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Matthias123
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Bx+2 α → Bx+1 α → Bx+0
*]Bx+0 ⊃□ B(x+2) α
*]Bx+0 ⊃ □ B(x+1) α
*]□ B(x+1) α ⊃ □ Bx+2 α
*]~ (Bx ⊃ ∃αB(x) α)
*]~B(x) α ⊃ ~ (Bx+2 α)
*]~ (Bx+2 α) ⊃ ~Bx+0 (1)
*]~Z ⊃ ~Bx+0
*]Bx+0 ⊃ □Z (1-5)
*]Bx+0
*]∴ □ Z
The movement of Bx+0 from potency to act implies that it is necessary for a prior mover B(x+1) α to exist. The movement of B(x+1) α from potency to act implies the existence of another prior mover Bx+2 α It is the case that the existence of Bx does not imply that Bx is a mover, because it cannot move-itself. (axiom of causality). If no entities that are movers exist, then the mover Bx+2 α does not exist. If the mover Bx+2 α does not exist, then the effect Bx+0 does not exist, because its existence is contingent upon Bx+2 α as stated in premise 1. If the hypothetical entity Z was did not exist, then the effect Bx+0 will not exist. So if Bx+0 exists then the existence of Z is necessary to it’s existence, as we have demonstrated from premise 1-5. Therefore since the effect Bx+0 exists, Z necessarily exists.
This argument has been constructed presupposing that a cause does not necessarily imply an effect.