The proofs of the Grundgedanke in Wittgenstein's Tractatus

The Tractatus contains two different proofs of the Grundgedanke, or the nonreferentiality of logical constants. In this paper, I explicate the first proof in TLP 5.4s and reconstruct the less explicitly stated second proof. My explication of the first proof shows it to be elegant but based on an invalid inference. In my reconstruction of the second proof, the main argument is that the sign of a logical constant does not denote because it possesses the punctuation-mark-nature. And it possesses the punctuation-mark-nature because, given the analyticity thesis in TLP 5, one can establish for everyday language an adequate symbolism with N as the sole fundamental operation such that its sign is a bar indicating merely the order and scope of its application.