I constructed the following Surreality Troikas in response to five proofs by Aquinas of the existence of God.
Zeroth Mover Troika.
If the First Mover is that which sets all other things into motion, then define the Zeroth Mover as that which set the First Mover into motion. Then either; there is no first mover, and motion has been eternal; there is a first mover but no zeroth mover, and hence an unmoved mover; or there is a first mover and a zeroth mover, which set each other into motion.
Let the Stooges take each of these positions; then these propositions pass: there is a First Mover, every mover is moved, there is no Zeroth Mover.
Zeroth Cause Troika.
Define a zeroth cause as that which causes the first cause. As above, then either there is no first cause because causation goes back infinitely deep; or there is an uncaused first cause; or first and zeroth cause cause each other.
Let the Stooges take each of these positions; then these propositions pass: there is a First Cause, every cause is caused, there is no Zeroth Cause.
Define a pre-necessary being as a being which necessitates the most necessary being. Proceed as before; either there is no most necessary being, or there is a most necessary being that is itself not necessary; or there are at least two beings necessary to each other.
Let the Stooges take each of these positions; then these propositions pass: there is a most necessary being, all beings are necessitated, there is no pre-necessary being.
Define a trans-maximal being as a source of the maximal being. Then, as before, either there is no maximal being, and an infinite sequence of ever-greater beings; or there is a maximal being not surpassed, and hence without source; or there are at least two beings greater than each other, and each other's source.
Let the Stooges take each of these positions; then these propositions pass: there is a maximal being, all beings have a source in something greater, there is no trans-maximal being.
Sub-Prime Intelligence Troika.
Define a Prime Intelligence as one that directs all things, or at least directs their directors. Now define a Sub-Prime Intelligence as an intelligence that directs the Prime Intelligence. Proceeding as before: either there is no prime intelligence, and there are directors to infinite depth; or there is a prime intelligence itself undirected by intelligence; or there are two intelligences which direct each other.
Let the Stooges take each of these positions; then these propositions pass: there is a Prime Intelligence, all intelligences are intelligently directed, there is no Sub-Prime Intelligence.
In each of these troikas, a putative maximum/prime/necessary/first entity is undermined by a transmaximal/sub-prime/pre-necessary/zeroth entity. What maximum, prime, necessary and first had in common was superior reality. Time for a troika!
So define ‘surreality’ to be that which exceeds a ‘greatest reality’. There are three possibilities; the Line, the Ray, or the Loop. Either the realness order is endless, with no greatest reality; or it ends at an edge, with an unsurpassed greatest reality; or it loops, with two realities exceeding each other. All three options are unintuitive; endless reality depth is incomprehensible, an edge of reality is chaotic, and a reality loop is paradoxical.
Let the Stooges take each of these positions; then these propositions pass: there is a greatest reality, any reality is exceeded, there is no surreality. That is, reality is founded, reality is transcended, reality is unparadoxical; choose two!
This resembles the Munchausen Trilemma mentioned previously; namely, that any explanation is at most two of: finite, complete, noncircular. We can phrase the Munchausen Trilemma as a Some-All-None Trilemma, thus: some explanation is final; every explanation is explained; there are no explanatory loops; choose two. The Stooges uphold each by 2/3, yet all agree that one must go. Finite, complete and noncircular is what we call normality; an illusion created by paradox, whose failures define deduction.