Spinozian Ontological Argument
First we will look at a Spinozian ontological argument, based on the philosophical work of Baruch Spinoza. This is an ontological argument which has not, as far as I can tell, received a lot of recognition in the literature, compared to the more popular arguments. Here is a syllogistic sketch of the argument.
1. Substance is something that exists independently and does not rely on anything else for its existence.
2. There can be only one substance with a particular attribute.
3. God is an absolutely infinite substance, having all possible attributes.
4. An attribute is a property that expresses the essence of a substance.
5. A substance necessarily exists if it has at least one attribute that necessarily exists (it’s essence entails or contains existence).
6. Since God has all possible attributes, God necessarily has an attribute that necessitates existence.
7. Therefore, God necessarily exists.
Spinoza's ontological argument for the existence of God is grounded in his metaphysical system, which is characterized by substance monism and the principle of sufficient reason (PSR). For Spinoza, a substance is a self-sufficient, independent entity that does not rely on anything else for its existence. In Spinoza's view, substances are characterized by their attributes, and they are causally independent of other substances. Here's an overview of the premises.
Premise 1. For Spinoza, a substance is something that exists in itself and is conceived through itself. In other words, it is self-existent and self-definable. It does not depend on anything else for its existence. That's just what a substance is in his metaphysics.
Premise 2. Spinoza asserts that there can be only one substance with a particular attribute, a principle that follows from his substance monism. He argues that it is impossible for two substances to share the same attribute, as they would then be indistinguishable from one another, thus contradicting the PSR. As there would be no sufficient reason for why they exist as two distinct entities.
Premise 3. Spinoza is taking God also known as Nature (Deus sive Natura).to be an "absolutely infinite substance", which refers to the concept of a being that encapsulates all possible attributes and is self-determined, meaning it exists and acts due to the necessity of its own nature. This substance isn't limited or restricted by anything external to itself, as it comprehends everything within its essence.
Premise 4. An attribute, in Spinoza's metaphysics, is a fundamental property that expresses the essence of a substance. Attributes are the ways in which we perceive and conceive the essence of the substance. For example, the attribute of extension is taken to express the essence of material substance, whereas the attribute of thought is taken to express the essence of mental substance.
Premise 5. A substance necessarily exist if it possesses an attribute that necessarily exists. This is because, in Spinoza's metaphysics, the existence of a substance is intrinsically linked to its essence, as expressed by its attributes.
1. Substance is something that exists independently and does not rely on anything else for its existence.
2. There can be only one substance with a particular attribute.
3. God is an absolutely infinite substance, having all possible attributes.
4. An attribute is a property that expresses the essence of a substance.
5. A substance necessarily exists if it has at least one attribute that necessarily exists (it’s essence entails or contains existence).
6. Since God has all possible attributes, God necessarily has an attribute that necessitates existence.
7. Therefore, God necessarily exists.
Spinoza's ontological argument for the existence of God is grounded in his metaphysical system, which is characterized by substance monism and the principle of sufficient reason (PSR). For Spinoza, a substance is a self-sufficient, independent entity that does not rely on anything else for its existence. In Spinoza's view, substances are characterized by their attributes, and they are causally independent of other substances. Here's an overview of the premises.
Premise 1. For Spinoza, a substance is something that exists in itself and is conceived through itself. In other words, it is self-existent and self-definable. It does not depend on anything else for its existence. That's just what a substance is in his metaphysics.
Premise 2. Spinoza asserts that there can be only one substance with a particular attribute, a principle that follows from his substance monism. He argues that it is impossible for two substances to share the same attribute, as they would then be indistinguishable from one another, thus contradicting the PSR. As there would be no sufficient reason for why they exist as two distinct entities.
Premise 3. Spinoza is taking God also known as Nature (Deus sive Natura).to be an "absolutely infinite substance", which refers to the concept of a being that encapsulates all possible attributes and is self-determined, meaning it exists and acts due to the necessity of its own nature. This substance isn't limited or restricted by anything external to itself, as it comprehends everything within its essence.
Premise 4. An attribute, in Spinoza's metaphysics, is a fundamental property that expresses the essence of a substance. Attributes are the ways in which we perceive and conceive the essence of the substance. For example, the attribute of extension is taken to express the essence of material substance, whereas the attribute of thought is taken to express the essence of mental substance.
Premise 5. A substance necessarily exist if it possesses an attribute that necessarily exists. This is because, in Spinoza's metaphysics, the existence of a substance is intrinsically linked to its essence, as expressed by its attributes.
Premise 6. Since God, as an absolutely infinite substance, possesses all possible attributes, it follows that God necessarily possesses at least one attribute that necessitates existence. This assertion is derived from the principle of sufficient reason, which posits that there must be an explanation for the existence of any substance, and that explanation is found in the substance's attributes.
With that explanation out of the way, we can move to objections.
Objection 1 - The Gap
The first, and perhaps most obvious objection which comes to mind is that this argument doesn't establish the existence of "God" in the sense of some theologically interesting set of attributes, including omnipotence, omniscience, moral perfection etc. Rather it defines 'God' as the totality of all possible attributes and argues for 'God' in this sense, which seems unproblematic for atheism. Of course, the theist might attempt to bridge the gap from "totality of all possible attributes" to a theologically interesting being. But then it is of course, on the theist to meet such a burden.
Objection 2 - Controversial metaphysical assumptions
Here are just a few examples of metaphysical assumptions the argument relies on which can be challenged or argued as outdated:
i) Substance ontology: Spinoza's argument is built on the concept of substances, which are entities that exist independently and do not rely on anything else for their existence. This substance ontology has been challenged by alternative views, such as process metaphysics and relational ontology. Process metaphysics emphasizes the dynamic, ever-changing nature of reality, and relational ontology posits that entities are constituted by their relations with other entities. Both views question the primacy and independence of substances, thus undercutting the foundations upon which Spinoza's argument is built.
ii) Attributes as properties: Spinoza's argument relies on the idea that attributes are properties that express the essence of a substance. This assumption has been criticized in contemporary metaphysics, particularly by proponents of trope theory, which posits that properties are particularized and only exist insofar as they are instantiated by objects. If properties (or attributes) are not abstract entities that can express the essence of substances but rather "substances" are just bundles of tropes, then Spinoza's argument is undercut.
iii) Identity of Indiscernibles: Spinoza's argument that two substances cannot share a particular attribute assumes the identity of indiscernibles. However, the identity of indiscernibles is controversial and might be questioned on the following basis; Imagine two completely symmetrical and isolated spheres with identical properties. According to the principle of the identity of indiscernibles, these spheres would be considered identical, however critics may argue they are in-fact distinct entities (Black 1952).
Objection 3: The PSR and modal collapse.
As said before, Spinoza's argument relies on the PSR. which states that everything that exists has a explanation or reason for it's existence either by the nature of the thing itself (i.e it's necessity), or in the nature of something else (it's contingency on something else). This leads to modal collapse (Van Inwagen 1983). Modal collapse is the elimination of contingency, and thus modal distinctions, such as possibility, necessity, actuality etc.
8. Start with the PSR, which states that everything must have a sufficient reason or explanation for its existence, either in its own nature or in the nature of something else.
9. Assume there are contingent facts (facts that could have been otherwise) with sufficient reasons for their existence.
10. This chain of sufficient reasons must eventually lead to a necessary fact or being (N) with its sufficient reason in itself, to avoid violating the PSR.
11. Since N is necessary and exists in all possible worlds and serves as the sufficient reason for all contingent facts, its existence entails the existence of all contingent facts in all possible worlds.
12. This results in modal collapse, as the distinction between possible and actual worlds is eliminated, and all possibilities collapse into a single necessary reality.
(8.) is a statement of the PSR, (9.) is an assumption for reductio. (10.) is accepted by the Spinozian argument I gave above, which argues that there must be a substance with an attribute which necessitates existence. (11.) is the most controversial. It assumes that the necessary explanation for all contingent things must be an entailing explanation, However, with the strong PSR Spinoza relies on, non-entailing explanations won't seem to cut it, it demands sufficient reasons after-all, not "good-enough" reasons. Further, non-entailing explanations run into problems, if we want to accept that all facts have an explanation. Here is the argument;
13. Suppose the necessary fact N explains contingent existential truth C through a non-entailing explanation.
14. The fact that N & C obtains rather than N & not-C would require an explanation, according to the PSR.
15. Let Q be a non-entailing explanation for why N & C obtains instead of N & not-C.
16. However, since Q is a non-entailing explanation, it does not necessitate the fact N & C.
17. This leads to a new fact (Q & N & C obtains rather than Q & N & not-C)
18. By the PSR, there must be an explanation for this new fact (Q & N & C obtains rather than Q & N & not-C).
19. This pattern continues indefinitely, where for any non-entailing explanation for C you give, there will be a further contingent fact in need of explanation
20. Therefore, given (19.) non-entailing explanations do not satisfy the requirements of the PSR, as they lead to an infinite regress of explanations without providing a conclusive account of why specific combinations of facts obtain.
As a result, it looks like if we accept the PSR, non-entailing explanations won't do, for every non-entailing explanation we need to terminate in an entailing explanation. Some proponents of the PSR might argue that contrastive facts do not require a further explanation, however, I'm not convinced that such a restriction is motivated, and it just seems to wind up accepting brute facts. In any case, the PSR required for the Spinozian argument is strong enough to lend itself to the modal collapse objection.
Modal collapse is a problem for several reasons. First, it goes against our common-sense intuitive understanding of the world, we make modal judgements all the time, it seems obvious that my foot could have been placed at one picometer further to the right at time t. Second, it appears to undermine free will, as there is no possible world where agents could have chosen otherwise. Third, if there is no distinction between possible and actual worlds, this undermines our ordinary understanding of modal logic as those terms lose their meaning, and the whole system becomes incoherent. Finally, it leads to difficulties in understanding causality and providing explanations for events. If everything that happens is necessary, it becomes unclear how we can determine causes or explanations for specific events, since it would seem the explanation for every event would be that it is necessary.
Objection 4; The Frege-Russell-Quine view of existence.
