marte's 𝟙-Object argument for God
most arguments for God's existence, as far as I'm aware, are birthed in metaphysics, cosmology, or modal logic (which to its credit, I have formed arguments with as well). however, one day, in the shower, I asked myself, does the category of all positive beings have a terminal object? if it does, then category theory is hiding a precise, universal, and mathematical way to talk about a "God-like" being, not because of theology or religion, but because of how structure itself literally behaves.
let 𝓟 = (Obj(𝓟), Hom(𝓟)) be a category
axioms:
A1. (positivity objects)
∀𝑋 ∈ Obj(𝓟), 𝑋 is a maximally consistent set of instantiated positive properties
A2. (morphisms preserve positivity)
∀X,Y ∈ Obj(𝓟), ∀f ∈ Hom(X,Y), f is a structure-preserving map:
f: X → Y ⇨ ∀p ∈ X, p ∈ Y and p retains positivity
A3. (well-formed category)
𝓟 satisfies:
a ∀X ∈ Obj(𝓟), idₓ ∈ Hom(X,X)
b ∀f: X → Y, g: Y → Z, g ∘ f ∈ Hom(X,Z)
c composition is associative
A4. (terminal object postulate)
∃𝔾 ∈ Obj(𝓟) such that ∀X ∈ Obj(𝓟), ∃! f: X → 𝔾
if my axioms A1–A4 hold, then:
∃! 𝔾 ∈ Obj(𝓟) such that ∀X ∈ Obj(𝓟), ∃! f: X → 𝔾
proof sketch: by A4, 𝔾 exists and satisfies the universal mapping condition. in category theory, terminal objects are unique up to isomorphism: ∀𝔾₁, 𝔾₂ terminal ⇒ 𝔾₁ ≅ 𝔾₂ hence, ∃! such 𝔾
if it makes sense to talk about positive beings in this kind of network, and if that network has a terminal object, then there must exist one uniquely perfect being, which everything else including me & you, is just a shadow or reflection of.