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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:


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)


Physicalism v. Hylomorphism


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.

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.