Justification of the subject matter proposed for the
VIII Congress
In a paragraph of Physics,
Aristotle states that in his days the mathematicians themselves stopped
feeling the need of the infinite. The Stagirite thus authorises a tendency in
the history of thought that repudiates this concept, which nevertheless
constitutes a true obsession for science itself. For, as much from the angle of
the infinitely large as from that of the infinitely small, the apeiron of the Greeks slipped like a
shadow, and sometimes like an essential resource, into all attempts to explain
the phenomena.
A labyrinth was the infinite for Leibniz, who although
being a co-founder of the calculus called infinitesimal,
declares on several occasions that, from the point of view of philosophical
rigour: “I do not believe that there are
neither truly infinite magnitudes nor truly infinitesimal magnitudes; they are
just useful fictions to abbreviate and speak in a general manner”. A
delicate labyrinth into which “entering
was not given to me” regretted Jorge
Luis Borges speaking about the Cantorian infinite that he just
contemplated “from Bertrand Russell’s
pages.”
The infinite likewise is a labyrinth for cosmologists,
confronted today with dilemmas about the geometric structure consistent with
the objective Universe. The Universe is unquestionably finite and closed only
on the supposition of the objective density of matter being superior to the critical
density, and on that of the universe having a positive curvature. For the
remaining hypotheses the universe is at least open, although it would be
perhaps useful to turn to the old Aristotelian distinction between potential
infinite and actual infinite to determine whether it is infinite or not.
The evolution of ideas about the universe is often
presented as the history of the incorporation of the infinite to the cosmos.
The sequence Aristotle/Newton appears like an almost unavoidable itinerary. To
prevent the aporias of the void, it pushes its way the idea that matter should
occupy space completely, be extended in all its infinitude. The property of an imagined infinite space was thus
attributed to matter. Since Netwon’s death this agreement was challenged. Cosmic matter was first formed by stars,
then by stars and nebulae, later by galaxies and finally by a group of stellar
bodies as varied as the natural species that developed on our planet. Astronomy
leaned on physics to explain the structure of matter.
It
is precisely this alliance between cosmos and physics that brings back the
problem of the infinite in the universe. A simple transfer from the world of
mathematics to physics is not enough to believe that the problem of its
interpretation has been removed. The cosmic infinite is much more complex. It
is the infinite of physical space, of the interpretation of time, of the
reformulation of causality and, above all, of the explanations of how
everything happened in a complex that shows restless, evolutionary and dynamic,
where bodies like stars appear and disappear, where the galaxies move at a
surprising speed, where it seems as if a large part of space cannot be seen,
where the look of the terrestrial observer is suspended at an instant of time
from where he can travel through the entire history of the universe. To look at
the heavens would be to look at the past if this word had the same meaning as
in a personal biography. But it does not, precisely because the notion of
infinity has stopped being the safe guide it was at the good Newtonian age, the
notion imagined, simple, and the receptacle where everything occurred in our
world, the reference of space and time.
Returning now to a strictly mathematical field, we
confirm that the question of infinity continues being a source of aporias as it
was at the time of Aristotle and Leibniz. First of all, the debate from the end
of the 19th century surged in relation to the Cantorian construction
of the transfinite numbers. Far from being settled, the discussion has been
re-ignited in the last several years. On the one hand, there are the criticisms
about the Cantorian infinite formulated by first class mathematicians such as
Solomon Feferman. On the other hand, there are the discussions about the
problem of the continuum, already dealt with by Cantor and brought up to date
very recently by mathematicians like W. H. Woodin.
A complementary problem is that of the infinitely small. Rejected by 19th
century mathematics (to such a degree that Mario Bunge could talk in a debate
with Abraham Robinson about Execution and
Burial of infinitesimals), Cantor confirmed
such repudiation by affirming that a theory of the infinitesimals en acto had nothing to do with the
Differential Calculus or with the theory of functions. And nevertheless, in the
middle of the 20th century Abraham Robinson restored the concept of
infinitesimal magnitude in the prodigious construction known as Non Standard Analysis. Is then the
infinitely small the basis of this vraie
metaphysique du Calcul differentiel
that D’Alembert ascribed to the notion of limit? The debate remains open…
The infinite should be a relative concept, assures cosmologist Joe Silk. It will also be a source of metaphors in order to be able to express the universe, to enable a notion of origin that allows to talk about before the origin, to tell a story that seems to ramify in all the directions of its meaning, to fulfill the physicists’ dream who desired from the beginning of the 20th century to find a unique source of explanation that allows to comprehend the world as if it were unique.
Since its first edition in 1993, the International Ontology Congress
(IOC) has had the objective of assessing the current state of the questions concerning
the key interrogations of fundamental philosophy, considered in the light of
contemporary reflection. That’s why appearing on the Permanent International
Scientific Committee next to philosophers are eminent representatives of
contemporary science and art. The successive Congresses have been held under
the sponsorship of UNESCO.
The 3rd and 4th
IOCs were centered on the concept of Physis.
From the emergence of this concept in presocratic texts until the subversion
that Quantum Mechanics represented for our representations of the Physis (and concretely, theorems like
Bell’s theorem), passing through the handling of the concept in Physics by Aristotle, all angles of
approach were considered.
The 5th congress
(held in October 2002) was focused on the concept of the living that once
again, and without ever leaving historical perspective aside, was considered
from fascinating contemporary debates. Biology played the role of pivotal
discipline but the discussion was enriched with foci stemming from linguistics,
semiotics, psychology, chemistry, physics itself, and of course, ethics and
aesthetics, all considered from the vantage-point of a Kantian order (is there
or not an horizon of aims that, in the heart of the living, “transcendentally”
singularizes what is human?).
At the 6th IOC the organizers intended to
extend the reflection started at the previous congress, jumping however towards
the consideration of the problems from the intersection of biology and
linguistics. That is the reason of the title From the gene to language: state of the question. The honorary
President of the meeting was Hilary Putnam.
The 7th IOC had as title From Plato’s cave to Internet: the real and the virtual. It was held
under the patronage of UNESCO and the honorary presidency of John Searle. Never
like in our modern era have our perceptions, our aesthetic and ethical
judgments, and our cognoscitive efforts been so influenced by information
(driven by digits) with two-dimensional rendering. Digital modeling has allowed
prodigious advances, for example, in the field of medicine. It has even been
said that, even purely theoretical reflection (scientific or philosophical)
would be de facto impossible today without digital paraphernalia. To what other
people object that Einstein, Niels Böhr and even John Bell are more a cause
than the fruit of technological sophistication and that science worthy of its
name continues meeting the everlasting objective of knowing, of which
technology must continue to be a mere instrument. The subject of reality and
virtual reality present different fronts that involve from mathematical
simulation to cybernetics, molecular biology, neurobiology, passing through
cognitive psychology, etc. Contemporary physics is as well a prominent aspect
where the term “virtual” is applied to phenomena that violate the classic laws
of conservation when that violation is directly undetectable. It was not left
aside the concept of “virtual” in art
and, very specifically, in music.