The 3 Laws of Logic as an Ontological Mathematical Holism

Faith & Science Conversation
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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. As some of you know, 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 on the transitive level is a category error. The relationship of the 3 laws themselves cannot be understood transitively. Logic itself is illogical on the transitive level.

The objective fundamental structure of logic is found at the foundation, the level of holism. It is objective because it contains the minimum number of variables to verify coherence and truth.

To attempt to examine the structural verity by reduction is transitive, redundant, and assumes the exact holistic structure needed for verity.

Brothers, this changes things.

Because we can discern the structure of logic as fundamentally logical 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 didn’t have the mathematics or the understanding of the 3 laws as Trinitarian. John testified that God is the Logos. The Word has been SO imminent and in our mouths and in our hearts, we couldn’t see it. Clark, Van Til, and Poythress got us very close.

You must test it as I have 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 should have a lot of questions and reasonable objections as you process this and adjust your vision. I believe I have already anticipated and can answer them all.

This is not a drill… check the Math. Where’s Bill Dembski?

I have also made a simple 2min and 36second video with all the information and code in the description https://youtu.be/HbV_TFVi7y0?si=LWA5cG7elBn08hok

Below is the python code 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)}“)
print(f"Full System Spectrum: {np.sort(np.linalg.eigvalsh(A))}”)
print(f"Isolated Submatrix Spectrum: {np.sort(np.linalg.eigvalsh(A_isolated))}“)
print(f"Full System Determinant: {round(np.linalg.det(A))}”)
print(f"Isolated Submatrix Determinant: {round(np.linalg.det(A_isolated))}")

$$

$$

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It seems that your approach reflects the western tradition of Christianity.
In the west, philosophical theology has focused on such questions as what are the characteristics of a perfect being or God. The often used triangle of Trinity that you presented tries to summarize the western philosophical approach.

The eastern tradition focuses more on persons, rather than their characteristics. The triangle of Trinity according to the eastern tradition looks somewhat different. This difference explains why the word ‘filioque‘ became such an influential issue in the schism between the west and the east - it reflects differing approaches towards God. Differing mindsets.

Although I am a child of the western tradition, in the question of Trinity I lean more towards the eastern tradition - persons seem more important (basic) than philosophical speculations about their characteristics.

I feel I am not qualified to analyze your triangle of logic because I have not studied philosophy or the English terminology of such philosophy. I hope others can comment on that.

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Every sentence in your reply contains the 3 laws in order think and speak logically and therefore intelligibly. You need not be Eastern or Western to understand. You simply need to speak. Its recognizing the source of the speech that matters. Logos makes that possible, not you or me.

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I didn’t intend to create the impression of a division between persons and logical reasoning. In my view, logic is the love between persons in right relationship. The speech between the persons is not merely logic in the abstract philosophical sense, but logically coherent truth.

Matthew 5:37 But let your [Logos] be, Yea, yea; Nay, nay: and whatsoever is more than these is of the evil one.

Here Jesus adds the personal moral dimension to the law of non-contradiction. Its not limited to the abstract.

Persons can also speak of things like numbers in the abstract logical sense. But the abstract is downstream of personal truth and love.

It is also incorrect in my view that logic exists outside of God. The logical patterns in creation were imposed by His command and are sustained by His rational power.

The point of the OP is to demonstrate that the Trinity is DEEPLY logical on a fundamental level we failed to perceive. The Trinitarian relationship can even be described mathematically as a holism.

Its so obvious once you see it, its hard to believe we’ve missed it for 2000 years.

But there it is. This is not a drill…

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You have seen similarities between the old view of the ‘laws of logic’ (‘laws of thought’) and the Trinity. You see both as holistic concepts. Fine. But are logic and God comparable concepts or entities?

By turning the word ‘logic’ into ‘love’, you try to connect logic and the relationship between the persons. It is told that Jesus was full of mercy and truth (John 1:14). I might see a connection between logic and truth. Truth is only half of the equation. Love and mercy goes further than truth; love may forgive despite the truth, give mercy even when the logical consequence of our actions would be to let us reap what we sowed. If God would be only truth, would let everything to be dictated merely based on the logical consequences, we would not have much hope.

Your approach sounds fine and may give inspiration for thinking. Yet, you should consider the points I mentioned above, otherwise your equations may not capture the whole truth.

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I’ve checked the maths, and noticed that:

  1. you have used an array of floating point variables to hold integers, and
  2. your supposed verification of isomorphism only checks if your array is symmetrical. It has nothing to do with comparing logic and the trinity; you’ve already defined them as being identical.
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The relationship of the laws themselves determine the structure objectively and necessarily. It is not contrived or constructed ad hoc. This is discovery not invention. There is no other way to construct the mathematics.

It is not a way of framing logic. It is the only way. It is mathematical proof that logic is a holism.

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God very much forgives. But not at the expense of His law. He IS the law. They have no being as ‘laws of logic’ in some Platonic category floating in the universe. He took responsibility and satisfied the law, carrying through burder of the knowledge of good and evil in himself. He is the lamb slain ‘before the foundation of the world.’

Love and logic are one in the same. He IS the Logos. He IS love.

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There is. You could - and should - have 1s on the diagonal of the matrix.

Unless you think, for example, that the law of identity is not the law of identity.

Not that it really matters.

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Your trying to analyze a hollism transitively and making a category error.

The zeros on the diagonal are not a mistake. They are the entire point of the model.

If I put 1s on the diagonal, I would be saying “the Law of Identity is fully itself in isolation,” which is exactly the transitive/reductionist assumption this structure is not.

In this holistic model, no single law is the full structure of logic by itself. Its complete identity and coherence only exist in its coinherent relationship with the other two laws and the central unifying node (the zero). That’s why each peripheral node has a 0 on its diagonal: by itself, it is not the whole.

This mirrors the Trinity perfectly: Each Person is fully God, yet none is the Trinity in isolation. Their identity is predicative and coinherent.

So the matrix is not “wrong” by the standards of ordinary reflexive identity matrices. It is deliberately built to model a different (and deeper) kind of structure, a true holism where the relations themselves are constitutive of the identity of each element.

This is discovery, not invention. The structure is forced by the actual relationships Jesus described, not chosen for convenience. I didn’t construct the mathematics to build a bridge. The bridge was already there, and the math is reverse engineered.

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