Jean
le Rond d'Alembert is a name more often heard in a history of
mathematics than in a history of philosophy. Yet, his connections to
the world of philosophy in French Enlightenment are not non-existent,
because he was one of the editors of the famous Encyclopédie,
an encyclopedia meant to cover all human knowledge of the time.
D'Alembert was particularly entrusted to care for all the articles
engaged with natural sciences, but he also wrote a preliminary
discourse explaining the purpose of the work and also engaging with
some philosophical underpinnings of it and presenting a general
framework for all sciences.
The
book I am engaged with here belongs on the surface to d'Alembert's
more scientific works, as even the name suggests. In effect, the
purpose of d'Alembert in this treatise is, firstly, to present some
fundamental principles for movement of material objects, such as
inertia, and secondly, based on these principles, to solve some
tricky problems, in which, for instance, the velocity of a body
hanging from a thread is to be determined.
The
topic of d'Alembert's treatise is then something that modern students
of physics might find useful to consider. On the other hand,
d'Alembert's method of presenting his result has some quaint
elements, which show his work to belong to a transitional period
between a geometric presentation of Greeks and algebraic presentation
familiar in modern mathematics and physics. This is firstly shown by
d'Alembert's assumption that everyone knows truths that have been
demonstrated by Euclid in his Elements, as he without any
explanation refers to a property of a circle that if two lines AB and
AC are drawn from the same point A outside circle so that AB touches
the circle on B and AC goes through a point D of the circle and then
cuts circle also in the point C, then the square of the side AB
equals a rectangle formed by AD and DC or AD x DC. While a modern
student of mathematics might even have some difficulties following
this description, let alone being convinced of it, any connoisseur of
mathematics from d'Alembert's time would instantly recognise this
statement as the proposition 36 in the third book of Euclid'sElements.
Even
more clearly this transitional nature is seen in d'Alembert's habit
of embodying quantities like velocity, time and others with lines,
which for an eye unused to geometric way of presentation seem to have
no connection with each other, although one acquainted with this
method could see what mathematical relation the different lines are
supposed to exhibit. Then again, in more difficult cases d'Alembert
prefers algebraic denotations of mathematical relation. What makes it
all even more confusing is that while d'Alembert clearly had an
inkling that some quantities (e.g. forces) have a direction, neither
the geometric presentations nor algebraic formulas clearly
distinguish between scalar and vector quantities. Add to all this the
rather muddled view of infinitesimals at the time, in which e.g.
differentials of various levels were represented by lines that are
supposed to be infinitely small, and a modern reader is bound to feel
some puzzlement.
Philosophically
most interesting part of the book is, as is often the case with such
treatises, the preface. Here we find d'Alembert's take on the muddled question of ”living forces”, seemingly physical problem that
still interested such philosophers as Descartes, Leibniz and Kant.
The controversy itself started from the apparently obvious notion that
something remains same in various interactions of bodies, such as
collisions and that this same element would represent the quantity of
motion itself. Descartes, among others, had suggested that this must
be what is nowadays called momentum or mv, in which m
means mass of the bodies involved and v their velocity. Some
people, such as Leibniz, objected that what is conserved is actually
a more intricate quantity, ½(mv^2). Leibniz also asserted that this
quantity expressed a living force of the moving bodies themselves,
while momentum was connected only with dead forces affecting bodies
externally.
D'Alembert
strategy, at least in the first edition of the treatise. is to deny
that there is any true controversy. Momentum is conserved in
momentanous collisions of bodies, while Leibnizian quantity of motion
is conserved in cases where e.g. a medium continuously resists the
movement of a body. Now, the case of a resisting medium can be
regarded as an infinite sum of infinitely small collisions, which
mathematically means that Leibnizian quantity of motion must be an
integral of momentum, as it truly is. Which one to take as the more
essential expression, d'Alembert concludes, is just a verbal quibble.
Although
d'Alembert's solution is, as far as I know, quite correct, it also
expresses a more general tendency of disregarding all philosophical
problems as verbal quibbles – something quite common for modern
scientists. This tendency is shown by d'Alembert also with a question
concerning the status of physical laws : are they necessary or
contingent? D'Alembert attempts once again to show that both sides are
in a sense correct: laws of physics are contingent, because world
could have worked according to different laws, but they are also
necessary, if you take into account the empirical evidence about the
motion of bodies. D'Alembert fails to notice that he has actually
endorsed one side of the dilemma – contingency – and rephrased
the other side, so as to fit with the first side. Furthermore, from a
modern viewpoint, he has accepted a rather strong position . Not many
would accept that empirical data would fit in with just one physical
theory and thus necessitate it.
So
much for d'Alembert, next time another philosopher from French
Enlightenment.
