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

 

Catholicism is Realism

A Modus Tollens of Rosenberg to God

Alex Rosenberg makes an unflinching case that strong atheism (the denial of God’s existence) leads one to adopt positions like eliminativism, mereological nihilism, and semantic nihilism. It would be too strong to say that Rosenberg proves that there is a direct implication between strong atheism and these subsidiary positions, but a more modest claim would be that strong atheism implies that one ought to treat these beliefs as “live options”. Thus:

P1. If strong atheism is true, then one ought to treat eliminativism, mereological nihilism and semantic nihilism as live options.

A “live option” is a belief that one can actively entertain as a real possibility. What one counts as a “live option” can vary from culture to culture and from time to time. The progress of scientific knowledge can preclude certain live options. For instance, I would not consider belief in a flat earth to be a live option. It is not a belief I could actively entertain or take seriously. Despite the relativistic and historicistic aspects of what might count as a “live option”, it would be bizarre to think that one has an epistemic duty to consider self-defeating beliefs as live options. This is not to say that one has a duty to reject these beliefs as live options, but certainly such an epistemic duty is under-cut by the fact that a belief is self-defeating. That is:

P2. If belief p is self-defeating, then it is not the case that one ought to treat p as a live option.

Now, William Lane Craig and Edward Feser have made very powerful cases that Rosenberg’s eliminativism, mereological nihilism, and semantic nihilism are self-defeating beliefs. So:

P3. Eliminativism, merelogical nihilism and semantic nihilism are self-defeating beliefs.

Thus is follows:

C1. It is not the case that one ought to treat eliminativism, mereological nihilism, or semantic nihilism as live options. [From P2,P3 Modus Ponens]

C2. It is not the case that strong atheism is true. [From P1,C1 MT]

or

C3. God exists. [C2 Semantic Equivalence]

La-la la-la, la-la la-la, I was on Elmo’s World Podcast

A Refinement on The Contingent Symmetry Argument Against Existential Inertia

P1. If contingent entities have existential inertia, then the facts by which identity and individuation principles are grounded are intrinsic to contingent entities.

P2. If the facts by which identity and individuation principles are grounded are intrinsic to contingent entities, then contingency is not symmetrical.

P3. It is false that contingency is not symmetrical.

C1. If contingent entities have existential inertia, then contingency is not symmetrical. (P1, P2 HS)

C2. It is not the case that contingent entities have existential inertia. (P3, C1 MT)

Ad P1. Suppose that identity and individuation principles are not grounded by facts intrinsic to contingent entities. If so, it would seem that identity and individuation is ungrounded or extrinsically grounded. Ungrounded identity and individuation is metaphysically absurd, or at least an untoward position to adopt to salvage EI and contingent symmetry. If a contingent entity’s identity and individuation is grounded extrinsically, then there are external facts that must be the case for the contingent entity to be sustained in existence, but that would be incompatible with existential inertia. For, if an entity has existential inertia, its sustenance, or persistence, cannot be explained by external facts happening to obtain and not failing to obtain.

Ad P2. Contingency is typically defined as two-way possibility, i.e. x possibly exists and possibly does not exist. Now, one might say that x is contingent if it is actual and could fail to exist, but that is only because it seems reasonable to say that whatever is actual is possible. However, such a claim is not the same as the notion of symmetrical contingency, in which an entity that exists could cease to exist and in situations or worlds in which that entity has ceased to exist, it could come to be again. If an entity’s identity and individuation is groundless, it would be a groundless claim to say that it has symmetrical contingency, i.e. that it could come back into existence in situations where it is not. There would not be any facts by which principles of identity or individuation are grounded such that one could appeal to make the claim that it is the same individual. Likewise, if identity and individuation are intrinsic to an entity, the intrinsic facts that ground those principles would go out of existence in situations where the entity does not exist. Thus, from the perspective of those situations, a counterfactual claim that the same individual entity could come to be would be groundless, since the facts that could have grounded the coming-to-be of that same individual would have ceased to be along with the entity and all of its other intrinsic properties.

