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, infiniteregressing Larry has an explanatory Line, and
circularreasoning 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 selfreferential paradox. Chaos, quantum and metamath are the 20^{th}
century’s threefold 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 oneway; 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 oneway; deny one!