5.136 There is no causal nexus that justifies such an inference.
How could a causal nexus (metaphysical) justify a logical inference? It couldn’t, but this underlines the importance of not confusing metaphysics and logic. Schopenhauer and Frege emphasize this point, in different ways.
Stenius (p. 60) says “By ‘causal nexus’ he obviously means the aprioristic certainty of causal connections.”
Black (p. 244) says “W. does not mean to deny the existence of causal regularities: he does deny that they are a priori.”
Frascolla (pp. 130-131) connects this remark and the next with 6.37. Wittgenstein is denying “that there is any necessity in the so-called causal nexus between the events of one type, identified as causes, and the events of another type, identified as effects of those cause.” (p. 130)
Schopenhauer refers to the causal nexus in The Fourfold Root of the Principle of Sufficient Reason (translated by E. F. J. Payne,
As for the law of causality being a priori, see Schopenhauer again, p. 110: “No one who himself has any intelligence will doubt its existence in the higher animals. But it is at times quite evident that their knowledge of causality is actually a priori, and has not resulted from the habit of seeing one thing follow another. A young puppy does not jump down from a table because he anticipates the effect.” He goes on to tell of his pet poodle’s being astonished by curtains that are moved by means of a cord pulled at the side. The dog naturally looked for the cause of the movement. Schopenhauer calls such a natural reaction a priori knowledge of the law of causality. If Wittgenstein denies that it is a priori, then what would he say instead? Has he an explanation?