Author Archives: Daniel Vecchio, PhD

The BOA with an Actuality Operator “@”

[Note: The following exploration of the Bonavaenturean Ontological Argument (hereafter, the BOA) uses Free Logic and an “actuality” operator.]

Expressed informally

D1) God is the absolutely complete being.
P1) If nothing that satisfies the definite description of God is actually absolutely complete, then God is not absolutely complete.
P2) If something that satisfied the definite description of God is actually absolutely complete, then God exists in reality.
C) God exists in reality

Explanation of D1: Here we stipulate that God is defined as complete in every positive simple attribute, which is to say that by “God”, we mean a perfect being. Given free logic, singular terms that are provided with a definite description do not carry existential import. Maydole (2009, “Ontological Arguments”, Blackwell Companion, 555) explains:

The presupposition is that some referring singular terms and definite descriptions could be free of existential import, and quantifiers should be allowed to range over possibilia (Girle 2003, chap. 4). Otherwise, some referential terms that refer to nonmental things, such as “God” and “the being than which nothing greater can be conceived,” would have to refer to mental things that have existence-in-the-understanding, which makes no sense; or those referential terms would have to have to refer to things that have existence in-reality, which would make the Anselmian ontological argument beg the question.

Maydole’s point with respect to the Anselmian ontological argument applies, mutatis mutandis, to the BOA. This definitions is definite, i.e. it refers to a singular term. Since absolute completeness implies omnipotence, and there can only be one omnipotent being. For, if there were two, one could will contrary to the other, and absurdity would follow, e.g. one wills that at time t1 a surface is entirely red, and another omnipotent being that at time t1 a surface is entirely green.

A stipulation is to be granted, so long as it is coherent, otherwise any conclusion could be deduced from it. As to whether the definition of an absolutely complete being is coherent, it should be noted that perfections, in being both simple and positive, cannot contain any explicit or implicit contradiction, and so the stipulation is logically coherent. For to have a contradiction, one perfection would have to negate the other, either in whole or in part. But for a whole perfection to negate another, the perfection would have to be a negative attribute. And for a part of perfection to negate another perfection, the perfection would have to be complex rather than simple. So perfections are compossible, and the definition coherent. This is based on the Leibnizian argument for the compossibility of perfections.  So here we have a non-question-begging, coherent, definite description.

Defense of P1: The key to defending this premise is to understand how “actually” functions in the argument. In the context of this argument “actually” means that it is the case in our reality. This could be thought in contrast to “imaginably”. For instance, we might say, simply, that Sherlock Holmes is the world’s greatest detective. In one sense, this is true, in that it can be imagined that Sherlock Holmes is the world’s greatest detective. In actuality, though, Sherlock Holmes is not the world’s greatest detective, so it is not completely true that Sherlock Holmes is the world’s greatest detective. That is, “Sherlock Holmes is the world’s greatest detective” is an incomplete expression. The principle behind this premise, then, is the idea that if something is not actually the case, then to say it is the case, simply, is not completely true. Applied, then, to the denial that a thing is actually absolutely complete, and we must infer that it is not completely true that it is absolutely complete. But to deny the complete truth that something is absolutely complete just is to deny that it is absolutely complete.

Defense of P2: This is, of course, not to claim God exists in reality, but is to provide a sufficient condition by which it could be said that God exists in reality. That condition is for an individual to exemplify the perfections of absolute completeness in reality

The Formal Proof

Let,

@… ≝ it is actually the case that…
Cx ≝ x is absolutely complete
Dxy ≝ x is the individual by which y is definitionally described
E!x ≝ x exists in reality
g ≝ (ɿx)Cx

1. (∀x)(Dxg → ~@Cx) → ~Cg (premise)
2. (∃x)(Dxg ∧ @Cx) → E!g (premise)
3. (∀x)(Dxg → ~@Cx) (IP)
4. ~Cg (1,3 MP)
5. (∃x)[Cx ∧ (∀y){[Cy →(y = x)] ∧ ~Cx} (4 theory of descriptions)
6. [Cμ ∧ (∀y){[Cy →(y = μ)] ∧ ~Cμ (5 EI)
7. [(∀y){[Cy →(y = μ) ∧ Cμ] ∧ ~Cμ (6 Comm)
8. (∀y){[Cy →(y = μ) ∧ [Cμ ∧ ~Cμ] (7 Assoc)
9. Cμ ∧ ~Cμ (8 Simp)
10. ~(∀x)(Dxg → ~@Cx) (3-9 IP)
11. ~(∀x)(~Dxg ∨ ~@Cx)(10 Impl)
12. ~(∀x)~(Dxg ∧ @Cx)(11 DeM)
13. (∃x)~~(Dxg ∧ @Cx) (12 QN)
14. (∃x)(Dxg ∧ @Cx) (13 DN)
15. E!g (2,14 MP)