One possible response is that identity and individuation are grounded intrinsically when a contingent entity is existentially inert, but is somehow buffered to an extrinsic source so that when the entity goes out of existence, there are extrinsic grounds for its identity and individuation are preserved. This response seems rather complicated and an ad hoc rescue. Buffering grounding principles seems like a kind of overdetermination of identity and individuation and so metaphysically implausible. Moreover, it is not entirely clear how a different set of facts that ground identity and individuation could preserve the possibility of the same individual. A regress would have to form, i.e. there would have to be something the grounds the identity between the intrinsic facts and the buffered facts, and such a grounding would suggest that there ultimately is an extrinsic ground for a contingent entity’s identity and individuation, since its supposed intrinsic facts are, themselves, grounded extrinsically.

Ad P3. Typically, we think of two-way possibility, or contingency, as symmetrical. So if EI is true, we must drastically modify our modal intuitions to accommodate that fact. Contingency would be more like a fuse than a circuit breaker, i.e. the current flows in a fuse but once broken, a different fuse, which would be a counterpart to the first, is needed whereas the same circuit breaker can be flipped back to complete the circuit. When I consider myself as a contingent being, I think that I could blip in and out of existence, as a teleporter might be able to decompose me and bring me back into existence. Christian theists, in particular, should think that God has the omnipotence to bring the same individuals back into existence after they have ceased to exist. So, those committed to EI must suppose that individual entities are not symmetrically contingent, but only contingent in the sense that they actually exist and can cease to exist, but can never come back into existence again. If EI is metaphysically necessary, then it would be impossible for any individual to ever be resurrected, person or object.

Brass Tacks: it seems, if this argument is sound, that a commitment to EI will require one to abandon modal Axiom B. That is, if EI is necessarily true, φ → ☐♢φ fails as would systems of modal logic that depend on Axiom B, e.g. system B, which adds Axiom B to system M, S5 which adds Axiom B to system S4, among others.

Some Thoughts on Existential Inertia

P1. If x has existential inertia, then necessarily, the actuality of x is not grounded in some actuality extrinsic to x.

P2. If x is symmetrically contingent and exists in the actual world, @, then there is a possible world where x does not exist and accessibility relations are such that x possibly exists in @.

P3. If necessarily the actuality of x is not grounded in some actuality extrinsic to x, then it is not the case that there is a possible world where x does not exist and accessibility relations are such that x possibly exists in @.

C1. If it is not the case that there is a possible world where x does not exist and accessibility relations are such that x possibly exists in @, then it is not the case that x is symmetrically contingent (P2 Transposition)

C2. If necessarily the actuality of x is not grounded in some extrinsic reality, then it is not the case that x is symmetrically contingent. (P3,C1 HS)

C3. If x has existential inertia, then it is not the case that x is symmetrically contingent. (P1,C2 HS).

P4. All contingent things that actually exist are things that are symmetrically contingent.

C5. No thing that actually exists and has existential inertia is a thing that is symmetrically contingent. (C3 Semantic Equivalence)

C6. No contingent thing that actually exists is a thing that has existential inertia. (P4,C5 Modus Camestres)

I am thinking about this argument. A defense of the premises would need to be made, but I think they are intuitively true.

The Cephas/Caiaphas Theory

Return of the Ontological Argument — Steven Nemes and Daniel Vecchio

The Possibility of God and Impossibility of Parodies

Cx ≝ x is complex
Gxy ≝ x is greater than y
©… ≝ it is conceivable that…
g ≝ (ɿx)~©(∃y)Gyx
Axiom M: ☐p ⊃ p

1. ~♢(∃x)(x = g) ⊃ ☐(∀x)©(∃y)Gyx (premise)
2. (∀x)(©(∃y)Gyx ≡ ©Cx) (premise)
3. (∀x)©Cx ⊃ ~(∃x)©~Cx (premise)
4. (∃x)©~Cx (premise)
5. ~~(∃x)©~Cx (4 DN)
6. ~(∀x)©Cx (3,5 MT)
7. (∃x)~©Cx (6 QN)
8. ~©Cμ (7 EI)
9. (∀x)(©(∃y)Gyx ⊃ ©Cx) ∧ (∀x)(©Cx ⊃ ©(∃y)Gyx) (1 Equiv)
10. (∀x)(©(∃y)Gyx ⊃ ©Cx) (9 Simp)
11. ©(∃y)Gyμ ⊃ ©Cμ (10 UI)
12. ~©(∃y)Gyμ(8,11 MT)
13. (∃x)~©(∃y)Gyx (12 EG)
14. ☐~(∃x)~©(∃y)Gyx ⊃ ~(∃x)~©(∃y)Gyx (Axiom M)
15. ~~(∃x)~©(∃y)Gyx ⊃ ~☐~(∃x)~©(∃y)Gyx (14 Contra)
16. (∃x)~©(∃y)Gyx ⊃ ~☐~(∃x)~©(∃y)Gyx (15 DN)
17. (∃x)~©(∃y)Gyx ⊃ ♢(∃x)~©(∃y)Gyx (16 ME)
18. ♢(∃x)~©(∃y)Gyx (13,17 MP)
19. ~~♢(∃x)~©(∃y)Gyx (18 DN)
20. ~☐~(∃x)~©(∃y)Gyx (19 MN)
21. ~☐(∀x)©(∃y)Gyx (20 QE)
22. ~~♢(∃x)(x = g) (1,21 MT)
23. ♢(∃x)(x = g) (22 DN)

