  Wittgenstein's paradoxical theses that unproved propositions are meaningless,
proofs form new concepts and rules, and contradictions are of limited concern,
led to a variety of interpretations, most of them centered on the
rule-following skepticism. We argue that his intuitions rather reflect
resistance to treating meaning as fixed content, and are better understood in
the light of C.S. Peirce's distinction between corollarial and theorematic
proofs. We show how Peirce's insight that "all necessary reasoning is
diagrammatic", vindicated in modern epistemic logic and semantic information
theory, helps explain the paradoxical ability of deduction to generate new
knowledge and meaning.
