# Blog Archives

## The Ontological Argument From Transcendence 2.0

I’ve presented my own version of Anselm’s ontological argument here and I’ve also argued for an ontological argument using “more transcendent” rather than “greater” here. Combining the two, and refining the argument, I got this:

1. Something is an Anselmian God if and only if it is conceivable, nothing can be conceived of which is more transcendent, and it necessarily exists (definition Θ).

2. There is something conceivable such that nothing can be conceived of which is more transcendent (premise).

3. For all x, if the possibility of failing to conceive of x implies the possibility that x doesn’t exist, x is mentally dependent (premise).

4. For all x, if x is mentally dependent, there is something conceivable that is more transcendent than x (premise). Therefore,

5. An Anselmian God exists.

Let

Cx – x is conceived
Mx – x is mentally dependent
Txy – x is more transcendent than y
Θx- x is an Anselmian God, that is: (∀x){Θx ≝ ([♢Cx & ~(∃y)(Tyx & ♢Cy)] & ☐(∃z)(z=x))} (Def Θ)

1. (∃x)[♢Cx & ~(∃y)(Tyx & ♢Cy)] (premise)
2. (∀x){[♢~Cx ⊃ ♢~(∃z)(z=x)] ⊃ Mx} (premise)
3. (∀x){Mx ⊃ [(∃y)(Tyx & ♢Cy)]} (premise)
4. (∀x){[♢Cx & ~(∃y)(Tyx & ♢Cy)] ⊃ [♢~Cx ⊃ ♢~(∃z)(z=x)]} (IP)
5. ♢Cu & ~(∃y)(Tyu & ♢Cy) (1 EI)
6. [♢~Cu ⊃ ♢~(∃z)(z=u)] ⊃ Mu (2 UI)
7. Mu ⊃ [(∃y)(Tyu & ♢Cy)] (3 UI)
8. [♢~Cu ⊃ ♢~(∃z)(z=u)] ⊃ [(∃y)(Tyu & ♢Cy)] (6,7 HS)
9. [♢Cu & ~(∃y)(Tyu & ♢Cy)] ⊃ [♢~Cu ⊃ ♢~(∃z)(z=u)] (4 UI)
10. ♢~Cu ⊃ ♢~(∃z)(z=u) (5,9 MP)
11. (∃y)(Tyu & ♢Cy) (8,10 MP)
12. Tvu & ♢Cv (11 EI)
13. ~(∃y)(Tyu & ♢Cy) (5 Simp)
14. (∀y)~(Tyu & ♢Cy) (13 QN)
15. ~(Tvu & ♢Cv) (14 UI)
16. (Tvu & ♢Cv) & ~(Tvu & ♢Cv) (12,15 Conj)
17. ~(∀x){[♢Cx & ~(∃y)(Tyx & ♢Cy)] ⊃ [♢~Cx ⊃ ♢~(∃z)(z=x)]} (4-16 IP)
18. (∃x)~{[♢Cx & ~(∃y)(Tyx & ♢Cy)] ⊃ [♢~Cx ⊃ ♢~(∃z)(z=x)]} (17 QN)
19. (∃x) ~{~[♢Cx & ~(∃y)(Tyx & ♢Cy)] ∨ [♢~Cx ⊃ ♢~(∃z)(z=x)]} (18 Impl)
20. (∃x){~~[♢Cx & ~(∃y)(Tyx & ♢Cy)] & ~[♢~Cx ⊃ ♢~(∃z)(z=x)]} (19 DeM)
21. (∃x){[♢Cx & ~(∃y)(Tyx & ♢Cy)] & ~[♢~Cx ⊃ ♢~(∃z)(z=x)]} (20 DN)
22. (∃x){[♢Cx & ~(∃y)(Tyx & ♢Cy)] & ~[~♢~Cx ∨ ♢~(∃z)(z=x)]} (21 Impl)
23. (∃x){[♢Cx & ~(∃y)(Tyx & ♢Cy)] & ~[☐Cx ∨ ♢~(∃z)(z=x)]} (22 ME)
24. (∃x){[♢Cx & ~(∃y)(Tyx & ♢Cy)] & [~☐Cx & ~♢~(∃z)(z=x)]} (23 DeM)
25. (∃x){[♢Cx & ~(∃y)(Tyx & ♢Cy)] & [~☐Cx & ☐(∃z)(z=x)]} (24 ME)
26. [♢Cu & ~(∃y)(Tyu & ♢Cy)] & [~☐Cu & ☐(∃z)(z=u)] (25 EI)
27. ~☐Cu & ☐(∃z)(z=u) (26 Simp)
28. ☐(∃z)(z=u) (27 Simp)
29. [♢Cu & ~(∃y)(Tyu & ♢Cy)] (26 Simp)
30. [♢Cu & ~(∃y)(Tyu & ♢Cy)] & ☐(∃z)(z=u) (28,29 Conj)
31. Θu (30 Def Θ)
32. (∃x)Θx (31 EG)

