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ernard burgoyne
as well as natural sciences, and, among other themes, detailed mathematics
(geometry, arithmetic, and “mathesis” generally), astronomy, grammar, and
the interpretation of dreams. 19 Koyré’s version of the rise of the mathematical
sciences revolves around his reading of these trajectories that started with
Agrippa’s text, De incertitudine et vanitate scientiarum (On the Uncertainty
and Vanity of the Sciences). As the supposed unity of the world “fell into
shreds” the questioning that had produced this effect itself became something
that was put into question. The questioning of world-views became
subject to analysis.
As Descartes took up the problems of what can be called a program of
“critical skepticism,” he found that the philosopher is constrained to adopt
a position that had already been forced on Montaigne: he “interrogates the
questioner.” This Socratic questioning of the subject is engaged in the early
parts of the psychoanalytic cure; 20 that it was a forced step in the Cartesian
development of science is part of the presentation that Koyré gives of these
developments. It was Descartes, according to Koyré, who pushed further
the “analyses” initiated by Montaigne; the mathematization of the world
introduced by Descartes appears simply, in this perspective, as a consequence
of taking such an analysis “to its end.”
Koyré stresses – contra the attempts of Bacon and Locke to move science
towards “presuppositionless” foundations – that any experience of, or experiment
on, the world “presupposes a previous theory.” He is even more
specific than this. Towards the end of his first lecture he says, “experience
(of the world) implies a language within which one addresses it.” It is “impossible,”
says Koyré, for any experience of the world not to draw on the
language used to give a formulation to it.
Koyré sees the heart of Descartes’ program in the formulation that he
gives to a proposition known since the time of classical Greek science and
philosophy, that nature speaks the language of mathematics. It is in this
language, says Koyré, that nature will respond to the questions that a science
puts to it. In this way the real conditions of our existence – questions of
physics and questions of the nature of the human soul – can be formulated
within a metaphysics of what Koyré calls “the real value of mathematicism.”
In putting it thus, Koyré is taking informal descriptions of the world – and
certainly “common sense” – to be clothed in what he calls the “imaginary”;
the virtue of mathematical structure is that it allows such imaginary formulations
to be left behind, as it opens up pathways that allow access to what
is real.
Any such restitution of the sciences places mathematical relations at the
center of its program. Koyré states that a science – in Descartes’ view –
needs a metaphysics: it is formulated and develops within a metaphysical
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