Tractatus on Causality

From Tractatus' logical point of view, outside logic everything is accidental (6.3). It is not at all surprising. To say so, we must first clarify what it means by accident. If we define an accident / contingency to be a fact (what is a fact anyway?) that are not necessarily true or necessarily false (a priori), then such a statement becomes clear. (Of course we shall thereby ask what it means by something being necessary / a priori. It may turn out that the claim at 6.3 just follows immediately from a definition!) As it is stated in Tractatus,

• in logic nothing is accidental (2.012);
• there are no pictures that are true a priori (2.225);
• all deductions are made a priori (5.133);
• this is connected with the fact that no part of our experience is at the same time a priori (5.634).

According to Tractatus, propositions in logic have no sense, not to mention the truth or falsity of the senses (e.g. 6.111). On the other hand, the totality of true propositions is the whole of natural science (4.11).

Furthermore, there is no causality in logic (5.135 and 5.136). We cannot infer the events of the future from those of the present. Belief in the causal nexus is superstition (5.1361). However, in natural science there are laws of the causal form, 'law of causality' (6.321). Buddhists believe in Karma, while Schopenhauer considered the principle of sufficient reason a priori. As stated at 6.34, the principle of sufficient reason is a priori insight about the forms in which the propositions of science can be cast.

Aristotle also says in Posterior Analytics that to know a thing’s nature is to know the reason why it is (Book 2, Part 2), and we think we have scientific knowledge when we know the cause (Book 2, Part 11). Natural science cannot tell us anything that happens for no reason. Consider the law of thermal expansion that states how the length of a metal bar changes according to the changes of its temperature. To an effect, there may be more than one cause. The length of a metal bar will also be changed if it is being hammered on the ends. When a physicist states such a law, he / she is in fact assuming implicitly not only that other causes to the effect do not happen, but also that the effect must happen for some reason. Thermodynamics can tell you the length of the metal bar after the change of its temperature if you know its initial length, assuming all other conditions such as pressure remain unchanged. If a metal bar would expand without any reason, how could thermodynamics predict the length of such a metal bar? Sciencists, including quantum physicists, also believe in the principle of sufficient reason (even though God does throw dice).

Wittgenstein then says at 6.41 that:
For all that happens and is the case is accidental. What makes it non-accidental cannot lie within the world, since if it did it would itself be accidental. It must lie outside the world.

Besides, Wittgenstein in fact has neither told us what in the world are states of affairs, nor given us any examples. It is because the facts, and the existence of states of affairs, are all accidental. Even the existence of the world is accidental. Not only Existentialists like Sartre think so! (Of course Existentialists mean differently by something being accidental.)

In Tractatus (philosophy), Wittgenstein tries to draw a limit to not only what can be said (natural science), but also what is not accidental (logic).