QED

Hope and the MOA

As I have argued elsewhere, hope is a habit of the will by which one desires a good and expects to receive it.  As in many virtues, hope is a mean between extremes, as one can desire a good in a disordered way (too much or too little in relation to other things good or bad), and ones expectations can be too high or too low depending on what is reasonable to expect.  Hope, then, involves achieving a mean in both what one desires and what one expects, which shows that there is a certain state of character that admits of a mean between extremes that tends towards our good.

Thus, if we can virtuously hope for p, we can rationally expect that p.  Moreover, it can be argued that if we are ignorant as to whether p is even metaphysically possible, we cannot rationally evaluate whether we ought to expect that p is true.  Now, I could contend that a person can virtuously hope for a perfect being, i.e. a being that has all perfections, including necessary existence.  If this is so, a perfect being exists.

Some atheists may endorse the virtue of hoping that there is a perfect being, but then they must either claim that one can virtuously hope for that which is inscrutable in terms of expectations (and so deny that such a mean is part of virtue), or they must hold that one can reasonably expect there to be a perfect being without knowing whether it is even possible.  I don’t find either very plausible.  In fact, I would say that under such conditions, we are not talking about hope, but the vice of presumption.

More modestly, I would endorse the conditional conclusion that if there can be a virtuous hope for a perfect being, such a being exists.

A Moral Argument for the Personhood of Being Itself

1) We act morally wrong when we treat Being Itself merely as a means to our own ends.
2) If we act morally wrong when we treat Being Itself merely as a means to our own ends, Being Itself is an end in itself.
3) Whatever is an end in itself has autonomy.
4) Therefore Being Itself is autonomous.
5) Whatever is autonomous has personhood, i.e rationally and freely wills the moral law.
6) Therefore Being itself has personhood, i.e. Being Itself rationally and freely wills the moral law.

Some Thoughts:

  • When we sin, we utilize existing things for our own ends. Those things exist insofar as they participate in Being Itself. So we are literally treating Being Itself like a tool, or an object for our own benefit. And that is sinful because Being Itself is not an object.  One ought not do this not only because it is a category error, but also because it is a failure to recognize the dignity of Being Itself. This bridges the is/ought divide and explains why our moral duties are grounded in reality. Divine Autonomy is realized in the teleology of beings. We sin when we subvert that telos in a way that completely instumentalizes their being, and so God’s as well.  To subvert the telos of beings in this way is nothing more than self-worship.
  • This is why evil cannot exist on pantheism or naturalism. You can’t sin against Being Itself, if Being Itself is merely objective. That is, you would be treating it as it is, not as it is not.  This is also why our own autonomy is threatened when we accept pantheism or naturalism.
  • Satan wanted to be a god without “recognizing” that his “being” is from God. Without that recognition, God is treated as a mere tool, which is blasphemy of the highest order. And yet saints are just those who want to be gods through “recognizing” that their “being” is from God. And thus it is God’s autonomy and grace by which the saints are divinized.  To treat Being Itself as autonomous is to recognize Being’s gratuitousness towards us and our own radical contingency.  It is also to recognize our humble place is not at the top or center of creation, let alone Being.
  • Animals cannot be treated as merely means even if they lack autonomy. Actually this might explain why they can’t be treated as mere means, despite not being autonomous. Mistreatment of animals is not a violation of animal autonomy, but the autonomy of Being itself. Thus, all violations of the moral law are violations against autonomy, be it in us, or in Being Itself.  The same may hold for plants, and ecosystems.  We can use such things, but not abuse them.  We cannot lose sight of the dignity of Being even as we consume the fruits of our labor and cultivate the land.

On “Is”

<<τὸ ὂν λέγεται πολλαχῶς…>> (Bill Clinton and Aristotle)

“Is” (to be) is a tricky word, and I think the ambiguous nature of this word has led to some misunderstandings of some of the arguments I present, which are typically written in Free Logic. “Is” has multiple meanings, and some of the meanings are more “ontologically committing” or “existentially loaded” than others. Some common logical notation that gets translated as “is” in ordinary language include: 1) “(∃x)”, 2) “=”, 3) “Px”, and 4) “≝”, and I would like to emphasize that they are not syntactically equivalent, and do not function in logical arguments in the same way.

