Hume challenged other philosophers to come up with a deductive reason for the inductive connection. If the justification of induction cannot be deductive, then it would beg the question. To Hume, induction itself, cannot explain the inductive connection.
Wittgenstein's early account of causation in TLP follows Hume in rejecting the idea of
causal necessity. There is only one kind of necessity, namely logical necessity;
'outside logic everything is accidental.' This means that there is 'no
causal nexus' to justify an inference from the existence of one situation
to that of another. Hence, too, there is no 'compulsion' that one
thing should happen because another has happened, and we cannot know
future events (TLP 5.135-5.1362, 6.3, 6.36311-6.372).
In other words, induction (TLP 6.3f.) has only a psychological justification; 'there are no grounds for believing that the simplest eventuality will in fact be realized.' For the 'law of induction', according to which nature is uniform - will carry on the way it has in the past - has no logical justification. Everything outside logic, in the domain of empirical science, is 'accidental'. In particular, causation is neither a real nor a necessary connection between events. Consequently we cannot know that the sun will rise tomorrow. "The events of the future cannot be inferred from those of the present.Superstition is the belief in the causal nexus". For reasoning yields knowledge only if the premises are known to be true and entail the conclusion; but the existence of one situation never entails the existence of another. Wittgenstein supposition is that knowledge requires certainty.
Like other so-called 'fundamental' laws of science, the 'law of causality',
according to which every event has a cause, is not a law, but 'the form of a
law'. This means that it is neither a law of logic, nor an empirical generalization,
nor a synthetic a priori proposition. Indeed, it is not
a proposition at all, since it tries to say what can only be shown. What it
indicates is a certain 'form of description' which is crucial to scientific theorizing
(TLP 6.321f.). Descriptions which connect events in a non-lawlike
manner are excluded from science. To characterize something as an event is
to imply that it is explicable by reference to some often unknown causal
law. Causation itself is a formal concept. It characterizes not reality, but the
'network' of an optional form of representing reality, such as Newtonian
mechanics (TLP 6.33-6.341, 6.36f., 6.362).
Wittgenstein's later thoughts after TLP on causation focuses on the way we
establish causal connections in everyday life, not in science, and the results challenge crucial aspects of the Humean position. Wittgenstein makes the claim that
the principle of causality, 'Every event must have a cause', is not a synthetic
a priori truth, as Kant thought, but a disguised rule of grammar.
If this means that our grammar simply rules out as nonsensical the expression
'uncaused event', it is wrong. But one might argue that it is a norm of
representation of classical mechanics that it always makes sense to look for
the cause of an event, even if no plausible candidate is in sight.