The Frege-Russell-Quine view of existence, otherwise known as the second-order predicate view, or existential quantifier view, holds that existence is not a property of individual objects but a property of concepts or predicates. In this view, to say that something exists is to say that a certain predicate applies to at least one object in the domain of discourse. However, Spinoza’s metaphysics, which the argument relies upon, is committed to existence as a first-order predicate, this is because it holds that existence inheres in a substance. Substances exist because their essence contains existence.
There are plenty of motivations for this second-order view, here are some that I find compelling;
iv) It resolves philosophical puzzles related to non-existent entities, like fictional characters or mythical creatures. If existence were a first-order property, statements about non-existent entities would be problematic, as they would seem to imply that these entities exist. By treating existence as a second-order property, this view allows us to make meaningful statements about non-existent entities without committing ourselves to their existence.
v) It provides a precise and consistent way of understanding and analyzing existence claims within the framework of formal logic. By employing quantifiers and variables, this approach allows for a more rigorous and systematic treatment of existence claims in logic, which in turn can help clarify and resolve philosophical issues related to existence. This also allows us to reduce the amount of primitive concepts in our vocabulary, as there is no property of existence over and above quantification over some predicate or definite description.
vi) Existential statements seem to be analogous to statements of number. Take the statement "unicorns do not exist." In the second-order predicate view, this statement can be understood as saying that the property of being a unicorn is not instantiated by any objects. This is similar to saying that the number of objects with the property of being a unicorn is zero.
vii) Peter Van Inwagen's Martian Language argument (Van Inwagen 2009)." Van inwagen asks us to imagine a race of intelligent Martians who speak a language that differs from ours in the way it treats existence. In their language, they do not have a word for "exists" or "existence." Instead, they have a word that translates to something like "exemplified" or "instantiated." When they want to say that something exists, they say that the concept, property, or set corresponding to that thing is instantiated.
For example, instead of saying "unicorns do not exist," the Martians would say something like "the concept of a unicorn is uninstantiated" or "the property of being a unicorn is unexemplified." In their language, existence claims are always made as claims about the instantiation or exemplification of concepts, properties, or sets, rather than about individual objects.
Van Inwagen argues that, from a Martian perspective, an understanding of existence as a first-order property is peculiar and confusing. The Martians would see such usage as making category mistakes by treating existence as a property of individual objects, rather than a property of concepts, properties, or sets. Further, it looks like the Martian language is no less capable of conveying the same semantic content without the use of terms like "existence" which seems to imply that our understanding of existence might be shaped by the particularities of our language, rather than reflecting some deep metaphysical truth about the nature of existence itself.
Objection 5: Invalid argument?
The final objection is one that is much more technical and more difficult to follow for those less familiar with first order logic (FOL). The objection in question originates from J.H Sobel’s Logic and Theism (Sobel 2003). In order to explicate the critique, Sobel advances a FOL symbolic interpretation of the argument. The argument he develops in his book is a bit different then the syllogism I sketched above. His formulation of the argument goes as follows;
21. If a thing can be conceived not to exist, its essence or nature does not involve existence: (x)(Kx ⊃ ∼Vx).
22. Existence belongs to the nature of a substance: (x)(Sx ⊃ Vx).
23. The infinite substance can be conceived not to exist. (∃y)((x)[(Ix & Sx) ≡ x = y] & Ky)
24. If an infinite substance exists, then God is the infinite substance: (∃x)(Ix & Sx) ⊃ (∃y)((x)[(Ix & Sx) ≡ x = y] & G = y).
25. What cannot be conceived not to exist, exists necessarily: (x)[∼Kx ⊃ X(x)]. ∴
26. God, the infinite substance, necessarily exists: (∃y)((x)[(Ix & Sx) ≡ x = y] & G = y) & X(G)
For Sobel, the problem herein lies with (23.). Sobel points out that (23.) is ambiguous between two interpretations.
23a. There is no such thing that is the only infinite substance and can be conceived not to exist.
23b. There is such a thing that is the only infinite substance and it cannot be conceived not to exist.
As Sobel points out, the interpretation you choose for (23.) impacts the validity of the argument. If you choose (23a.), the steps from (21.) and (22.) to (3a) are logically valid, but the leap from (23a.), (24.), and (25.) to the conclusion (26.) is not valid. If you choose (23b.), while the leap from (23b.), (24.), and (25.) to (26.) is valid, the leap from (21.) and (22.) to (23b.) is not valid.
What about the way I presented the Spinozian argument? To formalize the argument I used above in first order predicate logic we get something like this;
28. (2.) ∀x∀y∀z((S(x) & S(y) & A(x, z) & A(y, z)) ⊃ x = y) Translation: For all x, y, z, if x and y are substances and both x and y have attribute z, then x is equal to y.
29. (3.) ∀x(G(x) ⊃ (S(x) & I(x) & ∀y(A(x, y)))) Translation: For all x, if x is God, then x is a substance, x is infinite, and for every y, x has attribute y.
30. (5.) ∀x(S(x) & ∃y(A(x, y) & NE(y)) ⊃ NE(x)) Translation: For all x, if x is a substance and there exists an attribute y of x that necessarily exists, then x necessarily exists.
31.(6.) ∀x(G(x) ⊃ ∃y(A(x, y) & NE(y))). OR. ∃x(G(x) & ∃y(A(x, y) & NE(y))). Both translations covered below.
21. If a thing can be conceived not to exist, its essence or nature does not involve existence: (x)(Kx ⊃ ∼Vx).
22. Existence belongs to the nature of a substance: (x)(Sx ⊃ Vx).
23. The infinite substance can be conceived not to exist. (∃y)((x)[(Ix & Sx) ≡ x = y] & Ky)
24. If an infinite substance exists, then God is the infinite substance: (∃x)(Ix & Sx) ⊃ (∃y)((x)[(Ix & Sx) ≡ x = y] & G = y).
25. What cannot be conceived not to exist, exists necessarily: (x)[∼Kx ⊃ X(x)]. ∴
26. God, the infinite substance, necessarily exists: (∃y)((x)[(Ix & Sx) ≡ x = y] & G = y) & X(G)
For Sobel, the problem herein lies with (23.). Sobel points out that (23.) is ambiguous between two interpretations.
23a. There is no such thing that is the only infinite substance and can be conceived not to exist.
23b. There is such a thing that is the only infinite substance and it cannot be conceived not to exist.
As Sobel points out, the interpretation you choose for (23.) impacts the validity of the argument. If you choose (23a.), the steps from (21.) and (22.) to (3a) are logically valid, but the leap from (23a.), (24.), and (25.) to the conclusion (26.) is not valid. If you choose (23b.), while the leap from (23b.), (24.), and (25.) to (26.) is valid, the leap from (21.) and (22.) to (23b.) is not valid.
What about the way I presented the Spinozian argument? To formalize the argument I used above in first order predicate logic we get something like this;
- S(x) = "x is a substance"
- A(x, y) = "x has attribute y"
- E(x) = "x exists"
- G(x) = "x is God"
- I(x) = "x is infinite"
- NE(x) = "x necessarily exists"
28. (2.) ∀x∀y∀z((S(x) & S(y) & A(x, z) & A(y, z)) ⊃ x = y) Translation: For all x, y, z, if x and y are substances and both x and y have attribute z, then x is equal to y.
29. (3.) ∀x(G(x) ⊃ (S(x) & I(x) & ∀y(A(x, y)))) Translation: For all x, if x is God, then x is a substance, x is infinite, and for every y, x has attribute y.
30. (5.) ∀x(S(x) & ∃y(A(x, y) & NE(y)) ⊃ NE(x)) Translation: For all x, if x is a substance and there exists an attribute y of x that necessarily exists, then x necessarily exists.
31.(6.) ∀x(G(x) ⊃ ∃y(A(x, y) & NE(y))). OR. ∃x(G(x) & ∃y(A(x, y) & NE(y))). Both translations covered below.
32. (7.) ∃x(G(x) & NE(x)) Translation: There exists an x that is God and necessarily exists.
(We don’t need to translate (4.) in the original syllogism above, because (4.) is a definition and doesn't directly contribute to the logical structure of the argument, and wouldn't cleanly translate anyways. We will just take (4.) as enthymematic)
Might an invalidity charge be levied against this formulation of the argument? Echoing a Sobelian-style line of critique, I think we can show there is. The problem here lies in (31.). There are 2 interpretations of (31.), the first runs into an issue with validity, the second, fails to be inferred from the previous premises, and begs the question.
Universal interpretation: Under this interpretation we have ∀x(G(x) ⊃ ∃y(A(x, y) & NE(y))), which translates to "For all x, if x is God, then there exists some y such that x has attribute y and y necessarily exists". This is entailed from the previous premises, since by (29.) God is a substance and possesses all attributes, and since we are taking Spinoza's metaphysics for granted in the background, (In particular, through the use of a bridging premise such as ∃x(A(x) & NE(x)) "There is an x, such that x is an attribute and x necessarily exists" which may be argued for via the PSR, as well as premises (1./27.), (2./28.) and (4.) in the natural language formulation) God would have an attribute which necessarily instantiates existence. However, from (31.) and the subsequent premises, you cannot validly infer (32.) (That there is a God, that necessarily exists). All the subsequent premises do, is specify conditions which would obtain were God to exist, or were a substance to have a necessarily-existence-entailing attribute. None of them entail, even when taken together, that there actually is some x that satisfies the predicate G(x) (There is a God). The most you can get is ∀x(G(x) ⊃ NE(x)) (For all x, if x is God, then x necessarily exists). Or to put it in simpler terms. IF God exists, then God necessarily exists. But of course, the atheist need not lose sleep over such a conclusion.
(We don’t need to translate (4.) in the original syllogism above, because (4.) is a definition and doesn't directly contribute to the logical structure of the argument, and wouldn't cleanly translate anyways. We will just take (4.) as enthymematic)
Might an invalidity charge be levied against this formulation of the argument? Echoing a Sobelian-style line of critique, I think we can show there is. The problem here lies in (31.). There are 2 interpretations of (31.), the first runs into an issue with validity, the second, fails to be inferred from the previous premises, and begs the question.
