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

 

De Ente and the Falsity of Naturalism

Thomas Aquinas writes:

…[E]verything that is in a genus has a quiddity beyond its existence, since the quiddity or nature of the genus or species is not in the order of nature distinguished in the things of which it is the genus or species, but the existence is diverse in diverse things (De Ente V.).

Given some basic modal theorems and axioms, and the above considerations, the following argument occurred to me:

P1. If naturalism is true, everything is in the genus “nature”.
P2. If everything is in the genus “nature”, then everything has a quiddity beyond its existence.
P3. Necessarily, if there is some x such that its quiddity is nothing other than its existence, then necessarily there is some x such that its quiddity is nothing other than its existence.
P4. If there is something x such that its quiddity is nothing other than its existence, then not everything has its quiddity beyond its existence.
P5. Possibly, there is some x such that its quiddity is nothing other than its existence.
C. It is not the case that naturalism is true.

Defense of P1: Naturalism just is the thesis that everything that exists is natural, and so belongs to the generic class “nature”.

Defense of P2: According to Aquinas, if the quiddity, or essence, of a thing is in a genus, then its quiddity cannot be its existence, since a genus admits of more than one instance, and whatever has its existence as its quiddity cannot admit of more than one instance.

Defense of P3: If something has its existence as its quiddity, then it has existence per se and so necessarily so.  This is necessarily implied, since it is analytically true.

Defense of P4: This would be based on the notion that if a quiddity is the same as its existence, then its quiddity would not also be beyond its existence, for then the quiddity and existence could not be the same.

Defense of P5: This is just to say that it is at least metaphysically possible that something’s quiddity and facticty are the same.  There does not appear to be anything impossible about such a notion, at least prima facie.

Formal Proof:

Let,

N ≝ Naturalism is true
Gxy ≝ x is in the genus y
Q(F,x) ≝ F is ths quiddity of x
B(F,G,x) ≝ F is beyond G for x
E! ≝ existence
n ≝ nature
Theorem of K: ☐(p → q) → (♢p → ♢q)
Theorem of S5: ♢☐p → ☐p
Axiom M: ☐p → p

1. N → (∀x)Gxn (premise)
2. (∀x)Gxn → (∀x)(∀F)[(Q(F,x) → B(F,E!,x)] (premise)
3. ☐{(∃x){[Q(E!,x)∧(∀F)~(F = E!)]→ ~Q(F,x)} → ☐(∃x){[Q(E!,x)∧(∀F)~(F = E!)]→ ~Q(F,x)]}} (premise)
4. (∃x){[Q(E!,x)∧(∀F)~(F = E!)]→ ~Q(F,x)} → ~(∀x)(∀F)[(Q(F,x) → B(F,E!,x)] (premise)
5. ♢(∃x){[Q(E!,x)∧(∀F)~(F = E!)]→ ~Q(F,x)} (premise)
6. N → (∀x)(∀F)[(Q(F,x) → B(F,E!,x)] (1,2 HS)
7. ☐{(∃x){[Q(E!,x)∧(∀F)~(F = E!)]→ ~Q(F,x)] → ☐(∃x){[Q(E!,x)∧(∀F)~(F = E!)]→ ~Q(F,x)]}} → {♢(∃x){[Q(E!,x)∧(∀F)~(F = E!)]→ ~Q(F,x)]} → ♢☐(∃x){[Q(E!,x)∧(∀F)~(F = E!)]→ ~Q(F,x)]}} (Theorem of K)
8. ♢(∃x){[Q(E!,x)∧(∀F)~(F = E!)]→ ~Q(F,x)]} → ♢☐(∃x){[Q(E!,x)∧(∀F)~(F = E!)]→ ~Q(F,x)]} (3,7 MP)
9. ♢☐(∃x){[Q(E!,x)∧(∀F)~(F = E!)]→ ~Q(F,x)]} (5,8 MP)
10. ♢☐(∃x){[Q(E!,x)∧(∀F)~(F = E!)]→ ~Q(F,x)]} → ☐(∃x){[Q(E!,x)∧(∀F)~(F = E!)]→ ~Q(F,x)]} (Theorem of S5)
11. ☐(∃x){[Q(E!,x)∧(∀F)~(F = E!)]→ ~Q(F,x)]}(9,10 MP)
12. ☐(∃x){[Q(E!,x)∧(∀F)~(F = E!)]→ ~Q(F,x)]} → (∃x){[Q(E!,x)∧(∀F)~(F = E!)]→ ~Q(F,x)]} (Axiom M)
13. (∃x){[Q(E!,x)∧(∀F)~(F = E!)]→ ~Q(F,x)]}(11,12 MP)
14. ~(∀x)(∀F)[(Q(F,x) → B(F,E!,x)] (4,13 MP)
15. ~N (6,14 MT)

