Modal ontological argument

Last revised: 01/31/25

These are in progress and subject to revision. Feedback welcomed.
The subpoints provide further clarifying thoughts or definitions.
I offer two variants of the modal ontological argument.

First argument

Simplified

Definition: TETWNGCBC is that entity than which nothing greater can be conceived.

A contested entity with a nature that fulfills or satisfies the description of being TETWNGCBC (G) possibly instantiates. (Steps #1-10)

If true, the absence of G is metaphysically impossible in all comprehensive possible ways reality could be or is true, including the way reality actually is. (Steps #11-14)

G has or exemplifies all compossible greatness-making attributes, including intellect. (Steps #15-19)

If true, God exists. (Step #20)

God exists.

Full argument

Presuppositions

1. Self-contradictions cannot take place or be true.

2. Not everything that exists has a sufficient explanation (or possible explanation) or reason for its existence. For note, I offer arguments for the PSR linked here.

3. Universals exist as the principle or reason that explains why certain features are present in particular instantiations to varying degrees. Universals exist in things as the principles of their nature and in the intellect when abstracted. Universals are not arbitrary but instead based on real features found in things.

   1. For example, “greatness” exists in the intellect as a universal concept but is derived from particular instances in which it is found. However, this does not mean that “greatness” exists as a separate, concrete substance. Rather, universals are instantiated in particular things (as humanity is in individual humans) and exist in the intellect when abstracted from those particulars.

   2. A separate argument that universals do exist independently of language is linked here.

4. The argument uses the S5 axiom of modal logic. In S5, all possible worlds are accessible from each other. If something is possible, then it is possible in all possible worlds. If something is necessary, then it is necessary in all possible worlds.

   S5 also includes the principle that if something is possibly necessary, then it is necessary. This follows from the idea that possibility and necessity apply across all possible worlds without restriction.

   The modality used is metaphysical possibility. A proposition is metaphysically possible if it is not logically contradictory and follows from necessary truths and nature of things. For example, “a triangle has three sides” is necessarily true in all possible worlds, while “a triangle has four sides” is not possible in any.

Premises

Definition: TETWNGCBC is that entity than which nothing greater can be conceived.

1. If being self-sufficient and lacking deficiencies and dependence on the fulfillment or relief of any specific circumstance or state of affairs (B) constitutes greatness, then a contested entity with a nature that fulfills or satisfies the description of being TETWNGCBC possibly instantiates if it exemplifies B.

   1. This argument employs metaphysical modality by considering what is possible or necessary across all comprehensive ways reality could be. Metaphysical possibility applies to an entity or state of affairs that (a) is free from logical contradiction and (b) conforms to eternal or necessary truths and the nature of things, such as the requirement that a triangle must have three sides and cannot have four.

   2. Epistemic possibility concerns what is possible given our knowledge or beliefs (e.g., "It might rain this afternoon" reflects uncertainty based on what we know). The premise, however, is not about what we know or believe but about the nature and instantiation of an entity (TETWNGCBC) with specific properties (self-sufficiency and lacking deficiencies or dependence). An epistemic version of the premise might be: “We don’t know if TETWNGCBC exemplifies B, so it’s possible it does.” But the premise doesn’t frame the issue in terms of uncertainty or knowledge gaps—it frames it in terms of what is logically or ontologically possible given the entity’s nature.
      The word "possibly" here isn’t about your knowledge or uncertainty. It’s not saying, “for all we know, such a being might exist.” It’s saying, “such a being could exist given what it would be like.” It’s a comment on what kind of being can exist, given a set of traits.

   3. Let B denote “being self-sufficient and lacking deficiencies and dependence on the fulfillment or relief of any specific circumstance or state of affairs.”

   4. Let G denote "a contested entity with a nature that fulfills or satisfies the description of being TETWNGCBC."

   5. “Contested entity” means an entity whose ontological status as to whether it actually exists (or a referent can be described as it) is in dispute or being argued.

