Modal argument from perfection
Last revised: 05/08/25
These are in progress and subject to revision. Feedback welcomed.
Formal symbolic argument for Stage 1 linked here.
The subpoints provide further clarifying thoughts or definitions.
Simplified argument
An absolutely perfect particular possibly exists. (Steps #1-16)
If true, an actual absolutely perfect particular exists in all possible worlds, including our own. (Steps #17-24)
If an absolutely perfect particular exists, it would have the traditional properties that God minimally has. (Steps #25-47)
God exists.
Full argument
Presuppositions
Self-contradictions cannot take place or be true.
The argument adopts predicate nominalism and class nominalism, which are the views that universals do not exist independently of the language we use. Instead, "red" or "triangular" are just linguistic or conceptual groupings of particular things, without any real shared properties or traits. Under predicate nominalism, universals exist only in language as tools for talking about particulars, not as independent realities. Under class nominalism, universals are reducible to classes of particulars, defined by observed or inferred similarities, not by some deeper nature. For note, I offer an argument against nominalism linked here.
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. For example, “a triangle has three sides on a flat plane” is necessarily true in all possible worlds, while “all triangle are isosceles” is not a necessary truth.
Premises
Stage 1
The predicate “is absolutely perfect” applies to an intentional particular if and only if it has all and only those compossible tropes that are perfect without qualification or context-dependence.
Some tropes could be described as perfect only in specific context, so “is absolutely perfect” would not include those tropes. For example, the perfect size of a scalpel might differ from the perfect size of a bus, so some tropes like size or weight lend themselves to being perfect only in a limited context. Some particulars could be perfect for its assigned purpose. For example, a framing hammer might be perfect for its assigned purpose of driving nails into wood. It might have the right weight, balance and grip for that task. It fits your hand well, and the head strikes the nail cleanly. But this same framing hammer might be ill suited at other tasks. It could be too heavy for delicate work. It might rust if left outside. It could even damage softer materials if used carelessly. It is not perfect in every respect. It lacks qualities you would want for other tasks. A tool designed for many different tasks might need to sacrifice some perceived tropes to gain others. Every object or tool has limits built into its design. Those limits define where its perfection ends. Therefore, as perfect in some respects a hammer might be, it is only perfect with qualifications or for a certain context. Physical tropes like size and weight lend themselves to be context-dependent.
A particular trope's "perfection" is not context-dependent if and only if:
Its full character or specific quality is not subject to or altered by its relations to other particulars, external conditions, or any specific purpose. The trope is simply what it is, in its own particular instance.
It represents the maximal logically possible instantiation of its specific quality within that individual trope. This means there is no logical possibility for that individual trope to possess a greater degree of that specific quality. If a greater degree of that quality is possible for that particular trope, then it is not "perfect" in this sense. The "perfection" signifies that the trope fully embodies its specific quality, with no part of that quality being absent or incomplete within that instance.
Its completeness is not a judgment derived from an external criteria, subjective preference, or utility for an external goal. Instead, its "perfection" lies solely in its absolute, exhaustive presence of its own particular quality.
In other words, if the individual trope is all that it can possibly be, and its "being all it can be" is not contingent on anything outside itself, then its perfection is not context-dependent. It is self-contained in its completeness.
Intelligence is example of a trope judged to be perfect without qualification or context-dependence. By "intelligence" as a trope in a nominalist sense, I am not referring to a universal concept of "intelligence" existing independently. I mean the particular, individual instance of intelligence as it exists in a specific particular. For example, if this particular being possessed those cognitive faculties (such as understanding, reasoning, problem-solving, and knowledge acquisition) to their maximal degree, then that particular instance of intelligence would be perfect. Its perfection lies in its complete self-actualization as a particular instance of intelligence, not in its adherence to an external standard of intelligence or for some utility within a given context. It simply is fully intelligent, without qualification.
“Perfect” refers to the complete and exhaustive presence of a specific quality of an individual trope, such that no greater degree of that particular quality is logically possible for that individual instance.
By "intentional," the particular is being discussed or analyzed for the sake of argument or exploration. It's not necessarily something that is presumed to exist mind-independently in reality but is instead a construct for examining certain principles, tropes or relationships. Suppose we posit an intentional particular like “a perfect symphony,” a specific performance where every note, rhythm and emotion hitting every perceived trope we’d call "perfect" (harmony, beauty, precision). We don’t need to presume such a symphony exists if we’re just arguing whether it would qualify as “perfect” if it did match all those tropes.
By “particular,” I mean some real physical or non-physical entity, instance, event, process or state.
