Maydole's Temporal Contingency Argument

In 2009, Blackwell publishing release the Blackwell Companion to Natural Theology, which is the gold standard on arguments for the existence of a personal God. Since the book was written for professional philosophers, you should not get frustrated if the book seems challenging to read. Just a fair warning.

The book delivers a series of
1. cosmological arguments - arguments that the nature of the physical world requires an ultimate being
2. teleological arguments - arguments that the design in our world requires a designer
3. moral and axiological arguments - arguments that objective value, beauty, and obligation requires an ultimate being
4. ontological arguments - arguments from the definition of God to his existence

I believe there are sounds arguments for God in all of these categories. The one argument in this book that really piqued my interest, since it blends the strongest parts of different cosmological, axiological, and ontological arguments. Let me show you the argument first and then I'll go through it. The argument comes in two parts: the first section with all the T statements are premises with T15 as the conclusion. The second half of the argument is the full, technical version, which I will translate into plain English and explain in the rest of this post.



Here is what's going on: Robert Maydole is using a version of Thomas Aquinas' Third Way, his third argument for the existence of God, but Maydole is updating it to accommodate advances in both science and philosophy. It uses alethic S5 Modal logic, which is used to derive metaphysical truths. This is the system Alvin Plantinga uses in his works, such as in The Nature of Necessity. In order to understand the argument, you will need to be familiar with some of the terms such as being, necessity, possibility, sufficient reason, possible world, and the like, so here goes.

Being - anything that exists. Examples of beings include chairs, keyboards, phones, atoms, quarks, photons, cars, people, souls (if they exist), God (if he exists), books, computers, space, stars, galaxies, the universe, and your mom. Basically, the two criteria for a being are: (1) does it exist? and (2) can you name it?

Necessity and Possibility - Maydole uses Alvin Plantinga's definition of broad logical possibility and broad logical necessity. This is expressed in what's called possible worlds semantics. A possible world is a way reality might be or might have been. the actual world is the way reality is. A statement is possibly true if there is a possible world where the statement is true. A statement is necessarily true if it is true in all possible worlds. What's strange and confusing about this argument is that it uses BOTH metaphysical necessity AND temporal necessity, which are different terms entirely. Maydole does a good job of keeping the terms separate. He does not confuse the two and I will try my best to avoid mixing them as well.

Without limitations - It appears that, according to Maydole's use, a being is without limitations if it is the metaphysical ultimate. That is, the greatest metaphysically possible being. If we could describe a being greater than the metaphysical ultimate, then THAT would be the metaphysical ultimate. Such a being would have to be, at minimum, omnipotent, omniscient, and omnibenevolent in all possible worlds. This means that it would have to exist in all possible worlds. This means that a being without limitations would exist necessarily.

One objection to possible worlds semantics is that it is inconsistent with actualism. Acutalism is the belief that everything that exists is actual, and therefore merely possible worlds do not really exist. This is not a problem, however, as most actualists, such as Alvin Plantinga, still use possible worlds semantics, so there is no inconsistency here.

Sufficient reason - The principle that everything that exists has an explanation for its existence. This principle is not as controversial as it might at first seem. Science presupposes this principle, that there are reasons why the physical world works the way it does. It is also impossible to accept this principle for some things and reject it for others. Events without an explanation cannot be governed by probability so anyone who denies this principle cannot even say that unexplainable things are possible but improbable.

Equivalence - "A is equivalent to B" is the same as saying it is true that ("If A, then B" and "If B, then A")

The universe - for the sake of this argument, "the universe" means "all of physical reality" so if there are multiverses or other universes or other planes of existence, all of physical reality in its entirety is being defined, for the sake of this argument, under the title "the universe."

Remember that the premises of the argument are the 14 T statements (T15 is the conclusion) at the top of the chart. Every other step of the argument is a logically airtight deductive argument. If you want to deny the conclusion, you have to dispute at least one of the premises. But the real power of the argument lies in the following: because this is a modal argument, as long as there is ANY possible world where the 14 premises are true, even if it is not the actual world, then the argument is sound. Let me repeat that: as long as the 14 premises are even POSSIBLE, then the argument goes through.

The first part of the argument lays out the first 7 premises (T1 through T7)

1. (premise) Something presently exists
2. (premise) Only finitely many things (or beings) have existed to date
3. (premise) For every x, if x is temporally contingent, x begins to exist at some time and ceases to exist at some time
4. (premise) For every x, if x begins to exist at some time and ceases to exist at some time, then x exists for a finite period of time
5. (premise) for every x, if x exists for a finite period of time and only finitely many things have existed to date, then there was a time when nothing existed
6. (premise) if there was a time when nothing existed, then nothing presently exists
7. (premise) for every x, "x is temporally necessary" is equivalent to "x is not temporally contingent"
8. suppose that for every x, x is temporally contingent
9. then if the universe is temporally contingent, it begins to exist at some time and ceases to exist at some time
10. suppose the universe is temporally contingent
11. then the universe began to exist at some time and will cease to exist at some time
12. if the universe began to exist at some time and will cease to exist at some time, then the universe exists for a finite period of time
13. so the universe exists for a finite period of time
14. then for every x, x exists for a finite period of time
15. then everything exists for a finite period of time and only finitely many things have existed to date
16. therefore, there was a time (or state of affairs) where nothing existed
17. therefore, nothing presently exists
18. but something does presently exist!
19. therefore, it is not the case that for every x, x is temporally contingent
20. therefore there is something that is not temporally contingent
21. let's call this being that is not temporally contingent THE NECESSARY BEING (TNB).