Universal interpretation: Under this interpretation we have ∀x(G(x) ⊃ ∃y(A(x, y) & NE(y))), which translates to "For all x, if x is God, then there exists some y such that x has attribute y and y necessarily exists". This is entailed from the previous premises, since by (29.) God is a substance and possesses all attributes, and since we are taking Spinoza's metaphysics for granted in the background, (In particular, through the use of a bridging premise such as ∃x(A(x) & NE(x)) "There is an x, such that x is an attribute and x necessarily exists" which may be argued for via the PSR, as well as premises (1./27.), (2./28.) and (4.) in the natural language formulation) God would have an attribute which necessarily instantiates existence. However, from (31.) and the subsequent premises, you cannot validly infer (32.) (That there is a God, that necessarily exists). All the subsequent premises do, is specify conditions which would obtain were God to exist, or were a substance to have a necessarily-existence-entailing attribute. None of them entail, even when taken together, that there actually is some x that satisfies the predicate G(x) (There is a God). The most you can get is ∀x(G(x) ⊃ NE(x)) (For all x, if x is God, then x necessarily exists). Or to put it in simpler terms. IF God exists, then God necessarily exists. But of course, the atheist need not lose sleep over such a conclusion.
Existential interpretation: Under this interpretation we have ∃x(G(x) & ∃y(A(x, y) & NE(y))), which translates to "There is an x, such that x is God, and there exists some y such that x has attribute y and y necessarily exists". On this interpretation, (32.) can be validly inferred. The problem with this interpretation, however, is that this premise cannot itself be inferred from the previous premises, (27-30) as the universal interpretation can, none of them, even jointly, show that there is some x that satisfies the God predicate. Further, this interpretation begs the question by simply asserting that there is some x such that x is God, which is the very thing that is supposed to be shown.
I conclude that the Spinozian ontological argument, even when it's highly controversial metaphysical assumptions are taken for granted, fails either on the basis of invalidity, or begging the question.
Meinongian ontological argument
Next, we look at the Meinongian ontological argument, which is based on the philosopher Alexius Meinong's theory of objects. Although Meinong himself did not make the argument, the argument is based on his work. It can be formalized as follows;
1. Each instance of the schema “The F G is F” expresses a truth.
2. Hence the sentence “The existent perfect being is existent” expresses a truth.
3. Hence, the existent perfect being is existent.
4. Hence, God is existent (God exists)
Objection 1: Reject Meinongianism
The schema in the first premise is a characterization theorem used in the context of Meinong's theory of objects. which posits that objects can have properties regardless of whether or not they exist. As such, the argument will not be convincing to anyone who doesn't accept Meinong's view. The arguments I gave above for the second-order predicate view of existence, apply mutatis mutandis to Meinong's view. Non-existent objects don't exemplify properties on the second order view, existence just is the second-order property of properties being exemplified. Further, there is an additional reason to reject Meinongianism which is that it is ontologically unparsimonious, it posits a distinction between existent and subsistent objects, which seems to be an unnecessary ontological commitment. The distinctions he draws seem to just add more complexity, and may not even be intelligible.
Objection 2: Analytic-Synthetic Dilemma
The schema "The F G is F" can be understood in two ways. One way would be purely analytic, (i.e., true by virtue of the meanings of its terms), which would 'cancel-out' ontological commitment. Another would be as a synthetic statement, which is a substantive claim about the actual world, which does not 'cancel-out' ontological commitment.
If (2.) is taken as analytic, then it does not entail an ontological commitment to the existence of an existent perfect being in the actual world. It would simply be stating a tautology about the concept of an existent perfect being. So, the argument, insofar as it concludes that a perfect being exists in the actual world, is invalid.
On the other hand, if the statement is taken to imply ontological commitment, then it is no longer purely analytic, as it relies on the existence of an existent perfect being in the actual world. But no atheist would then accept (2.). The argument would need to provide additional justification for this ontological commitment, which is not provided by the characterization theorem alone. The argument, as it stands, would be simply question-begging. Thus, on either interpretation, the argument fails.
The Modal Perfection Argument
This will be the longest and most technical section. I will try my best to make the points easier to follow. The 'modal perfection' argument is a Godelian-style ontological argument and the most complicated ontological argument. I've seen forms of the argument claimed to be logical proofs of theism, or used as an intimidation tactic, to those less familiar with philosophy and logic, as the complicated logical structure and technical terms employed, make it very difficult to address for those lacking the proper tools/training. Which, in part, is what inspired me to make this post. An examination and critical analysis of the argument will demand a great deal of groundwork. First, I will need to provide some necessary context, we will start by briefly laying out the history of the argument. Next, we will formulate, and explain the Modal Perfection argument in it's strongest form, which I believe is provided my C'zar Bernstein. Lastly, I will provide objections, which, by my lights, show that the argument is either unsound, or at the very least extremely unconvincing to those not already predisposed to accept the conclusion.
Brief History of the Argument and Dialectic
The earliest formulation of what is now called "The Modal Perfection Argument" (Henceforth, MPA), would be Godel's ontological argument. Gödel's "Ontological Proof" is a dense and technical philosophical argument that is not well-known even among many philosophers and theologians. He presents this argument formally to deduce the existence of a 'God-like' being. This being is defined as having all 'positive' properties, but the term 'positive' itself remains undefined. Importantly, unlike other ontological arguments, Godel's argument does not assume that either existence or existence-in-reality is a property. The existence of something in his logic is established through existential quantification. His argument is constructed around three defined notions, five axioms, and three important theorems. Robert Maydole (Maydole 2009) formalizes the argument as follows;
Df 1 A being has the property of being God-like if and only if it has every positive
property.
Df 2 A property is an essence of something if and only if it has the property, and the
property entails each of its properties.
Df 3 Something has the property of being a necessary being if and only if every
essence it has is necessarily instantiated.
Axioms
Ax 1 A property is positive if and only if its negation is not positive.
Ax 2 Positive properties entail only positive properties.
Ax 3 God-likeness is positive.
Ax 4 Positive properties are necessarily positive.
Ax 5 The property of being a necessary being is positive.
Theorems
Tm 1 It is possible that something is God-like.
Tm 2 God-likeness is an essence of whatever is God-like.
Tm 3 Something is God-like.
This argument has been objected to on many grounds, the axioms are what is most often disputed. Notably Sobel 2003, has argued that the axioms lead to modal collapse (Just like how strong PSR above leads to modal collapse, but the way the entailment is derived is different). The basic idea is that for every proposition P, there is the property of existing alongside the truth of P. This property, which we'll call O would either be positive or not positive. If O is positive and there's a God-like being with all positive properties (Df 1), then this God-like being has O, but then since the God-like being exists and has all positive properties in all possible worlds, it would have O in every possible world. So, P would be true in all possible worlds. If O is not positive, then by axiom 1 the negation of O, ¬O (the property of existing alongside the falsity of P), would be positive, so the God-like being would have ¬O in all possible worlds, so P would be false in all possible worlds. In either case, P would be necessarily true or necessarily false. So all truths would be necessary truths.
However, emendations of the argument from the likes of Anderson, Hazen, Koons, and Hàjek avoid the modal collapse objection, typically by modifying axiom 1 in some way or other. Oppy 1996 argues that these modifications (in particular Andersons' although it may apply equal to the others) run afoul of parodies. In Andersons formulation, a being is defined as God-like if all its essential properties are positive. Oppy modifies this definition by allowing for certain exceptions, e.g a being is God-like if all it's essential properties are positive except for P1, or P2, or Pn. Oppy concludes that for each positive property, there's a God-like being that doesn't have this specific positive property but has all other positive properties. Which implies, absurdly, that there are as many God-like beings as there are positive properties.
This is where Robert Maydole's MPA (Maydole 2003) comes in. His argument is designed to rely on less axioms and therefore less avenues of objection, and avoid these parodies. It also replaces the term "positive property" with the term "perfection", the latter being a somewhat more clear notion. And, it replaces the term "God-like" with the term "supreme". A perfection is understood as a property that is necessarily better to have than lack. Supreme is understood as the property of being such that it is impossible for something to be greater and impossible for there to be something else than which it is not greater. With that, the argument starts out by laying out three axioms;
M1 A property is a perfection only if its negation is not a perfection.
M2 Perfections entail only perfections.
M3 The property of being supreme is a perfection.
From M1, M2, and M3, it follows that it is possible that a supreme being exists. The proof goes as follows;
1. Suppose being supreme is impossible
2. Since being supreme is impossible it entails being not-supreme
3. By M2, perfections only entail perfections
4. By M3, the property of being supreme is a perfection
5. From 2, 3 and 4, being not-supreme is a perfection
6. But this contradicts M1, if a property is a perfection it's negation cannot be a perfection
7. Therefore our initial assumption is false, being supreme is not impossible
From, here we deduce from the possibility that a supreme being exists, that a supreme being exists. This can be deduced in 2 ways. Here's one way.
8. It's possible that a supreme being exists
9. Necessary existence is a perfection
10. Since it's impossible for a supreme being to be greater, a supreme being must have all perfections (properties that are greater to have than lack)
11. From 9, and 10, a supreme being has necessary existence (e,g it exists in all possible worlds, if it exists at all).
12. From 8 and 11, it's possibly necessary that a supreme being exists
13 From 12, it's necessary that a supreme being exists (S5)
14. So, a supreme being exists
This argument however, is controversial. It may be disputed on the grounds of (9) (the assumption that necessary existence is a perfection), or on the grounds of (13), (the assumption of the S5 modal axiom). It also seems to make one vulnerable to the modal collapse objection sketched above, given that the supreme being has all perfections (10.) including necessary existence (11.), and given we accept M1. Maydole himself offers a different deduction, here is the formal derivation, and I'll now provide the argument in natural language;
M2 Perfections entail only perfections.
M3 The property of being supreme is a perfection.
