Witti-Buch2 2001.qxd - Austrian Ludwig Wittgenstein Society

The Net Metaphor Reconsidered: Wittgenstein's Conception of Science in the Tractatus
This can be illustrated by Wittgenstein's own example of the theory of heat borrowed
from Boltzmann. Heat is described completely when it is conceived as a movement of
the smallest particles. In the Notebooks Wittgenstein identifies the smallest particles with
the material points of physics: "The division of the body into material points, as we have
it in physics, is nothing more than analysis into simple components." (20.6.15).
At the end of 6.342 Wittgenstein contends that "we are also told something about
the world by the fact that it can be described more simply with one system of mechanics
than with another". He might allude here to different representations of mechanics as
discussed by Hertz in the introduction of The Principles of Mechanics. In the section of
the Notebooks where he unfolds the net metaphor, Wittgenstein refers to Hertz's hidden
masses. These play an important role in Hertz's representation of mechanics. However,
while Hertz leaves open the possibility of verifying these hidden masses empirically,
Wittgenstein states that Hertz's hidden masses are generally considered as pseudoobjects
(Scheingegenstände). This verdict Wittgenstein has probably taken from
Boltzmann who criticized Hertz's mechanics in his Populäre Schriften. Boltzmann
pointed out that he had been unable to find hidden masses that would lead to acceptable
solutions when Hertz's mechanics were employed. He concluded that "so long as even
in the simplest cases no systems or only unduly complicated systems of hidden masses
can be found that would solve the problem in the sense of Hertz's theory, the latter is
only of purely academic interest." (Boltzmann 1974, 90). The unwieldiness of Hertz's
mechanics led to Boltzmann's well-known statement: "I have often heard Hertz's
mechanics praised, yet never seen anyone pursue the path he indicated" (Boltzmann
1974, 88). I suggest that this brought Wittgenstein to saying that the world "can be
described more simply with one system of mechanics than with another."
The parallel between Wittgenstein and Boltzmann also explains why Wittgenstein in
his philosophy of science only takes mechanics into account. First, Wittgenstein, just like
Boltzmann, considers mechanics as the foundation of physics: "Just as with the numbersystem
we must be able to write down any number we wish, so with the system of
mechanics we must be able to write down any proposition of physics that we wish"
(6.341). Secondly, for Wittgenstein, as for Boltzmann, mechanics is not just the
foundation of physics. It is the foundation of every science; "All propositions used in the
description of the world must be obtained in a given way from a given set of propositions
- the axioms of mechanics." Both conceive mechanics as a general theory that is
applicable, at least in principle, to all kinds of phenomena, as a means to give an allembracing
picture of the world.
From the foregoing comparison of Wittgenstein with Boltzmann I conclude that
Wittgenstein's philosophy of science in the Tractatus was directly influenced by
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