“Perceived tropes” refers to those things we notice and associate with a given name, based on patterns across particular instances. They may be perceived through philosophical insight or by recognizing patterns or relations between things through conceptual perception.
“Compossible” refers to when when the particular quality described by tropes can belong to the same particular without conflict. Some sets of tropes are compossible if they describe the same thing without contradiction (e.g., having four legs and being brown). Others are not (e.g., having four legs and six legs simultaneously).
“Trope” refers to a particular quality we observe in specific instances that lead us to group particulars under the same name. For example, "flowing downhill" is a trope seen in individual cases like rivers or raindrops. We associate these similar tropes with the name "water" because they show a consistent pattern across those particular cases.
A subset of trope is a mode (how something under the same name can differ under certain conditions).Let P denote “the predicate ‘is absolutely perfect.’”
P is inconsistent with anything that compromises or precludes a perceived tropes judged, without qualification or context-dependence, to be perfect.
In other words, if something diminishes or prevents a trope we associate with “perfect,” those imperfections are inconsistent with being perfect, let along absolutely perfect.
“Compromise” refers to weakening, undermining or diminishing a particular’s ability to fully express or embody what it is understood to be.
A qualitative limitation, self-contradiction or deficiency compromise or preclude perceived tropes judged to be perfect.
A qualitative limitation prohibits the complete exhibition of the perceived tropes we consistently describe it with; a self-contradiction would compromise that exhibition altogether; and a deficiency represents the absence of a trope we associate with it that is necessary for it to fully and completely exhibit the perceived tropes tied to the concept or name we’ve given it (e.g., “water” as H₂O), based on observed or inferred resemblances among similar particulars.
Qualitative limitation: We commonly describe water as a universal solvent with a strong ability to dissolve substances, but this perceived trope is limited by the quantity of water, the substance to be dissolved and the time needed. This limitation means it exhibits the perceived trope of solubility, but not fully.
Contradiction: Water that is simultaneously described as H₂O and not H₂O (e.g., a sample claimed to be water but chemically identified as H₂SO₄ sulfuric acid). This contradicts a trope we predicate of water (that its molecular structure as H₂O), so making it impossible to exhibit "waterness" consistently. It can’t be water if it’s something else entirely; the description collapses under the contradiction.
Deficiency: Water from a contaminated source that lacks potability because it contains high levels of toxins like lead or bacteria make the water unsafe to drink. Water lacks the ability to prevent contamination. We commonly associate water with being drinkable or life-sustaining under normal conditions (a key trope we predicate of water based on its role in human experience and its H₂O composition). This water is still H₂O chemically, but the absence of potability means it fails to fully exhibit what we categorize as water in everyday use. You wouldn’t use it to hydrate without treatment, so it’s deficient in a functional way.
An absolutely perfect particular is perfect in its entirety, which means there is no deficiency even in a quality that might seem unrelated to its perceived tropes. It would be an improvement to not have a qualitative limitation, self-contradiction or deficiency, but there is nothing to improve a particular that is absolutely perfect.
Therefore, P is inconsistent with a qualitative limitation, self-contradiction or deficiency. (Definitional Substitution on #2-3)
If P does not entail adhering to logical and metaphysical principles (e.g., non-contradiction, necessity of internal coherence), then P is consistent with a qualitative limitation, self-contradiction or deficiency.
Qualitative limitation: If P does not require logical consistency, P could include a compromising or precluding tropes.
Self-contradiction: Without the principle of non-contradiction, P could embody contradictory or incompatible tropes. This would make P incoherent, as contradictory or incompatible tropes cannot coexist in the particulars we call perfect.
Deficiency: If a particular were to lack any trope or quality necessary for its complete expression, it would, by that very fact, not be perfect. The absence of such a quality would represent a limitation or an incompleteness.
Necessity of internal coherence: Conflicting tropes would introduce qualities like limitation or deficiency, which are incompatible with the tropes of perfection derived from particulars.
Therefore, P entails adhering to logical and metaphysical principles. (Modus Tollens on #4-5)
If P is inconsistent with a qualitative limitation, self-contradiction or deficiency (per #4), then P is inconsistent with an intentional particular that depends on anything or lacking anything for the particular’s actual existence.
If a particular depends on anything else or lacks something for existence, that dependence or lack signifies a limitation.
Therefore, P is inconsistent with an intentional particular that depends on anything or lacking anything for the particular’s actual existence. (Modus Ponens on #6-7)
If true, then the exemplification of P requires no ontologically prior or temporally prior fulfillment or relief of specific circumstances, states of affairs, or the prior existence of any particular to be metaphysically possible.