From M1, M2, and M3, it follows that it is possible that a supreme being exists. The proof goes as follows;
1. Suppose being supreme is impossible
2. Since being supreme is impossible it entails being not-supreme
3. By M2, perfections only entail perfections
4. By M3, the property of being supreme is a perfection
5. From 2, 3 and 4, being not-supreme is a perfection
6. But this contradicts M1, if a property is a perfection it's negation cannot be a perfection
7. Therefore our initial assumption is false, being supreme is not impossible
From, here we deduce from the possibility that a supreme being exists, that a supreme being exists. This can be deduced in 2 ways. Here's one way.
8. It's possible that a supreme being exists
9. Necessary existence is a perfection
10. Since it's impossible for a supreme being to be greater, a supreme being must have all perfections (properties that are greater to have than lack)
11. From 9, and 10, a supreme being has necessary existence (e,g it exists in all possible worlds, if it exists at all).
12. From 8 and 11, it's possibly necessary that a supreme being exists
13 From 12, it's necessary that a supreme being exists (S5)
14. So, a supreme being exists
This argument however, is controversial. It may be disputed on the grounds of (9) (the assumption that necessary existence is a perfection), or on the grounds of (13), (the assumption of the S5 modal axiom). It also seems to make one vulnerable to the modal collapse objection sketched above, given that the supreme being has all perfections (10.) including necessary existence (11.), and given we accept M1. Maydole himself offers a different deduction, here is the formal derivation, and I'll now provide the argument in natural language;
15. It's possible that a supreme being exists
16. If it's possible that a supreme being exists, then it is possible for there to be a being that is supreme.
17. Let's call the being that is possibly supreme ν.
18. Being supreme means that it's not possible that any being is greater than ν, and it's not possible that ν is less great than any being.
19. Therefore, both these conditions (it's not possible that any being is greater than ν, and it's not possible that ν is less great than any being) can be possible at the same time.
20. If it's possibly not possible that any being is greater than ν, then in actuality, no being can be greater than ν.
21. Similarly, if it's possibly not possible that ν is less great than any other being, then in actuality, ν isn't less great than any other being.
22. So, since both these conditions are met, ν must be a supreme being.
23. Therefore, there is a being that must be supreme
24. Therefore, there must be a supreme being. A supreme being exists
This out of the way, the MPA can also be formulated in the following way, without even using axiom M1, and instead simply using the plausible assumption that at least one property is not a perfection;
25. Perfections only entail perfections i.e., For all properties P and Q if a property P is a perfection and P → Q then Q is a perfection.
22. So, since both these conditions are met, ν must be a supreme being.
23. Therefore, there is a being that must be supreme
24. Therefore, there must be a supreme being. A supreme being exists
This out of the way, the MPA can also be formulated in the following way, without even using axiom M1, and instead simply using the plausible assumption that at least one property is not a perfection;
25. Perfections only entail perfections i.e., For all properties P and Q if a property P is a perfection and P → Q then Q is a perfection.
26. At least one property, call it L, is not a perfection.
27. The property of being supreme is a perfection.
28. Suppose it is not the case that the property of being supreme is possibly instantiated
29. Then the property of being supreme entails L. (Impossible properties entail everything)
30. But from (25.) and (27.) it's not the case that the property of being supreme entails L.
31. So, (28.) is false, the property of being supreme is possibly instantiated.
32. If the property of being supreme is possibly instantiated, then it is instantiated. (Established via the above two deductions)
33. So, the property of being supreme is instantiated. (Which is to say a supreme being exists) 31, 32 MP
27. The property of being supreme is a perfection.
28. Suppose it is not the case that the property of being supreme is possibly instantiated
29. Then the property of being supreme entails L. (Impossible properties entail everything)
30. But from (25.) and (27.) it's not the case that the property of being supreme entails L.
31. So, (28.) is false, the property of being supreme is possibly instantiated.
32. If the property of being supreme is possibly instantiated, then it is instantiated. (Established via the above two deductions)
33. So, the property of being supreme is instantiated. (Which is to say a supreme being exists) 31, 32 MP
Oppy 2004 however, argues that (25./M2) is false. He points out that a perfection entails any disjunctive property where one disjunct is the perfection in question and the other disjunct is an imperfection (where an imperfection is a property that is worse to have than not). For example, consider the property being supreme (S) or being a mass murderer (M). This is a disjunctive property S ∨ M. The perfection "being supreme" entails this property, but it is highly unintuitive that this disjunctive property is a perfection. Hitler, for instance, has this disjunctive property, but clearly it is the furthest thing from a perfection imaginable that he instantiates it. This is where C'zar Bernstein enters the fray with his formulation.
Berntein's Formulation
Bernstein 2014 has his own formulation of the Modal Perfection argument, intended to address Oppy's counterexample. He does this by first introducing the concept of 'neutral properties' which he defines as "properties whose instantiation does not
necessarily add to or subtract from the greatness of the beings in which they
inhere; properties that are neither necessarily better to have than lack nor lack than
have". Disjunctive properties such as "being supreme or else being a mass murderer" would fall into this category. With this, the premise:
25. Perfections only entail perfections.
is modified to:
25*. Perfections only entail perfections or neutral properties.
Oppy's objection does not apply to (25*.) since (25*.) allows for perfections to entail neutral properties. Berstein goes on to give a "plausibly sound" argument for (25.*) which I will formalize for ease of clarity and organization.
34. Assume that it's possible for a perfection P to entail an imperfection L. (Assumption for reductio)
35. If P entails L, then L is a necessary condition for the instantiation of P. (Definition of entailment)
36. If L is a necessary condition for the instantiation of P, then anything that has P also has L.
37. If anything that has P also has L, then anything that has P is imperfect because it has L. (Definition of L as a lesser-making property)
38. Therefore P is a lesser-making property
39. But perfections are great-making, not lesser-making. (Definition of perfections)
40. Thus, our initial assumption leads to a contradiction, so it must be false. It's not possible for a perfection P to entail an imperfection L. (From 35-39)
From here Bernstein argues that (25*.) in conjunction with a set of plausible premises, get you to the conclusion that the existence of a supreme being (God) is possible. The argument runs as follows, where;
41. (PA & ~GB) & ~NB "Being supreme is a perfection, and being evil is neither great-making nor neutral."
Assume, for reductio, that
42. ~◊(∃x) Ax "It is not possible that there exists a thing that is supreme."
43. (∀K)[(PA & ☐(∀x) (Ax→Kx))→(GK v NK)] (25.*, UI) "For every property K, if being supreme is a perfection and it's necessarily the case that everything that is supreme also has property K, then K is either great-making or neutral."
44. (PA & ☐(∀x)(Ax→Bx))→(GB v NB) (43, UI) "If being supreme is a perfection and it's necessarily the case that everything that is supreme is evil, then being evil is either great-making or neutral."
45. ☐~(∃x) Ax (42, MN) "Necessarily, there is nothing that is supreme."
46. ☐(∀x) ~Ax (45, QN) "Necessarily, everything is not supreme."
Since, necessarily, A is not exemplified,
47. ☐(∀x)(Ax→Bx) "Necessarily, everything that is supreme is evil."
48. PA & ~GB (41, &E) "Being supreme is a perfection and being evil is not great-making."
49. PA (41, &E) "Being supreme is a perfection."
50. PA & ☐(∀x)(Ax→Bx) (47, 49 Conj). "Being supreme is a perfection and necessarily everything that is supreme is evil."
51. GB v NB (44, 50, MP) "Being evil is either great-making or neutral."
52. ~NB (41, &E) "Being evil is not neutral."
53. GB (51, 52, DS) "Being evil is great-making."
54. ~GB (48, &E) "Being evil is not great-making."
55. GB & ~GB (53, 54, Conj.) "Contradiction: Being evil is both great-making and not great-making."
56. ~~◊(∃x) Ax (25*-55, RAA) "So, by reductio, it's not the case that it is not possible for there to be something that is supreme"
57. ◊(∃x) Ax (56, DN) "Thus, it is possible for there to be something that is supreme."
Not unlike Maydole's MPA, Berstein's argument can be simplified and shortened to the following;
25*. Perfections only entail perfections or neutral properties.
I will start by providing some motivations for thinking (25*.) is false. Then I will examine Berstein's arguments in favor of (25*.) and explain why they are probably unsound.
Incompossibility of Perfections
The first avenue of attack will be the incompossibility of perfections. This attacks (25*.) because if some perfections are not compossible, then the presence of some perfections will entail the absence of some other perfections. Berstein, in his paper, grants that the absence of perfections are themselves imperfections. It also straightforwardly falls out of our analysis of perfections and imperfections. Since, by definition, perfections are properties that are necessarily better to have then lack, so lacking a perfection would be to lack something that would make one better if they had it, which is just to say the property of lacking a perfection is lesser-making, i.e an imperfection. Now, I've already indirectly argued for the incompossibility of some perfections by defending a few incompatible properties arguments against theism here. Here are some more contenders not listed in my article.
Perfect Justice vs Perfect Mercy; We'll understand "perfect justice" as the property of giving all moral agents exactly what they deserve. We'll understand perfect mercy as the property of exemplifying maximal mercy and forgiveness including for moral agents who have committed great wrongs and do not deserve it. Both of these properties seem to be great-making, take a being that lacks either of these properties, and then add one of these properties to your concept of said being, it seems you end up with a more impressive being overall. So, plausibly, both of these properties are perfections. However, these perfections are not compossible. The presence of one entails the absence of the other.
Let;
The argument then goes as follows;
58. ∀x∀y(Jx → (Dxy → ¬Pxy)) "For all x and y, if x is perfectly just then if y deserves punishment by x, then x does not pardon y."
59. ∀x∀y(Mx → (Dxy → Pxy))) "For all x and y, if x is perfectly merciful, then if y deserves punishment by x, then x pardons y."
From this, it follows,
60. ∀x∀y((Mx ∧ Jx) → (Dxy → (¬Pxy ∧ Pxy))) "For all x and y, if x is both perfectly merciful and perfectly just, then if y deserves punishment by x, then x both does not pardon y and pardons y."
61. ¬(∃x∃y(Dyx → (¬Pxy ∧ Pxy))) "It is not the case, that there is an x and there is a y, such that if y deserves punishment by x, then x pardons y and does not pardon y)
From (60.), and (61.) we get our conclusion,
C. (∀x)[J(x) → ¬M(x)] "For all x, if x is perfectly just then it's not the case that x is perfectly merciful"
25. Perfections only entail perfections.
is modified to:
25*. Perfections only entail perfections or neutral properties.
