Date: Mon, 25 Feb 2002 23:09:14 +0100
From: artefact-AT-t-online.de (Michael Eldred)
Subject: Re: Method - Axiomatic casting


Cologne 25-Feb-2002

Anthony Crifasi schrieb   Mon, 25 Feb 2002 15:06:07:

> Michael, please tell me you already had all of these texts on your
> computer, and didn't actually type it all in just to reply to me! Either
> way, thank you very much. I have always wanted to read the exact text where
> Heidegger discusses this issue.

Anthony,

Isn't Heidegger's lecture course available in English translation?

Heidegger says in the same text:

"Teaching is a giving, offering; but what is offered in teaching is not what can
be learned, but rather, only the instruction is given to the pupil to take for
him/herself what s/he already has. When the pupil only adopts something that has
been offered, s/he does not learn anything. S/he only comes to learning when
s/he experiences what s/he takes as something which s/he him/herself properly
speaking already has. Genuine learning only takes place where the taking of what
one already has is a _giving-to-oneself_ and is experienced as such. Teaching
therefore means nothing other than allowing the others to learn, i.e. mutually
bringing each other to learn. Learning is harder than teaching, for only those
who can truly learn -- and only as long as they can -- can genuinely teach. The
genuine teacher is distinguished from the pupil only in that the teacher can
learn better and wants to learn more properly. In all teaching, the teacher
learns most." (S.56)

The essence of the mathematical is taking what one already has. This is
learning. This taking of what one already has is radicalized in modernity to the
self-certain subject taking what is self-evident or what can be brought into
self-evidence through stepwise deduction.


> Anthony, This is one of
> >those big topics. It could be helpful if you would provide a couple of
> >references to Artistotle to see what he says. What, for instance, does
> >Aristotle understand by "mathematical position"?
>
> This is the text I had in mind. I don't have a hard copy with the line
> numbers  with me, so I will just post the section from an online version.
> You should find it in chapter one of the fourth book of Aristotle's Physics:
>
> "Further, the typical locomotions of the elementary natural bodies-namely,
> fire, earth, and the like-show not only that place is something, but also
> that it exerts a certain influence. Each is carried to its own place, if it
> is  not hindered, the one up, the other down. Now these are regions or
> kinds of place-up and down and the rest of the six directions. Nor do  such
> distinctions (up and down and right and left, &c.) hold only in  relation to
> us. To us they are not always the same but change with the  direction in
> which we are turned: that is why the same thing may be both  right and left,
> up and down, before and behind. But in nature each is  distinct, taken apart
> by itself. It is not every chance direction which is  'up', but where fire
> and what is light are carried; similarly, too, 'down' is  not any chance
> direction but where what has weight and what is made of  earth are
> carried-the implication being that THESE PLACES DO NOT  DIFFER MERELY IN
> RELATIVE POSITION, BUT ALSO AS  POSSESSING DISTINCT POTENCIES. This is made
> plain also by  the objects studied by mathematics. Though they have no real
> place,  they nevertheless, in respect of their position relatively to us,
> have a right  and left as attributes ascribed to them only in consequence of
> their  relative position, not having by nature these various
> characteristics."
>
> The line I capitalized is the part I am focusing on, since he mentions both
> mere position and power or potency as attributes of place. The former is
> mathematical position, as is clear from the subsequent two sentences, in
> which he describes mathematical position as mere relative position without
> any distinguishing natural powers or potencies that would make  this down
> not just down relative to something, but REALLY down ("where  what has
> weight and what is made of earth are carried"), and this up not  just up
> relative to something, but REALLY up ("where fire and what is light are
> carried").

The capitalized line reads in Greek:
_hos ou taei thesei diapheronta monon alla kai taei dynamei._ (208b20)
"how they [above and below] do not differ solely according to position, but
according to potency".

For Aristotle, geometrical points are abstracted from natural beings in their
place to become placeless points (_atopoi_) which nevertheless have a position
(_thesis_). Arithmetical number results from a further abstraction to placeless
and positionless entities. Thus geometrical points can have relative position,
but numbers cannot, since numbers themselves are positionless.

I.e. whereas the _topos_ belongs to natural beings, the _physei onta_, Aristotle
separates off from these the geometric and arithmetic entities, that is, the
point (_stigmae_), which is placeless (_atopos_), and the unit (_monas_), which
is both placeless and positionless (_athetos_).

You may find my online paper, Casting of a Digital Ontology, helpful in this
connection.
http://www.webcom.com/artefact/dgtlon_e.html

This makes it clear that Aristotle does not think natural beings in their being
as 'point masses', i.e. mathematically in the narrower sense. And yet you claim
that this difference (which lies at the heart of how natural beings are
conceived in their essence) is no essential difference from
Newton/Descartes/Galileo.


