do they mean anything?, we hear the analytic logician, Russell, ask. Not if you ensconce yourself behind the defences of logic and refuse to interrogate logic itself as a phenomenon in the world — and not just in words and statements. Which is one of questions — the question concerning the _logos_ and _legein_ — Heidegger's thinking raises, without going off the rails into merely gestural irrationality. Viewed from this angle, it is the philosopher, Bertrand Russell, who is "fleeing from thinking".

For Heidegger, if the nuclear bombs don't fall, we humans are confronted with an immeasurably greater, eery danger, namely, the destruction of human being itself by the modern scientific way of thinking. The eeriness consists in the danger's not being seen due to ubiquitous thoughtlessness and the self-satisfied refusal — including especially by philosophers such as Bertrand Russell and his multitudinous successors throughout the world — to painstakingly learn to think, of course, while at the same time steadfastly asserting the superiority of their own blinkered thinking.