1) The “is” of existential quantification: There is an x, e.g. there is something green, or (∃x)Gx,. This can be interpreted as a “particular quantifier” indicating that there is at least one individual x. Depending on the domain of discourse, the existential quantifier can be more or less ontological committing. One could say, there is a fictional detective that Arthur Conan Doyle wrote about, and use the existential quantifer, and one would not be committed to the reality of fictional beings, i.e. (∃x)(Fx & Wax) [read: there is an x such that x is fictional and Arthur Conan Doyle wrote about x], s = x satisfies the formula in this case, where “s” means “Sherlock Holmes”.

2) The “is” of identity: (x = y), e.g. Tully is Cicero, or (t = c). Sometimes the “is” of identity is combined with the existential quantifier to make strong existential claims, e.g. there is a planet named Venus: (∃x) [Px & (x = v)]. There are rules around identity that are, themselves, metaphysically complicated, and it is controversial how those rules should apply to logic. For instance, it is sometimes granted that (∀x)(x = x) can be introduced at any stage of an argument simply because everything is self identical. Also, if a = b, then b can be substituted for a in an argument in some, but not all, contexts. The contexts were such substitutions cannot occur are called “referentially opaque contexts”. For example, Clark = Superman. Lois believes Superman = Superman. But it doesn’t follow that Lois believes Superman = Clark.

3) The “is” of predication:  x is purple, or simply Px. This “is” is not very existentially committing, but merely ascribes properties to individuals, on could say Sherlock, where “s” is Sherlock, and “B” is the predicate “Brave”: Bs. In “Free Logic” to make strong “existentially loaded” or “existentially committing” claims, you might specify “Real Existence” as a kind of predicate said of an individual. This might run contrary to “Kant’s Dictum” that existence is not a real predicate, but alternative ways of forming existential claims about what exists in the world are problematic for other reasons. When I construct ontological arguments, I tend to use Free Logic. This is because free logic allows you to quantify over things that may or may not exist in reality, which is needed, if one is not to beg the question in ontological arguments.

4) The “is” of definition: for example, the name “God” is “the x such that x is perfect”, or g ≝ (ɿx)Px.  I might stipulate such a definition in an argument by writing “D1: God is perfect.” This is not an existentially committing sentence, but a stipulation of the meaning of a term. Definitions are not really propositions in the fullest sense, as they are not true or false, but merely what one means when one uses a term in a proposition. As such, a definition is usually assessed in terms of clarity and coherence rather then whether it is true.  The scholastics would make this point by saying that definitions pertain to the first act of the mind, not the second.  Explicitly adding predicates into a definition in order to prove that the thing defined has those predicates can be question-begging, this would include adding “real existence” as a predicate in the definition, e.g. A shmunicorn is a unicorn that exists, therefore shmunicorns exist would constitute a question-begging proof. Adding “existence” directly into a definition also entails that the thing defined would exist necessarily, since one can add necessity to any conclusion derived from zero premises. It would be unclear and possibly incoherent to say that shmunicorns exist of necessity, so such a proof should not command assent. My ontological arguments for God are never zero-premise, and always require one or more premises to reach the conclusion.

So this can help us to disambiguate.  Consider the following sentence: “There is an individual who is the author of this blog and who is Daniel, who is the only son of James and Kathy Vecchio, and who is.”

Axy ≝ x is the author of y
Sxyz ≝ x is the only son of y and z
d ≝ (ɿx)Sxjk
j ≝ James Vecchio
k ≝ Kathy Vecchio
b ≝ Vexing Questions blog

(∃x){[Axb ∧ (x = d)] ∧ E!x}

There are a lot of “ises” in that expression, but we can now see how each has its own function.