If P excludes all forms of dependency and lack, then no quantifier need precede P temporally or ontologically to make it possible. Exemplification of P must be possible without needing anything outside or prior to it.
If the particular required a prior state (e.g., a cause, a context, or a specific circumstance) to exist, it would be dependent, introducing a limitation inconsistent with the predicate. For example, a perfect logical proof (either in the form of concrete written symbols or as a thoughts in a mind) would be stands on its own without needing external validation. It couldn’t be “absolutely perfect,” because it would still depend on those symbols or thoughts in a mind to exist.
“Ontologically prior” refers to a relationship between two or more things that occurs whenever a thing exists only because another thing exists. It only becomes an ontological priority when at least one thing exists before (prior) another thing (posterior), even if temporally they exist simultaneously.
Therefore, the exemplification of P requires no ontologically prior or temporally prior fulfillment or relief of specific circumstances, states of affairs, or the prior existence of any particular to be metaphysically possible. (Modus Ponens on #8-9)
If (per #6) P entails adhering to logical and metaphysical principles, and (per #10) the exemplification of P requires no ontologically prior or temporally prior fulfillment or relief of specific circumstances, states of affairs, or the prior existence of any particular to be metaphysically possible, then there is no metaphysically necessary reason, principle, factor or cause preventing or negating the existence of an intentional particular that exemplifies or realizes P.
Something is metaphysically necessary if it must be the case due to the fundamental nature of reality, beyond just logical necessity (like "2+2=4") or physical laws (like gravity). It’s about what cannot be otherwise given the deepest structure of existence, regardless of contingent facts or circumstances. A metaphysically necessary reason not just a contingent or practical hurdle.
Put another way, there is no underlying rule, concept, or law (principle), nor any metaphysically necessary reason, factor, or cause that could logically argue against or prevent the actual existence of a particular that fulfills or satisfies P.
Finitude and imperfection objections: These objections posit that if reality itself is metaphysically finite or inherently imperfect (e.g., everything decays, nothing lasts forever, or imperfection is baked into existence), then no particular could exemplify P because the fundamental nature of reality prevents it. Therefore, P would be incoherent. However, this objection is blocked by the conclusion of step #10. The fact that the exemplification of P requires no ontologically prior or temporally prior fulfillment or relief of specific circumstance (including the finitude of reality) means that finitude cannot block the exemplification of P. The definition of fully exemplifying every compossible trope we associate with the name "perfect" across all meanings and extents must in principle be achievable independent of whether reality is finite or not. Finitude, as a circumstance, can’t be a prerequisite that P relies on. P’s independence from finitude or any other state of affairs means nothing is preventing P from being exemplified.
Logical contradiction objection: If P is self-contradictory or entails a contradiction, it’s metaphysically impossible for a particular to exemplify it. This objection is blocked by #6, which holds that P entails adhering to logical and metaphysical principles. “Perfect” is just what we call a set of perceived trope that exhibits no flaws, no gaps, and nothing left to improve. It’s a coherent description based on all the concrete, individual qualities we’ve tied to the name “perfection.”
Causal requirement objection: This objection suggests it’s possible that reality requires all particulars to arise from causes, and causes are inherently imperfect or contingent, so P can’t be exemplified because it’d depend on an imperfect source, contradicting its “no dependence” clause of #8. This objections overcome with the conclusion of #10, which states that P’s exemplification doesn’t need any ontologically prior states of affairs, including a perfect cause.
Nonexistence of anything capable of being perfect: This objection states that if reality metaphysically forbids particulars that can bear every perceived trope associated with the name "perfect” in every respect (e.g., no entity can be "perfect in every respect"), then P can’t be exemplified, not because of finitude, but because no suitable particular is possible. I think this objection would land, but it’s only I agree that not every perceived trope could be perfect in every possible respect. The argument just state that for those perceived tropes in which is possible to be perfect, then something can exemplify that name “perfection.” Stage 3 of the argument is meant to explore what are possible extents of perfection. So if hypothetically, it were impossible to be omniscient, then that would not prevent the exemplification of P; it would only mean that whatever exemplifies P cannot be omniscient. Later, in Stage 3, I will discuss omniscience and the other omni-attributes, but that is getting ahead of the argument.
Let (p) denote “an intentional particular that exemplifies or realizes P.”
Therefore, there is no metaphysically necessary reason, principle, factor or cause preventing or negating the existence of (p). (Modus Ponens on #10-11)
If the existence of an intentional particular is impossible, then there would be a metaphysically necessary reason, principle, factor, or cause preventing or negating its existence.