QED

Physicalism v. Hylomorphism

3jqqon.jpg

Well, he didn’t

Let

Fx ≝ x is a financier
Rxy ≝ x ran a sex trafficking ring out of y
Kxy ≝ x killed y
j ≝ (ɿx)(Fx ∧ Rxl)
l ≝ Little St. James Island

1. ~(∃x)[(Fx ∧ Rxl) ∧ Kxx](premise)
2. Kjj (Assumption for Indirect Proof)
3. (∃x){[(Fx ∧ Rxl) ∧ (∀y)[(Fy ∧ Ryl)→ (y = x)] ∧ Kxx} (2 theory of descriptions)
4. [(Fμ ∧ Rμl) ∧ (∀y)[(Fy ∧ Ryl)→ (y = μ)] ∧ Kμμ (3 EI)
5. (∀x)~[(Fx ∧ Rxl) ∧ Kxx] (1 QN)
6. ~[(Fμ ∧ Rμl) ∧ Kμμ] (5 UI)
7. [(Fμ ∧ Rμl) ∧ (∀y)[(Fy ∧ Ryl)→ (y = μ)] (4 Simp)
8. Fμ ∧ Rμl (7 Simp)
9. Kμμ (4 Simp)
10. (Fμ ∧ Rμl)∧ Kμμ (8,9 Conj)
11. [(Fμ ∧ Rμl)∧ Kμμ] ∧ ~[(Fμ ∧ Rμl) ∧ Kμμ] (6,10 Conj)
12. ~Kjj (2-11 Indirect Proof)

QED

Hempel’s Raven Paradox and God’s Existence

elsa
Hempel’s Raven Paradox: a red apple is evidence that “all ravens are black things”, since it counts as evidence for the logically equivalent proposition “all non-black things are non-ravens”.
 
Likewise, the fictional character, Elsa of Arendelle, is evidence that God is non-fictional, since “All things identical to God are non-fictional beings” is logically equivalent to “All fictional beings are non-identical to God”.
 
If it is evidence, it isn’t very good evidence, I would admit. But, even if it isn’t very good evidence, there is a potential infinity of fictional characters that are non-identical to God. How would you block that from generating a cumulative case for God, simply by increasingly inventing fictional characters that are not God?
 
This is an honest question I have. I am not trying to provide some bizarre cumulative case for God’s existence, as I perceive that this would prove too much.
 
I suppose this just is Hempel’s paradox, but I don’t think I have seen it applied to existential claims about singular terms before.

An Abductive Cosmological Argument

Let us define God as the non-natural sufficient explanation of nature.  If so, I think the following abductive argument presents a plausible reason to believe in God.

P1: If God is not the best explanation for nature, i.e. the whole of natural reality, then either nature is self-explanatory, or we ought to think nature is brute, i.e. it has no explanation.

P2: If nature is self-explanatory, then the quiddity of nature, i.e. what nature is, includes its facticity, i.e. that nature is.

P3: It is not the case that the quiddity of nature includes its facticity, i.e. the existence of nature is not an analytic truth.

P4: If we ought to think something, x, is brute, then then all things are among those which have been eliminated as possible explanations for x.

P5: God is not among that which has been eliminated as a possible explanation for nature.

P6: If God is the best explanation for nature, then it is probable that God exists.

C: It is probable that God exists.

The deduction is as follows:

C1: It is not the case that nature is self-explanatory [from P2 and P3 by Modus Tollens].

C2: If we ought to think nature is brute, then all things are among those which have been eliminated as possible explanations of nature [from P4 by Universal Instantiation].

C3: Some things are not among those which have been eliminated as possible explanations for nature [from P5 by Existential Generalization].

C4: Not all things are among those which have been eliminated as possible explanations of nature [from C3 by Contradiction].

C5: It is not the case that we ought to think nature is brute [from C2 and C4 by Modus Tollens].