This first section is basically Aquinas' section of the argument. Objects (or beings) either begin to exist or they do not. Also, there are either an infinite number of objects that have existed in the past or there are not. Since the existence of an actual infinite number of objects would violate the laws of set theory (you would be able to perform invalid operations such as subtraction and division of actual infinites), it follows that there are only a finite number of objects in the past.

If everything that exists began to exist, and there are a finite number of objects, then it follows logically that there was some state of affairs where there was not anything that existed. However, such a state of affairs would lack even the potential for something to exist, so that nothing could ever come into existence. But something did come into existence. Hence, there is at least one object (or being) that did not begin to exist.

22. "TNB is temporally necessary" is equivalent to "TNB is not temporally contingent"
23. therefore, if something is temporally necessary, it is not temporally contingent, and vice versa
24. therefore, if TNB is not temporally contingent, TNB is temporally necessary
25. hence, TNB is temporally necessary
26. therefore, TNB exists

This conclusion may seem to jump out at you. How did we established that a TNB exists? Maydole made the assumption that all beings are temporally contingent, showed that it leads to a contradiction. If not everything is temporally contingent, then something is temporally necessary and 22 through 26 just show the coherence of such a concept.

The next section is going to add the rest of the premises.

27. (premise) for every x, there exist a y such that y is a sufficient reason for x
28. (premise) if for every x, there exists a y such that y is a sufficient reason for x, then there exists a z such that [z is a sufficient reason for x and z is a sufficient reason for z]
29. (premise) for every x and for every y, if x is temporally necessary and y is a sufficient reason for x, then y is temporally necessary
30. (premise) for every y, if y is temporally necessary and y is a sufficient reason for y, then y is without limitations
31. (premise) for every y, if y is without limitations then necessarily [for every z, if z is not y, then y is greater than z]
32. (premise) it is not possible that there is a y such that y is greater than itself
33. (premise) necessarily, for every x and every y, if x is greater than y, then y is not greater than x

Most of these premises are pretty uncontroversial. 27 is just a statement of the principle of sufficient reason, which needs to be presupposed in order to make sense of empirical investigation. 28 states that explanations are not circular. Hence, something has to be self-explanatory. 30 states that only an ultimate being i.e. a being without any limitations could explain why it exists.

34. therefore, there exists a y such that y is a sufficient reason for TNB
35. therefore, if there exists a y such that y is a sufficient reason for TNB then there exists a z such that such that z is a sufficient reason for TNB and is a sufficient reason for z (z is a sufficient reason for itself)
36. therefore, there exists a z such that z is a sufficient reason for TNB and z is a sufficient reason for z
37. hence, there exists TNB such that TNB is a sufficient reason for TNB and TNB is a sufficient reason for itself

To prevent an infinite regress, which would render everything inexplicable, there needs to be some sort of explanatory stopping point. That stopping point cannot be a temporally contingent being, because it could not explain any temporally necessary beings.

38. if TNB is temporally necessary and is a sufficient reason for itself, then it is not temporally contingent
39. TNB is a sufficient reason for itself
40. TNB is temporally necessary and is a sufficient reason for itself
41. TNB is not temporally contingent
42. "TNB is temporally necessary" is equivalent to "TNB is not temporally contingent"
43. if TNB is temporally necessary then TNB is not temporally contingent, and if TNB is not temporally contingent, then TNB is temporally necessary
44. if TNB is not temporally contingent, then TNB is temporally necessary
45. so TNB is temporally necessary
46. hence, TNB is a sufficient reason for itself

I may have messed up the interpretation here. 39 and 46 seem to be identical, but I am not sure if there is a distinction in the formula between v and v1.

47. TNB is temporally necessary and is a sufficient reason for itself
48. if TNB is temporally necessary and is an explanation for itself, then TNB is without limitations

Only the metaphysical ultimate, or that than which nothing greater can be conceived can serve as the ultimate explanatory stopping point.

49. if TNB is without limitations, then necessarily, for every z, if z is not TNB, then TNB is greater than z
50. therefore, necessarily, for every z, if z is not TNB, then TNB is greater than z
51. necessarily, for every z, either z is not TNB or TNB is greater than z
52. necessarily, for every z, either z is not TNB or it is not the case that TNB is not greater than z

If TNB is the metaphysical ultimate, and therefore the greatest possible being, then any other object you pick cannot be greater than TNB.