Oppy's objection does not apply to (25*.) since (25*.) allows for perfections to entail neutral properties. Berstein goes on to give a "plausibly sound" argument for (25.*) which I will formalize for ease of clarity and organization.
34. Assume that it's possible for a perfection P to entail an imperfection L. (Assumption for reductio)
35. If P entails L, then L is a necessary condition for the instantiation of P. (Definition of entailment)
36. If L is a necessary condition for the instantiation of P, then anything that has P also has L.
37. If anything that has P also has L, then anything that has P is imperfect because it has L. (Definition of L as a lesser-making property)
38. Therefore P is a lesser-making property
39. But perfections are great-making, not lesser-making. (Definition of perfections)
40. Thus, our initial assumption leads to a contradiction, so it must be false. It's not possible for a perfection P to entail an imperfection L. (From 35-39)
From here Bernstein argues that (25*.) in conjunction with a set of plausible premises, get you to the conclusion that the existence of a supreme being (God) is possible. The argument runs as follows, where;
- PJ = J is a perfection
- GK = K is a great-making property
- NK = K is a neutral property
- Ax = x is supreme (or x has the property of being supreme)
- Bx = x is evil (or x has the property of being evil)
41. (PA & ~GB) & ~NB "Being supreme is a perfection, and being evil is neither great-making nor neutral."
Assume, for reductio, that
42. ~◊(∃x) Ax "It is not possible that there exists a thing that is supreme."
43. (∀K)[(PA & ☐(∀x) (Ax→Kx))→(GK v NK)] (25.*, UI) "For every property K, if being supreme is a perfection and it's necessarily the case that everything that is supreme also has property K, then K is either great-making or neutral."
44. (PA & ☐(∀x)(Ax→Bx))→(GB v NB) (43, UI) "If being supreme is a perfection and it's necessarily the case that everything that is supreme is evil, then being evil is either great-making or neutral."
45. ☐~(∃x) Ax (42, MN) "Necessarily, there is nothing that is supreme."
46. ☐(∀x) ~Ax (45, QN) "Necessarily, everything is not supreme."
Since, necessarily, A is not exemplified,
47. ☐(∀x)(Ax→Bx) "Necessarily, everything that is supreme is evil."
48. PA & ~GB (41, &E) "Being supreme is a perfection and being evil is not great-making."
49. PA (41, &E) "Being supreme is a perfection."
50. PA & ☐(∀x)(Ax→Bx) (47, 49 Conj). "Being supreme is a perfection and necessarily everything that is supreme is evil."
51. GB v NB (44, 50, MP) "Being evil is either great-making or neutral."
52. ~NB (41, &E) "Being evil is not neutral."
53. GB (51, 52, DS) "Being evil is great-making."
54. ~GB (48, &E) "Being evil is not great-making."
55. GB & ~GB (53, 54, Conj.) "Contradiction: Being evil is both great-making and not great-making."
56. ~~◊(∃x) Ax (25*-55, RAA) "So, by reductio, it's not the case that it is not possible for there to be something that is supreme"
57. ◊(∃x) Ax (56, DN) "Thus, it is possible for there to be something that is supreme."
Not unlike Maydole's MPA, Berstein's argument can be simplified and shortened to the following;
25*. Perfections only entail perfections or neutral properties. i.e., For all properties P and Q if a property P is a perfection and (P → Q) then Q is either a perfection or neutral.
26*. At least one property, call it L, is an imperfection.
27*. The property of being supreme is a perfection.
28*. Suppose it is not the case that the property of being supreme is possibly instantiated
29*. Then the property of being supreme entails L (Impossible properties entail everything)
30*. But from (25*.) and (27*.) it's not the case that the property of being supreme entails L.
31*. So, (28*.) is false, the property of being supreme is possibly instantiated.
32*. If the property of being supreme is possibly instantiated, then it is instantiated.
33*. So, the property of being supreme is instantiated.
Where (32*.) is established through either of the two deductions I sketched above, (8-14) or (15-24). With all this groundwork out of the way, it is finally time to proceed with objections.
The first objection will be to reject one of the central premises of Bertstein's argument. 27*. The property of being supreme is a perfection.
28*. Suppose it is not the case that the property of being supreme is possibly instantiated
29*. Then the property of being supreme entails L (Impossible properties entail everything)
30*. But from (25*.) and (27*.) it's not the case that the property of being supreme entails L.
31*. So, (28*.) is false, the property of being supreme is possibly instantiated.
32*. If the property of being supreme is possibly instantiated, then it is instantiated.
33*. So, the property of being supreme is instantiated.
Where (32*.) is established through either of the two deductions I sketched above, (8-14) or (15-24). With all this groundwork out of the way, it is finally time to proceed with objections.
Objection 1 - Rejecting 25*.
25*. Perfections only entail perfections or neutral properties.
I will start by providing some motivations for thinking (25*.) is false. Then I will examine Berstein's arguments in favor of (25*.) and explain why they are probably unsound.
Incompossibility of Perfections
The first avenue of attack will be the incompossibility of perfections. This attacks (25*.) because if some perfections are not compossible, then the presence of some perfections will entail the absence of some other perfections. Berstein, in his paper, grants that the absence of perfections are themselves imperfections. It also straightforwardly falls out of our analysis of perfections and imperfections. Since, by definition, perfections are properties that are necessarily better to have then lack, so lacking a perfection would be to lack something that would make one better if they had it, which is just to say the property of lacking a perfection is lesser-making, i.e an imperfection. Now, I've already indirectly argued for the incompossibility of some perfections by defending a few incompatible properties arguments against theism here. Here are some more contenders not listed in my article.
Perfect Justice vs Perfect Mercy; We'll understand "perfect justice" as the property of giving all moral agents exactly what they deserve. We'll understand perfect mercy as the property of exemplifying maximal mercy and forgiveness including for moral agents who have committed great wrongs and do not deserve it. Both of these properties seem to be great-making, take a being that lacks either of these properties, and then add one of these properties to your concept of said being, it seems you end up with a more impressive being overall. So, plausibly, both of these properties are perfections. However, these perfections are not compossible. The presence of one entails the absence of the other.
Let;
- Jx = x is perfectly just
- Mx = x is perfectly merciful
- Pxy = x pardons y
- Dxy = x deserves punishment by y
The argument then goes as follows;
58. ∀x∀y(Jx → (Dxy → ¬Pxy)) "For all x and y, if x is perfectly just then if y deserves punishment by x, then x does not pardon y."
59. ∀x∀y(Mx → (Dxy → Pxy))) "For all x and y, if x is perfectly merciful, then if y deserves punishment by x, then x pardons y."
From this, it follows,
60. ∀x∀y((Mx ∧ Jx) → (Dxy → (¬Pxy ∧ Pxy))) "For all x and y, if x is both perfectly merciful and perfectly just, then if y deserves punishment by x, then x both does not pardon y and pardons y."
61. ¬(∃x∃y(Dyx → (¬Pxy ∧ Pxy))) "It is not the case, that there is an x and there is a y, such that if y deserves punishment by x, then x pardons y and does not pardon y)
From (60.), and (61.) we get our conclusion,
C. (∀x)[J(x) → ¬M(x)] "For all x, if x is perfectly just then it's not the case that x is perfectly merciful"
(58.) follows from the definition of perfect justice I sketched above, since a perfectly just being gives all moral agents exactly what they deserve, they wouldn't pardon someone who deserves punishment from them. (59.) seems to as well fall out of our conceptual analysis of "perfect mercy". If a being perfectly, and maximally exemplifies mercy and compassion they will show such mercy and compassion even to those who don't deserve it. Perhaps one might object that perfect mercy may involve mitigation of punishment rather than absence of any punishment at all. This appears quite implausible, as it seems if we have a being which merely mitigates punishment, you could have a more merciful or forgiving being that pardons rather than simply mitigates punishment. In any case, we can just redefine Pxy as x mitigates punishment of y, and the argument would still go through (a perfect being would not mitigate punishment if such mitigation isn't deserved). (60.) is entailed from the previous premises. I take it that (61.) is just a logically necessary truth, there cannot be a x and y, such that x both does and does not pardon y, that's obviously a contradiction. Our conclusion, C is then derived via proof by contradiction.
One might be tempted to avoid the argument by redefining the notions of perfect justice or perfect mercy. Where e.g perfect justice does not involve retribution, but rather, the reformation and rehabilitation of an individual. As tempting as a move like this might be, such a move would just be to not engage with the argument, which is that given the way I stipulated the terms, perfect justice and perfect mercy are not compossible. What would engage with the argument, is if one were to dispute that either perfect justice, or perfect mercy (or perhaps both), as I construed are not perfections. However, independent of the incompossibility argument I laid out, it is as plausible to me that those properties, taken in isolation, are perfections, as the thesis that the divine properties (omnipotence, omniscience, omnipresence etc.) are perfections.
Necessary Moral Perfection vs Contingent Moral perfection: Here we will understand necessary or essential moral perfection as the property of being morally perfect in every possible world. In every world in which a being with this property exists, their nature entails they will do the morally best action. Then we have contingent, or non-essential, moral perfection. This would be the property of being morally perfect contingently in virtue of happening to freely choose to do the best actions in this possible world, and there being other possible worlds where the being doesn't do the morally best action. Now, necessary moral perfection seems to be a perfection, since it entails doing the morally best action in every possible world, as opposed to only doing the morally best action in some but not all possible worlds. However, contingent moral perfection also seems to be a perfection, since it is plausible that if the morally best action is x and you have 2 agents A and B, and both choose to do a morally best action x. The only difference being, A upon reflecting on it's options freely chooses to do x and could have chosen otherwise in some possible world, and B chooses x out of necessity. It looks like A is praiseworthy for doing x, because it freely chose x and could have chosen differently, whereas B does not seem to be praiseworthy for doing x because it is completely incapable of doing anything else. Insights like these have lead some to conclude that 'perfect goodness' or 'moral perfection' simpliciter is an incoherent property (Keller 2010). However, I do not need to make that strong of a claim, all I need is that both necessary, and contingent moral perfection, are perfections, yet they are not compossible.
