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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In a recent discussion that I had, my interlocutor claimed that “contingency” was an outdated scholastic concept.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:


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)


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”.

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.

A Video on the Modal Epistemic Argument

[H/T Inspiring Philosophy]

The above video presents the following argument:

1. For all p, if p is unknowable, then p is necessarily false (premise).

2. The proposition “God does not exist”, is necessarily unknowable (premise).

3. Therefore, the proposition “God does not exist”, is necessarily false.

I find this argument interesting, especially since (1) is very similar to a crucial premise in my knowability argument for omniscience. So my premise states: (∀p)(p ⊃ ◊(∃x)Kxp), or for all p, if p is true, then it is possible that p is known by someone.  The modal epistemic argument above tells us something like: (∀p)(~◊(∃x)Kxp) ⊃ □~p). It would be interesting if one could derive the existence of omniscient mind, and the existence of God from two independent arguments that utilize the same knowability premise.  This means that knowability really stands against the naturalist, and I think some good arguments can be made to support it.  My ears perked up when the narrator mentioned some of the realists and idealists who would be willing to grant the knowability premise: Aristotle and Hegel.  I’ve noticed that anti-realists like Dummett and realists like Aquinas also endorse the knowability premise.  So, it is something to consider.

A Mystico-Ontological Argument

I was considering the idea of evidence in the last post. This argument occurred to me.  Criticisms, as always, are welcome (Also, this is my 100th post!!):

A Mystico-Ontological Argument

1. If the probability of a hypothesis is greater on a given piece of evidence than the probability of the hypothesis alone, and no fact makes the evidence impossible, then the probability of the hypothesis, given the evidence, is greater than zero.
2. If the probability of a hypothesis given the evidence is greater than zero, then possibly the hypothesis is true.
3. There is a hypothesis that necessarily there exists an all-perfect being.
4. There is evidence from the testimony from those who have had a mystical experience of an all-perfect being.
5. The probability of the hypothesis that there necessarily exists an all perfect being is greater on the testimonial evidence from mystical experience than the probability of the hypothesis alone.
6. No fact makes the testimonial evidence of the mystical experience of an all-perfect being impossible.
7. Therefore, an all-perfect being exists.

P(h|e) – the probability of hypothesis h given evidence e
P(h) – the unconditioned probability of h
Πx – x is all-perfect
Tx – x is testimony that one has mystical experienced an all-perfect being

1. (∀h)(∀e){[(P(h|e) > P(h)) & ~(∃φ)(P(e|φ) = 0)] → (P(h|e) > 0)} (premise)
2. (∀h)(∀e)[(P(h|e) > 0) → ◊h] (premise)
3. (∃h)(∃e){[(h = ☐(∃x)Πx) & (e = (∃y)Ty)] & [(P(e|h) > P(h)) & ~(∃φ)(P(e|φ) = 0)]} (premise)
4. (∃e){[(h = ☐(∃x)Πx) & (e = (∃y)Ty)] & [(P(e|h) > P(h)) & ~(∃φ)(P(e|φ) = 0)]} (3 EI)
5. [(h = ☐(∃x)Πx) & (e = (∃y)Ty)] & [(P(e|h) > P(h)) & ~(∃φ)(P(e|φ) = 0)] (4 EI)
6. [(P(e|h) > P(h)) & ~(∃φ)(P(e|φ) = 0)] (5 Simp)
7. (∀e){[(P(h|e) > P(h)) & ~(∃φ)(P(e|φ) = 0)] → (P(h|e) > 0)} (1 UI)
8. [(P(h|e) > P(h)) & ~(∃φ)(P(e|φ) = 0)] → (P(h|e) > 0) (7 UI)
9 (P(h|e) > 0) (6,8 MP)
10. (∀e)[(P(h|e) > 0) → ◊h] (2 UI)
11. (P(h|e) > 0) → ◊h (10 UI)
12. ◊h (9,11 MP)
13. (h = ☐(∃x)Πx) & (e = (∃y)Ty) (5 Simp)
14. h = ☐(∃x)Πx  (13 Simp)
15. ◊☐(∃x)Πx (12,14 ID)
16. ☐(∃x)Πx (15 axiom S5)
17. (∃x)Πx (16 NE)

Support for the premises:

Premise 1: This premise tells us that when there is evidence that raises the probability of a hypothesis even slightly, then the probability of the hypothesis on the evidence cannot equal zero. To counter the charge that the evidence is only apparent, I’ve added the condition that there should not be any fact that makes the evidence, itself, impossible.

Premise 2: If the probability for some hypothesis is greater than zero it has to be possible. Put another way, if a hypothesis is impossible, the probability for the hypothesis is not greater than zero. And that is just what it means to be impossible.

