There is a visual here that is helpful. And it provides the mathematical description of holism that the formal proof cannot provide.
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Your’re right about the 3 laws being foundational. Since I currently don’t possess the knowledge for that I’ll have to take the word of experts.
The other logics are variants that apply to specific domains. Schrodinger logic is a for electrons that lack identity.
The holy trinity is illogical. Newton, presumably a very logical man, rejected it. He was a unitarian. The idea had many opponents, all of them silenced in typical orthodox fashion i.e. my way or the highway.
It seems Frege and Wittgenstein were of the opinion that A = A is a tautology. AI says it’s got to do with, inter alia, equivocation. Wikipedia says the exact opposite. The first to formulate A = A was medieval scholar Antonius Andres - sparked off a debate on which, A = A or the LNC, was prior. You seem to derive the 3 laws from each other, which I’ve alreay copied to my notes. Thanks.
Aristotle thought the answer to, “why is a man a man?” is “a man is a man”. To him the question is dubious. He never got around to A = A.
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Scorpion, your comprehension of the laws as fundamental is important. That is recognizing logic in its most basic form as ontological.
The point of holism is how to coherently understand the 3 in one structure. The three laws aren’t derived one from another in a linear chain. They mutually indwell each other simultaneously, each already containing the other two.
That’s the holism. I don’t blame Newton or the Orthodox theologians for struggling with the Trinity. They were working with Greek abstract categories and trying to force a formal proof onto the very laws that make any formal system possible in the first place. That results in the circular or tautological flavor you’re seeing.
Only when we see logic itself as this simultaneous, indivisible structure does the Trinity become visible as logical in the same ontological sense.
The 4x4 matrix in the BioLogos thread shows that relational symmetry directly.
Logic is a fundamental relationship of 3 laws in precisely the same way as the persons of the Trinity. So to say the Trinity is illogical is to say that logic is illogical.
The reason Newton and pretty much everyone else struggled with understanding the Trinity, is because we never really understood logic.
The real shock for me was discovering that the Trinitarian relationship could be described mathematically as a holism and as totally and fundamentally logically coherent.
Agree or not, do you understand my position now?
A little bit, not that much. It definitely is a novel idea that I haven’t encountered before.
It has a long history, the 3 laws, and it seems Antonius Andreas’ formulation A = A was some kind of a breakthrough. Leibniz seems to have attempted to bring some clarity to the issue. I guess those days communication wasn’t easy, being mostly snail mail.
I have to concur that the derivations aren’t as important as the co-inherency of the 3 laws.
The 3 laws perfectly relate to the holy trinity. The 3-ness kind of jumps out at us. We then triangulate to the truth, as you so correctly laid out.
Schrodinger logic is about electrons. They all look alike. This isn’t due to experimental conditions that one might think of. Intriguingly you could put electrons at the 3 corners of your trinity and still get the same result. Just a hunch of mine.
Paraconsistent logic seems to appear in computer systems. The domain is inconsistent databases.
Polyvalent logic comes into play when a 3rd truth value is posited. The one I’m familiar with is U, for unknown. It’s fascinating but I only got a brief glimpse. You seem familiar with the system. I’m sure you’ll get more out of it than I ever can.
Peace upon you Rob.
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Scorpion, I appreciate you engaging this and seeing the co-inherency point.
It can feel new at first—I’ve been sitting with it for months myself. But we’ve actually encountered this structure before; we just didn’t recognize it.
The prologue of John’s gospel lays it out: “In the beginning was the Word (Logos), and the Word was with God, and the Word was God. He was with God in the beginning. Through him all things were made.”
The Logos isn’t an extra idea added later. it’s the same simultaneous, mutual-indwelling structure we’ve been mapping in the laws. John simply recognized the Logos as personal rather than abstract as in the Greek paradigm.
Take your time with it. If questions or thoughts come up, feel free to hit me up.
Truth be told, I’ve been sitting with it since the early 2000s, that’s roughly 2 decades. On and off, on and off. Your post was very helpful. Thanks.