One objection that might come to mind is compatibilism which allows for free will even if ones actions are determined, so a being that is necessarily morally perfect might still make free choices even though they couldn't have done otherwise. However, compatibilism doesn't entail that there are no possible worlds where a free agent couldn't have chosen otherwise, only that one couldn't have chosen otherwise given the present antecedent conditions and laws of nature in the actual world. In other words, compatibilism allows for possible worlds where the antecedent conditions or laws of nature are different and you choose otherwise. Further, this response seems inapplicable in the case of God, for surely God would not have antecedent conditions outside of Himself which determine his actions.
Omniscience and the ability to experience surprise: Omniscience which is taken to be a perfection by theists, is defined as the state of knowing all true propositions. On the other hand, surprise is understood as the discovery of something previously unknown or not expected. It follows from these definitions that an omniscient being cannot be surprised; they already know everything, including all future events, and therefore cannot discover anything unknown or unexpected. Experiences of surprise, discovery, and learning are plausibly valuable and enriching as they contribute to the dynamism and depth of existence. Therefore the ability to experience surprise can plausibly be taken to be a perfection, one that is not compossible with the perfection of omniscience. (Note; this is inapplicable to open theists)
Besides these, there are many, many more potential examples of incompossible perfections, see; (Martin 1990) (Martin & Monnier 2003) (Everitt 2010) (Cray 2011) (Shand 2010).
As it happens, Bernstein (2014 & 2018) also has a direct argument against the claim that there are perfections which are not compossible. The argument goes as follows:
62. Suppose it is impossible that something has all perfections
63. If it is impossible that something has all perfections, then there is a perfection that is sufficient for not having some other perfection. (namely the one with which it is inconsistent)
64. If a property is sufficient for not having some perfection, then that property is sufficient for being imperfect.
65. If a property is sufficient for being imperfect, then it is not a perfection.
66. There is some perfection that is sufficient for not having some perfection (62, 63)
67. There is some perfection that is sufficient for being imperfect (64, 66)
68. There is some perfection that is not a perfection (65, 67)
69. So, (62.) is false. Possibly something has all perfections.
What are we to make of this argument? The problem is going to lie with either (64.) or (65.), indeed, whether one accepts the conjunction of (64.) and (65.) is going to be a function of whether one is antecedently committed to thinking all perfections are compossible. If 'being perfect' is understood as the property of having some maximal compossible set of perfections, and 'being imperfect' as the negation of being perfect (i.e not having a maximally compossible set of perfections). Then obviously anyone who thinks some perfections are not compossible will reject (64.), because having a certain perfection may, given what we've laid out, entail not having another, incompatible perfection. However, this would not entail ' being imperfect' in this sense so long as the bearer still possesses a maximally compossible set of perfections. If however, we understand 'being perfect' as having the set of all perfections, and 'being imperfect' again as the negation of being perfect, then anyone who thinks some perfections are not compossible will reject (65.). This is because, if some perfections are not compossible, then having some perfection which we'll call P, since P is incompossible with some other perfection, would mean that the bearer does not have all perfections, which would lead to 'being imperfect' in this sense. But P would still be a perfection in this scenario, it would just be the case that not all perfections are compossible. So, in either case, one who thinks some perfections are incompossible has good reason to think that one in the conjunction of (64.) and (65.) is false, and the argument is dialectically powerless to change the mind of anyone who holds that some perfections are incompossible.
Perfections and negative outcomes
Next, we will look at cases where a being having a perfection, a property that is necessarily better to have than lack, entails negative outcomes which I'll define as states of affairs which are such that, at least when taken in isolation, ceteris paribus their occurrence is either worse than not, or entails the lack of some good. Negative outcomes, are, of course, neither perfections nor neutral properties. Here are a couple examples;
Omniscience and complete lack of privacy: Omniscience entails the outcome of there being a lack of privacy for all agents which would co-exist with the omniscient being in question. This is so because an omniscient being would know everyone's deepest thoughts, feelings, desires, intentions, past actions, future actions, and so on. However, privacy - having moments that one keeps to oneself, and thoughts that are not immediately accessible to anyone but the thought-haver is plausibly a good (and an outcome which entails the absence of a good is a negative one), since it allows persons to decide when, how, and to what extent information about themselves is made public and communicated to others. It is closely tied to ones sense of personal freedom and autonomy. Further, were the omniscient being to coexist with privacy-valuing beings, it's omniscience would entail a violation of the consent of these privacy-valuing beings, which it seems to me, is a negative outcome (this may be true even if privacy from God is not a right created beings have).
Generosity and economic need: Generosity which is the property of being liberal with giving to those in need, is generally taken to be a virtue and is plausibly a perfection. However, consider that acts of generosity entail that there must be a recipient in need, someone who is lacking, or in want of something. One might have a mere disposition for generosity in the absence of any needs, but one cannot actually be generous or exemplify generosity in the absence of needs. If actually exemplifying generosity is a perfection, and a state of affairs that involves some lacking, or needing on the part of the recipient, is a negative outcome, then it looks like we have another perfection which entails a negative outcome.
Some other examples
Courage and fear/hardships: Courage can be understood as the property of overcoming fear or dangerous tasks, and enduring hardships in pursuit of a good purpose. Courage, is plausibly a perfection as it is a cardinal virtue in the works of Aristotle, Cicero, and the ancient Stoics and most theists, particularly Christians are committed to thinking courage is a virtue. However, fear seems to, quite clearly, be an imperfection, as it implies being either fragile enough so that something is a threat to you (an imperfection of weakness), or having a mistaken belief about something being a threat to you (an imperfection of error). Experiencing hardships and difficulties as well, seem like imperfections, as they imply a lack of power.
This also suggests another incompatibility between perfections, if we take courage to be a perfection as is plausible, and we take omnipotence and omniscience to be perfections. An omnipotent being can't experience hardships, because hardships imply a lack of power or control. A being that is both omnipotent and omniscient can't experience fear because there is nothing that can cause any harm to, or threaten an omnipotent being, and being omniscient said being would know that nothing can harm or threaten them. Thus an omnipotent, omniscient being can't exemplify courage.
This also suggests another incompatibility between perfections, if we take courage to be a perfection as is plausible, and we take omnipotence and omniscience to be perfections. An omnipotent being can't experience hardships, because hardships imply a lack of power or control. A being that is both omnipotent and omniscient can't experience fear because there is nothing that can cause any harm to, or threaten an omnipotent being, and being omniscient said being would know that nothing can harm or threaten them. Thus an omnipotent, omniscient being can't exemplify courage.
Temperance and temptations: Temperance is another cardinal virtue, which can be understood as the property of exercising moderation, or restraint over temptations/improper impulses of the mind. Temperance is plausibly a perfection, yet it seems to imply that one can experience temptation/improper impulses, which is an imperfection. It may be objected that temperance does not require experiencing temptation, and that one can exemplify temperance by having a sufficiently strong character that is immune to temptation. Even granting this, it appears that temperance which involves overcoming temptations is associated with a unique sense of moral admirableness, and thus is plausibly a perfection. Consider two agents, C and D, C lacks any temptation to do some bad action y, and D does have a temptation to do y but resists it. There appears to be a sense in which agent D is more praiseworthy than agent C, as C had nothing to overcome when presented with the option to do y since they lacked any temptation to do y, and D was tempted to do y but successfully overcame her temptation which seems admirable in itself.
Perfect experiential knowledge and negative what's-it-likeness: Perfect experiential knowledge can be understood as the property of being able to perfectly understand or comprehend all experiences from the first-person, rather than just through description, inference, or conjecture. Knowledge is uncontroversially a perfection, and knowledge is generally considered better the more complete and accurate it is. Perfect experiential knowledge represents the pinnacle of understanding - a state where one has a complete and accurate comprehension of experiences. Further, perfect experiential knowledge can be argued to be morally enriching as it involves a profound understanding of the lived experiences of others, enabling one to fully empathize with their joys, sufferings, and struggles. However, perfect experiential knowledge entails that one knows what it's like to experience great emotional distress, to feel afraid and vulnerable, sin, and to have perverse desires. But these seem like imperfections, as these states seem to entail suffering, moral impurity, or other forms of negativity that we would not expect a perfect being to have. Thus, plausibly, we have another instance of a perfection entailing an imperfection,
Let us now lastly consider the argument Berstein laid out to directly motivate (25*.). Recall the reasoning goes as follows;
34. Assume that it's possible for a perfection P to entail an imperfection L. (Assumption for reductio)
35. If P entails L, then L is a necessary condition for the instantiation of P. (Definition of entailment)
36. If L is a necessary condition for the instantiation of P, then anything that has P also has L.
37. If anything that has P also has L, then anything that has P is imperfect because it has L. (Definition of L as a lesser-making property)
38. Therefore P is a lesser-making property.
39. But perfections are great-making, not lesser-making. (Definition of perfections)
40. Thus, our initial assumption leads to a contradiction, so it must be false. It's not possible for a perfection P to entail an imperfection L. (From 35-39)
I think the problem with this argument is going to be similar to the problem with Berstein's argument to the conclusion that, possibly, there is a being with all perfections. The problem here will lie with (37.), if the property of 'imperfect' is understood as the negation of the property of having 'the maximally consistent set of perfections and lack of imperfections it is possible to exemplify' in other words if we take 'imperfect' to entail falling short of being as perfect as it it is possible for a being to be, then the consequent of (37.) does not follow from the antecedent. A being that has L might yet still exemplify the most comprehensive and coherent combination of perfections and lack of imperfections that can be co-instantiated. If, in (37.), 'imperfect' is understood as having any imperfection or lacking some perfection, then the consequent does follow from the antecedent, but (38.) does not follow from (37.). P may be a property of a being that is as perfect or great as is possible to be, even though P entails that an entity isn't perfect, (where 'perfect' is understood as the property of having all perfections and no imperfections) because 'being perfect' wouldn't be a possibly instantiated property since some perfections entail imperfections, but it is surely no mark against a being if it does not achieve a level of perfection that isn't possibly attained. Surely, if 'being perfect' is an impossible property, it itself is not a perfection.