53. necessarily, for every z, it is not the case that [z is not TNB and TNB is not greater than z]
54. necessarily, it is not the case that there is a z such that [z is not TNB and TNB is not greater than z)
55. therefore, it is not possible that there is a z such that [z is not TNB and TNB is not greater than z]

These steps deliver implications from 49, that all other objects besides TNB are inferior to TNB.

56. necessarily, there is no y such that y is greater than y
57. therefore, necessarily, for every y, it is not the case that y is greater than y
58. for every y, y is not greater than y
59. it is not the case that the universe is greater than the universe
60. either the universe is not greater than the universe or TNB is not the universe
61. either TNB is not the universe or the universe is not greater than the universe

60 and 61 are the same statement in reverse order. This is to set up the next steps of the argument.

62. if TNB is the universe, then the universe is not greater than the universe
63. if the universe is TNB, then TNB is the universe
64. if TNB is the universe, then the universe is not greater than TNB
65. for every y, if y is not greater than y, then here is what follows: [if the universe is TNB, then the universe is not greater than TNB]
66. necessarily, for every y, y not being greater than y implies that if the universe is TNB then the universe is not greater than TNB
67. necessarily, if the universe is TNB, then the universe is not greater than TNB

Here comes the hard part. It is technical and hard to understand, but I will state it and then explain it.

68. necessarily, for every x and for every y, if x is greater than y, then y is not greater than x, also, for every z, if z is not TNB, then TNB is greater than z
69. "necessarily, for every x and for every y, if x is greater than y, then y is not greater than x, also, for every z, if z is not TNB, then TNB is greater than z" implies that "necessarily, for every x and every y, if x is greater than y, then y is not greater than x, also, for every x, if z is not TNB, then TNB is greater than z"
70. necessarily, for every x and every y, if x is greater than y, then y is not greater than x, also, for every z, if z is not TNB, then TNB is greater than z
71. necessarily, the fact that "for every x and every y, if x is greater than y, then y is not greater than x, also, for every z, if z is not TNB then TNB is greater than z" implies that if the universe is not TNB, then the universe is not greater than TNB
72. necessarily, if the universe is not TNB, then the universe is not greater than TNB

So we've established the dilemma. Look at 72 and 67. The universe is not greater than TNB, regardless of whether or not the universe is TNB. This seems obvious just by looking at the two statements, but Maydole is thorough and will prove this deductively in steps 73 through 79.

73. necessarily, if the universe being identical with TNB means that the universe is not greater than TNB and if necessarily the universe not being identical with TNB means that the universe is not greater than TNB, then necessarily, the fact that either the universe is TNB or is not TNB means that necessarily, the universe is not greater than TNB
74. necessarily, the universe being identical with TNB means that the universe is not greater than TNB, and necessarily, the universe not being identical with TNB means that the universe is not greater than TNB
75. necessarily, whether or not the universe is TNB, the universe is not greater than TNB
76. necessarily, the universe either is or isn't TNB
77. therefore, necessarily, either the universe is not greater than TNB or the universe is not greater than TNB (damned if you do or damned if you don't)
78. therefore necessarily, the universe being either not greater than TNB or not greater than TNB means that the universe is not greater than TNB
79. therefore, necessarily, the universe is not greater than TNB

Now we go into the home stretch. we have established that the universe is not greater than The Necessary Being and cannot be greater than The Necessary being. Maydole will also establish that TNB has nothing greater than it and also has no equal. Something that has no equal and nothing greater is by definition supreme.

80. for every z, necessarily, no z is greater than TNB
81. if, for every z, necessarily there is no z greater than TNB, then necessarily, for every z, z is not greater than TNB

81 uses the Barcan formula, which is somewhat controversial. Graham Oppy has objected to it in the journal Philo. Yet I do not think his objections apply to this version of the argument. Both the if and then statements in 81 are basically the same thing re-worded. They both state that it is a necessary truth that nothing is greater than TNB.

82. necessarily, for every z, z is not greater than TNB
83. necessarily, there is no z that is greater than TNB
84. therefore, it is not possible that there is a z such that Z is greater than TNB
85. therefore, it is not possible that there is a z such that z is greater than TNB, and it is not possible that there is a z such that [z is not TNB and TNB is not greater than z]

This is the same as saying that it is not possible for anything to be greater than or even equal to TNB. The second half of 85 was derived from 55.

86. therefore TNB is supreme
87. Therefore, there exists a being that is supreme

Therefore, some being is supreme. It is either the universe or something distinct from the universe. This commits us to either theism or pantheism, and I think the latter is indefensible. If the universe is God (the metaphysical ultimate) then it follows with logical certainty that the universe cannot be improved upon, as it is the greatest conceivable being. This would mean that evil and any other deficiencies in the universe are illusory, and that the universe is temporally necessary. This would mean that the universe never began to exist, and will never go out of existence.

Hence, God exists, and is distinct from the universe.