It isn’t clear what else you want to do with your wonderful discovery. It’s got that hang-me-on-your-wall vibe. I can see it as an ice breaker with your guests. You can talk about the father, the son, and the holy spirit and how they’re synced to the LI, LNC, LEM. The father-son and holy spirit will certainly bless you with whatever you desire, Rob.
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Same. I’m 56 years old and have been chasing this rabbit since my conversion at age 30.
Glad it is a help.
Its actually of great practical import. This is a true paradigm shift in logic, philosophy, theology, and even physics. Old paradoxes melt away. And some materialists will not be happy about it either.
As you sit with it, and if it fully resolves in your own mind, you’ll begin to see what I mean. But for now, your perception adjustment will be a little disorienting. You’ll find your mind flipping back and forth from the old paradigm to the new, like one of those optical illusions with overlapping images. Ask me how I know…
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56 and you’ve learned so much!? 
I’m thereabouts but my body feels 70ish. I’ve seen world leaders age during their term in office. Not the supreme leader of NK though. He maintains his cherubic features. Must be the peace and tranquility that he brings to his people. 
Indeed some flipping and flopping has already happened and is happening with me. I studied the trinity in my spare time and realized it’s nonsense but I still held onto it because it makes sense in a curious, cultish, kind of way. It’s one of those problems Einstein would’ve grabbed at … to solve. As a materialist I look up to Einstein who was a determinist or at least had to be. Did you know Einstein was friends with Godel. Godel was a genius par excellence, but he developed a poisoning paranoia and left for his heavenly abode from starvation. 
I was not aware that Einstein knew Gödel but I’m not surprised. That era was a marvel of individuals free to think outside of the box. That’s why so much changed during that time. You can’t make new discoveries when you’re not allowed to threaten the paradigm.
I’m just a truck driver, so nobody cares what I think anyway. If I appear to be going off the deep end, its almost a prerequisite for the profession. Hours of time to think and listen to lectures away from the prying eyes of micromanagers.
Yes. Einstein would have loved this. But he was more of a Spinoza theist and he almost certainly felt there was nothing to see here. But this Trinity business does require an intuitive grasp first. Everything in the current paradigm of philosophy is set against it. In that sense it is foreign to accepted conventions. Its dismissed out of hand.
Think of the challenge Galileo faced. His own Christian establishment resisted hard. Paradigm shifts are difficult.
That may sound like hyperbole and megolomania on my part. Its not. Its apocalyptic in the true sense of an ‘unveiling’. Its a process Jesus started a very long time ago. It was HIS revelation.
He gave us the coordinates to understand it. We just didn’t fully perceive the laws and notice their Trinitarian relationship. And we wouldn’t have matrix algebra for another 1900 years.
The church was often too heavy handed, and that hindered discovery. But they also held the doctrine on intuition. It was non-negotiable because the source was Jesus’s own lips. Overprotection preserved the coordinates. It just meant professional clergy weren’t free to risk heresy and explore.
But ‘weirdos’ can! 
Glad you found your channel. I try broadcasting on all frequencies so to speak 
.
You didn’t know Einstein and Gödel were friends? 
He used to say he looked forward with the utmost joy to walk Gödel to his home. I think they were in Princeton those days.
Nuff said about Einstein.
Galileo was another great man. He looked up at the starry heavens and discovered something that made the vicarius christi (the pope) very agitated. Flipped an old, dusty, but institutionally or otherwise inherited switch on inside the Pope’s head. The rest is history.
Explore? Some peeps like a quiet life in a log cabin up in the mountains somewhere … far from the hustle and bustle of urbanity. There’s probably the occasional outing with family and friends. It’s difficult to triangulate but we can make educated guesses. It’s weird but my hunch is it gets weirder.
There is a lot I don’t know. My interest has never been primarily about collecting knowledge, but how to make sense of the knowledge.
I was a conversationalist early, asking philosophical questions before I knew the term ‘philosophy’. And I love debates, especially with people who I don’t agree with.
The debates helped direct my research. I didn’t waste time with what wasn’t relevant at the moment. But as my worldview picture widens, other areas become relevant and therefore interesting.