   6. “Constitutes” means to be considered as something.

   7. "Exemplifies" means to illustrate or demonstrate a quality or characteristic in the same sense that a unicorn exemplifies or possesses the defining characteristic of one-hornedness, even if unicorns are not real.

   8. “Possibly instantiates” means that there is a possible way reality could be in which G is present.

   9. The intent of this conditional premise is to establish a symmetry breaker for common counter-modal arguments that presumes God (or some entity that entails as much) possibly doesn’t instantiate. Meeting this condition of exemplifying B gives credence to metaphysical possibility and through reductio it shows that the premise “G possibly instantiates” satisfies the condition of exemplifying B. Meanwhile, the premise “G possibly doesn’t instantiate” will not satisfy the condition of exemplifying B. In order to be a valid symmetry breaker, it needs to be the case that G’s possible instantiation meets the condition, while G’s possible non-instantiation would not, which this inference achieves.

      1. If an entity fails to meet these condition of exemplifying B, it cannot be TETWNGCBC, because something greater (i.e., an entity that does meet these criteria or that is not subject to them at all) is conceivable. This doesn’t define existence or necessary existence in all possible worlds as part of the definition of a TETWNGCBC. Rather, it derives its possible instantiation through inference via reductio and then a further inference on #13 to conclude its necessary instantiation.

      2. An entity like an island, pizza or proposition than which nothing greater can be conceived inherently rely on other factors or causes, like space-time or the facts of the matter to exist, so an island, pizza or proposition cannot have or exemplify B, which cuts off those parodies since they fail to meet a necessary condition of greatness (self-sufficiency and lack of dependence on external factors). As great as any conception of an island or pizza may be, neither could exemplify B.

2. B constitutes greatness.

   1. "Greatness" is the quality of pursuing or fulfilling one's nature with the highest degree of excellence. This doesn’t require committing that things have a teleological or intrinsic purpose. A rock has properties that describes what it is (it has mass, occupies space, and is composed of minerals), and it has a nature. By “nature,” I mean a thing’s inherent disposition or natural inclination based on what it is. So a certain type of rock may be disposed for a kind of hardness, stability or heat-resistance, and a particular rock could express those characteristics in better or worse degrees. For example, the essence of a human being is rationality, and the nature of a human being is to act rationally and seek truth even if they sometimes don't do so.

   2. This premise is grounded in the idea that self-sufficiency reflects a higher degree of intrinsic greatness because it means a thing can pursue its inherent disposition or natural inclination without interruption under all possible conditions.

   3. Deficiencies and dependence imply a limitation on the way in which one’s nature is pursued or fulfilled, and greater entities are, by definition, less limited, so an entity would be greater still if it were not limited at all.

   4. An omnibeing that is also omnimalevolent (all evil) and a God who knows all but one true proposition are not greater than can be conceived since evil (the absence of good that is due) and lack of knowledge are deficiencies.

3. Therefore, G possibly instantiates if it exemplifies B. (Modus Ponens from #2-3)

4. Assume for reductio that G does not exemplify B.

5. If a contested entity does not exemplify B, then G has an inherent contradiction or a metaphysically possible reason, principle, factor, or cause external to its own nature that prevents or negates its actual presence in a comprehensive possible way reality could be or is true.

   1. This follows because if something's presence is not dependent on external conditions, then the only relevant factors determining whether it instantiates must arise from its own nature.

6. Therefore, assuming G does not exemplify B, G has an inherent contradiction or a metaphysically possible reason, principle, factor, or cause external to its own nature that prevents or negates its actual presence in a comprehensive possible way reality could be or is true. (Modus Ponens from #4-5)

7. If a contested entity has an inherent contradiction or a metaphysically possible reason, principle, factor, or cause that prevents or negates its actual presence in a comprehensive possible way reality could be or is true, then it is without a nature that fulfills the description of being than which nothing greater can be conceived.

