Causation and Effectuation Troikas
Define the First Cause as the cause of all causes. The Paradox of the First Cause is; what caused the first cause? If there be any such cause, then let us call it a zeroth cause. Is there a zeroth cause? There are three possibilities.
One is “the Line”: there is no first cause, but instead an endless backwards sequence of causation. The Line is a theory of infinitely deep causation.
Another is “the Ray”: there is a first cause but no zeroth cause; so the first cause is uncaused. The Ray is a theory of chaotic causation.
And a third is “the Loop”: there is a first cause and a zeroth cause; and these cause each other. The Loop is a theory of circular causation.
The Line corresponds to chaos theory, with infinite fractal complexity. The Ray corresponds to quantum theory, with intrinsic random chance. The Loop corresponds to Goedelian metamath, with self-referential paradox. Chaos, quantum and metamath are the 20th century’s three-fold retort to determinism. Of the three:
In two of the three (the Line and the Ray), causation does not loop;
In two of the three (the Ray and the Loop), causation has finite depth;
In two of the three (the Loop and the Line), causation is recursive;
So by 2/3 majorities: causation is linear; causation is finite; causation is recursive; but not all three! That’s the Causation Troika. Cause is one-way, cause has a beginning, every cause has a cause; but choose two!
Dual to the First Cause is the Final Effect; the effect of all effects. Does the Final Effect have any effect? Either there is no Final Effect, or the Final Effect is ineffectual, or there is a Postfinal Effect.
This translates, as before, into three possibilities: Line, Ray and Loop. In the Line, effect is linear, recursive and infinite; there is no final effect. In the Ray, effect is linear, nonrecursive, and finite; the final effect has no effect. In the Loop, effect is circular, recursive and finite; postfinal and final are effects of each other.
Of Line, Ray and Loop, by 2/3 majority each: effect is linear; effect is finite; effect is recursive: but never all three.
That’s the Effectuation Troika. Effect is one-way, effect has an end, every effect has an effect; but choose two!
In general, Line/Ray/Loop yields this trilemma:
linear, finite, boundless; choose two.