[Update 11/9/204] I’ve noticed that some did not understand why if possibility that failing to conceive x implied that x possibly didn’t exist, then a greater could be conceived than x.  I’ve tried to make this more explicit by explaining this in terms of mental dependence.  Here, a concept is not an abstract object, but an object in the mind.

## An Argument from Transcendence

In a previous post, I attempted a version of the ontological argument that makes use of a comparative relation other than “greater than.” In the argument, I used “more actual.” Of course, I meant “actual” in a sort of Aristotelian-Thomistic sense, and so it depends upon understanding that particular set of metaphysical jargon. It occurs to me that one might make use of other comparatives to similar effect. This post can be considered a “Part 2,” as I attempt a similar argument with “more transcendent” as the comparative (though I have made a few modifications to the original version that I think strengthen it). Of course, there will still be some metaphysical unpacking to do. As I have said, it is impossible to avoid metaphysics when considering arguments for God’s existence. First, we must consider what it means to “transcend” and why it might be appropriate to define God this way. For, if an ontological argument is to be successful, the definition must at least implicitly contain the traditional divine attributes.  So we must consider if “transcendence” entails those other attributes.  I think it does. That which transcends goes beyond some limit, whether it is the physical laws, space, time, or any of the fundamental categories of existence. God is often defined as transcendent, but not in the sense that He is completely detached from us and in no way relates—transcendence and immanence seem to be related attributes of omnipresence, but from different perspectives.. For, in a sense, to say that God lacks immanence is to say that God cannot transcend those limits back into our finite existence. So I don’t see transcendence and immanence as true opposites, but as two perspectives by which one can refer to the omnipresence of God. The concept of transcendence can also help us understand other divine attributes. God is said to be omniscient, transcending anything that would limit knowledge. Likewise God is omnipotent, transcending, for instance, the physical laws that limit the amount of power finite creatures possess. God is also morally perfect, transcending anything that might limit His ability to perfectly express his being good and loving towards others.  So a if we conceive of God as that than which none more transcendent can be conceived, it seems that we will arrive at a being that exists infinitely perfect and a se (self-existent and not limited to depending on other things to exist). Such a being would be omnipotent, omniscient and morally perfect (so personal), and transcending time and space.  Now one might consider whether it is conceivable that God transcends existence itself.  Some theological traditions flirt with this idea, but I strongly suspect that the idea that something transcends existence is logically incoherent.  That is, it would be something not limited by being something.  I have no idea what that would mean, but if it means that God is something or someone who doesn’t exist, then it is incoherent.  It may just be that “transcending existence” is just meaningless. Anselm defined God as that than which none greater can be conceived, and I think we can understand “greatness” in terms of “transcendence.” As I mentioned in a previous blog, “greatness” can be difficult for some people to grasp. Is it supposed to be defined subjectively? For Anselm, “greatness” was conceived in terms of the Great Chain of Being, and so was an objective evaluation of existing things. But today, most people think of “greatness” as something that is in the eye of the beholder–and opinion with no factual basis whatsoever. When I have presented Anselm’s argument in the classroom, a few of my students inevitably ask, “Why must anyone agree that it is greater to exist in reality than in the mind alone?” Responding with neo-platonic metaphysics might help the student to understand what Anselm was thinking, but it makes the argument seem irrelevant, antiquated, and weak. Transcendence, though, is more clearly an objective feature. One may simply observe whether some being goes beyond a certain limit. Now one might say that it makes no sense to say that there is a limit if something transcends the limit. But we speak of things moving beyond limits all the time. Voyager I has recently transcended the limits of our solar system. When you drive too fast, you transcend the legal limit at which you can drive (though you might not use such a grandiose term as “transcend” when the cop pulls you over for speeding). So the existence of something surpassing a limit is not inconsistent with there being limits. The physical laws of nature are physical limits on the way natural objects can behave. If naturalism is true, there is nothing that transcends those limits. Whether something transcends those limits is an objective question, not a question dependent upon one’s opinions, desires, or tastes. So perhaps we can modify Anselm’s definition and say that God is that than which none more transcendent can be conceived. Just as Anselm initially invites us to consider, we may ask ourselves if such a God could merely exist in the mind, as some idea, imaginary thought, or mental construct. Surely ideas, imaginary thoughts, and mental constructs are limited by the mind in which they inhabit. They are limited not only by the mental capacity of the mind conceiving of them, but also insofar as their existence depends upon and so are limited by the very existence of minds. An argument from transcendence would look like this:

