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?