From: "Anthony Crifasi" <crifasi-AT-hotmail.com>
Subject: Re: Method - Axiomatic casting
Date: 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.

Michael Eldred wrote:

> > I think you've discussed this with me before, so I don't want to > 
>unnecessarily beat dead horses, but I would very much appreciate it > if 
>you would discuss it with me again because the current topic of > my 
>dissertation is precisely the foundation of Cartesian philosophy. > In 
>short, I don't see why the rule you cite above implies a > different 
>casting of being from that of Aristotle because the > emphasis on 
>quantifiable measurability around Descartes' time was > the result of 
>numerous new scientific findings which discredited > certain long-standing 
>positions that Aristotle argued through > non-quantifying techniques. 
>Although "new scientific findings" of > course cannot be simply pasted from 
>one casting of being to another, > this is possible within essentially the 
>same casting of being. In > this case, Aristotle's scientific method 
>included BOTH quantifiable > and non-quantifiable techniques. A prime 
>example of this is > Aristotle's explicit description of place (Phyics 4?) 
>as having not > only mathematical position, but also power (the power to 
>draw things > to their natural place). He explicitly says both. But after 
>certain > observations (esp. by Galileo) discredited the idea that things 
>move > due to a tendency towards their natural ending place, the only thing 
> > left was place as mathematical position. So such mathematical > analyses 
>are simply the remnants of Aristotelian philosophy after > specific 
>conclusions resulting from his non-quantifiable techniques > were rejected 
>due to certain observations. Examples like this are > what make me think 
>that Descartes' emphasis on mathematical > precision was not the result of 
>an essentially different casting of > being, but of new scientific findings 
>within essentially the same > casting of being.  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").

>You seem to be suggesting that the Cartesian casting of being is merely a 
>stripped down version of the Aristotelean casting forced upon it in the 
>face of empirical evidence, i.e. facts. Here it would be worth your while 
>having it out with Heidegger _The Question Concerning the Thing_ Part I 
>Section 5 esp. Subsections d), e), f). Heidegger writes, for instance:  
>"The greatness and superiority of natural science in the 16th and 17th 
>centuries is based on the fact that those researcher were all philosophers; 
>they understood that there are no naked facts, but rather that a fact is 
>only what it is in the light of the concept which grounds it and in each 
>case according to the reach of such a grounding." (_Die Frage nach dem 
>Ding_ WS 1935/36 3rd ed. Niemeyer, Tuebingen 1987 S.51)  "Apart form the 
>two characterizations of modern science that are always mentioned (it is 
>factual science and experimental research), a third characteristic is 
>mostly also given. It underscores that the new science is calculating and 
>measuring research. That is correct; but it holds also for ancient [Greek] 
>science; it too worked with measurement and number. The question is again, 
>in what way and in what sense the calculations and measurements are 
>designed and carried out and what bearing they have for the determination 
>of the objects themselves." (S.52)  "The fundamental trait must consist in 
>what permeates and rules the fundamental movement of science as such in an 
>equiprimordial and definitive way: it is the work-dealings with things and 
>the metaphysical casting of the thingness of things. How are we to grasp 
>this fundamental trait?" (S.52)  H. says that this fundamental trait is 
>"the mathematical". "The decisive question is: What do mathematics and 
>mathematical mean here?" (S.52)  With regard to Newton's First Law of 
>Motion H. writes: "Up until well into the seventeenth century, this law was 
>not at all self-evident. In the preceding one-and-a-half millennia it was 
>not only unknown, but nature and beings in general were experienced in such 
>a way that this law would not have made any sense. In the discovery of this 
>law and in positing is as a fundamental law there lies a revolution which 
>is one of the greatest in human thinking and which first provides a ground 
>for the turn from the Ptolemaeic to the Copernican understanding of the 
>whole of nature." (S.61)

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 incline 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.

