[D-G] Deleuze-Guattari Digest, Vol 74, Issue 4

[Harald Wenk]

Dear group,

I am a litle bit puzzled, as the firs sentencenes in
WiP II.5:  Funktives and Notions are:

"SCience does not hav enotions to its object, but functions, which are
represented as prpostioen in discusive systems. Th
e elemnets of teh functivs are called funcztions.
A SCIENTIFIC NOTION  wil not be determined by a NOTION; but by 
functions or propositions.

That scientfic logic is teh on eof Frege an dRussel si the befginning 
of WiP II.6.


In II.5 teree is  te dsicussion about teh differnt approoaches of 
science, especially mathematics of set theroy of cantor, to chaos.

Now, ther ha sbeen progress, as te arguemnt in "EXample X" where
the final failinng of keeeping teh phsilophicala notion and scientfic function
identical of Cantor.

Herre are Rreferences to teh impossibility of a uniovrsl al aset or 
set ogf all sets and to Gödel.

Now, there are improvements of set tehroey, even beyond Quine mentioend in WiP,
especially by Weydert, who keeps the line to clasical philosophical logic.

"Set Thories with a universal set"  are described in Forster (namely!!)
There are a lot. The are even more from a eastern states  originating 
from Skala.

The connection to Kant lies in the "overflight" argumen t odf phsilophical
notions.
Here Spinoza may come in.

Science is concerned with "prosepcts2 in differncve to Notions",
an abbrvaition for schentfic notion.

But there maybe depper reasons fpr thsi naming.
.
There is also the attempt of catgory tehory whioich is verx 
ydriectly teh notion of notion in mathematics.

The classical solution is a split of class tehory, allowing teh cals 
of all classes (whoch is "CHaos shown by Russel according to Example 
X in WiP II.5)
and then projecting to a set theory with comprehension axiom.

The discusson od set tehroy os very vast, biut in order of
"upward comapbilirty2 (s o to speak "Hsotorocal§"",
a real change is  to a fully satisfying system is not to expect.
This is NOT, because there ARE `NONE!!!

There is universal set too and has been worked out by the strucuralis 
schhol of Bourbaki, especially Grothendick, which were well known by 
D&G.
The polemic against mathematical structuralism looks a bit
"literal".

But a category is bigger than set theory and even class theory, not a 
set or a class.

It gives "Functors" which are used by Guattari in his late books.

Category theory  comes from (and for) algebraic toplogy, McLane and 
Eilenberg,  and thereby is much better for the "topological" asepcts 
of D&G.

The notion of a manifolfd itself is desrcibed as ovthrowing out 
hegleina thinking,, a philsophical hero deed of first rank by 
Riemann, if true.


As the notion of manifold is used very "ontological" for immancence 
by G&D, espcially in "thosand Plateaus",
it is very surprising to see that notion not to be accepted as being 
mathematical and philosophical  togetehr, being one notion?

But, Riemanns "ontologocal" ideas, including something like Connan Doyle's
thesis of a nervous sytem of the earth WiP p. 253 in german edition,
is not mathematical any more and even little konwn among them.
To be honest, most of the  active riemannian geometers would fiercly 
deny such a ontological "view" of Rieman until they read it in the 
collected works.





After the great clash between Einstein and Kant in favour to Einstein
concerning space and time,
things are very "interesting" here.

Stengers and Prigorin, as "sceintsits",  are a bit "pragmatic" for a 
phsilophical taste ovf
crating a notion odf space an time.
THey are "open" to new scientfic reserch, so to write.
The prize is a little bit undefined notion.


greetings Harald

Ps. Especailly  the peadoxes and antinomies are solved,
already by Kutschera in the line of "circle definfitions", very 
refined, semanticly.