That particular information about Einstein never crossed my path until now.
I get plenty of solitude and time to meditate. And since I believe that God is the Logos, thinking often becomes indistinguishable from prayer.
There is an interesting complexity to thought, as if there is more than one voice in my head. That mystery of consciousness is not any more or less baffling than the Trinity itself.
Letting go and allowing the mind to open is exhilarating and terrifying. It can have a Dark Side of the Moon vibe.
Maybe the real difficulty has always been in recognizing the source of some ideas? I find our minds are entangled with other ‘beings’. All thoughts SEEM to originate from within my own mind, but DO they?
To even ask the question is more exploration than some desire, because that’s a REAL adventure that requires giving up the illusion of control.
Further reading if you’re interested. Covers some of the practical considerations and explanatory power.
A persistent error in logical calculus is the attempt to isolate, prioritize, or formally “prove” the three fundamental laws of classical propositional logic. Such attempts commit a fatal circularity, as any deductive calculus must implicitly smuggle in the laws to validate its own operational steps.
Through standard material implication, commutation, double negation, and De Morgan’s laws, any one of these expressions can be syntactically transformed into the other two without loss of semantic content.
This is in the OP.
To state, utilize, or presuppose one law is to structurally invoke the entirety of the triad. This internal symmetry behaves as a conceptual perichoresi, a mutual indwelling of distinct yet inseparable principles. Logic is fundamentally a holism; it cannot be reduced to standalone, modular building blocks.
This is acceptable
Do you maintain a distinction between LI, LNC, LEM? The holy trinity does. Also I’m not comfortable with the way you relate the 3 laws to the holy trinity. A clearer way to do that is in order.
I’m blown over by how you talk about the QM potentiality in the wave function and "The earth was without form and void and darkness was over the deep. The spirit of god was hovering over the surface of the waters?
That just it. The distinctions are real. Each law represents a unique perspective or operation. Yet they are one.
The move from abstract laws to persons is an excellent observation and question. Its the difference between structure and essence. Persons are not laws.
I’ve thought a lot about this. We need to work through it…
Firstly, in stating it the way I just did, notice we’re treating the 3 fundamental laws of thought as abstract and impersonal. Its the millenia old habit of the Greek paradigm we’ve accepted. We end up doing philosophy with a disposition ‘acting’ as if we’re computers.
We’re not. We’re persons. And in our attempt to be objective and ‘logical’ we inadvertently block out the obvious.
Thought is not impersonal. Rocks don’t do logic. Animals do, but I suspect (I do not know) that they are more computer or Ai-like, creatures of instinct. Minds like ours are conscious in a way few would argue is not utterly unique.
If that is the actual case, then these laws are necessarily personal and essential to consciousness, not just intelligence.
Secondly, the same apostle who tells us that God is Logos, also tells us God is love. And thats worth exploring…
Logic and love share the same Trinitarian structure. I contend they are two sides of the same coin. Our consciousness is able to reason about abstract entities like atoms, but our reasoning must be ‘truthful’. In other words, MORAL reasoning is both logical and honest.
Jesus did not give us the law of non-contradiction as a Greek philosopher. He incorporated it with the personal dimension as a ‘truth claim’.
Matthew 5:37 Let your logos be yes yes, or no no. Anything more comes from the evil one.
(more on that)
He was pointing back to the original deception and contradiction. It was when the serpent suggested we could attain God’s omniscient knowledge via direct empirical experience and sense perception (touch, sight, taste, etc).
Genesis 3 might use Hebrew vocabulary, but the philosophy of empiricism is plain to see. Its an epistemology lesson.
Empirical data and sense perception imparts zero knowledge. The data must be interpreted LOGICALLY.
Logos (God’s Word) is the “true light that gives light to everyone” John 1. Our true epistemological food and drink is Logos.
So, the serpent used WORDS to suggest the empirical was the way to acquire autonomy and all knowledge. Its a flat contradiction.