I conclude that the arguments that Berstein gives in favor of (25*.) are unconvincing, and the extant counterexamples to (25*.) remain in tact, at least insofar as perfections are construed, just as great-making properties, in such a way that doesn't make it a trivial analytic truth that perfections only entail perfections or neutral properties. So, (25*.) is probably false.
Objection 2 - A Dialectical Issue
But let's suppose we avoid any and all counterexamples to (25*.) by simply building into the concept of 'perfection' that an imperfection cannot be a necessary condition for the instantiation of a perfection, in other words, that perfections only entail perfections or neutral properties. Does this then save the argument? Not even close. What needs to be shown to show that 'supremity' or 'maximal greatness' or 'God-likeness' or the like is possibly exemplified, is that there is some property which meets all of the following conditions, (Van Inwagen 2009), (i) it belongs to maximal greatness/supremity/God-likeness (ii) it is closed under entailment (or in this case, it just doesn't entail a certain class of properties) (iii) it is not a property of everything. But once we define a perfection in such a way that condition (ii) holds, and the notion of "entailment" we are using is explosive (see: principle of explosion), this would mean no impossible properties are perfections, since impossible properties vacuously entail everything. The property of "supremity", "maximal greatness", or any equivalent concept would then be a perfection only if it is possibly instantiable. In other words, in order to know condition (i) in this case holds, one would have to know that maximal greatness/supremity/God-likeness is a possible property. To simply assert that maximal greatness/supremity/God-likeness is a perfection, would just be to assert that it is possible. But that's precisely what the MPA is supposed to prove, making the argument, inasmuch as it has a premise which asserts that maximal greatness/supremity/God-likeness is a perfection, problematically circular and dialectically inadequate. On the other hand, perhaps we might be using a notion of entailment that is non-explosive (e.g., relevance logic or a counterfactual analysis which permits non-trivial counterpossibilities). In this case, impossibilities don't vacuously entail everything. But then, in this case no valid inference to the possibility of "supremity" or "maximal greatness" can then be drawn. This is because non-explosive logics avoid vacuous entailments, but at the cost of not enabling a straightforward inference from a property's being a perfection in this sense to its possibility.
The upshot is, if we use the standard semantics for 'perfection', then (25*.) is probably false (see objection 1), if we abandon the standard semantics and build into the concept of 'perfection' that perfections can only entail perfections and neutral properties, then if the sense of entailment we are using is explosive, to then claim that being supreme is a perfection just is to claim that being supreme is possibly exemplified, which is the very thing that needs to be shown, and the very thing atheists will deny. If the sense of entailment we are using is non-explosive then the MPA becomes invalid. Until the theist can provide a non-question-begging reason to suppose that there is a property which is such that conditions (i)-(iii) hold, a reason which of course isn't provided by the MPA alone, the argument lacks any dialectical bite.
Objection 3 - Axiological non-realism
Another possible line of attack to the argument would be to attack an implicit assumption of the argument, the assumption of axiological realism - the view that there are objective values, and in this case, objective properties that can be categorically deemed as "lesser-making" or "great-making", that these properties are actual features of the world that exist independently of human beliefs, opinions, or cultural practices. If one were to take an axiological non-realist view, such as for instance, a subjectivist, relativist, or constructivist view of value, then this would be to deny that there are such stance-independent value properties. Therefore, there are no properties which are 'perfections' or 'great-making', or 'imperfections' or 'lesser-making', as these must be understood as properties which detract or add to a beings greatness in a stance-independent sense. One might even think the problem is even more serious, that the very concept of stance-independent value properties is in some way, inherently defective or unintelligible and so the premises in the MPA which invoke these concepts, fail to even be propositions. I will not get in the weeds of defending axiological non-realism, I will just point out that it is a view which renders the argument unsound, in particular premises (26*.) and (27*.) would be false.
Objection 4 - Some Parodies
Lastly, as a final objection. We will consider whether the MPA in it's current form is susceptible to parodies. A parody would be an argument that mirrors the structure of the parodied argument, to deliver an absurd, or unwanted conclusion. As many readers may already know, the practice of deploying parodies as responses to ontological arguments, goes back as far as Gaunilo of Marmoutiers, who famously argued that the reasoning used for Anselm's ontological argument for 'A being than which no greater being can be concieved', can just as easily be used to establish the existence of 'An island than which no greater island can be concieved' which is absurd!
Is there a possible avenue for parodying the MPA? I think there is. We will understand "maximally bad" as the property of being such that it is impossible for something to be worse and impossible for there to be something else than which it is not worse. Now, consider the following argument:
25#. Imperfections only entail imperfections or neutral properties
26#. At least one property, call it U, is a perfection.
27#. The property of being maximally bad, is an imperfection.
28#. Suppose it is not the case that the property of being maximally bad is possibly instantiated
29#. Then the property of being maximally bad entails U.
30#. But from (25#.) and (27#.) it's not the case that the property of being maximally bad entails U.
31#. So, (28#.) is false, the property of being maximally bad is possibly instantiated.
32#. If the property of being maximally bad is possibly instantiated, then it is instantiated.
33#. So, the property of being maximally bad is instantiated.
The reasoning involved in Bersteins' argument for (25*.) can as well be mirrored in favor of (25#.) as follows;
34#. Assume that it's possible for a imperfection L to entail a perfection P. (Assumption for reductio)
35#. If L entails P, then P is a necessary condition for the instantiation of L. (Definition of entailment)
36#. If P is a necessary condition for the instantiation of L, then anything that has L also has P.
37#. If anything that has L also has P, then anything that has L is greater because it has P. (Definition of P as a great-making property)
38#. Therefore L is a great-making property.
39#. But imperfections are lesser-making, not great-making. (Definition of imperfections)
40#. Thus, our initial assumption leads to a contradiction, so it must be false. It's not possible for an imperfection L to entail a perfection P. (From 35#-39#)
This argument for (25#.) seems to mirror the structure and plausibility for the argument for (25*.). I for one, can think of no reason, to reject this argument that wouldn't equally be a reason to reject the original deduction. Furthermore, Robert Maydole's deduction in favor of (32.), can be mirrored in favor of (32#.).
15#. It's possible that a maximally bad being exists
16#. If it's possible that a maximally bad being exists, then it is possible for there to be a being that is maximally bad
17#. Let's call the being that is possibly maximally bad ν.
18#. Being maximally bad means that it's not possible that any being is worse than ν, and it's not possible that ν is less bad than any being.
19#. Therefore, both these conditions (it's not possible that any being is worse than ν, and it's not possible that ν is less bad than any being) can be possible at the same time.
20#. If it's possibly not possible that any being is worse than ν, then in actuality, no being can be worse than ν.
21#. Similarly, if it's possibly not possible that ν is less bad than any other being, then in actuality, ν isn't less great than any other being.
22#. So, since both these conditions are met, ν must be a maximally bad being.
23#. Therefore, there is a being that must be maximally bad
24#. Therefore, there must be a maximally bad being. A maximally bad being exists.
The first deduction I offered (8-14), can also be mirrored, if we suppose, as is plausible, that if necessary existence is a perfection, then the conjunctive property being evil & necessarily existent, is an imperfection. However, even if the deduction didn't work, the mere possibility of a maximally bad being would itself cause problems for the classical theist or perfect being theist, since a maximally bad being would be omnipotent and evil, as Bernstein himself acknowledges. To quote Bernstein:
"According to classical theism, God exists necessarily, in every possible world. If it is possible that there exists a supremely imperfect being, then there is a possible world W in which both God and this being exist. Since the supremely imperfect being has all imperfections essentially, and since the conjunctive property being omnipotent and evil is an imperfection, in W there exists an omnipotent being that is not identical to God!"
We can also argue that two omnipotent beings with diverging desires, such as one that is wholly good which we'll call G (God) and one that is wholly evil, which we'll call E (the maximally bad being), coexisting in the same world is logically impossible. Since G is wholly good, G desires to actualize all-things-considered good states of affairs, and prevent all-things-considered evil states of affairs, since E is evil, E desires the opposite. Suppose G and E exist in the same world. Then, there will exist states of affairs that G wants to actualize and that E wants to prevent, and vice versa. This is because the states of affairs that G desires (good states) are precisely the states of affairs that E desires to prevent, and the states that E desires (evil states) are precisely the states that G desires to prevent. Further, given the omnipotence of both G and E, each has the power to actualize their desired states of affairs and prevent the actualization of their undesired states of affairs. But it is logically impossible for a state of affairs and its negation to be co-actualized in the same world, because this would entail a contradiction. So, it's impossible for G and E to co-exist. However through our parody argument, it's possible that E exists in some possible world, but then G cannot co-exist with E in such a world. Yet, on perfect being theology and classical theism, if God exists, He necessarily exists, He exists in all possible worlds. So the classical theist/perfect being theist cannot accept that E is possible.
Yet the reasoning for the possibility of E in (25#-33#) mirrors the structure, and seems just as plausible as the reasoning favoring the possibility of a supreme being. In response to this, Bernstein argues that (25#.) is palpably false, because the property of being evil is an imperfection yet this property entails being a moral agent and a person, which are perfections. So, the parody fails, we have a good reason to think (25#.) is false and no comparably good reason to think (25*.) is false. Problem: that's wrong. As I've shown in the first objection, there are comparably good reasons to think (25*.) is false, as there seem to be many equally plausible instances of perfections entailing imperfections. So the symmetry then, doesn't seem to be broken, insofar as we accept counterexamples to (25#.) there seem to be equally good counterexamples to (25*.). I conclude that the parody stands.