My Top 13 Best Arguments for God

Here is a list of the 13 best argument for God’s existence that I have written or formulated:

  1. The Bonaventurean Ontological Argument
  2. The Modal Ontological Argument from Divine Simplicity
  3. The Modal Ontological Argument from Anselm’s Apophatic Definition
  4. The Anselmian Ontological Argument
  5. The Cartesian Ontological Argument
  6. The Argument for an Omnipotent Being from Aristotelian Actualism
  7. A Mereological Interpretation of Aquinas’s Third Way
  8. The Argument from Essential Uniqueness
  9. The Indispendability Modal Ontological Argument (Voltairean Variation)
  10. A Deontic-Ontological Argument from Gratitude
  11. The Argument from Hope
  12. An Induction based on the Modal Ontological Argument
  13. The Knowability Argument for an Omniscient Mind

 

Improving the Formulation of Bonaventure’s OA

The following formulation relies on one less premise than my previous formulation, and avoids the implication that there are not objects which refer to God and which are not completely God, i.e. that there are not objects of thought to which “God” refers (a problem that resulted from the way I formulated P2 in the earlier version).

D1) God is absolutely complete
P1) If no objects to which “God” refers  are objects that truly and completely possess the divine essence, then God is not absolutely complete.
P2) If there is an object to which “God” refers and it truly and completely has the divine essence, then God exists in reality.
C) God exists in reality

Let,

Cx ≝ x is absolutely complete
Dx ≝ x truly and completely has the divine essence
Rxy ≝ x is the entity to which “y” refers
E!x ≝ x exists in reality
g ≝ (ɿx)Cx

1. (∀x)(Rxg → ~Dx) → ~Cg (premise)
2. (∃x)(Rxg ∧ Dx) → E!g (premise)
3. (∀x)(Rxg → ~Dx) (IP)
4. ~Cg (1,3 MP)
5. (∃x)[Cx ∧ (∀y){[Cy →(y = x)] ∧ ~Cx} (4 theory of descriptions)
6. [Cμ ∧ (∀y){[Cy →(y = μ)] ∧ ~Cμ (5 EI)
7. [(∀y){[Cy →(y = μ) ∧ Cμ] ∧ ~Cμ (6 Comm)
8. (∀y){[Cy →(y = μ) ∧ [Cμ ∧ ~Cμ] (7 Assoc)
9. Cμ ∧ ~Cμ (8 Simp)
10. ~(∀x)(Rxg → ~Dx) (3-9 IP)
11. ~(∀x)(~Rxg ∨ ~Dx)(10 Impl)
12. ~(∀x)~(Rxg ∧ Dx)(11 DeM)
13. (∃x)~~(Rxg ∧ Dx) (12 QN)
14. (∃x)(Rxg ∧ Dx) (13 DN)
15. E!g (2,14 MP)

QED

A Formulation of Bonaventure’s Ontological Argument

franc3a7ois2c_claude_28dit_frc3a8re_luc29_-_saint_bonaventure

Image Source: Wikipedia “Bonaventure

<<Si Deus est Deus, Deus est.>>

Bonaventure writes the following argument:

No one can be ignorant of the fact that this is true: the best is the best; or think that it is false. But the best is a being which is absolutely complete. Now any being which is absolutely complete, for this very reason, is an actual being. Therefore, if the best is the best, the best is. In a similar way, one can argue: If God is God, then God is. Now the antecedent is so true that it cannot be thought not to be. Therefore, it is true without doubt that God exists (Bonaventure, De mysterio trinitatis 1.1 fund. 29 (ed. Quaracchi V 48).

The overly-simplified version of the argument is:

P1) If God is God, then God is.

P2) God is God.

C) God is.

Noone and Houser (2013) write, “…the premise If God is God is not an empty tautology (Seifert 1992, 216–217). It means ‘if the entity to which the term God refers truly possesses the divine essence.’ And the conclusion means that such an entity must exist.”  This inspired me to reconstruct Bonaventure’s argument as best I can.

Informally the argument is:

D1) “God” is the absolutely complete being.
P1) There is an object to which the term “God” refers.
P2) If the object to which the term “God” refers does not truly and completely possess the divine essence, then God is not absolutely complete.
P3) If object to which the term “God” refers truly and completely possesses the divine essence, then God exists in reality.
C) God, the being who truly and completely possesses the divine essence, exists in reality.
Explanation of D1: Here we stipulate that God is defined as complete in every positive simple attribute, which is to say that by “God”, we mean a perfect being. This definitions is a definite description, i.e. it refers to a singular term, since absolute completeness implies omnipotence, and there can only be one omnipotent being. For, if there were two, one could will contrary to the other, and absurdity would follow. A stipulation is to be granted, so long as it is coherent, otherwise any conclusion could be deduced from it. As to whether the definition of an absolutely complete being is coherent, it should be noted that perfections, in being both simple and positive, cannot contain any explicit or implicit contradiction, and so the stipulate is logically coherent.
Defense of P1: This is to say that the term “God” refers to some imagined, conceived, or real object. The atheist should agree that “God” refers to some object, even if the object is just something in the theist’s fancy.
Defense of P2: Since the antecedent of (P2) specifies a way in which object to which the term “God” refers would be incomplete, it follows of analytic necessity that the object named by “God” is not absolutely complete, i.e. God is not absolutely complete.

