A Further Reconstruction of the Fourth Way

1.There are, among things that can exist, degrees of value (goodness, nobility).
2.The assignment of degrees of value consists in comparing things as more or less similar to a possible thing of maximum value.
3.Therefore, there is a possible being of maximum value. (From 1, 2)
4.A being has maximum value if and only if it has maximum existence. (Convertibility of goodness and being)
5.Therefore, there is a possible being M of maximum existence. (Conclusion of the first part)
6.There is a necessary being (or plurality of necessary beings) N that is, in every possible world, possibly the cause of all existing things in that world. (From the Second and Third Ways)
7.Necessarily, if x is possibly the cause of the existence of y, then x has existence to the same or greater degree than y does. (Aristotle’s Alpha the Lesser principle)
8.Therefore, in every possible world w, N has the greatest degree of existence of anything that exists in w. (From 6, 7)
9.A being of maximum existence exists in some world w. (From 5)
10.Therefore, N has maximum existence in w. (From 8, 9)
11.A necessary being has the same degree of existence in every world.
12.Therefore, N has maximum existence in every world. (From 10, 11)
13.Therefore, N has maximum value in every world. (From 4, 12)
 
There is a potential problem with this reconstruction: step 5 (conclusion of the first half) isn’t strictly necessary. If N didn’t have existence to the maximum possible degree, then there would be a world w containing something with existence to a higher degree. But, then, N could not be the cause of that thing.

Perhaps we could take 1-5 as merely establishing the possible existence of a being of maximum value, which provides some independent support to the conclusion 13. But it would be nice to find some way to make 1-5 directly relevant to 6-13.