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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

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.
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