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This is a first-order theory of causality, so some familiarity with first-order logic is assumed. The goal of this theory is not to prove anything useful or unexpected, but to describe the structure of causal systems and to develop an elegant terminology to talk about causality.
According to this theory, the structure of causal systems is probably that of a directed acyclic graph.[1]
This theory makes heavy use of the formal dictionary.
b is an individual constant with intended reading "Big Bang".
This is a primitive term. You can help the formal dictionary by finding a good definition for it. |
Event is a primitive term, an undefined term used to define others. You can get an intuitive grasp of the intended meaning of the term by reading the article Event (philosophy) at Wikipedia.
Ex is a one-place predicate with intended reading "x is an event".
This is a primitive term. You can help the formal dictionary by finding a good definition for it. |
Cause is a primitive term, an undefined term used to define others. You can get an intuitive grasp of the intended meaning of the term by reading the article Cause at Wikipedia.
xCy is a two-place predicate with intended reading "x is a cause of y".
The definitions in this section are all taken from the Formal dictionary.
Let c and e be events. Then e is an effect of c means: c is a cause of e.
Let c, d and e be events. Then c is a direct cause of e means: c is a cause of e and there is no d such that c is a cause of d and d is a cause of e.
Let c and e be events. Then c is an indirect cause of e means: c is a cause of e, but c is not a direct cause of e.
Let c and e be events. Then c is causally independent of e means: c is not a cause of e and e is not a cause of c.
Let e be an event. Then e is a first cause means: there is no event c that is a cause of e.
Let e be an event and ε be a set of events. Then ε is a full set of causes of e means: for every event c that is a cause of e, c is an element of ε.
A sequence of events (e1, e2, e3 ..., en) is a causal chain means: e1 is a cause of e2, e2 is a cause of e3 and so on until en-1 is a cause of en
The Big Bang is a first cause.
Every event has at least one effect.
If event c is a cause of event e, then e is not a cause of c.
If event c is a cause of event d, and d is a cause of event e, then c is a cause of e.
Let c and e be events. Then:
No event is a cause of itself (causality isn't reflexive).
For a proof by contradiction, suppose some event e is a cause of itself. Then by the axiom of asymmetry, e is not a cause of itself. But this is a contradiction, so no event can be a cause of itself. QED
If event c and event d are both direct causes of event e, then c and d are causally independent.
For a proof by contradiction, suppose c and d are both direct causes of e, but are not causally independent. Then c must be a cause of d, or d must be a cause of c, or both. It cannot be both, because causality is asymmetric. So suppose c is a cause of d. Then c is an indirect cause of e, as well as a direct cause. But this is a contradiction. The same happens if we suppose d is a cause of c. Therefore, c and d must be causally independent. QED
The Big Bang is in every full set of causes.