The Modal Third Way

Robert Maydole has recently presented a modal cosmological argument, known as the "Modal Third Way," which modifies Thomas Aquinas' Third Way in the Summa Theologiae. Maydole's paper can be found here: http://www.bu.edu/wcp/Papers/Reli/ReliMayd.htm

This will be my own take on the argument, with some premises simplified.

Where x = a thing; C = temporally contingent; t = time; P = past time; y = explicandum; and Eyx = x explains y.


1. (x) (Cx □ → ◊ (t) ~xt).
2. (x) ◊ (□t) ~xt □ → ◊ (□t) (x) ~Pxt.
3. ~(x) (◊x □ → ◊(y) (x ^ Eyx)).
4. ~[(□x) ◊ (□y) Eyx □ → ~(□t) (x) ~Pxt].
5. ~Pxt → ~C(x).
6. :. ~C(x).

In English:

1. Every temporally contingent thing possibly fails to exist at some time.
2. If all things possibly fail to exist at some time, then it is possible that all things collectively fail to exist at some past time.
3. It is necessarily the case that possible truths are explicable.
4. It is necessarily the case that something is explicable if and only if there was not a time when nothing existed.
5. If there could never have been a time when nothing existed, then something temporally necessary exists.
6. Therefore, something temporally necessary exists.