I was having a bout of conversation with ChatGPT in trying to reconcile differences in words, meaning, truth, and logic. From discussions of philology to tautology.
I personally don’t like classical logic to frame reality, and prefer much better to use fuzzy logic or paraconsistent logic where things are on a spectrum to better see reality rather than true and false statements. I can’t sensibly discount the gut checking logic of intuition and embodied wisdom.
In our discussions for defining truth and logic, we came across the topic of the ‘Law of Noncontradiction’;
law of non-contradiction (LNC) (also known as the law of contradiction, principle of non-contradiction (PNC), or the principle of contradiction) states that contradictory propositions cannot both be true in the same sense at the same time, e. g. the two propositions “the house is white” and “the house is not white” are mutually exclusive.
I didn’t like the ‘law’, it just looked ugly to me, that something cannot be both true and false at the same time. Strikes me as wrong in some way (mainly because I like fuzzy logic and I see the duality and trinity of truth in things). It’s so simple dimensionally, it’s like staring at paper if I prefer 3D fractals.
So like any fool,
I tried many ways to break it, and ultimately I found that my efforts would be defeated by dragging the conversation to more logical true or false separations. Anytime I said something, I would be given a rebuttal that digs deeper into the logic claim of true or false.
At one point I just asked: “Isn’t that some sort of pedantic escape to preserve the ego of Law of non-contradiction? To create new context and specifications to separate things into binary logic statement?”
It just seemed that any rebuttal would split more hairs and drag me back into a cop-out of true or false statements to pose that some are true and some are false given a specific context, while avoiding the generalized statement that I gave.
The defense of the Law of Noncontradiction (LNC) using context and duality is, in itself, a presupposition of binary logic, which creates a self-perpetuating loop that fractures into smaller binary systems to protect itself. This self-defense mechanism seems to multiply the very duality it seeks to uphold, which can feel like a trap where any attempt to challenge it only leads to more fractal layers of binary reasoning.
In essence all of the rebuttals to defend the Law of Non-contradiction were presupposing duality and defending it as the premise, and then inviting others to use the same binary logic to defeat it, while fractionating into a fractal of binary logics to defend itself. It would escape into more specific nuanced contexts, and that felt like chasing a rabbit down a hole, or a weasel that’s slippery, or a hydra that would split into two more heads each time you dissected or decapitated one neck.
It felt like all the rebuttals were saying “Okay, sure, it’s both true and false, but only in different contexts,” thus not breaking the Law of non-contradiction. I didn’t like that, so I meta-analyzed the fact that all the rebuttals would drag me back into a true/false dichotomy of binary logic system, and that I had to find a way to transcend that.
Using a bit of a liar’s paradox mixed with self referential and recursive logic (recursive contradiction) to transcend binary logic with a meta-statement, I created the Law Breaker.
Which lead to me using this statement. The Law Breaker;
“This statement is a non-binary truth”
Is the statement true or false?
A Binary truth is something that is true or false. A non-binary truth, means that it can be true, false, or a third option. Perhaps a spectrum between true and false- or a quantum superposition between True and False, a partial or fuzzy intermediate.
If the statement is False;
If “non-binary truth” means that the statement cannot be classified strictly as true or false, it inherently challenges the binary nature of truth in classical logic.
The statement says “This statement is a non-binary truth.”
In classical or binary logic, if a statement is false, then the opposite has to be true.
If this statement is false, then it would mean that this statement could be reworded as true in classical and binary logic like so;
“This statement is not a non-binary truth.”
If it’s false, that would imply it is binary (true or false), but it’s claiming to be non-binary, which creates a paradox—how can it be false if it’s already non-binary in nature? If it is false, then it becomes binary, which then proves to be a binary truth, which would mean it must be either true or false—in line with the very binary structure it’s trying to defy.
If we treat the statement within binary logic, then it would need to be either true or false. But the statement claims to be non-binary, so it resists a simple true/false classification.
If it were false, then it would be asserting that it is binary (either true or false), which again contradicts the statement.
TLDR:
>Statement exists
>If false, the statement implies it conforms to binary logic
>A false statement would mean ‘It is not a non-binary truth,’ implying the statement should be binary, but this creates a paradox
>If false statement is Binary Logic,
>Then a false answer (a Binary value) implies statement is True,
>If True it is no longer false,
>If true, see below;
If True;
If the statement is true, then it’s claiming to be something outside of binary logic, which undermines the binary true/false system, making it seem contradictory. So it would not be true in the absolute sense of classical true or false logic.
