Witti-Buch2 2001.qxd - Austrian Ludwig Wittgenstein Society

Remko van der Geest
Wittgenstein commentators have sofar neglected the example of the theory of heat
that Wittgenstein has given for his philosophy of science 3 . The main reason for this
neglect, I suggest, is that one has concentrated on the influence Hertz had exerted on
Wittgenstein via his Principles of Mechanics. In this work, of course the theory of heat
doesn't appear as subject matter at all.
By further investigation of Boltzmann's writings we find more similarities between
Wittgenstein's and Boltzmann's thought. Throughout his work Boltzmann has
emphasized the importance of model building in science. "[O]ur thoughts stand to things
in the same relation as models to the objects they represent. The essence of the process
is the attachment of one concept having a definite content to each thing [...]. What
resemblance there is lies principally in the nature of the connexion, the correlation being
analogous to that which obtains between thought and language, language and writing,
the notes on the stave and musical sounds, etc." (Boltzmann 1974, 214). This modelconcept
is, of course, remarkably similar to the Tractarian relation world-languagethought,
in which each element is a picture of the others. I refer the reader especially to
theses 2.12, 3.21, 4.01 and 4.011, where Wittgenstein discusses models and even uses
the same examples as Boltzmann.
Now, in what way are models used in mechanics? "In theoretical mechanics models
are often used to exhibit the physical laws of motion in interesting or special cases e.g.
the motion of a falling body or of a spinning-top, the movement of a pendulum on the
rotating earth, the vortical motions of fluids, etc." (Boltzmann 1974, 216). In these
mechanical models "we express longitude, mileage, temperature, etc. by numbers,
which should be looked upon as arithmetical analogies. Of a kindred character is the
representation of distances by straight lines, of the course of events in time by curves,
etc." (Boltzmann 1974, 214). In the same manner Wittgenstein describes in 6.341 and
6.35 how we apply to the world a purely geometrical network, the properties of which are
given a priori by the principles of mechanics. Mechanics "thus supplies the bricks for
building the edifice of science, and it says, 'Any building that you want to erect, whatever
it may be, must somehow be constructed with these bricks alone.'" (6.341)
According to Wittgenstein "the possibility of describing the world by means of
Newtonian mechanics tells us nothing about the world: but what does tell us something
about it is the precise way in which it is possible to describe it these means." (6.342).
This can be clarified by using Boltzmann's example of model building mentioned earlier.
That we can represent distances by straight lines and the course of events in time by
curves tells us nothing about the world. Only the result of imposing such a form of
representation to the description of the world gives us information. We obtain a complete
description of the world by choosing a form of representation that is sufficiently detailed.
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