Another parody, from Joseph Schmid in this video, can be formulated as a parody of Bernstein's MPA as well;
25*. Perfections only entail perfections or neutral properties
26*. At least one property call it L is an imperfection
70. The property of knowing God does not exist is a perfection
71. Suppose it is not the case that the property of knowing God does not exist is possibly instantiated
72. Then the property of knowing God does not exist entails L. (Impossible properties entail everything)
73. But from (25*.) and (70.) it's not the case that the property of knowing God does not exist entails L.
74. So, (72.) is false, the property of knowing God does not exist is possibly instantiated.
Of course, no classical or perfect being theist will accept (70.), as knowing God does not exist, on their view is an impossible property, since God necessarily exists. But then, it's clear that, analogously no atheist is going to accept (27*.) in the original argument, for the very same reason. The point, herein, is not that the above argument is a good one, on the contrary, it is that, it is equally uncompelling as the original argument for the possibility of a supreme being. No one who doesn't already accept that knowing God does not exist is possible will accept (70.), and conversely, no one who does not accept that being supreme is possible will accept (27*.).
So, I conclude that the Modal Perfection Argument is dialectically powerless and probably unsound.
The Maximal God Argument
The final ontological argument I will be examining will be Yujin Nagsawa's 'Maximal God' argument, from his book "Maximal God: A New Defense of Perfect Being Theism" (Nagasawa 2017). Nagasawa's project in this book is to propose a conceptual revision of the 'Perfect Being Thesis' arguing that that thesis only entails that God is the being with the maximal consistent set of great-making properties such as knowledge, power and goodness etc. (where this could be had in maximal amounts as the omni-properties, or not). He calls this revised concept "A real maximally great being". The ontological argument he proposes, then, is similar to Plantinga's modal ontological argument. The difference being, the premise "it is possible that a maximally great being exists,"—given the revised maximally-great-theism concept that Nagasawa defends, is changed to "it is possible that a real maximally great being exists". The argument then runs just as Plantinga's modal ontological argument;
1. Possibly, a real maximally great being exists.
2. If possibly, a real maximally great being exists, then necessarily, a real maximally great being exists.
3. Therefore, necessarily, a real maximally great being exists.
The possibility premise (1.). is the main premise that is in dispute in the original argument. However, given the revised concept Nagasawa uses as a being which by definition possesses the maximally consistent set of great-making properties, the possibility premise, so Nagasawa claims, comes for free. It is just built into the concept of a real maximally great being, that such a being is possible.
Objection 1 - Consistency to Possibility?
Nagasawa takes it as a given that consistency entails possibility. But this seems false, as there seem to be plausible counterexamples to this. Some x might be such that it is logically consistent in the sense that the set of properties it is composed of are individually coherent and jointly compatible yet this x could be metaphysically impossible for it is incompatible with the existence of some necessary y. Or conversely, some necessary x might be such that it is completely consistent in the sense that the set of properties it is composed of are individually coherent and jointly compatible yet this x could be metaphysically impossible (given S5) for it is incompatible with the existence of some y.
Furthermore, the argument seems to be subject to parodies, suppose we conceptualize an 'atheistic universe'—a universe devoid of any gods, including the one postulated by Nagasawa. We can construct this concept in such a way that the universe possesses properties that are both individually coherent and jointly compatible. But then, given Nagasawa's reasoning, the logical consistency of this atheistic universe would entail its possibility. However, this contradicts Nagasawa's argument that a maximal God (one with the maximal consistent set of knowledge, power, and goodness) exists in every possible world. In order to resist this one would need to either reject S5, or the consistency-to-possibility inference, both of which Nagasawa's argument requires.
To avoid this Nagasawa is going to have to revise the concept of a real maximally great being to something like a being with the maximal compossible set of great-making properties (knowledge, power and goodness etc.), rather than a being with the maximal consistent set of great-making properties.
Objection 2 - Would it be God?
From this point, we'll assume a 'maximal being' is a being with the maximal compossible set of great-making properties. Once we do that, that leaves us with an open question, why think such a being would be anything like a God as conceived in religious traditions or theology, understood as the very ground of being beyond the created order, an independent ase being, a personal creator, and a being that is worthy of worship? Perhaps the maximally compossible set of great-making properties isn't even an agent, as plausibly there are certain limitations entailed from being an agent. But even if it is an agent, why think such a being would not just be something like a very powerful, very knowledgeable, and highly virtuous alien or AI?
Even further, the argument assumes, in (2.), that necessary existence will be among the maximally compossible set of great-making properties. No-one who does not already believe that necessary existence is exemplified, or at-least exemplified for concreta, will believe that necessary existence is a possible property (for concreta). And even if one does accept that necessary existence is exemplified, there needs to be a further reason given to think that the contents of the set of all maximally compossible great-making attributes would include necessary existence. Then, yet further argued that a being with the maximally compossible set of great-making attributes would be something even non-naturalistic, let alone theistic.
Indeed, whether one accepts that a being with the maximally compossible set of great-making properties is the theistic God, seems to be a function of whether one is already a theist. If one is an atheist, one already doesn't believe that, possibly, there is a necessary being with the divine attributes. So of course, if one is an atheist, one wouldn't believe that a being with the maximally compossible set of great-making attributes is a necessary divine being. Until, and unless justification is given for thinking the contents of the maximally compossible set of great-making properties is something distinctly theistic, and necessarily existent, then the argument need not worry atheists.
Objection 3 - No Maximal Being
This last objection is a direct attack on the concept of a 'maximal being'. It doesn't seem like there can be a being with the maximally compossible set of divine attributes, including maximal goodness, knowledge and power. In particular, because knowledge, and power seem like degreed properties with no intrinsic maxima. For any particular degree of knowledge or power n, there is a possible higher degree of knowledge and power n+1, so there is no upper limit on what constitutes maximal knowledge or power. The Anselmian has a straightforward answer to this problem. By defining God as omnipotent and omniscient, where omnipotence is the ability to actualize any metaphysically possible state of affairs, and omniscience is knowing all true propositions. It is impossible for there to be a being greater than an omnipotent, or an omniscient being. However, recall that Nagasawa is revising the Perfect Being Thesis, away from the Omni-God Thesis, which is the thesis that God is defined as possessing the omni-attributes (omnipotence, omniscience etc.), to the maximal God thesis, which is the thesis that God has the maximal compossible set of great-making attributes. But once that is done, the theist leaves themselves open to the criticism that, just as there is no best possible world as some may argue, there is no 'maximal being'. For every set of great-making properties that can be instantiated, there is a potentially greater set. Of course, the maximal God thesis does not necessarily rule out Omni-theism, but if Omni-theism turns out to be impossible then the maximal God thesis runs afoul of this problem.
Nagasawa briefly covers this objection, saying it relies on a bottom-up approach to understanding the limits of knowledge and power. That is, where knowledge/power are incremental and can be made greater by adding units to it. Nagasawa argues this approach is flawed, as knowledge and power in fact have infinite gradations. Thus, having infinite gradations cannot entail that there is no intrinsic maxima in the case of knowledge and power. Nagasawa then suggests a top-down approach where instead of asking "How much more can be added?", we posit an intrinsic maximum which views all lesser degrees in relation to it. I will address this in turn and explain why I don't find this response compelling.
In regards to knowledge, Nagasawa invokes the KK thesis, to show that knowledge has infinite degrees, (if one knows p, then one knows that one knows p, and so on ad infinitum) the KK thesis is by no means universally accepted. Yet, even granting the KK thesis, it only demonstrates a single instance of knowledge has infinite recursive or self-referential depth. This means that knowing a single proposition, such as "p", would entail an infinite series of meta-knowledge (knowing that one knows that p, knowing that one knows that one knows that p, and so forth). In this context, the lack of a maxima is not an issue. It is possible to possess infinite meta-knowledge because it is possible to know p, and given the KK thesis, an infinite series of meta-knowledge is simply entailed from knowing p. On the other hand, when we think about what it means to have maximal knowledge, we are thinking about the breadth of ones knowledge, that is the range of distinct propositions one knows. In this case, the problem of intrinsic maxima does appear to be an issue. For every being who's knowledge encompasses some finite set of distinct propositions n, it looks like it is always possible for there to be a being who's knowledge encompasses n+1 set of distinct propositions.
In regards to power, Nagasawa shows that there are infinite gradations of power, such as being able to lift 3 kg and 3.3 kg, and 3.33 kg and so on ad infinitum. However, these gradations operate within a boundary. For instance, if my lifting capability peaks at 100 kg, this means I can lift any weight up to that limit, encompassing all the infinite gradations below it. The problem is unlike my lifting example bound by a 100 kg ceiling, there appears to be no upper threshold for power it is possible to have, if we exclude omnipotence, for any given degree of power you have, there's a greater possible degree of power beyond it. That is where the problem of intrinsic maxima rears it's ugly head.
Finally, Nagasawa's top-down approach simply assumes that there is an intrinsic maxima for knowledge, power and goodness to begin with. We would only be able to posit a possible intrinsic unsurpassable maxima of knowledge, power and goodness if there was such a maxima, but that's the very thing being called into question here by this objection!
Finally, Nagasawa's top-down approach simply assumes that there is an intrinsic maxima for knowledge, power and goodness to begin with. We would only be able to posit a possible intrinsic unsurpassable maxima of knowledge, power and goodness if there was such a maxima, but that's the very thing being called into question here by this objection!
Conclusion
I have examined 4 ontological arguments for theism, ones that are less well-known. A classical one, from Spinoza, a semi-contemporary one based on Meinongianism, and 2 contemporary ones from within the past decade from Yujin Nagasawa and C'zar Berstein. I have concluded that all of these arguments are subject to undercutting and rebutting defeaters, and are thus extremely uncompelling and shouldn't change the minds of anyone who doesn't already accept the conclusion. From the 11th century to today, there have been many ontological arguments, arguments which seek to prove the existence of God from the concept or essence of God alone, and through a-priori armchair reasoning, and yet none of them have been successful. None, I would contend, have come remotely close. It looks to me, then, that the project of deriving God's existence a-priori, from the concept/essence of God alone, is a dead project.
References
Lucas Collier. The Failure of the Ontological ArgumentOppy, Graham (2014). Ontological arguments. Stanford Encyclopedia of Philosophy.
Waller, Jason. Benedict de Spinoza: Metaphysics. Internet Encyclopedia of Philosophy
Waller, Jason. Benedict de Spinoza: Metaphysics. Internet Encyclopedia of Philosophy
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