Author Archives: Daniel Vecchio, PhD

Well, he didn’t


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)


Hempel’s Raven Paradox and God’s Existence

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


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].


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


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)


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


@… ≝ 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)


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.