Leibniz decomposed "philosophy, or the complete knowledge of all things"
in three areas :
* logic : Leibniz is indeed the founder of symbolic logic, as opposed to =
old =
aristotelian logic and scholastic rethorics
* ars memoriae : the antique tradition of the "Art of Memory", =
cf. F. Yates or P. Rossi's books for details
* ars inventendi : combinatorics, following the Lullian tradition.
Logic is the way to derive new knowledge from old one (but no new ideas c=
an
be created in that way), ars memoriae the way to record knowledge in an =
efficient manner (and _images_ played there an important role),
ars inventendi is the way to produce new knowledge and ideas.
How can we produce new ideas ? We cannot just start from our previous =
knowledge,
because then the "new" would follow from the old and would not be so new =
indeed.
Therefore one has to find an external (and in some sense mechanical) way =
of
generating all possible knowledge. And then "choose" the interesting thin=
gs.
This is combinatorics, but how can we be sure to generate all possibiliti=
es
without being bound by our own limits ?
The point is to consider a blind, formal (in the logical sense) combinato=
rics :
first associate ideas to symbols, then start a combinatorial generation o=
f all
combination of symbols and then "decode" the results.
This has been first proposed by Raymond Lulle in his Ars Magna at the end=
of =
the XIIIth century with a limited vocabulary of 9 basic ideas symbolized =
as =
letters (corresponding to the attributes of God, Ramon Llull was a franc=
iscan =
monk from Catalunia) that could be combined in all possible groups of two=
or =
three by an interesting device made of 3 rotating wheels =
(the first computer ?). However Raymond was a trickster
and removed from the possible sentences those that were incompatible with=
his
religion ... therefore showing that a pure application of combinatorics w=
as
indeed a way of getting out of the realms of the accepted ideas of his ti=
me !
The interesting point to note here is that the combinatorics is done in a=
purely mechanical way on un-interpreted symbols (letters), rotating wheel=
s
acting here as a "blind thought" trying to explore all possibilities.
Lullian tradition was quite vivid in the medieval an Renaissance times,
culminating with Giordano Bruno that designed a device with 8 rotating =
wheels of 33 symbols each.
Leibniz was the last philosopher to refer to Lullism, which has been
too much linked with the Renaissance occult/hermetic tradition
for the century of the Enlightments ... (Giordano Bruno was burned by the=
=
inquisition in 1600, Leibniz wrote his early "arte combinatoria"
in 1666, but his famous Monadology in his later days in 1712).
Nevertheless leibniz has kept all his life the belief that the "blind tho=
ugh"
of combinatorics was the only way to create new knowledge.
He, for instance, said that he discovered infinitesimal and differential =
calculus by purely combinatorial ideas. =
OK, let's come to Duchamp. =
Many readings of his works have been done, let me increase the noise.
Many of Duchamp's works can be reconsidered as attempts to explore in
a combinatorial way the limits of art. When the space of possibilities be=
comes
infinite, chance become a good approximation of combinatorics.
"3 metres etalons" fits therefore exactly in these lines.
Readymades, and "Fountain" above all, can be considered as choosing in th=
e
combinatorics of "real-life" objects that enlarge the field of art
(le champ du pensable artistique).
The Large Glass ("the bride ...") has been generating an infinity =
of interpretations, all accepted by Duchamp with a grin.
Together with the notes in the Green Box (1914), "un guide de lecture" (=
M.D.),
it indeed reifies the separation between symbol and signification,
abstract forms and meaning, the "blind though" of the canvas,
"une logique d'apparence" (M.D.). =
Is its sole purpose to be an interpretation generator ?
Generating "news concepts" for the spectator ?
This work could be explained both in terms of semiotics
(cf. the work of M. de Barros, EIDOS no 13, 1997) =
or in terms of logic in the opposition (also due to Leibniz) between the
"lingua characteristica" approach (Frege, Russel, first Wittgenstein) =
and the "calculus ratiocinator" approach (Boole, Skolem, Tarski).
Duchamp was well aware of the modern logic of his time (cf. the interview=
with P. Cabanne) and indeed played with a few logical notions in his
works (e.g. the "principe de (non) contradiction" that he mentionned in h=
is
notes and the open/closed door of "13, rue Lautey")
His last work, "Etant donnees", brings us back to combinatorics. It is =
described as "la figuration d'un possible" (M.D.) ("possible worlds" bein=
g
anything that obey the "principe de (non) contradiction", if we follow
Leibniz again). =
As if, again, its sole purpose was to generate an infinite number of
interpretations, of "new ideas" in the head of the viewer, in an even mor=
e
radical manner than the Large Class. =
BTW, art historians and critics have indeed been much less talkative =
on "etant donnees" ... =
One could even find an actual link between Leibniz and Duchamp in the
french mathematician Raymond Poincare', well-known to artists of the earl=
y
XXth century through his work on the 4th dimension, reprinted by
Theo van Doesburg in De Stijl.
Poincare' developed Leibniz's infinitesimal calculus =
(he reused Leibniz's term : "analysis situ") and was
one of the founder of modern topology.
His idea of scientific discovery (Science et M=E9thode, 1908) is that int=
uition
"choose" good ideas from the "blind" "automatic combinations" of the =
"unconscious" (Poincare's words).
Duchamp knew and admired Poincare' (cf. Le Lionnais, fellow chess playing=
=
friend
of M.D.). He certainly read his book "Science et methode", and might have=
been
influenced by his idea about creation and intuition.
(cf. Rhonda Shearer's paper in The Sciences, NY academy of Science, =
March/April 1997)
One can therefore wonder if there are in contemporary art any followers o=
f =
Duchamp is this sense ...
I have no real idea up to now.
Anyway there is here a real benefit in using computers for exploring some=
combinatorics and moving to a radically new notion of space,
dynamic versus static.
Philippe