The Modesty of Maydole’s Temporal Contingency Argument
In a recent discussion that I had, my interlocutor claimed that “contingency” was an outdated scholastic concept. Really it is just a modal property. Sometimes it is called “two-way” possibility, i.e. x is contingent iff possibly and possibly not x. Temporal contingency the possibility of existing at some point in time and not existing at some point in time. We experience temporal contingency all the time. Anyways, I promised to explain how contingency is still relevant today in the philosophy of religion. In fact, I think it is relevant in one of the most powerful arguments for God’s existence. I can’t really imagine a good reason to deny any of the premises, and it is of course logically valid. So I am compelled to conclude that it is a sound argument for the existence of a supreme being, which I call “God”.
In a sense, The argument originates with Thomas Aquinas’s third way, but is developed by Robert Maydole, who fuses it with a modal ontological argument to devise an ingenious new argument.
Maydole defines a supreme being as follows:
D1. A supreme being is such that it is not possible that there exists anything greater than it and it is not possible that it is not greater than anything else that is non-identical to it.
He then proves the following, which we will call T1:
T1. If possibly a supreme being exists, then a supreme being exists.
Maydole does this by making use of a few theorems, like Barcan Formula, and other theorems in modal logic (I will reproduce the argument below, for those who are interested, see the conditional proof on lines 4-19 for the exact proof). Then Maydole constructs an argument for the possibility of a supreme being. He lists the following premises (but don’t attack them straight off, something interesting happens):
P1. Something presently exists.
P2. Only a finitely many things have existed to date.
P3. Every temporally contingent being begins to exist at some time and ceases to exist at some time.
P4. Everything that begins to exist at some time and ceases to exist at some time exists for a finite period of time.
P5. If everything exists only for a finite period of time, and there have been only a finitely many things to date, then there was a time when nothing existed.
P6. If there was a time when nothing existed, then nothing presently exists.
P7. A being is temporally necessary if and only if it is not temporally contingent.
P8. Everything has a sufficient reason for its existence.
P9. Anything that has a sufficient reason for its existence also has a sufficient reason for its existence that is a sufficient reason for its own existence.
P10. No temporally contingent being is a sufficient reason for its own existence.
P11. Every temporally necessary being that is a sufficient reason for its own existence is a being without limitations.
P12. A being without any limitations is necessarily greater than any other being.
P13. It is not possible for anything to be greater than itself.
P14. It is necessarily the case that “greater than” is asymmetric.
From P1-P14 one can prove C1:
C1. A supreme being exists.
The proof from P1-P14 to C1 is a bit long, and I believe Maydole even made a few typographical mistakes along the way. Here is my adaptation of this part of the argument, if you are interested.
Next consider what was said, before, that if it is possible that a supreme being exists, then a supreme being exists, i.e. T1. Maydole’s argument is surprisingly modest. What he does is argue that POSSIBLY (P1-P14) is true. Since C1 is provable from (P1-P14), we can say POSSIBLY C1 is true, which is to say that possibly a supreme being exists. Given T1 and the possibility that a supreme being exists, we can conclude that a supreme being exists (which is rightly called God)!
Now, the argument is very strong, because it is plausible that P1-P14 are actually true. However, Maydole only requires that the premises be possibly true rather than actually true, which is to say that they are not logically or metaphysically incoherent, or that they are true in some metaphysically possible world (as contemporary modal logicians would say). The deduction is valid, and it is very hard for me to think any of the premises are false. So I am compelled to think that this is, indeed, a sound argument for God’s existence.
