Finite Boundless Lines
Consider this Time Troika:
Moe says that time is linear, bounded, and finite; an interval.
Larry says that time is linear, unbounded, and infinite; a line.
Curly says that time is circular, unbounded, and finite; a loop.
2/3 (KM) say: time is finite.
2/3 (LK) say: time is unbounded.
2/3 (ML) say: time is linear.
But all agree that time can’t be all three.
If Moe gives time a beginning but no end, then the trilemma is: time is finite; past time is unbounded; past time is linear. If Moe gives time an end but no beginning, then the trilemma is: time is finite; future time is unbounded; future time is linear.
These are both what I call a Line/Ray/Loop Troika. The line, ray and loop needn’t be in time; they can be any ordered sequence, continuous or discrete. In a line/ray/loop troika:
Moe sees a Ray: the sequence has an endpoint.
Larry sees a Line: the sequence extends to infinity.
Curly sees a Loop: the sequence cycles.
Majorities affirm this “Finite Boundless Line” trilemma:
The sequence is finite;
The sequence is unbounded;
The sequence is linear;
- but all agree that the sequence is not all three!
Now consider this “Agrippa Troika”:
Moe: There is an unexplained first explanation.
Larry: Explanations regress to infinity.
Curly: Explanation is circular.
In this troika, dogmatic Moe has an explanatory Ray, infinite-regressing Larry has an explanatory Line, and circular-reasoning Curly has an explanatory Loop. Majorities affirm:
Explanation is finite;
Explanation is complete;
Explanation is noncircular.
But not all three! That is the “Munchausen Trilemma”:
Any explanation can be at most two of:
Finite; that is, some explanation explains all others;
Complete; that is, every explanation is explained;
Noncircular, that is, there are no explanatory loops.
The Munchausen Trilemma describes a finite boundless line of explanations. Finite, complete and noncircular is called normality; an illusion created by paradox.
The line/ray/loop troika applies to the Paradox of the First Cause. Define the First Cause as the cause of all causes; then 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:
In the Line, there is no first cause, but instead an endless backwards sequence of causation. The Line is a theory of infinitely deep causation.
In 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 in 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, based upon 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 Ray and Loop, causation has finite depth;
In Loop and Line, causation is recursive;
In Line and Ray, causation does not loop.
So by 2/3 majorities: causation is finite; causation is recursive; causation is linear; but not all three! That’s the Causation Trilemma, a finite boundless line. Cause has a beginning, every cause has a cause, cause is one-way; deny one!
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 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 Trilemma, another finite boundless line. Effect has an end, every effect has an effect, effect is one-way; deny one!