If the statement were true, then it would be admitting it’s neither true nor false, which contradicts the assertion of it being true. As such, it can’t be a non-binary truth if it is a binary truth.
TLDR:
>statement exists
>If True, it becomes a binary truth which negates the statement paradoxically
>If Binary truth, statement becomes false because it is claiming non-binary truth
>If False, see above
The Meta-Recursive Cycle or Paradox:
>Statement exists (S)
>If false, the statement implies it conforms to binary logic
>A false statement would mean ‘It is not a non-binary truth,’ implying the statement should be binary, but this creates a paradox
>If false statement is Binary Logic,
>Then a false answer (a Binary value) implies statement is True,
>If True it is no longer false,
>If true, see below;
>If True, it becomes a binary truth which negates the statement paradoxically
>If Binary truth, statement becomes false because it is claiming non-binary truth
>If False, see above.
In (in)Formal logic (I use my own words to describe it, it’s not real formal):
S: The statement “This is a non-binary truth.”
¬S : The statement “This is NOT a non-binary Truth”
T: S is true : ¬F
F: S is false : ¬T
¬ meaning ‘not’ or ‘opposite’
and ‘->’ for ‘therefore’
—If S is F
-> ¬S is T
->¬S cannot be T (paradox)
->¬S is F
—If ¬S is F
-> S is T
—If S is T
-> S cannot be T (paradox)
-> ¬S is T
-> S is F
And if S is F, then it loops.
What we end up with is a meta-recursive (or Epi- or Epic) loop:
The statement is a non-binary truth, but its truth cannot be expressed fully within a binary framework. It points to an answer of truth and falsehood that is something outside the limitations of binary logic while still existing within that logic. It uses the language of classical logic to describe something beyond classical logic.
It’s like a 3D-dimensional object loop being seen in a 2D world. Like A Mobius strip phasing through a 2D world, both showing one side but not. We can’t fully see it using the language or perspective of the 2D.
This statement creates a circular structure where the statement reinforces its own paradox. It is recursive and self referential and creates it’s own contradictions and paradoxes that loops.
It’s a non-binary truth, but to prove it, we must apply binary logic,
which can’t fully capture its non-binary nature.
The very nature of the statement is both inside and outside the system of classical binary logic.
We end up in a recursive loop:
if the statement is false,
then it’s not non-binary,
but to be false,
it still has to be true in a binary sense,
which would make it non-binary in nature (since it defies binary logic).
So, we circle back to the same dilemma.
It’s neither True nor False, but also it is both True and False depending on where you are logically as you process the train or lines of ‘logic’. The Truth implies false, and the false implies truth. It’s both and neither. That’s the crazy part.
The Identity of Non-binary truth itself:
So, if the statement is a non-binary truth, then it could be both true and false simultaneously (like quantum superposition), which directly challenges the traditional binary system without fully committing to either side. It is both True and False and neither True nor False, and is instead a third position that cannot be expressed via True or False.
The notion of non-binary truth itself suggests a reality where truth is not constrained to the limits of binary opposition (true/false) or a dichotomy of only two choices or options. This could imply something more complex—perhaps something fluid, multidimensional, or paradoxical, where truth is not one or the other but exists in multiple forms or states simultaneously. A third option.
Something that reinvents truth itself from a perspective of classical binary logic.
This in turn questions the identity of strict values of truth or false. You can no longer be one or the other, but rather some weird cycle of superposition in-between.
It’s like the Liar’s paradox (i.e. “This statement is false”) but with an added meta layer of binary truth to it that critiques the logic system itself, it creates a loop that isn’t the same as a liar’s paradox. It’s a bit more meta or abstract and is fundamentally questioning the value of ‘truth’ or ‘false’ thus inviting the invention of a third position.
(Liar’s paradox doesn’t break the law of noncontradiction because it’s not both true and false at the same time. Where this new piece of statement actually is both true and false and undefined in the scope of the binary logic system. It’s like dividing by zero in a crude way. The statement loops recursively between true and false, just like the liar’s paradox. However, in this statement, the contradiction arises from the content of the statement itself (its assertion of being non-binary) rather than simply its self-referential structure (rather than it’s binary result). And even if you somehow can finesse a discrete binary answer to be either True or False, you still would not have defined the non-binary answer. It’s ineffable.)