   1. If there were some self-contradiction or explanation that actively kept it from instantiating in comprehensive possible way reality could be or is true, then an entity that isn't actively blocked would be in a better position to pursue or fulfill its nature (all else being equal).

8. Therefore, assuming G does not exemplify B, then G (a contested entity with a nature that fulfills or satisfies the description of being TETWNGCBC) is without a nature that fulfills or satisfies the description of being TETWNGCBC, which is a self-contradiction. (Modus Ponens #6-7)

9. Therefore, the assumption that G does not exemplify B is false, which entails G exemplifies B. (Reductio from #4-8)

10. Therefore, G possibly instantiates. (Modus Ponens from #3 and #9)

11. If true, then in virtue of B, the absence of G is impossible in at least one comprehensive possible way reality could be or is true.

    1. An entity that exemplifies B, like G, is self-sufficient and doesn't depend on external states of affairs, so its own self is sufficient for its existence, and nothing can prevent or interrupt it from instantiating. If an entity’s nature is such that nothing can prevent it from instantiating, then its presence must be continuous rather than temporary. Otherwise, something must explain why it stops and starts, which contradicts its self-sufficiency. If its were such that G only existed for some period of time, for example, then that means G is subject to the passage of time, which would contradict its self-sufficiency. If it stopped and started randomly and without reason, then it lacks control of itself, contradicting its self-sufficiency and independence from the relief of any specific circumstance or state of affairs (including random probability). If a self-sufficient entity could decide to cease existing, the that would mean its own nature is not sufficient for its existence and is dependent upon its state of mind, contradicting its self-sufficient nature.

12. Therefore, the absence of G is impossible in at least one comprehensive possible way reality could be or is true. (Modus Ponens on #10-11)

13. If a state of affairs is metaphysically impossible in a comprehensive possible way reality could be, then it is metaphysically impossible in all possible ways reality could be or is true, including the way reality actually is.

14. Therefore, the absence of G is metaphysically impossible in all comprehensive possible ways reality could be or is true, including the way reality actually is. (Modus Ponens on #12-13)

15. If an attribute is necessary for maximizing the value of other greatness-making attributes, then it is a greatness-making attribute.

16. Intellect and will are attributes necessary for maximizing the value of other greatness-making attributes.

17. Therefore, intellect and will are greatness-making attributes. (Modus Ponens on #15-16)

18. If a contested entity lacking a greatness-making attribute would be inferior to one with that attribute, then G has or exemplifies all compossible greatness-making attribute, including intellect and will.

19. Therefore, G has or exemplifies all compossible greatness-making attributes, including intellect and will. (Modus Ponens on #17-18)

20. If a contested entity has or exemplifies all compossible greatness-making attributes, including intellect and will, is present in all comprehensive possible ways reality could be or is true, including the way reality actually is, is what people mean by God, then God exists.

21. Therefore, God exists. (Modus Ponens on #19-20)

Second argument

1. A contested entity with a nature that fulfills or satisfies the description of being TETWNGCBC (E) possibly instantiates.

2. If true, E exist in all metaphysically possible worlds.

3. Therefore, E exist in all metaphysically possible worlds, which entails it is metaphysically necessary. (Modus Ponens on #1-2)

4. If a property enables the maximization of other greatness-making qualities, then it is itself a greatness-making property.

5. Intellect is a property that enables the maximization of other greatness-making qualities.

6. Therefore, intellect is a greatness-making property. (Modus Ponens on #4-5))

7. If an entity lacking a greatness-making property would be inferior to one with that quality, then E must possess that greatness-making property.

8. Therefore, E must possess intellect. (Modus Ponens on #6-7)

9. If an entity with every great-making property (including intellect) existing in every logically possible world is what people mean by God, then God exists in our actual world.

10. Therefore, God exists. (Modus Ponens on #8-9)