“must have in common with reality in order to be able to represent it.” This
form is shown but it is not said in the proposition; in order to do so “we
should have to be able to station ourselves with propositions somewhere
outside logic, that is to say outside the world” (Tractatus 4.12).
Similarly, in discussing Frege’s technique of functions and their contents,
the fundamental break from the subject-predicate logic, Wittgenstein points to
a category of formal concepts beyond those discerned by Frege. These are not
represented or said by the function but are shown by the kind of sign being
used: name signifiers for objects, number signs for numbers, operation signs
for operations, and so on (Tractatus 4.126–4.1272). In effect this is a gener-
alization of Frege’s founding of the number system on cardinal numbers,
Platonic essences of numbers which are beyond the ordinal numbers of em-
pirical counting. The most innovative part of Wittgenstein’s version is that
Platonic forms are no longer taken as the highest species of the rationally
intelligible; quite the opposite, they are what is unsayable. With the weapon
of the unsayable/showable, Wittgenstein is able to defend still further realms,
the higher reality of ethics and mystical religion, unaffectable by anything that
can be said on the merely verbal level.
Wittgenstein’s distinction between saying and showing crystallizes from
several aspects of Frege and Russell’s work: Platonism, knowledge by acquain-
tance, and the difficulties of the theory of types. Saying/showing is supposed
to obviate the theory of types. Actually it grows out of it, a reformulation and
extension of the basic thrust of Frege and Russell in exploring the relations
among hierarchical levels in propositions. Wittgenstein declares that the theory
of types is unnecessary to avoid paradox because the different kinds of symbols
used in a logical language directly show that various kinds of realms are to be
treated differently and cannot be mixed. Implicitly, one knows that the kind
of thing symbolized by “a” or “b” plays a different role from those symbolized
by “x,” “y,” “z.” The source of Wittgenstein’s discovery of the saying/showing
distinction is his explicit investigation of the way symbols do their work
(Monk, 1990: 92; Tractatus 4.0312–4.0411). He resists the habit of seeing
symbols as purely conventional, which had blinded previous logicians from
seeing how symbols are chosen through their success or failure in expressing
various things.^20
Frege and Russell had developed logic symbols in the course of developing
their programs; now Wittgenstein turned the technique of meta-attention,
which he had learned from his predecessors, on what they were doing. Wittgen-
stein’s move was like breaking a gestalt frame, since it is virtually impossible
to see the structures of symbol use while we are wielding them for some
purpose. This is why Wittgenstein had such an intense and painful struggle to
realize what could be done next, and to express in words an insight about
716 •^ Intellectual Communities: Western Paths