So the proof looks something like this:
Let
Gxy ≝ x is greater than y
Sx ≝ (~◊(∃y)Gyx & ~◊(∃y)(x≠y & ~Gxy))
1. ◊(P1-P14) (premise)
2. (P1-P14) ⊢ C1 (premise that C1 is provable from P1-P14)
3. {◊(P1-P14) & [(P1-P14) ⊢ C1]} ⊃ ◊C1 (premise)
4. ◊(∃x)Sx (Assump CP)
5. ◊(∃x)Sx ⊃ (∃x)◊Sx (BF theorem)
6. (∃x)◊Sx (4,5 MP)
7. ◊Su (6 EI)
8. ◊(~◊(∃y)Gyu & ~◊(∃y)(u≠y & ~Guy)) (7, df “Sx”)
9. ◊(~◊(∃y)Gyu & ~◊(∃y)(u≠y & ~Guy)) ⊃ (◊~◊(∃y)Gyu & ◊~◊(∃y)(u≠y & ~Guy)) (theorem)
10. ◊~◊(∃y)Gyu & ◊~◊(∃y)(u≠y & ~Guy) (8,9 MP)
11. ◊~◊(∃y)Gyu (10 Simp)
12. ◊~◊(∃y)(u≠y & ~Guy) (10 Simp)
13. ◊~◊(∃y)Gyu ⊃ ~◊(∃y)Gyu (theorem, by “S5”)
14. ◊~◊(∃y)(u≠y & ~Guy) ⊃ ~◊(∃y)(u≠y & ~Guy) (theorem, by “S5”)
15. ~◊(∃y)Gyu (11,13 MP)
16. ~◊(∃y)(u≠y & ~Guy) (12,14 MP)
17. ~◊(∃y)Gyu & ~◊(∃y)(u≠y & ~Guy) (15,16 Conj)
18. Su (17, df “Sx”)
19. (∃x)Sx (18 EG)
20. ◊(∃x)Sx ⊃ (∃x)Sx (4-19 CP, which proves T1)
21. {◊(P1-P14) & [(P1-P14) ⊢ C1] (1,2 Conj)
22. ◊C1 (3,22 MP)
23. ◊(∃x)Sx (22, def “C1”)
24. (∃x)Sx (20,23 MP)
QED
To me, it is P11 that needs more explanation. It certainly seems right that a temporally necessary being who is the sufficient reason for its own existence has the sort of existence that is not limited by time nor by the existence of any other thing. But to say that the existence of x is not limited by time nor any thing seems a bit different from saying thag such a being is essentially without limitations. I believe the idea is that if there is no time nor state of affairs in which such a being would cease to exist or lack a reason for existing, then it is not limited by anything at all, and must be greater than every other thing.
Another person noted that P5 did not make sense to him because time is something that exists, so there could never be a time when nothing exists. Maydole, however, is quantifying over things in a way that is distinct from moments (in his “Modal Third Way” you see a more careful distinction between moments and things). With the right qualifications, and stipulations, this worry can be alleviated, e.g. one might say “no concrete things” or “no subsitent things” rather than “nothing”.
Reference:
Maydole, R. 2012. “The Ontological Argument”. In The Blackwell Companion to Natural Theology. Ed. W.L. Craig & J.P. Moreland. Malden, MA: Blackwell Publishing, pp. 580-586.
Posted on June 2, 2015, in Arguments for God and tagged Aquinas, God, Maydole, modal, ontological argument, temporal contingency argument. Bookmark the permalink. 2 Comments.
vexing questions 
Someone asks “By what means are any of the premises shown to be true?”
—
Maydole explains, “Now I know of no reason to believe that there could not be a possible world ω where the propositions [P1], [P2], [P3], [P6], [P8], [P9], [P10], and [P11] express logically contingent facts about ω. Propositions [P4], [P5], [P7], [P13], and [P14] appear to be self-evident analytic truths which are true in every possible world, including ω. Only [P12] requires special justification:
Assume x is a being without limitations in ω. Then x possesses every great making property in ω. In particular, x possesses the property in ω of not being limited in world ω1 by anything. In other words, if x is a being without any limitations in ω, then x possesses every great making property in ω. But the property of not being limited in ω1is a great making property of ω. So it is true in ω that it is true in ω1 that x is unlimited. But for any statement p, if it is true
in world α that p is true in world β, then p is true in world β. Hence, x is unlimited in world ω1. Now if x is unlimited in ω1, then in ω1 x is greater than any other being in ω1; otherwise x would be limited by not possessing a great making property possessed by something else. Hence it is true in ω1 that x is greater than every other being. Since ω1 is an arbitrarily selected possible world, it follows that it is true in every possible world that x is greater than every other being. Consequently, it is necessarily the case that x is greater than every other being. So [P12] is true in ω.” (Maydole 2012, “The Ontological Argument” p. 585-586).
