Further to the connections between meaning and use, it seems useful to consider the (explanation of the immediate) consequences one is allowed to draw from a proposition as something directly related to its meaning/use. And indeed, Wittgenstein's references to the connections between meaning and the consequences, as well as between use and consequences are sometimes as explicit as his celebrated ‘definition’ of meaning as use given in the Investigations. Here we attempt to collect some of these references, discussing how an intuitive basis for the construction of a more convincing proof-theoretic semantics (than, say, assertability conditions semantics) for the mathematical language can arise out of this connection meaning/use/(explanation of the immediate) consequences.1

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