Premise 3: This tells us that there is a hypothesis on the table, namely that necessarily there exists a maximally great being. That is the God hypothesis, which is the central dispute in this debate. To deny that there is even a God hypothesis is absurd, for it is to deny the debate altogether.

Premise 4: This tells us there is evidence for that hypothesis in the form of testimony from religious experience.  Indeed, Mark Webb (2011, Religious Experience) confirms, “Some subjects of religious experiences report… [experiences of] an infinitely perfect, personal creator.”  Here are some examples of such testimony: i) There is the mystical writing of St. John of the Cross, “O gentle touch, and most gentle, for you touch me with your most simple and pure essence, which being infinite is infinitely gentle, therefore it is that this touch is so subtle, so loving, so deep, and so delicious that it savors of eternal life” (St. John of the Cross,The Living Flame of Love, Stanza II, emphasis mine). ii) There is the mystical writings of Pseudo-Dionysius the Aeropagite, “Through these, Its incomprehensible Presence is manifested upon those heights of Its Holy Places; that then It breaks forth, even from that which is seen and that which sees, and plunges the mystic into the Darkness of Unknowing, whence all perfection of understanding is excluded, and he is enwrapped in that which is altogether intangible, wholly absorbed in it that is beyond all, and in none else (whether himself or another); and through the inactivity of all his reasoning powers is united by his highest faculty to it that is wholly unknowable; thus by knowing nothing he knows That which is beyond his knowledge” (Mystical Theology, Ch. 1). Pseudo-Dionysius goes on to say, “…we can neither affirm nor deny it, inasmuch as the all-perfect and unique Cause of all things transcends all affirmation, and the simple pre-eminence of Its absolute nature is outside of every negation- free from every limitation and beyond them all” (Mystical Theology, Ch. 5, emphasis mine). iii) Augustine reports in the Confessions a mystical experience of God that he shared with his mother, Monica, in Ostia, “ Our colloquy led us to the point where the pleasures of the body’s senses, however intense and in however brilliant a material light enjoyed, seemed unworthy not merely of comparison but even of remembrance beside the joy of that life, and we lifted ourselves in longing yet more ardent toward That Which Is, and step by step traversed all bodily creatures and heaven itself, whence sun and moon and stars shed their light upon the earth. Higher still we mounted by inward thought and wondering discourse on your works, and we arrived at the summit of our own minds; and this too we transcended, to touch that land of never-failing plenty where you pasture Israel for ever with the food of truth. Life there is the Wisdom through whom all these things are made, and all others that have been or ever will be; but Wisdom herself is not made: she is as she always has been and will be forever. Rather should we say that in her there is no “has been” or “will be,” but only being, for she is eternal, but past and future do not belong to eternity. And as we talked and panted for it, we just touched the edge of it by the utmost leap of our hearts; then, sighing and unsatisfied, we left the first-fruits of our spirit captive there, and returned to the noise of articulate speech, where a word has beginning and end. How different from your Word, our Lord, who abides in himself, and grows not old, but renews all things” (Confessions IX, 24 emphasis mine). iv) Even the logical positivist and well-known atheist, A.J. Ayer, is reported to have had an religious experience of some sort, “I was confronted by a red light…Aware that this light was responsible for the government of the universe. Among its ministers were two creatures who had been put in charge of space…” (P. Foges 2010).  These mystical experiences of an infinite, all-perfect, self-abiding, eternal being is testimonial evidence that there is a being that has all-perfections, including omnipotence, omniscience, moral perfection, and necessary existence. That is precisely what our hypothesis is.

Premise 5: Testimonial evidence of the truth of some hypothesis raises the probability of that hypothesis higher than the hypothesis possesses intrinsically. This is testimonial evidence that some mystics have had experiences of a perfect personal God.

Premise 6: While one may be skeptical of such mystical experiences, or attempt to explain it away as a deception, neurological illusion, some other psychological delusion, or mere poetry none of these facts make the testimony that these people actual experiences a personal all-perfect being impossible. That is, attempts to explain this evidence away does not establish that there is zero probability that it is evidence at all. Nor is there any fact that makes a personal all-perfect being intrinsically possible, given that the plausibility that apparent inconsistencies in the divine attributes can be resolved, and arguments like Robert Maydole’s Modal Perfection argument or Alexander Pruss’s Gödelian Argument, which argues that positive perfections are compossible.