C6: It is not the case that nature is self-explanatory, and it is not the case that we ought to think nature is brute [from C1 and C5 by Conjunction].

C7: It is not the case that either nature is self-explanatory or we ought to think nature is brute [from C6 by DeMorgan’s Theorem].

C8: It is not the case that God is not the best explanation for nature [from P1 and C7 by Modus Tollens].

C9: God is the best explanation for nature [from C8 by Double Negation].

C10: It is probable that God exists [from P6 and C9 by Modus Ponens].

 

 

A Private Language Argument Against Unitarianism

Nature is semiotic.  The intelligible, effable, and teleological characteristics of creation, and the alethic, aesthetic, and moral values it intrinsically possesses, are best explained by the existence of a non-unitarian God.  The One, Eternal God “spoke” creation into existence such that it is suffuse with meaning.  Thus, all things are pros hen analogically comparable insofar as they reflect, to varying degrees, ipsum esse subsistens.  “For from the greatness and the beauty of created things their original author, by analogy, is seen” (Wisdom 13:5).  Nature did not gain this meaning with the advent of other intelligent beings.  The meaning was embedded in nature by its “author” from eternity.  Yet, there are no private languages.  So, from eternity, the analogical meaning communicated ad extra to each created thing must be grounded in a kind of non-private ad intra divine communication, which is impossible on the supposition that God is but one person.

An Argument from Wayne and Garth

749956

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.

An Ontological Argument from Pure Actuality

Informal Argument

D1. God is the being of pure actuality.
P1. For all x, if x exists in the intellect but not in reality, then there is a y such that x is causally dependent on y.
P2. For all x, if x is purely actual, then there is not a y such that x is causally dependent on y.
P3. God is in the intellect.
C. God is in reality

Defense of Definitions and Premises

It should be noted, at the outset that this argument is in Free Logic. As such, the existential quantifier carries no existential import in the argument. This prevents any inference of the existence of God from the definition alone.

D1: A being of pure actuality is simply a being that lacks any potentiality. Such a being has, as Aquinas argues, the divine attributes of omnipotence, omniscience, immutability, eternity, immateriality, and uniqueness. It is this last feature, uniqueness, that justifies the use of a definite description, since there can be only one such being. Instead, existential claims are made by the predicate “R” in the formal argument below, which means that something exists in sense of being real, as opposed to existing in a fictitious or imaginary way.

P1: This premise is motivated by the fact that if something exists in the intellect alone, then its existence is causally dependent on some mind.

P2: A being of pure actuality exists a se, and uncaused, as Thomas proves in his five ways.

P3: Every Thomist who contemplates the implications of a being of pure actuality has the Thomistic conception of God in mind.

The Formal Proof

Let,

Ix ≝ x is in intellectu
Rx ≝ x is in re
Dxy ≝ x is is causally dependent on y
Ax ≝ x is purely actual
g ≝ (ɿx)Ax

1. (∀x)[(Ix ∧ ~Rx) → (∃y)Dxy] (premise)
2. (∀x)(Ax → ~(∃y)Dxy) (premise)
3. Ig (premise)
4. (Ig ∧ ~Rg) (IP)
5. (Ig ∧ ~Rg) → (∃y)Dgy (1 UI)
6. (∃y)Dgy (4,5 MP)
7. Dgμ (6 EI)
8. (∃x){[Ax ∧ (∀y)[Ay → (y = x)]] ∧ Dxμ} (7 theory of descriptions)
9. [Aν ∧ (∀y)[Ay → (y = ν)]] ∧ Dνμ (8 EI)
10. Aν ∧ (∀y)[Ay → (y = ν)] (9 Simp)
11. Aν (10 Simp)
12. Aν → ~(∃y)Dνy (2 UI)
13. ~(∃y)Dνy (11,12 MP)
14. (∀y)~Dνy (13 QN)
15. ~Dνμ (14 UI)
16. Dνμ (9 Simp)
17. Dνμ ∧ ~Dνμ (15,16 Conj)
18. ~(Ig ∧ ~Rg) (4-17 IP)
19. ~Ig ∨ ~~Rg (18 DeM)
20. ~~Rg (3,19 DS)
21. Rg (20 DN)

QED

The Paradox of the Inconsistent Triad

  1. This is an inconsistent triad.
  2. If, at most, two of the propositions in this triad are true, then this is an inconsistent triad.
  3. At most, two of the propositions in this triad are true.

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