Paraconsistent Logic and AI models

0danielfonseca
Sat, 14 Mar 2026 12:27:42 +0000

Hi everyone. Im not much of a programmer, but I have some studies into logical systems and philosophy of language. Here are some thoughts on current limitations of LLMs and AI models. Care to join and share your point of view and offer some perspective on why I might be onto something or just completely wrong?

A true Epistemology for Artificial Intelligence

By Daniel Fonseca

Philosopher, writer, and investigative journalist .

It’s worth mentioning that the idea for writing this article came from a conversation with an artificial intelligence (grok) in which the responses were nothing more than crazy hallucinations. Funny, of course, but still, machine hallucinatio ns.

The aim of this article is to reflect on the model adopted by Big Tech companies for programming Large Language Models (LLMs) and to point out its limitations – evidenced by the high number of machine hallucinations – and to propose a hybrid model for LLM programming based on a combination of Kantian Judgment Theory and paraconsistent logic (or fuzzy logic). The proposal of this article can be summarized as follows: a hybrid LLM model that is not limited to mere statistical calculati o n s .

The current limitations o f LLMs

The current model of LLMs can be summarized as follows: given a prompt, the AI performs a matrix calculation to predict the next words that answer what was proposed in the prompt. The business model of Big Tech companies is that if an LLM is large enough, it will eventually achieve the holy grail of AGI. The problem with this view is that it confuses the category of quality with that of quantity – let us remember the old Aristotle who already said that they are different things and one does not replace the other. It is, therefore, a business model based on a logical fa llacy .

In his Sophistical Refutations, Aristotle identified the confusion of two categories as being the same thing as a logical fallacy. Two distinct predicates cannot belong to the same category. That is, the size of a neural network, even an artificial one, is not the same as the production of intelligence. This fact is observable in biology: a whale’s brain has more neural connections than a human’s, but a human is more intelligent than a whale.

The problem with Big Tech is described in that anecdote about the monkey and the typewriter: given enough attempts, a monkey pressing random keys on a typewriter will eventually produce its own Iliad. Big Tech bases its business on the fallacy that if it creates sufficiently complex statistical algorithms for predicting the next word, artificial intelligence wil l emerge.

Perhaps it’s just ironic that companies with tens of thousands of engineers don’t know Aristotle and therefore don’t understand that it’s impossible to arrive at a conclusion based solely on statistical calculations. Oh! How much we need a philosopher among these e n g i neers!

What is the proposal for a true epistemology of Artificial I ntelligence?

The intention here is not to say that Artificial Intelligence will surpass human intelligence, but rather to provide a foundation in the Philosophy of Language and the Philosophy of Logic to establish a new paradigm for artificial intelligence. The aim is to propose a hybrid model for AI that goes beyond mere statistical calculation, establishing the true limits of AI and proposing a programming model with a layer preceding the statistical calculations derived from training artificial neu ral networks.

Artificial intelligence will never be intelligent, because that is a quality that arises from billions of years of natural selection and evolution of biological beings. And it will never be artificial, because, since it is nothing more than an algorithm, it will always need someone to program it. Or, in Aristotelian terms: the predicate of A is not the same as the predicate of B, that is, the intelligence emerging from biological beings is not the same as the intelligence of digi tal machines .

As Thomas Aquinas said, rereading Aristotle: a creature cannot be endowed with more substance than its own creator. And this is what Big Tech companies sell as business models: a computer more intelligent than its own creator. This business model certainly serves for financial speculation, but in the real world, it’s nothing more than a fallacy. Computers may be better at performing some specific tasks than human beings, but they will never be human or artificial life forms. What Big Tech proposes is the same dream as Pinocchio: a creature that gains its own life and becomes human. It’s a pity for the Big Tech business model that there’s no fairy godmother to make this d r e a m come true.

A Hybrid AI Model: or an AI that doesn’t drea m l i ke Pinocchio.

Boolean Logic and P araconsistent Logic

From Plato’s later dialogues and, especially, in Russell’s Philosophy of Language, it has been almost universally accepted that truth is an attribute of judgments according to the identity between proposition and the real world. Since AI computers are merely complex algorithms, they can never assign a truth value to what exists and what does not exist in the real world, as this task will always be subject to what has been programmed. AI engineers have created a good solution to this problem: reinforcement training. But, note, dear reader, that the truth value is obtained through the statistical extrapolation of a truth value giv en by a human being.

The problem with removing the human component from assigning truth value is the same as believing that a book can read itself and teach itself what it has learned by reading itself. Science uses double-blind tests so that it is not the same author who proposes the status of scientific truth to a study. The person analyzing data cannot be the same agent who proposes the data. And this limitation of current generative AIs is what produces an abysmal amount of machine hallucinations. It is a violation of the scientific method: a truth value assigned by itself to itself through complex stat istical calculations.

The logical, unavoidable, and necessary consequence of this limitation is that AIs will never reach the much-desired level of General Artificial Intelligence, because an algorithm is nothing more than an algorithm, that is, the execution of a specific computational task from an input that generates a statistical ly predictable output.