Defense of P3: To grant that there is an object which truly and completely possesses the divine essence is semantically equivalent to granting that that which everyone calls “God”, i.e. a perfect being, exists in reality.

Further notes:

  • In other words, it is asking whether the object to which “God” refers is a perfect being. If it is not a perfect being, then “God” means an absolutely complete being and does not refer to an absolutely complete being. There is an “incompleteness” inherent in this relationship, which means that if “God” fails to refer to that which is truly God, then we mean that God, a complete being, is not a complete being. Our sense of “God” would be contradictory in nature.
  • We cannot include in the sense of what “God” is, the notion that “God” refers to something that isn’t completely God.
  • The only consistent alternative is to mean that the object which we name “God” exists in reality, and completely has the divine essence.
  • What Bonaventure is saying is that the sense of “God” must include that it references God, or else the the sense is incoherent. So to grant that there is an object to which the sense of “God” refers is sufficient to prove there is God.

Formally:

Let,

Cx ≝ x absolutely complete
Dx ≝ x truly and completely has the divine essence
Rxy ≝ x is the entity to which “y” refers
E!x ≝ x exists in reality
g ≝ (ɿx)Cx

1. (∃x)Rxg (premise)
2. (∀x)[(Rxg ∧ ~Dx) → ~Cg] (premise)
3. (∃x)(Rxg ∧ Dx) → E!g (premise)
4. Rμg (1 EI)
5. Rμg ∧ ~Dμ (IP)
6. (Rμg ∧ ~Dμ) → ~Cg (2 UI)
7. ~Cg (5,6 MP)
8. (∃x)[Cx ∧ (∀y){[Cy →(y = x)] ∧ ~Cx} (7 theory of descriptions)
9. [Cν ∧ (∀y){[Cy →(y = ν)] ∧ ~Cν (8 EI)
10. [(∀y){[Cy →(y = ν) ∧ Cν] ∧ ~Cν (9 Comm)
11. (∀y){[Cy →(y = ν) ∧ [Cν ∧ ~Cν] (10 Assoc)
12. Cν ∧ ~Cν (11 Simp)
14. ~(Rμg ∧ ~Dμ) (5-13 IP)
15. ~Rμg ∨ ~~Dμ (14 DeM)
16. ~~Rμg (4 DN)
17. ~~Dμ (15,16 DS)
18. Dμ (17 DN)
19. Rμg ∧ Dμ (4,18 Conj)
20 (∃x)(Rxg ∧ Dx) (19 EG)
21. E!g (3,20 MP)

QED

References:

Noone, Tim and Houser, R. E., “Saint Bonaventure”, The Stanford Encyclopedia of Philosophy (Winter 2014 Edition), Edward N. Zalta (ed.), URL = <https://plato.stanford.edu/archives/win2014/entries/bonaventure/&gt;.

Seifert, Josef, 1992. “‘Si Deus est Deus, Deus est’: Reflections on St. Bonaventure’s Interpretation of St. Anselm’s Ontological Argument,” Franciscan Studies, 52: 215–231.

Using Logic and Definitions to Prove God

Often when I share my arguments, atheists will respond by pointing out that one cannot define God into existence. I don’t think my arguments do that, since each of them require axioms and premises that move beyond mere definitions to establish their conclusions. At any rate, when someone makes this objection, this is what I visualize:

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I’ve also heard it said that you cannot use logic to prove the existence of something:

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Combining Aquinas and the MOA

Here is a variation on my argument from Anselm to Plantinga:

P1) Possibly, there is an absolutely metaphysically simple being.
P2) Necessarily, that there is an absolutely metaphysically simple being implies that there is a maximally great being.
P3) If it’s possible that something is maximally great, then it’s possible that necessarily there is an omnipotent, omniscient, and omnibenevolent.
C) There is an omnipotent, omniscient, and omnibenevolent being.

