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An Argument from Wayne and Garth

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P1.  If a maximally great being is impossible, then it is possible that I am worthy of worship.

P2. It is not possible that I am worthy of worship.

C1. A maximally great being is not impossible [from P1 and P2 Modus Tollens].

C2. A maximally great being is possible [from C1 by Obversion].

P3. If a maximally great being is possible, there is a maximally great being.

C3. There is a maximally great being [C2 and P3 Modus Ponens].

QED

Defense of Premises:

P1.  If there are no possible worlds where there is a being that has a maximal set of compossible great-making properties, then there is at least some possible world where I, or my counter-part, is the greatest being that happens to exist, and so I would be of greatest worth, i.e. worthy of worship.

P2. I know, through direct intuitional self-knowledge, that it is metaphysically impossible that I am a being worthy of worship.

P3. A maximally great being is a being that, if it exists in any possible world, exists in all possible worlds, including in the actual world.

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

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 incompossible properties or attributes.  Moreover, since it is the ground of all contingent facts, an absolutely metaphysically simple being cannot be inconsistent with any possible contingent fact. 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 “moderate” realism over Platonic “extreme” 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

The Dilemma Theodicy

  1. By definition, God is a maximally great being, i.e. an omnipotent, omniscience, morally perfect being in every possible world.
  2. Any argument against God’s existence that depends on a premise of the form “If God were to exist, then we would expect there to be x” (hereafter, the “counterfactual” premise) must have a justification, either by way of a trivial entailment, given the incoherence of the concept of God, and so the impossibility of the existence of God, or by way of the defense of a substantive counterfactual implication, given a thoroughgoing conceptual analysis of the concept of God, and the sorts of states of affairs implied by God’s existence.
  3. If the justification for the “counterfactual” premise is by way of a trivial entailment, given the incoherence of the concept of God, and so the impossibility of the existence of God, then the justification for the “counterfactual” premise begs the question of any argument against God’s existence that depends upon the “counterfactual” premise, which means the argument containing the “counterfactual” premise is informally fallacious.
  4. If the justification for the “counterfactual” premise is by way of a defense of a substantive counterfactual implication, given a thoroughgoing conceptual analysis of the concept of God, and the sorts of states of affairs implied by God’s existence, then the justification depends upon the metaphysical possibility of God, and the sorts of states of affairs that obtain in the nearest possible worlds where God exists, which also serves as a justification for the possibility premise of the modal ontological argument, by which the existence of God can be directly demonstrated from His metaphysical possibility, based upon an axiom of S5.
  5. But, a successful argument cannot be informally fallacious, nor can a successful argument depend on a justification that directly implies the contradictory of the its conclusion.
  6. So, no argument against God’s existence that depends on the “counterfactual” premise is successful.

Escaping the horns would require a substantive justification of the counterfactual premise that does not imply any real metaphysical possibility of God.  Would such a justification be compelling enough for a theist, or neutral party to accept the truth of the counterfactual premise? 

Ontological Argument Improved Again

Let,

Rx ≝ x exists in re
Ix ≝ x exists in intellectu
Gx ≝ x admits of more greatness
G[Px,~Px] ≝ x having P is greater than x not having P
Gxy ≝ x is greater than y
©… ≝ it is conceivable that…

g ≝ (ɿx)(~©Gx ∧ ~©(∃y)Gyx)