In virtue of being absolutely perfect, there is nothing preventing or negating the actual existence of an intentional particular that exemplifies or realizes P. This guarantees there are no internal or external absences, constraints or negating factors.
One straightforward metaphysically necessary reason anything that could exist doesn’t exist is because it’s not self-existent.
When we say something is impossible, we mean that there exists no possible world where it could be instantiated. For example, if "a golden mountain" is impossible, then there must be no possible world or the way reality could be where such a mountain exists. Likewise, if absolute perfection is possible, then some particular can instantiate it in at least one possible world or way the world could be.
This does not presume that existence is a predicate. Instead, a modal ontological argument overcomes the objection by framing existence as a modal property (necessary existence), not a first-order predicate, and by grounding the argument in the logical structure of possible worlds rather than treating existence as a quality added to a concept. What entails from being absolutely perfect is that there is no reason metaphysically necessary reason, principle, factor, or cause preventing or negating its existence. If so, then it's not impossible.
Therefore, the existence of (p) isn’t impossible. (Modus Tollens on #12-13)
If the existence of a particular isn’t impossible, then there is at least one possible world where it would actually exist.
Therefore, there is at least one possible world where (p) would actually exist. (Modus Ponens on #14-15)
Stage 2
If there were W, a possible world where (p) would actually exist, then had that world been actual, an actual (p) would exist.
Let (p)a denote “an actual (p).”
Let W denote “a possible world where (p) would actually exist.”
Therefore, had W been actual, (p)a would exist. (Modus Ponens on #16-17)
If a particular that would actually exist in a world doesn’t dependent on anything or lack anything for its own existence, then it cannot fail or cease to exist in that world, so its non-existence is impossible in that world.
Therefore, (p)a cannot fail or cease to exist in W, so its non-existence is impossible in W. (Modus Ponens on #18-19)
Whatever is impossible in one world is impossible in all possible worlds, including our actual world.
Therefore, the non-existence of (p)a is impossible in all possible worlds, including our actual world. (Modus Ponens on #20-21)
If the non-existence of a particular is impossible in all possible worlds, then it exists necessarily in all possible worlds, including our actual world.
Therefore, (p)a exists necessarily in all possible worlds, including our actual world. (Modus Ponens on #22-23)
Stage 3
If an actual particular did not exist concretely but abstractly (like a concept), or if it had physical or metaphysical parts, or if it were fragmented, then it would depend on either: (1.) instances or participants to be an actual instantiation in the world, (2.) its parts being co-existing or (3.) it being assembled or unified by its parts into a single whole.
To exist concretely means to exist as an independent substance with actuality (the here-and-now present state), rather than merely as an idea or a potentiality (the aptitude or capacity to receive a different state).
Per #10, P is incompatible with a dependence on the fulfillment or relief of any specific circumstances or states of affair.
Therefore, (p)a exists concretely, without parts and unfragmented. (Modus Tollens on #25-26)
If an actual particular doesn’t depends on anything or lack anything for existence, then its concrete existence, tropes and actions are wholly self-determined.
Its existence and actions would be the epitome of autonomy, uninfluenced and unrestricted by anything outside itself.
Therefore, (p)a is wholly self-determined. (Modus Ponens on #27-28)
If an actual particular is wholly self-determined , then it must possess the capacity for intellect and will.
If something lacks a will, it might understand things, but it can’t choose. It has no power to act on what it knows or to make certain reasons efficacious. Without a will, it’s passive and moved by what it happens to understand, not by a free decision to act as cause in a given respect.
A wholly self-determined particular would make certain reasons efficacious or determining. The reasons do not make efficacious (determine) a wholly self-determined particular.
If the particular didn’t have these capacities, it might act from within, but it wouldn’t understand or guide why it acts. That would leave its behavior shaped by unexamined impulses or fixed dispositions. It would not determine its reasons. Reasons would determine it.
If an entity is wholly self-determined, then nothing outside itself explains its behavior. Self-determination means being the source and reason for one’s own actions. That requires not just the ability to do anything, but the ability to decide what to do and why. Without intention, there’s no decision, just causation. To be wholly self-determined, the entity must direct itself in light of what it understands because otherwise its internal movements are just the playing out of fixed patterns or dispositions, not expressions of will. True self-determination requires that the entity knows what it is doing and chooses it. So the control has to come from deliberate, goal-directed action.
“Intentional self-determination” means acting in full alignment with its intellect and will and exercising the greatest degree of autonomy. This implies freedom from constraints, ignorance, instinct or external coercion.