Q.E.D. It is possible that there is the Anselmian God, i.e. that than which none greater can be conceived.

Ad (1): This premise tells us that if it is not possible that there is something that is the Anselmian God, then necessarily everything is such that a greater can be conceived. We might see this better by contraposition, i.e. the possibility that there is an x that is such that none greater can be conceived implies the possibility of the Anselmian God, so defined. Now, if the Anselmian God is not possible, it is hard to think anything that contains the Anselmian definition but adds parody elements to it (is island-like, is unicorn-like) would be possible. So the impossibility of the Anselmian God would necessarily mean everything is such that a greater can be conceived.

Ad (2): If something is such that a greater can be conceived, then it is conceivably complex. For, whatever is such that a greater can be conceived can, itself, be conceived to be greater through conceptual additions of various qualities and quantities, which is what is meant by conceivably complex. Likewise, if something is conceivably complex, then a greater can be conceived of it through conceptual additions of various qualities and quantities. Thus, this biconditional statement is true.

Ad (3): If everything is conceivably complex, then it is not the case that there is something that is conceivably not complex, i.e. something that is conceivably simple. That is, everything would be such that it could be conceived to have a more complex nature than it has. This is just what it would mean if everything is conceivably complex.

Ad (4) There is something that is conceivably not complex. That is, it cannot be conceived in such that it could be thought to be complex, viz. that which is essentially simple. The God of classical theism is conceived to be essentially simple, and so it is inconceivable that this God should be complex. To conceive of a complex God is to conceive of something essentially distinct from the God of classical theism. Surely the God of classical theism is an object of theological contemplation, so we must accept this premise.

NB: Parodies involve descriptions of individuals that are, in part, conceivably complex, i.e. unicorns, pizzas, lost islands, etc. They are necessarily conceivably complex in that they describe things that include the Anselmian description, i.e. they are those than which none greater can be conceived, at least in part. Thus, by the Anselmian definition, they are such that none greater can be conceived, while by (2) above, they are conceivably complex, e.g.. Anselmian + unicorn-like, and so a greater can be conceived than them. Thus, true parody is impossible.

The Real and the Non-Real



Rx ≝ x is real
R̅x ≝ x is non-real
Gxy ≝ x is greater than y
©… ≝ it is conceivable that…
g ≝ (ɿx)~©(∃y)Gyx

1. (∀x)(R̅x ⊃ ©(∃y)Gyx) (Premise)
2. (∀x)(Rx ∨ R̅x) (Premise)
3. R̅g (IP)
4. R̅g ⊃ ©(∃y)Gyg (1 UI)
5. ©(∃y)Gyg (3,4 MP)
6. (∃x){{~©(∃y)Gyx ∧ (∀z)[~©(∃y)Gyz ⊃ (z = x)]} ∧ ©(∃y)Gyx} (5 theory of descriptions)
7. (∃x){{(∀z)[~©(∃y)Gyz ⊃ (z = x)] ∧ ~©(∃y)Gyx} ∧ ©(∃y)Gyx} (6 Comm)
8. (∃x){(∀z)[~©(∃y)Gyz ⊃ (z = x) ∧ {~©(∃y)Gyx ∧ ©(∃y)Gyx}} (7 Assoc)
9. (∀z)[~©(∃y)Gyz ⊃ (z = μ) ∧ {~©(∃y)Gyμ ∧ ©(∃y)Gyμ} (8 EI)
10. ~©(∃y)Gyμ ∧ ©(∃y)Gyμ (9 Simp)
11. ~R̅g (3-10 IP)
12. Rg ∨ R̅g (2 UI)
13. Rg (11,12 DS)

Q.E.D.

