¿Ayudaría la lógica matemática a demostrar la existencia de Dios?

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Attempts to prove the existence (or non-existence) of God by means of abstract ontological
arguments are an old tradition in philosophy and theology. G¨odel’s proof [12,13] is a modern
culmination of this tradition, following particularly the footsteps of Leibniz. G¨odel defines God
as a being who possesses all positive properties. He does not extensively discuss what positive
properties are, but instead he states a few reasonable (but debatable) axioms that they should
satisfy. Various slightly different versions of axioms and definitions have been considered by G¨odel
and by several philosophers who commented on his proof (cf. [19,2,11,1,10]).
Dana Scott’s version of G¨odel’s proof [18] employs the following axioms (A), definitions (D),
corollaries (C) and theorems (T), and it proceeds in the following order:3
A1 Either a property or its negation is positive, but not both: ∀φ[P(¬φ) ↔ ¬P(φ)]
A2 A property necessarily implied
by a positive property is positive: ∀φ∀ψ[(P(φ) ∧ ∀x[φ(x) → ψ(x)]) → P(ψ)]
T1 Positive properties are possibly exemplified: ∀ϕ[P(ϕ) → ♦∃xϕ(x)]
D1 A God-like being possesses all positive properties: G(x) ↔ ∀φ[P(φ) → φ(x)]
A3 The property of being God-like is positive: P(G)
C Possibly, God exists: ♦∃xG(x)
A4 Positive properties are necessarily positive: ∀φ[P(φ) →  P(φ)]
D2 An essence of an individual is
a property possessed by it and
necessarily implying any of its properties: φ ess. x ↔ φ(x)∧ ∀ψ(ψ(x) → ∀y(φ(y) → ψ(y)))
T2 Being God-like is an essence of any God-like being: ∀x[G(x) → G ess. x]
D3 Necessary existence of an individual is
the necessary exemplification of all its essences: NE(x) ↔ ∀φ[φ ess. x → ∃yφ(y)]
A5 Necessary existence is a positive property: P(NE)
T3 Necessarily, God exists: ∃xG(x)

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