We miss the deepest fundamental level of logic when we treat the 3 laws of thought as separate axioms.
We can mathematically describe the structure of logic as 3 coinherent fundamental laws. In mathematics this is called a holism.
The Trinity shares the identical mathematical structure. In mathematics this is called an isomorphism.
Attempts to make logical sense of the Trinity by way of the transitivity of identity is a category error. The relationship of the 3 laws themselves cannot be understood transitively. They are prior to and sit below classical principles.
The objective structure of logic sits at the ontological foundation, the level of holism. It is objective because it contains the minimum number of perspectives necessary to triangulate coherently and reliably verify truth. It does so not as a linear process by way of transitivity, but simultaneously.
The attempt to examine the structure by reduction is transitive, redundant, and assumes the exact holistic structure needed for verity.
This changes things.
Because we can discern the structure of logic as fundamentally Trinitarian, and can describe it mathematically, we can do the same for the Trinity. No more appeals to mystery. Its not a paradox. It is deeply logical.
Jesus gave us the information necessary. We just didnât have the mathematics or the correct understanding of the 3 laws. John testified that God is the Logos.
The Word has been so imminent and in our mouths that we couldnât see it. Clark, Van Til, Frame, and Poythress got us very close.
Test it and let it settle in. Logic is not a series of independent axioms any more than the Trinity is 3 Gods. They are one. They are the same structure because He IS the Logos.
You likely have questions and objections as you process this and adjust your vision. I have anticipated some of them. Subjective systems like intuitionistic and paraconsistent logics do not escape the objectivity of the 3 fundamental laws. They cannot produce a specific output without them.
Below is the python script for the mathematics of logic and the Trinity as a holism. The formatting here distorts the code slightly for some reason. But every Ai should be able to recognize and autocorrect it without difficulty. Just copy and paste:
import numpy as np
Define the shared Relational Matrix
A = np.array([
[0, 1, 1, 1],
[1, 0, -1, -1],
[1, -1, 0, -1],
$$
1, -1, -1, 0
$$
], dtype=float)
Extract the isolated peripheral submatrix (Center removed)
A_isolated = A[1:, 1:]
print(f"1:1 Structural Isomorphism Verified: {np.array_equal(A, A.T)}â)
print(f"Full System Spectrum: {np.sort(np.linalg.eigvalsh(A))}â)
print(f"Isolated Submatrix Spectrum: {np.sort(np.linalg.eigvalsh(A_isolated))}â)
print(f"Full System Determinant: {round(np.linalg.det(A))}â)
print(f"Isolated Submatrix Determinant: {round(np.linalg.det(A_isolated))}")