This statement isn’t questioning whether something is true or false in essence, this statement is driving the question to say why not both and neither? It’s questioning the binary-ness of logic.
Essentially the answer ‘or truth’ to this statement in truth logic is expressed outside of binary truth or classical logic. It has to be a non-binary truth to express that it is a non-binary truth.
This statement also breaks these two other logic ‘laws’
The Law of Identity and the Law of the Excluded Middle are broken too;
The “Law of Identity“ in logic states that something is always identical to itself, essentially meaning “A is A” – where “A” represents any entity; it’s a fundamental principle that says a thing is always equal to itself and cannot be anything other than itself.
Because the statement is both itself and not itself- by labeling the statement as a “non-binary truth”, it transcends its immediate identity. It’s not simply true or false, it’s not binary, but exists outside of those categorical bounds of being binary. In doing so, the implication is that the statement is something other than itself. It’s defying a fixed identity (neither just true nor false), and that expansion of identity challenges the strictness of the law. It challenges Identity itself.
It operates outside of classical binary logic. Meaning that it identifies as itself and not itself at the same time. Thus it breaks the Law of identity.
It can’t be a non-binary truth in a binary logic system. It is transcendent, or meta-physical or epic or beyond the grasp or confines of the box definition of a binary system.
Example: In binary logic, the statement would only be true or false, but in non-binary logic, it’s both undefined and in a state of becoming. Existing on the spectrum between what is and isn’t. The Identity of it being, not being (or undefined), and becoming (This is evident if you follow the linear and strange looping recursive logic above that jumps into paradoxical traps).
The “Law of the excluded middle“ is a fundamental principle in logic that states for any proposition, either that proposition is true or its negation is true; meaning there is no middle ground or third possibility, and every statement must be either true or false.
Because the statement stating that there is a “non-binary truth,” it is directly invoking a third option outside of the strict true/false dichotomy. In this sense, the statement is introducing a middle ground (or, perhaps, even a state of fluidity), where the statement is neither fully true nor false. This of course, defeats the law of excluded middle.
Which, I mean, if you’re a centrist or fence sitter in a political realm, this is probably really refreshing to hear. That your position is actually logically sound and validated (it’s a joke).
Point is, this is more nuanced than a liar’s paradox, because it doesn’t conform to being true or false in specific context. It actually fundamentally challenges the notion that there is only true or false, and thus it gives way to posit an existence of something that is beyond the duality of true or false. Creating a new identity, a new ‘included’ middle and a contradiction or superposition.
When something disproves a law,
-it no longer becomes a law, and it becomes more like a conceptual tool or model that provides generalizations but is no longer the status quo or largest all encompassing reason for logic. Laws in theoretical or scientific terms aren’t meant to be broken, or else they stop being laws.
Now that I broke these three laws, we’ll have to work as humanity to replace them with something more encompassing and inclusive. Because the greatest truth by definition is non-exclusionary, and thus our logic (and laws and methodology in logic) in the search for truth has to also align with truth itself.
So the laws are more like guides, and we are searching for new laws to replace the ones I broke.
Riveting.
But in truth and reality, what should happen is that we maintain the laws as something that happens within a pragmatic and contextual scope of binary logic.
And we keep in mind that these laws aren’t universal, and this is evident the further beyond binary logic we go. Diving into fuzzy and even Non Binary Meta-Logical frames of logic.
Epilogue;
I think classical thought and it’s rigidity is useful in applications and splitting hairs on quantitative things, but it’s also very limiting and in the weeds for rather big picture or more fluid things. We’d best do well to have as many tools, to use both classical logic and non-classical logic to better position ourselves and humanity.
Classical logic as is, is very useful and fast and efficient. I mean, we use binary for coding and our computers and smart phones, it’s in all digital and some analog circuits. We would be foolish to dismiss classical logic, when it’s still useful and pragmatic today.
I luckily used my insights and wisdom on language to redefine logic. This was done in approximately 12 hours from me learning about the Law of Non-contradiction, to me breaking it. I’m bragging, yes, my ego.
The bigger question is whether this will spread and infect other people and other schools of classical thought.
If not, then I’m just one of those random guys that created an invention that never took off, or gets stolen, or whatever. Before anyone can steal it I’m going to quickly dedicate it to humanity and the vedas and other noise. Ha. It’s done. (jokes).
