Witti-Buch2 2001.qxd - Austrian Ludwig Wittgenstein Society

Is Logic Syntax of Language?
contained in the insight that knowing the syntax of a sign-language is sufficient for
knowing all the logical truths thereof. (6.113 and 6.124) 4 There is further agreement that
for a sentence to be analytic, synthetic, or contradictory is for it to have a certain formal
structure. (See 1.2 below.) Here Carnap reports having followed Weyl, but the
agreement with Wittgenstein remains. 5
1.2 The Truths of Logic are Tautologies, Lacking Content
Wittgenstein states in the Tractatus that whenever a combination of signs is such
that every possible state of affairs is consistent with it, then it is tautologous. (4.46ff)
Since a proposition only has sense insofar as it is a possible picture of reality, and
tautologies do not represent any particular state of affairs, tautologies have no sense.
Wittgenstein then claims, "The propositions of logic are tautologies. Therefore the
propositions of logic say nothing. (They are the analytic propositions.) All theories that
make a proposition of logic appear to have content are false." (6.1-6.111)
Carnap employs a similar conception of content, holding that the content of a class
of sentences is the class of its non-valid consequences. (LSL, p. 175) That is, the
content of some sentence S will be the set of all states of affairs it entails and contradicts.
Since logical truths have only valid entailments, they have no content. Commenting on
the influence of the Tractatus on his thought, Carnap mentions as one of the most
important theses, "Logic is tautological, says nothing about the world (Bracket: 'that is
entirely new.')" 6
1.3 Logical Consequence is a Syntactic Relation between Sentences
The view that logical consequence is governed by rules of syntax is clearly
expressed in the Tractatus: "When the truth of one proposition follows from the truth of
others, we can see this from the structure of the propositions." (5.13) Later, in his
conversations with Schlick and Waismann, Wittgenstein states: "That inference is a
priori means only that syntax decides whether an inference is correct or not." (WVC, p.
92) 7 Remembering that for Carnap syntax governs the formation and transformation of
sentences, we see a symmetrical view of logical consequence: "We have called a
sentence C a consequence of a class P of sentences - the premises - if there is a chain
of sentences constructed according to the transformation rules connecting the class P
with the sentence C." (PLS, p. 51) The upshot here is that the consequence relations
change whenever there is a change in the syntax.
1.4 Convention Alone Determines What Logical Syntax is Employed
The idea that nothing dictates a correct syntax is a departure from the Tractarian
view that "[l]ogic is […] a mirror-image of reality." (6.13) The view that we postulate the
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