A Couple of Anticipated Objections:

1. One might attack (2) by saying that there is a shift between subjective probability and logical possibility, and that this is tantamount to shifting between conceivability and possibility. Then again, if the hypothesis is itself impossible, that should be established by the atheologian given the positive arguments for the coherence of h (found in 3D above). But given those positive arguments, combined with the testimonial evidence of mystics, we might say that we have some good positive reasons to think that the P(h|e) is higher than zero, and so possible. Perhaps this argument does shift between conceivability and logical possibility in (2). What it might tell us something interesting about our intuitions, namely, that if we have a sense that mystical testimony in anyway increases the probability that the hypothesis is true, then we should believe it. But if we have the sense that no amount of mystical evidence raises the probability that there is an all-perfect being, then that would be consistent with the impossibility of such a being.

2. One might argue that the testimonial evidence offered in (3) is not an encounter of an all-perfect, or maximally great being. But for this argument to be a defeater, they would need definitive proof that it was not, since even if it is the slightest bit probable that they did have such a genuine encounter, the probability of h is raised slightly, and we can conclude that h is possible.

1For the purposes of this argument, I’ve condensed premises 3-6 in natural language into the third premise of the formal deduction.

A simple deontic-ontological argument

Here is a simple deontic ontological argument:

1. I ought to attain the highest form of happiness.
2. I ought to attain the highest form of happiness only if is possible that I attain the highest form of happiness.
3. ‘I attain the highest form of happiness’ is identical to ‘there is a perfect being and I am in communion with it’.
4. If it is possible that there is a perfect being and I am in communion with it, then it is possible that there is a perfect being, and it is possible that I am in communion with it.
5. A perfect being is identical to a necessarily existing maximally excellent being.
6. Therefore, a perfect being exists.

Some Helpful Videos on the Modal Ontological Argument

Here are some really interesting and helpful videos on the modal ontological argument that I’ve recently discovered.

This first video (by The Messianic Drew) adds the flourish of a sub-argument for the Triune God of Christianity. Enjoy!

These two videos (by Inspiring Philosophy) form a series. The first walks through the argument in a step-by-step fashion, and the second addresses common objections.

Am I My Body?

Aside from the fact that Dr. Plantinga isn’t quite sure how many legs a beetle has–come on, eight, really?!?–I think he presents a really good argument against physicalism.

The argument runs something like this:

1.  If I am my Body, then anything possible with regard to me is also possible with regard to my body.

2.  It is possible that I exist when my body does not exist.

3.  It is not possible that my body exists when my body does not exist.

4.  Thus, “I exist without my body” is something possible with regard to me that is not possible with regard to my body.

5.  Therefore, I am not my body.

The argument demonstrates a discernible difference between the body and the self.  But does it matter that we are talking about mere possibilities here?  Plantinga’s point is that there is no possible world where a body exists without itself.  Yet, it does not seem logically impossible to imagine a possible world where the self exists without its body.  We take such stories to be supernatural, fantastical, or fictional, but not logically incoherent.  So, it seems reasonable to suppose the logical possibility of a disembodied self.

This means that proving an identity relationship between the self and the body requires a lot more than empirically proving a causal relationship between physical states and mental states.  One must also prove that it is logically incoherent to suppose that there are any possible worlds where the self is disembodied.  So it seems that while this burden is heavily placed upon the physicalist, the supernaturalist can merrily go along believing that she is her soul.  Right?

Not so fast, my friend Shaun Miller has pointed out to me that this argument, if anything, proves too much (Shaun was inspired by Shelly Kagan, ff about 43 min in for the appropriate part).  Kagan points out that we could imagine that the same body is possessed by different souls. His point is not that we are not our soul, but that our soul doesn’t seem sufficient to establish personal identity.  As far as I can tell, Shaun’s response to Plantinga is original, and quite difficult to overcome.  He points out that we could substitute just about anything in the argument, including the soul, and prove it to be non-identical with the self.  Does this mean that I am not my soul?!? My initial reaction to this was, “Well, it’s just not possible that I exist without my soul, since I am my soul.”  But now I’m guilty of special pleading.  This fallacious soul-ution is to stipulate that “soul” is simply defined as “self”.  But then we have just stipulated our way to victory, which is not very satisfying.  What would prevent the physicalist from stipulating “body” as “self”?  We’re back to square one.

Upon further reflection, I think the argument achieves something.  It proves that unless we have good reason to think that it’s not possible for X to exist when Y doesn’t exist, then we don’t have good reason to think X and Y are identical.   I have no good reason to think I am my body, because I think it is at least logically possible to be disembodied and survive.  But then I should be willing to bite the bullet and concede that I have no good reason to think I am my soul.  So be it.  I have no good reason to think I am my soul either.  As I said before, we could substitute just about anything for body–just about.  However, I cannot substitute “self”.  Whatever “self” is, it cannot both exist and not exist, at the same time, and in the same possible world!  So I do have good reason to think at least this…  I am myself.

But is this an adequate response?  Are there other problems with the argument that I am not mentioning here?