>
> This is a text (again from Physics IV) where Aristotle directly opposes his
> own view to exactly what Newton says in his first law of motion:
>
> "Further, [if there were a void] no one could say why a thing once set in
> motion should stop anywhere; for why should it stop here rather than  here?
> So that a thing will either be at rest or must be moved ad infinitum,
> unless something more powerful get in its way." (Physics IV.8)
>
> So Aristotle himself sees that Newton's First Law would be a necessary
> implication of a void, since in a void, places would not be differentiated
> by  any natural characteristics which would result in a mobile stopping here
>   instead of there. So Aristotle himself explicitly opposes Newton's First
> Law  to his own teleological view that things tend to stop in certain
> places. The  reason is easy to see - Aristotle's view is that things in
> linear motion tend to stop, while Newton's First Law states that they do not
> tend to stop. They are exact opposites, so the rejection of one naturally
> entails the other.  So again, it seems to me that the changeover to
> Newtonian physics is  better explained in terms of the new scientific
> observations favoring inertial  tendency (esp. Galileo's inclined plane
> observations) within the same casting  of being. If two different castings
> of being were involved, it would never have  occurred to an ancient Greek
> like Aristotle to oppose the two views.

How do these "new scientific observations" come about? They are guided by a
certain thinking, which in turn also develops through the observations. What
kind of thinking is at work here in this historical transition?

It is the Aristotelean casting of natural beings in their being, i.e. as having
of their nature a place toward which they tend, which excludes infinite
unhindered linear motion. As Heidegger points out, there is no possible
experience of infinite unhindered linear motion. On the contrary, experience
supports rather the notion of infinite circular motion for those bodies which
are in their place in the heavens. Galileo's casting has to be thought prior to
him conceiving experiments with inclined planes and making observations. What
happens in the Galilean/Newtonian/Cartesian casting is that natural beings are
stripped of their inherent nature and place and instead cast as beings that can
be mastered mathematically, i.e. the subject gives itself the axioms on the
basis of which the motion can be mastered in scientific-mathematical thinking.
It is the abstraction from natural beings which enables this mastery and also
dictates a certain kind of experience with natural beings. I.e. there is no
empirical observation that is outside a casting of being and could judge over
it. Rather, experience and thinking are intermeshed.

>
> It may be true that (as he says) no body can ever be completely "left to
> itself" without anything impinging on it whatsoever, but this does not mean
> that a clear progressive pattern cannot be observed in how bodies behave as
> external  impingement decreases. Is he saying that this is the same as "the
> merely dialectical invention of concepts in medieval scholasticism and
> science"?

Not at all. He says that the casting of the being of natural beings is prior to
any experiments with them and cites Galileo's prior reflections in support of
this. No observation is able to induce a recasting, but rather, the recasting
itself comes from a metaphysical recasting of beings as a whole and the being of
beings in which human existence itself adopts another fundamental stance towards
the world. Experimental observation itself plays an ancillary role in this
metaphysical recasting and only in tandem with it.

>
> I would have to see exactly how Galileo's opponents tried to explain this
> experiment. I am almost certain that their alternate explanation would have
> observable consequences which could also be (and probably were) tested by
> another experiment. If that is the case, then once again, the changeover is
> explained by empirical evidence within the same casting of being.

Only it is not the same, since the being of natural beings and beings as a whole
is now cast in a totally different way -- axiomatically from the mathematical
subject. A sign of this total revolution is the revolution in the meanings of
the words 'subject' and 'object'.

"Up until Descartes the word 'subject' was applied to every existing thing; Now,
however, the 'I' becomes the subject par excellence, i.e. that in relation to
which the other things are first determined as such. Because they only obtain
their thingness -- mathematically -- through the founding relation to the
highest principle and its 'subject' (the I), they are essentially something
which stands as something else in relation to the 'subject', lie against it as
obiectum. The things themselves become 'objects'. ... This inversion in the
meaning of the words subiectum and obiectum is not simply a matter of the use of
language; it is an earth-shattering transformation in human being (Dasein), i.e.
in the clearing of the being of beings on the foundation of the rule of the
_mathematical_. _It is a stretch in the path of history proper which is hidden
to the common eye_ which is always the history of the openness of being -- or
else nothing at all." (S.81, 82)

I suppose you would say that there is nothing "earth-shattering" going on in
this historical transformation. But think about it.

>
> Yes Newton states them as axiomatic, but if you look at the development of
> physics in the 100 years preceding Newton's Principia, you can find very
> specific observations which led to those axioms, supporting the view that
> things in motion do not tend to stop over the view that things in motion
> tend to stop. If that is the case, then again, the changeover is explicable
> in terms of new evidence within the same casting of being, not a new casting
> of being. This obviously does not threaten Heidegger's view that empirical
> facts do not stand alone, but are facts only under some casting of being.
> The only thing I am disputing is that the changes to which he refers above
> are the result of a new casting of being altogether, instead of developments
> within the same casting of being.

The only way forward here, it seems, would be for you to write down the
Aristotelean casting of being and the Cartesian casting of being and see if they
are different and how radically different they are. You keep on saying that it
is the observations that lead to the recasting of beings in their being. But all
observations are such only within a cast of thinking, i.e. observations are
always already understood in some way or other, and this understanding relies on
the overall metaphysical casting of the being of beings within which it is
situated.

What is the significance of Newton's laws being given an _axiomatic_ cast? You
don't seem to appraise the import of this axiomatic character.

Michael
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