Back to the structure…
The Triune structure is the same from abstract to personal. There is no separation between logic and love. Real love is always truthful. The real complexity in logic isn’t differential algebraic equations. It’s in whether or not to tell the truth and how MUCH of that truth to reveal.
Finally, the coordinates for the Trinitarian structure were not arrived at mathematically. They were communicated by a 1st century Jewish carpenter who claimed to BE the truth who came from heaven from the Father.
Once we could intuit the structure logically, we could then seek to model it mathematically. The insight is top down from the personal dimensions.
That is the only way I can presently see to bridge the apparent gap. The essence or substance of a multipersonal eternal being who transends physicality and created it is beyond me. I can’t even comprehend a single biological cell.
But if Jesus is who he claimed to be (as I believe). He revealed the structure of his essence in a way he created us to comprehend. And that is logically.
What’s more, the mathematics that reveal the structure show it as scale invarient. In other words, God’s essential Trinitarian nature (or shape) does not change from alpha to omega.
Its like when we first learn basic arithmetic. The light comes on and suddenly we know math! And though we have barely begun to understand math, we really do ‘get it’. Math doesn’t change shape. It simply adds dimensions and complexity.
See how easy this is if we just slow WAY down and observe the simple and foolish things carefully?
I guess so. The 3 laws are co-inherent, just as the 3 persons are. The Father \ne The son \ne The holy spirit is truthful in that LEM \ne LI \ne LNC.
True also that God = Love. Also, God = The ground of all being and that God = Infinity.
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As far as QM and Genesis 1:1-2, what surprises me is that no one seems to notice the obvious!
Einstein rightly mocked the idea that human consciousness was necessary to collapse the wave function. But there is a real difficulty in separating conscious observation from collapse.
There is even a question designed to illustrate the problem. “If a tree falls in the forest and no one is around to hear it, does it make a sound?”
The question rules out the possibility of an omnipresent observer. It assumes human consciousness is the ONLY consciousness. Einstein was doing the same thing.
There are no laws, rules, or ideas, that are “self-evident”. No truth stands without justification. Self-evidence is just a cop-out, used when we don’t want to admit that an idea, possibly a deeply reverenced one, is unjustified or unjustifiable. We use “axiom” for a similar purpose, I think.
What’s so very bad about just admitting honestly what we’re doing? Is it really so bad to say “I don’t really know that this is true, but it seems so to me, and so I suggest that we proceed as if it was true…”?
I think (?) the three ‘laws’ that you mention come under this 
category?
The 3 laws are necessarily fundamental and ‘self revealing’ ( that’s more suggestive than ‘self evident’) if we bother to look.
You just identified, distinguished and excluded in your own comment. The quote you referenced did the same.
If it REALLY boils down to ‘just admitting that we don’t know’, then I agree we are not omniscient and must live by faith.
And since we’re all using the same 3 laws to express and justify our beliefs, your denial of the laws rests on the same justification of the laws. We’re in the same boat, friend.
The laws are simultaneously present in every thought and spoken word, identifying, distinguishing, and excluding. They provide what is essential precisely so that we CAN understand.
The 3 provide the minimum number of perspectives/witnesses/variables to triangulate and verify objectively.
That is itself a law… “No testimony is valid unless it is in the presence of at least two or three witnesses.”
Why?
6×i=u
We can’t ‘know’ anything apart from triangulation.
I have to agree with what you say. The point is that these 3 laws are foundational to discourse. That’s what I’ve gleaned from the discussion. These laws aren’t pulled out of a magician’s hat.
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Oh no, not “denial”. If anything, I question the use of the term “laws” to describe them. Laws implies authority, justified authority, so it might look to some like an attempt to bolster something that can’t be justified at all.
A while ago, I read of one theory-of-everything idea whereby the universe is remade, recreated, every instant. That there is no historical/temporal continuity. I don’t subscribe to this theory, but I would hesitate to say that it is wrong. At least, not without something to back up my assertion(s). Maybe a bit of evidence?
The laws you refer to lack any sort or form of justification, yes? Except that they seem “self-evident” to some, yes?