So:
P1: there is a possible world ω where something presently exists. Yep
P2: there is a possible world ω where only a finite many things have existed to date. Sure, why not (nothing contradictory about that, unless there is some reason that every world must have an actual infinity of these concrete things)
P3: Every temporally contingent being begins to exist at some time and ceases to exist at some time. Well, that seems definitionally true, but there is at least some possible world ω where it is true.
P4: It is analytically true that everything that begins to exist at some time and ceases to exist at some time exists for a finite period of time. It has a beginning and an end!
P5: It is analytically true that if everything exists only for a finite period of time, and there have been only a finite many things to date, then there was a time when nothing existed. Why? The longest stretch of time you could have is if you had one thing exist at a time, one after another. Finite quantity existing for a finite duration means you eventual have a time when there is nothing (concrete objects, as I explained to Robert).
P6: Even if you do not agree that it is actually true that from nothing nothing comes, it is hard to argue that there could not be a world ω where if there was a time when there was nothing, then there would presently be nothing.
P7: it is analytically true that temporal necessity is defined as not being temporally contingent.
P8: Even if you disagree that the principle of sufficient reason actually holds, it is really hard to maintain that there is no possible world ω where this principle obtains.
P9: Again, Leibniz gave us reason to think that it must be actually true that all contingent things require an explanation that is its own sufficient reason for existence. Suppose you don’t think it is actually true, are you really prepared to say that there isn’t a possible world ω where this isn’t the case?
P10: If something is the sufficient reason for its own existence, then nothing else is need to explain why it exists, so then why would such a thing begin and cease to exist? There is at least a possible world ω where such a thing is true, it actually seems reasonable to hold this, after all. Contingent things seem to need other things beyond themselves, to explain why they are the case.
P11: If a being’s existence is not limited in duration and not dependent on anything else, or any state of affair being the case or not being the case (because it sufficiently explains its own existence), then it is without limitation. This is at least true in some possible world ω, as it seems to be reasonable to hold for something if it were to have such properties in the actual world.
P12: See Maydole’s special justification above.
P13: It is necessarily true that there isn’t anything that could be greater than itself.
P14: To say that the “greater than” relation is “asymmetric” is to say that if x is greater than y, it can’t also be the case that y is greater than x in the same sense and respect. This is a necessary truth.
All necessary truths are true in ω, and it is reasonable to suppose that all contingent truths could be true in some possible world ω, thus P1-P14 is possibly true. P1-P14 need to be compossible for the argument to work, and I think it is reasonable to think they are.
An objector mentioned that Oppy doesn’t think the argument is successful. I respond as follows:
…Before punting to Oppy’s authority, I think you should understand what his argument amounts to. He basically argues that there could be this capital N Naturalist, who takes modal possibility to be constrained to the point where all possible worlds have universes that share the same initial conditions, i.e. a physically necessary state that gives rise to a singularity, and that all possible worlds share the same physical laws of nature, and differ only due to the out-workings of chance.
To take this position is to place oneself in an extreme minority of modal conservatives (I don’t even know anyone who holds the position Oppy commits the Fool to). Moreover, if the only reason one adopts such modal conservativism is to avoid the conclusion of this argument, one has begged the question against the argument. One needs an independent reason to adopt such a position. As Maydole points out, this is nothing more than equivocating between alethic and nomic possibility. I hardly take it as reasonable to make such an equivocation just for the sake of avoiding a conclusion one does not like. Finally, to address Oppy’s argument, he is only saying that the argument does not convince the committed Naturalist (who performs the sort of mental contortions Oppy describes). Who cares? Why should an argument have to convince the person Oppy describes? No argument is able to convince everyone. But a good argument convinces the intelligent open minded person.
Alethic modality shouldn’t be so constrained. There is no reason to think that it is logically impossible for anything other than Naturalism to be true. At the very least, I’d like even a small argument for why Naturalism is metaphysically necessary!
Oppy’s objections and Maydole’s response can be found in this book: http://www.degruyter.com/viewbooktoc/product/209124