Therefore, (p)a must possess the capacity for intellect and will. (Modus Ponens on #29-30)
If there were more than one (p)a, then the distinguishing tropes between or among them would either imply dependence on an external condition or indication of an incompleteness in each (implying a limitation in each that prevents any one from possessing the trope of necessary existence), both of which are contrary to the trope of (p)a.
Therefore, only a single (p)a exists. (Modus Tollens on #31-32)
If an actual particular cannot have a qualitative limitation, self-contradiction or deficiency to a trope of its being, then it cannot have whatever entails a qualitative limitation, self-contradiction or deficiency.
Self-limiting tropes entail a qualitative limitation, self-contradiction or deficiency.
Qualitative trope (such as knowledge, power and moral goodness) are compatible with being unlimited if they are not defined by limitation, deficiency, dependency or lack.
For example, to possess self-limiting tropes like being physical (having a specific shape, size or location in space) would be constraining by spatial dimensions, which contradicts the idea of unlimited existence.
Therefore, (p)a cannot possess self-limiting tropes. (Modus Tollens on #34-35)
If an actual particular is qualitatively unlimited and without self-limiting tropes, then it necessarily possess all maximally compossible non-self-limiting tropes.
Having realized the full and complete expression of every perceived tropes, (p)a necessarily possess all maximally compossible non-self-limiting tropes.
Therefore, (p)a necessarily possesses all maximally compossible non-self-limiting tropes in their maximum form. (Modus Ponens on #36-37)
If a relational trope depends on an external particular or implies deficiency, then the trope is self-limiting.
The relational trope of an absolutely perfect being arise necessarily from its own essence and do not depend on anything external or imply deficiency.
Relationality is compatible with perfection when it reflects fullness (rather than need), unity (internal to the being itself) and self-sufficiency (unchanging and eternal).
Therefore, the relational tropes of an absolutely perfect being are not self-limiting. (Modus Tollens on #39-40)
The concept of freedom means having the ability to act according to one’s will or essence without being coerced by external forces or limitations.
If an actual particular is described as having certain a perceived trope (for instance, those we call "absolutely perfect"), then consistently acting in accordance with the perceived tropes we associate with it reflects the uncoerced exhibition of the qualities tied to the concept or name we’ve given it, based on observed or inferred resemblances among similar particulars, and is not a limitation on its freedom.
Therefore, consistently acting in accordance with the perceived tropes we associate with it reflects the uncoerced exhibition of the qualities tied to the concept or name we’ve given it, based on observed or inferred resemblances among similar particulars, and is not a limitation on its freedom. (Modus Ponens on #42-43)
If an actual particular is perfectly morally good, then its qualitative tropes are inherently and necessarily aligned to express its perfect goodness.
Therefore, the qualitative tropes of a perfect being are inherently and necessarily aligned with its perfect goodness. (Modus Ponens on #44-45)
If what people mean by God is an actual particular that is absolutely perfect, is not dependent on anything external to itself, necessarily exists in all metaphysically possible world, has intellect and will and is singularly unique, the expression of moral goodness, then God exists.
Therefore, God exists. (Modus Ponens on #46-47)
Formal symbolic argument for Stage 1
P (Definition)
P→¬L(x)
L(x)→D(x)
P→¬L(x)¬D(x) (Definitional Substitution on 2-3)
¬(P→adhering to logical and metaphysical principles)→(P→L(x))
P→adhering to logical and metaphysical principles (Modus Tollens on 4-5)
P→¬D(x)→¬C(x)
P→¬C(x) (Modus Ponens on 6-7)
¬C(x)→¬N
P→¬N (Modus Ponens on 8-9)
(P→adhering to logical and metaphysical principles)∧(P→¬N)→¬N
¬N (Modus Ponens on 10-11)
□¬E(x)→N
¬□¬E(x) (Modus Tollens on 12-13)
¬□¬E(x)→◊E(x)
◊E(x) (Modus Ponens on 14-15)
Symbol Definitions
P = "is absolutely perfect"
E(x) = "x actually exists"
L(x) = "x has a qualitative limitation, self-contradiction, or deficiency"
D(x) = "x is dependent on something or lacks something for its actual existence"
C(x) = "x is contingent on specific circumstances or states of affairs for its actual existence"
N = "there is a metaphysically necessary reason, principle, factor, or cause preventing or negating x’s actual existence"
◊E(x) = "x possibly exists"
Logical Symbols Used
∀ = "for all"
∃ = "there exists"
¬ = "not"
→ = "if...then"
↔ = "if and only if"
∧ = "and"
∨ = "or"
□ = "necessarily"
◊ = "possibly"