>This passage indicates just how much your thesis of an essentially same 
>casting of being is opposed to Heidegger's way of seeing the difference 
>between ancient and modern science.  For Aristotle, "the kind of movement 
>of a [natural] body and the relation to its place depend on the nature of 
>the body". (S.66) Place belongs to the nature of the body, and the natural 
>bodies are distinguished according to the places to which they naturally 
>belong.  In Newtonian physics. natural bodies do not of their very nature 
>belong to a place. All bodies are of the same nature with regard to motion 
>and do not have a natural place where they belong. There are no places as 
>such in Newtonian physics, but only positions. The 'where' a being 
>presences no longer belongs to its own nature. Positions are measurable, 
>i.e. completely determined by quantity, whereas places are not. The natural 
>movement for all bodies without distincation is now to move in a straight 
>line. This is nothing inherent in the body's nature that determines its 
>motion, but rather nature itself is "the mode of the multitude of the 
>changing relative positions of bodies". (S.68)  "It should only become 
>visible that and how, in positing the First Law of Motion, all the 
>essential changes are also posited. These changes are all interlinked and 
>all equally founded in the new fundamental stance which comes to expression 
>in the First Law and which we call the mathematical fundamental stance." 
>(S.69)  "What is the situation regarding this Law? It speaks of a body, 
>corpus quod a viribus impressis non cogitur, a body left to itself. Where 
>do we find such a body? There is no such body. There is also no experiment 
>which could ever bring such a body to a directly intuitive representation. 
>But modern science, in contrast to the merely dialectical invention of 
>concepts in medieval scholasticism and science, is supposed to be based on 
>experience. Instead of this, such a law is placed at the edifice. It talks 
>of a thing which does not exist. It demands a fundamental notion of things 
>which contradicts the usual notion of things.    In such a claim rests the 
>mathematical, i.e. the positing of a determination of the thing which is 
>not derived from it itself on the basis of experience and which at the same 
>time forms the basis for all determination of things, enables such 
>determination and first makes room for it." (S.69)

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"?

>With regard to Galileo's experiment dropping objects from the leaning tower 
>of Pisa:  "Galileo and his opponents both saw the same 'fact', but both 
>made the same fact, the same happening visible to themselves differently, 
>interpreted it differently. What for each of them appeared as the proper 
>fact and truth was different in each case. Both thought something with 
>regard to the same phenomenon, but they each thought something different, 
>not in detail, but fundamentally, with regard to the body's essence and the 
>nature of its motion. What Galileo thought in advance with regard to motion 
>was the determination that the motion of any body is uniform and linear if 
>every obstacle is excluded, but that it changes uniformly if the same force 
>works on it." (S.70)  What Galileo "thinks in advance" is the fundamental 
>positing or casting of the First Law of Motion, which also casts what a 
>thing _is_. It is something which he gives to himself in thinking (mente 
>concipere). The experiment itself is neither decisive nor conclusive; it is 
>only a consequence of what is thought in advance. What the experiment 
>demonstrates depends on what is thought in advance.

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.

>"In this mente concipere something is grasped together in advance which is 
>to be uniformly determining for every body as such, i.e. for all 
>bodiliness. All bodies are equal. No motion is special. Every place is 
>equal to every other place. Every point in time is equal to every other 
>point in time. Every force is determined only according to what it causes 
>by way of change of motion, change of motion understood as change of place. 
>All the determinations of the body are inscribed in a basic cast according 
>to which a natural happening is nothing other than the spatio-temporal 
>determination of the motion of mass-points. This basic casting of nature 
>defines at the same time its domain as a domain which is uniform 
>everywhere." (S.70f)  "1. The mathematical, as mente concipere, is a 
>_casting_ of the thingness of things which, so to speak, leaps over them in 
>advance. The casting first opens the room for play within which the things, 
>i.e. the facts, show themselves. 2. In this casting, what things are 
>properly held to be is posited, as what and how they are to be appraised 
>from the outset. Such appraisal and holding-to-be is called _axioo_ in 
>Greek. The determinations grasping in anticipation in the casting are 
>_axiomata_. Newton therefore gives the heading: 'Axiomata, sive leges 
>motus' to the section in which he posits the fundamental determinations of 
>things as in motion . The casting is axiomatic." (S.71)

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.

Anthony Crifasi

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