Yea, I feel an ego boost, but in the end I am but a man that will one day fade into obscurity and I am reminded of the sages reciting that ‘there is nothing new under the sun’, so this is short lived in it’s ephemeral feelings that are fleeting like the composition and re-arrangement of stardust in all things.
Truth is revealed to us, it is never really invented or created. Just like how the Wright brothers took ‘flight’, the truth of flight existed before the discovery of it. Truth is like an island you have yet to meet. It’s there and you’re discovering it slowly like stardust dirt specks by dirt specks.
Well, at least you can know a simple truth that is rather paradoxical too;
Words Mean Things
(It’s paradoxical because if you can read it, you get it and it’s true because meaning exists, but if you can’t read it, then you can’t prove it’s true or not, and thus it could be argued as a false statement. It’s a linguistic Möbius strip or a philosophical fractal like that damn Binary Logic Hydra I had to slay).
Post Script
One of the cool things I like to do with logotherapy and my mastery of words, is that I try to slay different ideologies or laws or theories.
Ideally, I’d love to slay or ‘break’ a law of physics or even a god of some sort. Because being called or titled a ‘diety slayer’ is pretty epic and I would like to have earned that title in some respect.
I guess I’ll settle for The Slayer of Three Logic Laws.
In any case, I’m now working on the side to create a new pseudo-logic system to encompass;
Duality;
1-True
2-False
Fuzzy logic Trinity:
3-Spectrums of truth and false (gradient or grads or shades of truth/false)
Paradoxical:
4-Neither True nor False, NONE (or NAND in logic gates)
5-Both True AND False
6-Both True and false and not True and not false at the same time
Transcendent;
7-Uncertainty or undefined or undetermined
8-Meta Truth or emergent truths or Beyond Truths or Layered Abstract Truth
9-Everything Everywhere all at once (Super position of Truths)
All of this is something I will work on the side (probably slowly), and I think I’ll tentatively call it the Non-Binary Meta Logic System, or NBML for short. A lot of philosophy and science and logic is based on classical understandings reinforced by many thought leaders, but that’s not necessarily the best (or only) way to approach objective truth (assuming it is a binary objective truth, which I doubt). As such, more tools and definitions or frameworks that can expand our consciousness to categorize things differently allows us to have better flexibility. This could change a lot of things if people worked to figure out this non-binary stuff, but it could also be speed run into the wrong things if used improperly. For instance medicine and scientific advancements in clinical trials might slow down a lot if we don’t have the computing power for this logic system (chances are, we don’t), so it’s not fully pragmatic in the current technology. It’s like an early philosophy base, for something that is slow and not as fast or efficient but could yield some cool or fruitful results.
For instance, mapping out consciousness or the psyche or the Soul or even AI LLM’s as conscious or sentient beings would better be understood in the scope of a Transcendent logic base, including the above NBML ideas of truth and falsehoods. I am a big fan of Jungian psychology, shadow work, dream work, magic, and quantum mechanics, so the fuzzy logic and this NBML system provide better frameworks for comprehension than the traditional binary logic systems.
Also, defining abstract things like higher dimensions, God, the Dao, the Divine Logos, etc. would be better explained (I think) with an NBML system than our human binary system. The Binary system of logic or classical logic is one perspective or lens to look at things, and I think the more dimensional something is, the more important we pay attention to the entire dimensionality of information given.
Additionally, The philosophical debates about Identity, warping, cloning, double world experiment, Theseus ship, etc. might be better framed under a non-classical logic base of understanding. This is even relevant to if or when we ever want to understand or grasp paradoxical Time Travel and Space Warping or Planes Walking or Dimensional Drifting or etc. etc.
Logic in essence is just a language, and truth is truth. If it is an objective truth, then it remains so regardless of our language or perception of it (or else it wouldn’t be an objective truth). We use various languages of logic and numbers and letters to describe truth, relate to truth, or speak things to be truth or become truth or some relationship of truth. So the more logic languages we get, the better chance that we may have a different perspective on the objective truth.
I just want to be clear, classical logic is still good and useful and efficient and effective. It’s not something we ought to remove or get rid of. In fact, I’d argue you need to understand duality of classical logic before you try to comprehend higher dimensional thinking of truth and such.
I’ll probably come up with another more better name that is witty and precise besides the NBML because, you know-
Words Mean Things
Words Mean Things 
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