// a spatial meditation on formal logic
論理
Three axioms. Three axes. One emergent truth.
XY
The Foundation — three axioms anchor the plane.
If a thing is, it is itself.
∀x. x = x
A thing cannot both be and not be in the same respect.
¬(p ∧ ¬p)
Either a thing is, or it is not — no third.
p ∨ ¬p
XZ
The Extension — propositions multiply along Z; inference draws its line.
All ravens are black.
This bird is a raven.
Therefore this bird is black.
∴ q
Modus ponens preserves truth across implication.
p, p→q ⊢ q
Inference is a line traced through the space of propositions.
A chain holds only as long as its weakest link.
⟨p→q→r⟩
YZ
The Depth — premises near, conclusions far. Foreshortened reasoning.
Premise: things have natures.
A nature determines what is possible for the thing.
What is necessary cannot fail to be.
□p → p
Conclusion: the necessary defines the contour of the actual.
∴ □p ⊨ p
(0, 0, 0)
CONVERGENCE
Where the three axes meet, an emergent truth resides — visible only from this single point.
∀x ∈ X ∀y ∈ Y ∀z ∈ Z → (x ∧ y ∧ z) ⊨ 論理