1. (∀x)[(Ix ∧ ~Rx) ⊃ ©Rx] (premise)
2. (∀x)G[Rx,~Rx] (premise)
3. (∀x){[[~Rx ∧ G] ∧ ©Rx] ⊃ ©Gx}(premise)
4. Ig (premise)
5. ~Rg (IP)
6. Ig ∧ ~Rg (4,5 Conj)
7. (Ig ∧ ~Rg) ⊃ ©Rg (1 UI)
8. ©Rg (6,7 MP)
9. G[Rg,~Rg] (2 UI)
10. ~Rg ∧ G[Rg,~Rg] (5,9 Conj)
11. [~Rg ∧ G[Rg,~Rg]] ∧ ©Rg (8,10 Conj)
12. {[~Rg ∧ G[Rg,~Rg]] ∧ ©Rg} ⊃ ©Gg (3 UI)
13. ©Gg (11,12 MP)
14. (∃x){{[~©Gx ∧ ~©(∃y)Gyx] ∧ (∀z){[~©Gz ∧ ~©(∃y)Gyz] ⊃ (z = x)]}} ∧ ©Gx} (13 theory of descriptions)
15. {[~©Gμ ∧ ~©(∃y)Gyμ] ∧ (∀z){[~©Gz ∧ ~©(∃y)Gyz] ⊃ (z = μ)]}} ∧ ©Gμ (14 EI)
16. {(∀z){[~©Gz ∧ ~©(∃y)Gyz] ⊃ (z = μ)]} ∧ [~©Gμ ∧ ~©(∃y)Gyμ]} ∧ ©Gμ (15 Comm)
17. {(∀z){[~©Gz ∧ ~©(∃y)Gyz] ⊃ (z = μ)]} ∧ [~©(∃y)Gyμ ∧ ~©Gμ]} ∧ ©Gμ (16 Comm)
18. {(∀z){[[~©Gz ∧ ~©(∃y)Gyz] ⊃ (z = μ)]} ∧ ~©(∃y)Gyμ] ∧ ~©Gμ} ∧ ©Gμ (17 Assoc)
19. (∀z){[[~©Gz ∧ ~©(∃y)Gyz] ⊃ (z = μ)]} ∧ ~©(∃y)Gyμ] ∧ {~©Gμ ∧ ©Gμ} (18 Assoc)
20. ~©Gμ ∧ ©Gμ (19 Simp)
21. ~~Rg (5-20 IP)
22. Rg (21 DN)

Vexing Links (2/13/2016)

Happy St. Valentine’s Day readers!  I have been busy with my dissertation, so I have not had an opportunity to post any new arguments or articles.  In the meantime, here are some links of note:

  1. The  Vatican Library Digitizations Project is very exciting!  I imagine there will be some extraordinary treasures in there.
  2. The true history of Socrates’s last day on Earth.  Plato (or maybe Phaedo) had it all wrong.
  3. Wisecrack has an awesome video on Philosophy and the Walking Dead.  See the connections to Rome, and the ways in which the Walking Dead makes us confront the meaning of life and death.
  4. Dr. Larycia Hawkins claimed that Christians and Muslims worship the same God.  Subsequently, she was placed on administrative leave following a controversity at Wheaton College.  It looks like she will be terminated.  Many philosophers have weighed in on the question, including Dr. Francis Beckwith, Dr. Bill Vallicella, Dr. Dale Tuggy, Dr. William Lane Craig, and Dr. Lydia McGrew.  I think I am close to Vallicella’s position in that I think the question may be intractable, or at least depend upon what features one is going to insist upon as fixed, when determining the reference.  Perhaps the bigger issue is the disturbing trend in academia to discipline and fire professors when they voice positions with which the administration disagrees.  The fact that so many thinkers have arrived at completely different positions may tell you that Dr. Hawkins was taking a position that is not settled within Christian orthodoxy.  Indeed, if we construe this as a question in the philosophy of language and the question of reference, then it seems that one can reasonably agree with Dr. Hawkins and be a staunchly orthodox Christian.
  5. On the same theme of academic freedom, the President of Mount St. Mary’s College in Maryland, Simon Newman, decided to implement a plan to identify and cull out freshman who were unlikely to flourish and graduate (rather than, you know, help your students succeed).  He alledgly compared such freshmen to fuzzy bunnies who need to be drowned.  Faculty and administration who disagreed with Newman were terminated, even if they had tenure.  A provost was removed from his position.  It now looks like Newman is under pressure to take it all back.  At the same time, it is coming to light that Newman wants to rid MSM of her Catholic tradition and identity.  This is a troubling trend in Catholic education, to say the least.
  6. On the Stanford Encyclopedia of Philosophy Graham Oppy has updated his entry on Ontological Arguments, Daniel Nolan has updated his entry on Modal Fictionalism, and Christopher Menzel has an updated entry on Possible Worlds.
  7. Read Dr. Ed Feser’s review of Jerry Coyne’s Faith versus Fact.  It has to be the most scathing and hilarious review ever written.
  8. Dale Tuggy poses his “Jesus is God” challenge.  Perhaps when I have time, I will offer a substantive critique, but I think there are issues with P2 and P4, which render the argument unsound.  The first issue is that I suspect that identity statements about God are not subject the Leibnizian laws.
  9. This may be an older site, but it is new to me and it looks like it has a ton of resources for anyone interested in Early Church History and various original language documents: Documenta Catholica Omnia.
  10. I’ve been enjoying the music of Mikis Theodorakis lately.