Ad (1):

If some x is non-real, then we can conceive of something greater than x, viz. some counterpart to x which shares the same description except is real rather than non-real. Since the real has causal powers that non-real object lack, the description of x would include causally effective properties, and so would necessarily be metaphysically greater, where “greater” mean “of greater power” or “of greater capacity”.

Ad (2):
R and R̅ are class complements, and so this is a perfect dichotomy. Thus the disjunction between the two is necessarily exhaustive of our universe of discourse.

Either/Or OA

Here is a variation on an ontological argument:

P1. If a thing is fictional, then it is conceivable that there is something greater than it.
P2. If there is the Anselmian God, i.e. the being than which none greater can be conceived, then it is either fictional or non-fictional.
C. The Anselmian God is non-fictional

Ad (P1): That which is fictional is a creation of the imagination. The imagination is capable of adding more to the fiction, making it greater as a fictional object. For example, Miles Morales has all of the powers Peter Parker has, plus the ability to camouflage and “venom strike” opponents.

Moreover, one could conceive of a fictional object as something real, which is often the very aim of fiction, i.e. to imagine the fiction as real for entertainment purposes. To have all of the same properties as a fictional object, but to have them in reality is greater.

Ad (P2): This premise claims that if there is an Anselmian God, i.e. if such a thing is within our universe of discourse, then the Anselmian God must either be fictional or non-fictional. As fictional and non-fictional are class complements, such a division would be exhaustive of all items within the universe of discourse, including the Anselmian God.

Fx ≝ x is fictional
F̅x ≝ x is non-fictional
Gxy ≝ x is greater than y
©… ≝ it is conceivable that…
g ≝ (ɿx)~©(∃y)Gyx

1. (∀x)(Fx ⊃ ©(∃y)Gyx) (Premise)
2. (∃x)(x = g) ⊃ (Fg ∨ F̅g) (Premise)
3. Fg (IP)
4. Fg ⊃ ©(∃y)Gyg (1 UI)
5. ©(∃y)Gyg (3,4 MP)
6. (∃x){{~©(∃y)Gyx ∧ (∀z)[~©(∃y)Gyz ⊃ (z = x)]} ∧ ©(∃y)Gyx} (5 theory of descriptions)
7. (∃x){{(∀z)[~©(∃y)Gyz ⊃ (z = x)] ∧ ~©(∃y)Gyx} ∧ ©(∃y)Gyx} (6 Comm)
8. (∃x){(∀z)[~©(∃y)Gyz ⊃ (z = x) ∧ {~©(∃y)Gyx ∧ ©(∃y)Gyx}} (7 Assoc)
9. (∀z)[~©(∃y)Gyz ⊃ (z = μ) ∧ {~©(∃y)Gyμ ∧ ©(∃y)Gyμ} (8 EI)
10. ~©(∃y)Gyμ ∧ ©(∃y)Gyμ (9 Simp)
11. ~Fg (3-10 IP)
12. ~(∃x)(x = g) (IP)
13. (∀x)~(x = g) (12 UI)
14. ~(g = g) (13 UI)
15. (∀x)(x = x) (IR)
16. (g = g) (15 UI)
17. (g = g) ∧ ~(g = g) (14,16 Conj)
18. ~~(∃x)(x = g) (12-17 IP)
19. (∃x)(x = g) (18 DN)
20. Fg ∨ F̅g (2,19 MP)
21. F̅g (11,20 DS)

Q.E.D.

Note: At step 15, I use the Identity Rule to generate a contradiction, so that I can infer (∃x)(x = g). For some, this might appear to be illicit, as though I have conjured an existence claim about the Anselmian God out of thin air. I contend that (∃x)(x = g) does not carry robust existential import. It does not mean that the Anselmian God exists in reality, in actuality, or in any other more robust sense of “to exist”. Rather, this merely establishes that “g” is set within our universe of discourse. And, of course, “g” is within our universe of discourse, as are many fictional, abstract, and perhaps even impossible objects. Hence, I adopt something of a “Free Logic” stance with respect to the “existential operator”. It does not indicate the existence of an individual in reality, but within the universe of discourse. If the universe of discourse is maximal, then it includes non-real objects, and so the argument does not beg the question. This is the appropriate way to understand the logic of this argument. A strong existential claim about the Anselmian God only occurs, then, when one reaches the conclusion that the Anselmian God is part of the universe of discourse that is non-fictional.