Many attempts to define determinism, the philosophical notion that everything that happens in the universe is pre-ordained or pre-decided, involve the notion of causality. A causal chain or graph of events, driven by the laws of physics, is supposed to explain how determinism can be. In this view, the state of the universe at any time is determined once we have an initial state of the universe and a set of physical laws which allow us to compute the state of the universe at any time. Of course, since we are also part of the universe and are thus subject to its laws, some thinkers construct these arguments from the viewpoint of a hypothetical “demon” residing outside the universe and unaffected by the universe’s laws.
In what follows, I will argue that the most common notion of causality, based on counterfactual outcomes, is meaningless in a deterministic universe. We may have to adopt a definition of causality which relies on computability within the universe: A causes B if we can start with state A and compute a sequence of state changes induced by the laws of the universe, ending in B.
Counterfactual Causality Fails in a Deterministic Universe
According to the Wikipedia entry on determinism:
Causal (or nomological) determinism is the thesis that future events are necessitated by past and present events combined with the laws of nature.
The Wikipedia entry on Causality has this to say:
The philosopher David Lewis notably suggested that all statements about causality can be understood as counterfactual statements. So, for instance, the statement that John’s smoking caused his premature death is equivalent to saying that had John not smoked he would not have prematurely died.
The incompatibility between determinism and causality is now easy to see: if causality is defined counterfactually, then any event A which occurs before an event B is causally responsible for B. This is because the statement “If A had not occurred, then B would not have occurred” is meaningless in a deterministic universe. “If A had not occurred” is like saying “If 1 equals 2″, because determinism says that A occurring is the only possibility. Thus, if A occurs before B, then A is causally responsible for B.
Causality as Computation
Perhaps a modified definition of causality will help take care of this problem. Suppose that, by “A causes B”, we mean that a computer within the universe is able to find a chain of applications of the laws of the universe which takes the universe from state A to state B (via some sequence of intermediate events). Then we can say that A causes B. Note that this definition refers to the ability to compute or the ability to understand.
The definition is not yet valid, however. What if, given any two events A and B, we can compute such a sequence of intermediate events? Then this definition would be no more useful than the previous one based on counterfactuals. We may have to abandon an attempt to define causality as either true or false (A causes B or A does not cause B) and accept a definition based on degrees of causality. Thus, if the chain of intermediate events going from A to B is long, we say the relationship is “less causal”, and if it is short, we say it is “more causal”.