Defense of P1: An absolutely metaphysically simple being, insofar as it is being, is attributed positively, cannot contain a part that negates its essential nature, which means it does not contain inconsistent properties or attributes.  Now, it has been objected, by none other than Plantinga, that the concept of a metaphysically simple being is incoherent, but as Vallicella (2019) points out, one need not adopt the metaphysical framework by which that incoherence is pressed.  Thus the metaphysical possibility of an absolutely metaphysical being will depend on the supposition of a “constituent”  metaphysical frame work.  Vallicella (2019) writes, the “constituent” metaphysicians “…did not think of individuals as related to their properties as to abstracta external to them, but as having properties as ontological constituents.”  This roughly tracks Aristotelian realism over Platonic realism, which I think is a decisively preferable metaphysical framework, given the third-man objection to Platonism.  With these considerations in mind, I think it is highly plausible to defend the metaphysical possibility of an absolutely simple being.

Defense of P2: Aquinas demonstrates that an absolutely metaphysically simple being is metaphysically necessary (since its has existence essentially, see [3]-[4]), omnipotent (since God is infinite, which is derived from His simplicity), omniscient (see, in particular, [3]), and the good of every good (see [3]) and the highest good (see [5]), so omnibenevolent.  Now one might object that a maximally great being has many divine attributes and is, therefore, not absolutely metaphysically simple, but Aquinas explains that the plurality of divine attributes is not opposed to divine simplicity.  Since the attributes of a maximally great being can be deduced from an absolutely simple being, we can conclude that the existence of an absolutely simple being necessarily implies an maximally great being (where maximal greatness is defined as a necessarily existing, omnipotent, omniscient, and morally perfect being).

Defense of P3: This implication follows from Plantinga’s stipulative definitions of maximal greatness, and maximal excellence, with a slight deviation from moral perfection to omnibenevolence, defined in Thomistic terms.  So this is an analytically true implication.

Let,

Mx ≝ x is maximally great
Ox ≝ x is omnipotent, omniscient, and omnibenevolent
Sx ≝ x is absolutely metaphysically simple
Theorem of K: ☐(p → q) → (♢p → ♢q)
Theorem of S5: ♢☐p → ☐p
Axiom M: ☐p → p

1. ♢(∃x)Sx (premise)
2. ☐[(∃x)Sx → (∃y)My](premise)
3. ♢(∃y)My → ♢☐(∃z)Oz (premise)
4. ☐[(∃x)Sx → (∃y)My]] → [♢(∃x)Sx → ♢(∃y)My] (Theorem of K)
5. ♢(∃x)Sx → ♢(∃y)My (2,4 MP)
6. ♢(∃y)My (1,5 MP)
7. ♢☐(∃z)Oz (3,6 MP)
8. ♢☐(∃z)Oz → ☐(∃z)Oz (Theorem of S5)
9. ☐(∃z)Oz (7,8 MP)
10. ☐(∃z)Oz → (∃z)Oz (Axiom M)
11. (∃z)Oz (9,10 MP)

QED

References:

Vallicella, William F., “Divine Simplicity”, The Stanford Encyclopedia of Philosophy (Spring 2019 Edition), Edward N. Zalta (ed.), URL = <https://plato.stanford.edu/archives/spr2019/entries/divine-simplicity/&gt;.

 

Anselm’s God to Plantinga’s God

Prefatory Remarks:

There is a slight difference in the way Anselm and Plantinga define God.  Anselm’s definition is that God is that than which none greater can be conceived.  Plantinga’s God is a maximally great being, i.e. a necessarily existing being that has omnipotence, omniscience, and morally perfection.  Anselm’s definition is negative, while Plantinga’s is positive.  Anselm’s definition fits with the apophatic tradition of a negative theology, i.e. God is not among those things of which a greater can be conceived.  It is because Anselm’s definition is negative that I contend that Thomas Aquinas is incorrect in his central critique of the ontological argument.  Anselm isn’t offering a positive account of God’s essential nature.  I agree with Aquinas that a positive account of God’s essential nature cannot be completely and univocally known to us, but I should also say that although Plantinga’s definition is positive, it is not claimed to be complete and it need not be interpreted as perfections of “power”, “knowledge”, and “goodness” as those terms are understood univocally.

