Negation, material incompatibilities and inferential thickness: a Brandomian take on Middle Wittgenstein
Abstract
By 1929, after the full acknowledgment of the colour–exclusion problem, Wittgenstein had to admit that material incompatibilities presented in conceptual systems (Satzsysteme) could not be reduced to formal tautologies and contradictions. Wittgenstein then, in his middle period, had to examine the kind of negation which, for instance, colour systems should render, which expose not just one but many or, in some cases, infinite inferentially articulated alternatives. Here, inspired by Brandom’s inferentialism (1994, 2000, 2008), I explore the idea that Wittgenstein, in his middle period, advocated a form of inferentialism based on the inferentially articulated content of propositions in Satzsysteme. At that time, Wittgenstein suggested that every sentence should be logically connected to many others. I call this feature inferential thickness. Therefore, I use Löf’s (2013) normative read of verificationism to explain Middle Wittgenstein’s holist solution to problems concerning the use of negation related to material incompatibilities and determination of propositional sense. I also investigate the distinction between contrariety and contradiction and some possible connections to a mandatory restriction of the principle of excluded middle in Satzsysteme.
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