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, Open Court, La Salle, Ill., 1974), p. 56. On pp. 55-56 he writes: “it is most important for us clearly to recognize first and foremost that the law of causality relates solely and exclusively to changes of material states, and to nothing else whatever. Consequently, it must not be introduced when these are not mentioned. Thus the law of causality is the regulator of the changes undergone in time by objects of external experience; but all these are material. Every change can take place only through another having preceded it, which is determined according to a rule, but by which it then takes place as having been necessarily brought about. This necessity is the causal nexus.” (Italics in the original translation.) He begins this book with an emphatic distinction between the idea that there must be a reason for all things and the idea that the existence of each thing must have a cause. He also emphatically rejects all forms of the cosmological argument, and mocks the Hegelian “Absolute” as a ruse to get around Kant’s demolition of all attempts to prove the existence of God. His points against Hegel might be used against Heidegger. Or at least, the attempt to do so would appeal to many analytic philosophers, possibly including Wittgenstein. Schopenhauer might accept 5.135 and 5.136. He surely would reject 5.1361. For Schopenhauer, the relation between cause and effect is necessary, and the law of causality is a form of the principle of sufficient reason, on which all necessity is based. See p. 63.

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?