There is still a strong relationship between the Anselmian definition of God and the Plantingan definition.  Namely, one can derive from the Anselmian definition various divine attributes like necessary existence, omnipotence, omniscience, and moral perfection, among other perfections.  So one can argue that if there is an Anselmian God, then there is a maximally great being, in the Plantingan sense.  Indeed, that impication necessarily holds, given that it analytically follows from the Anselmian definition.  As an aside, I would argue that the two definitions are not equivalent in that one cannot derive the Anselmian definition from the Plantingan definition.  So, the existence of a maximally great being would not necessarily imply the existence of Anselm’s God.

Another interesting aspect of Anselm’s definition is that, since it is negative, I think the case for its metaphysical possibility can be firmly established.  Now, I am not suggesting that Anselm makes a modal inference that the metaphysical possibility of God, as he defines it, entails his actual existence.  Still, it is often disputed that conceivability does not entail metaphysical possibility. However, in this particular case, the conceivability of the Anselmian God makes the following falsehood self-evident, viz. that it is somehow metaphysically necessary that for any object, there will always be something else one could conceive of which would be greater.

Given that Plantinga’s maximally great being is a necessarily existing omnipotent, omnicient, and morally perfect being, I think there may be a powerful way to combine the fact that we can understand the Anselmian God, and show the Anselmian God possible, and use that to demonstrate the existence of a being that is omnipotent, omniscient, and morally perfect.  In what follows, I exploit Anselm to vindicate Plantinga.

Informal Expression of the Argument:

P1) If I can understand the Anselmian definition of God, then it is not necessarily the case that, for any given thing, there will be something conceivably greater.
P2) If it is possible that there is something than which none greater can be conceived, then it is possible that there is an Anselmian God.
P3) The existence of the Anselmian God necessarily implies the existence of a maximally great being.
P4) I can understand the Anselmian definition of God.
P5) If it’s possible that something is maximally great, then it’s possible that there is a necessarily existing, omnipotent, omniscient, and morally perfect being.
C) There is an omnipotent, omniscient, and morally perfect being.

A Formal Expression of the Argument:

P1) If it is possible that the Anselmian God is in the understanding, then it is not necessary that, for all x, it is conceivable that there is y and y is greater than x.
P2) If it is possible that there is something, x, such that it is not conceivable that there is some y and y is greater than x, then it is possible that there is something, z, and z is the Anselmian God.
P3) Necessarily, if there is something that is the Anselmian God, then there is something that is maximally great.
P4) It is possible that the Anselmian God is in the understanding
P5) If it is possible that there is something that is maximally great, then it is possibly necessary that there is something that is omnipotent, omniscient, and morally perfect.
C) There is something that is omnipotent, omniscient, and morally perfect.

Formal Deductive Proof of the Argument:

Let,

Mx ≝ x is maximally great
Ox ≝ x is omnipotent, omniscient, and morally perfect
Ux ≝ x is in the understanding
Gxy ≝ x is greater than y
©… ≝ it is conceivable that…
g ≝ (ɿx)(~©(∃y)Gyx)
Theorem of K: ☐(p → q) → (♢p → ♢q)
Theorem of S5: ♢☐p → ☐p
Axiom M: ☐p → p

1. ♢Ug → ~☐(∀x)©(∃y)(Gyx) (premise)
2. ♢(∃x)~©(∃y)(Gyx) → ♢(∃z)(z = g) (premise)
3. ☐[(∃z)(z = g) → (∃x)Mx] (premise)
4. ♢Ug (premise)
5. ♢(∃x)Mx → ♢☐(∃y)Oy (premise)
6. ☐[(∃z)(z = g) → (∃x)Mx] → [♢(∃z)(z = g) → ♢(∃x)Mx] (Theorem of K)
7. ~☐(∀x)©(∃y)(Gyx) (1,4 MP)
8. ~~♢~(∀x)©(∃y)(Gyx)(7 ME)
9. ♢~(∀x)©(∃y)(Gyx)(8 DN)
10. ♢(∃x)~©(∃y)(Gyx)(9 QN)
11. ♢(∃z)(z = g) (2,10 MP)
12. ♢(∃z)(z = g) → ♢(∃x)Mx (3,6 MP)
13. ♢(∃x)Mx (11,12 MP)
14. ♢☐(∃y)Oy (5,13 MP)
15. ♢☐(∃y)Oy → ☐(∃y)Oy (Theorem of S5)
16. ☐(∃y)Oy (14,15 MP)
17. ☐(∃y)Oy → (∃y)Oy (Axiom M)
18. (∃y)Oy (16,17 MP)

QED