[D-G] Concepts seen as functions

malgosia askanas ma at panix.com
Thu Apr 28 16:41:45 PDT 2011

Dear Jeff,

I wouldn't dream of discouraging you from a study of calculus, but to 
me it seems that the passage you quote from WiP doesn't call upon any 
special knowledge of calculus, or mathematics in general.  I think 
that "limit" here does not have any specialized mathematical sense, 
but just refers to restricting something, setting limits upon it - 
and that "something", in this case, is the virtual.  As for 
"abscissa", I think that the important point here is that in the 
virtual there is no external "clock", or standard, which "clocks" the 
variation of the differential elements (i.e. those elements whose 
differences are responsible for the continuous variation within the 
given virtual domain).  The differential elements thus form what D&G 
call "intensive ordinates" - their variations don't depend on 
anything extraneous, and neither are there any internal dependencies 
between the differential elements (that's why they all form 
"ordinates" and there is no "abscissa", i.e. no variable on which 
they are all considered to be dependent).  They vary freely, 
continuously and unrestrictedly.  For example, the gradations of the 
phonemes in the Idea (or virtuality) of Language would not be 
restricted by considerations of discernability by ear, 
pronounciability, etc.

Science, on the other hand, imposes limits on the virtual in more 
ways than one, if only through its stringent methodological 
requirements: that it be based on experiment, that the experimental 
results be reproducible, that the theoretical results have a close 
connection to the experimental and be formulated according to certain 
standards of shared intelligibility, and so on.  And since the 
language in which it expresses its results is the language of 
functions, the first step of any scientific project is to choose the 
variables under study - the variables whose changes express the 
natural phenomena under study, and whose functional dependencies the 
study will pertain to.  And every scientific project has to limit 
itself to studying the given phenomena under a certain set of 
conditions - which, in turn, sets limits on the possible values which 
the variables can range over.  So: the first two components of every 
scientific function - i.e. the first two functives, to use D&G's 
language - are the limit (or limits) and the variable (i.e. the 
choice of variables).  It is these two components that constitute the 
scientific plane as a plane of reference.  And why is "the variable" 
an "abscissa of speeds"?  I think it is because the introduction of 
these two components (or perhaps even just the choice of variables, 
qua potential functives and with their limits) sets a "clock" (like a 
sampling rate, but in a more profound sense) to the free variations 
within the virtual - the "sampling" will only take place according to 
certain methods, and only on certain terms, at certain "speeds" of 
thought, according to a certain experimental protocol, etc.  So if 
the variation of the virtual is described as taking place intensively 
and "at infinite speeds", then the scientific actualization is 
achieved by slowing down the virtual to speeds dictated extensively, 
by the methods of science, which thus effectuate an "abscissa".

These are just the general lines along which I would tease that 
passage, and perhaps completely off.


At 6:42 PM +0000 4/28/11, Cain, Prof. Jeffrey P. wrote:
>RV, thanks for the interesting comments.  I do understand, I think, 
>a reasonable part of this issue with regard to 
>schizoanalysis--though I will never claim to have any of D&G's 
>concepts completely or even mostly exhausted, especially not 
>schizoanalysis. But the part of _What is Philosophy?_ that has 
>always seemed a bit vague to me (and I blame it on my own lack of 
>mathematical sophistication, not Deleuze and Guattari), is Part Two, 
>Section Five, "Functives and Concepts."  Specifically, the English 
>translation says that "the first functives are the limit and the 
>variable and reference is a relationship between the values of the 
>variable, or, more profoundly, the relationship of the variable, as 
>abscissa of speeds, with the limit" (118-119).
>I'd be gratified to resolve a gnawing question about how this 
>relates to differential calculus, the limit theory, the asymptote, 
>mathematical functions, etc; particularly since D&G do make remarks 
>elsewhere that implicate the calculus. Perhaps an unfocused but 
>well-intentioned question would be: "how is schizoanalysis like 
>differential calculus?" But I already sense that it isn't formulated 
>rigorously.  Again, I assume this is my own ignorance--I can say 
>that I've been working fairly hard on my math for the last couple of 
>months, have arranged to audit a calculus class and am definitely 
>trying to get there by myself. (My Ph.D. is in English!) But it 
>occurred to me earlier today that someone on the list might have a 
>complete understanding from a mathematical point of view.  Just 
>thought I'd clarify my reasons for writing.
>"Abscissa," by the way, seems to be a somewhat outdated word in 
>English--I understand it as simply the term one plots on the x or 
>horizontal axis of a Cartesian grid. My pre-calculus book doesn't 
>use the term, so I'm also wondering whether it has any other meaning 
>for D&G.
>Thanks again, RV, for your very kind help.
>Jeffrey P. Cain, Ph.D.
>Chair, Department of English HC221A
>Sacred Heart University
>Fairfield, Connecticut 06825
>Office Hours Spring 2011: Mondays 12:00-2:00; Wednesdays 12:00-2:00; 
>Fridays 11:30-12:15
>From: deleuze-guattari-bounces at lists.driftline.org 
>[deleuze-guattari-bounces at lists.driftline.org] on behalf of 
>saphiregnauld [saphi.regnauld at numericable.fr]
>Sent: Thursday, April 28, 2011 1:37 PM
>To: deleuze-guattari at lists.driftline.org
>Subject: Re: [D-G] Concepts seen as functions
>  dear all
>  according to D+G and at least in french "concepts" are not "functifs"
>and will never be..
>Concepts are able to mobilize the movement whereas  functifs are said to
>immobilize the movement in order to build a  true equation..   This is
>one the worst D+G idea : concepts are only for philo and science is left
>with  second order ideas which are called  functifs.
>  The basis of this is in "cartographies schizoanalytiques" by G (alone)
>when he dismisses neuro sciences  and wants to promote schizio analysis
>(in the french edition it is page 47 to 51)
>  " notre souci principal est de developper un cadre conceptuel qui
>prémunisse la schizo A contre toute tentation de s'abandonner à l'idéal
>de scientificité qui prévaut ordinairement dans le domaine "psy"  "..
>which in english is something like :
>"our main  aim is to develop a conceptual framework which may prevent
>schizo A to be leaning toward the idealistic scientist model which
>usualy dominate the "psy" field..."
>  Good idea , absolutely great idea for the "psy" field. But the problem
>is that other sciences do not fit with this local epistemic model. For
>so called "natural sciences" such as geology or physical geography or
>ecology.. there is no need to separate the concept (which ables the mind
>to move) and the functif which stops the minds and reduces it to a set
>of neuronal interactions.
>There no mind in natural sciences.. and this difference between self
>concious minds and incouncious minds does mean anything.
>  So D+G should not have taken the model of neuro science vs schizo A as
>a universal model of the relation between science and philosophy..
>Hopelessly this is not a main topic in the excellent book about Deleuze
>and space..
>  Anyhow
>  it is of the most tricky aspect of D+G work and working about it is a
>difficult task.. You have to get back to the early book on Hume and to
>all the difficults relations between D and G at the end of their lives
>(see Dosse's book) .
>  See, above all,  A Sauvagnargues'  mega excellent book on "empirisme
>transcendantal" (in french) and some papers in in Chimères..
>  amicalement  RV
>    malgosia askanas a écrit :
>>  Dear All,
>>  When D&G, in WiP, refer to the view that concepts are functions, are
>>  they referring to Frege, or is there an earlier philosophical
>>  tradition that proposes this view of concepts?  I recently chanced
>  > upon a text that claimed the latter, but now I cannot locate it
>>  again.  Your help will be much appreciated.
>>  -m
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