(1): It is possible that the first contingent thing is caused to exist. (Premise)
(2): In the possible case where the first contingent thing is caused to exist, a
causally powerful necessary being must cause it to exist. (Premise)
(3): A causally powerful necessary being possibly exists. (From 1 and 2)
(4): A possibly causally powerful necessary being necessarily exists. (From 3, using the S5 theorem from the intro)
A “Sum-styled” Contingency Argument.^{1}
(1): Everything not existing by necessity (i.e. everything that could fail to exist) owes its existence to something external to itself. (For example, planets, lightning, and humanity each owes existence to something else.)
(2): Something exists (call it “Universe” or “Big Contingent Sum”) which is the sum of all these things which do not exist by necessity.^{2}
(3): Therefore, “Big Contingent Sum” owes its existence to something external to itself.
(4): Whatever exists externally to “Big Contingent Sum” obviously cannot itself be contingent (i.e. cannot be part of that sum).
(5): Therefore, whatever exists externally to "Big Contingent Sum" is not contingent; by definition it exists of necessity.
Conclusion: Therefore, “Big Contingent Sum” owes its existence to something that exists by necessity.
A “Start-styled” Contingency Argument.^{1, 2, 3}
(1): It is metaphysically possible for a first contingent thing's existing to be caused.
(2): In this possible (even if non-actual) scenario, a non-contingent causer must exist to cause that first contingent thing.
(3): So this non-contingent (necessary) causer exists in this possible scenario.
(4): If a necessary entity exists in any truly possible scenario, then it exists in all possible scenarios. (Existing in all possible scenarios is just what it means to be necessary.)
(5): Therefore, the necessary causer in that actual or non-actual scenario exists.
Alexander Pruss's Contingency Argument (2009)^{1} is presented as a series of steps:
(1): Every contingent fact has an explanation.^{2}
(2): Some contingent fact includes all other contingent facts.
(3): Therefore, there is an explanation of this fact.
(4): This explanation must involve a necessary being.
(1): Any genuinely possible event is possibly caused.
(2): A Big Bang event in which there is an ultimate beginning of contingent things is a genuinely possible event.
(3): Therefore, such a Big Bang event is possibly caused.
(4): Only a necessary being could cause an ultimate beginning of contingent things.
(5): Therefore, a necessary being is possible.
(6): If a necessary being is possible, then a necessary being exists.^{1}
(7): Therefore, a necessary being exists.^{2}
Joshua Rasmussuen's Modal Argument from Beginnings (2011)^{1, 2} Paraphrase:
(1): Normally, for any intrinsic property p that (i) can begin to be exemplified and (ii) can be exemplified by something that has a cause, there can be a cause of p ’s beginning to be exemplified.
(2): The property c of being a contingent concrete particular is an intrinsic property.
(3): Property c can begin to be exemplified.
(4): Property c can be exemplified by something that has a cause.
(5): Therefore, there can be a cause of c’s beginning to be exemplified.
(6): Therefore, if (5), then there is a necessary being.
(7): Therefore, there is a necessary being.
Christopher G. Weaver's Argument from Beginnings (2013)^{1, 2}
(1): Possibly, there is at least one entity x, such that x is a first purely contingent event.
(2): Necessarily, for any entity x, if x is a first purely contingent event, then possibly, there is at least one entity y, such that x is the first purely contingent event, and y causally produces x.
(3): Necessarily, for any entity x, and for any entity y, if both x is the first purely contingent event and y causally produces x, then y is an event that is not purely contingent.
(4): If, possibly there is at least one entity y, such that y is an event that is not purely contingent, then possibly there is at least one entity z, such that z is an individual and z exists necessarily.
(5): Therefore, possibly there exists a z, such that z is an individual and z exists necessarily.