1. God is that than which none more transcendent can be conceived. [Definition]
2. If God exist only as an idea in the mind, something can be conceived more transcendent than God. [Premise]
3. If it is not the case that something exists only as an idea in the mind, then it exists as an extra-mental reality. [Premise]
4. If something can be conceived more transcendent than God, something can be conceived more transcendent than God. [Tautology]
5. If something can be conceived more transcendent than God, something can be conceived more transcendent than that which none more transcendent can be conceived. [From 1, 4 Definition]
6. If something can be conceived more transcendent than that than which none more transcendent can be conceived, then that than which none more transcendent can be conceived is not that than which none more transcendent can be conceived. [Premise]
7. It is not the case that that than which none more transcendent can be conceived is not that than which none more transcendent can be conceived. [Law of Non-Contradiction]
8. It is not the case that something can be conceived more transcendent than that which none more transcendent can be conceived. [From 6, 7 Modus Tollens]
9. It is not the case that something can be conceived more transcendent than God. [From 5, 8 Modus Tollens]
10. It is not the case that God exists only as an idea in the mind. [From 2, 9 Modus Tollens]

Therefore,

1. God exists as an extra-mental reality. [From 3, 10 Modus Ponens]

Is this argument subject to parody? I think not, and much for the same reason I did not think an ontological argument using the comparative “more actual” is susceptible to parody. Consider, for instance, Gaunilo’s perfect island. It seems incoherent to define an island as “that island than which none more transcendent can be conceived.” The very nature of an island is such that it does not transcend the limits of water on all of its sides. Otherwise, it would cease to be an island! “Very well,” you might think, “let’s say that it does not transcend watery limitations, but it does transcend all other limits.” Well, which ones must such an island transcend? Must it transcend all limits as to the amount of sand it has on its beach? Would it have an actual infinity of sand on the beach? Perhaps there is some physical restriction you would want to place on the amount of sand, otherwise the gravitation would be so great that it would be more like a super-massive black hole than an island resort. Ah, but it transcends all physical limitations, and so it would not be bound to obey gravity or other physical laws. But now it is sounding less and less like an island, which seems to at least be bound by physical laws to do with water and land. Would it be limited such that it could not be conscious? Would it be limited in power? If you grant that it would, so that it could remain island-like, then it becomes more and more ad hoc that you should insist that one of the ways in which the island than which none more transcendent is transcendent is insofar as it must exist beyond the mental. If you insist that it would be conscious, even all knowing, and all powerful to boot, then it sounds less and less like you are really talking about an island, and more and more like you are really talking about God. Perhaps you are really just saying that God could choose to manifest himself as a physical island. And perhaps this is true. But then the island isn’t so much a parody as it is a reiteration of the actual proof, while insisting that we consider God in this odd manifested form. So, if we strictly hold to the concept of “island” it is not clear that the concept of an “island than which none more transcendent can be conceived” is coherent, or physically possible. If we ditch the idea that it really is an island, as islands are traditionally conceived, the parody crumbles apart and just becomes a reiteration of the proof. There are, of course, other objections to ontological arguments. Perhaps you could mention your objections to the argument in the comments below.