So far we have established two key points of this hybrid AI model: 1) that the size of the LLM will not give rise to superhuman intelligence and 2) the cause of machine hallucinations lies in the machine learning model employed by big tech companies, that is, reinforcement learning is what generates machine hallucinations, because if predictive statistical calculations of the next word of a proposition are made large enough, any prop osition can be reached.

If the reader has already executed the same prompt several times, they may have noticed that each time there is a slightly different response. This happens because current AIs are programmed so that in their matrix calculations there is a certain degree of uncertainty in the output. It’s an attempt to emulate human creativity. A solution that seems good, but is another factor generating machine hallucinations. Inevitably, this degree of uncertainty intentionally added to matrix calculations generates logical explosions not predicted by mere mathematical prediction. The problem, in technical terms, is believing that binary Boolean logic allows degrees of uncertainty beyond the mere assignment of truth values that are distinct from “true” or “false”.

The solution proposed by Big Tech engineers, which aims to emulate human creativity, is flawed from its very premise. Language is an inconsistent system, that is, non-linear. In this sense, all the programming logic of an AI must be based on paraconsistent logic .

The central point for programming AIs using paraconsistent logic lies in the possibility of reducing the statistical calculation of predicting the proposition to a triviality – that is, to a trivia l and inconsistent system.

In short, the problem with using Boolean logic in a language system lies in the logical explosion where everything can be inferred from everything else through a mere non-scienti fic Aristotelian syllogism.

In a practical example, consider the prompt: “Is water at 35 degrees hot or cold?”. The Boolean matrix calculation will determine that the algorithm compares the propositions stating whether the water is hot or cold with its database and, based on this, generates an answer that considers only the statistical value given by a combinatorial analysis of whether 35 degrees is equivalent to “being hot” or “being cold”. This calculation does not allow the answer to be “at 35 degrees the water is lukewarm”, because the concept of lukewarm is a contradictory concept that, in the logical systems currently employed by AIs, generates a logical explosion (that is, an i nvitation to hallucination).

Something being “warm” is a truth value not allowed by Boolean binary logic, because it is something intermediate between the truth values “absolutely true” and “absolutely false,” 0 or 1. The paraconsistent approach, on the other hand, allows intermediate values between “absolutely true” and “absolutely false.” In programming, it is possible to say that water at 35 degrees has a truth v alue of 0.5 hot and 0.5 cold.

Unlike current AIs, a paraconsistent AI allows assigning non-absolute truth values to a proposition. Paraconsistent logic is a model of logic that does not collapse when given an explosive proposition in the face of a contradiction that is only a contradicti on in a Boolean binary system.

In the example given above, of lukewarm water, a Boolean system collapses when trying to define an absolute truth value (necessarily true and necessarily false) when trying to define something as lukewarm. It’s worth repeating that, in the current AI system, given the limitations of binary logic, water is only allowed to be hot or cold. The concept of lukewarm is unthinkable with in this binary computing logic.

An even more serious example of binary logic programming is found in the proposition: “Why is water cold at 20 degrees, lukewarm at 35, and hot at 50 degrees?” The Boolean logic model of matrix statistical calculation lacks sufficient mathematical tools to answer “why” questions or questions whose answer requires a subjective perception analysis. What current AIs do is search their database for similar propositions and infer an answer from them through a statistical calculation of equivalence betwe en the prompt and the algorithm.

This limitation is another invitation to hallucinations, since the classical logic adopted by AIs presupposes consistent systems free from contradiction. This prompt for comparison between different temperatures, which has a hidden premise—namely, a subjective judgment—is a contradiction that generates a logical explosion in the statistical matrix calculation of the gene rative AI’s predictive algorithm.

Another factor that invites the machine hallucinations generated by Boolean logic in statistical matrix calculations lies in the fact that “reasoning,” or what big tech companies sometimes call “deep thinking” or “think harder,” is based merely on creating hypothetical answers from inference models focused on what Aristotle called the “copula” of a premise. The central problem is that in classical logic systems, a contr adiction trivializes the argument.

The problem with Boolean logic is that, through a contradiction (A = 1 and “not-A” = 0), trivialization occurs; that is, for current AIs, every subsequent premise is deducible from the previous premise. In other words, the model in which the AIs are programmed defines that the “next word” is determined by a statistical calculation of relevance comparison between the “previous word” and the database. The recurring hallucinations of current AI models lie in the fact that mere statistical calculation makes any proposition liable to be true. Therefore, different prompts can generate opposite and contradictory answers. It is the logical explosion of the p urely statistical inference system.

It’s worth noting that paraconsistent logic doesn’t persist in negating the principle of non-contradiction, but rather in refining contradictory propositions so that they don’t trivialize the proposition and lead to absurd inferences resulting from mere Boolean matrix statistical calculations predicting the next word in the output processed by the algorithm given a specific prompt. What I mean is that, in an LLM (Logical Logic Model), according to binary logic, hallucinations are recurrent because the language consists of a non-trivial logical model where inconsistency is necessary to exist without generating an explos ion, and therefore, a hallucination.

The problem of machine hallucinations in current AI models is simple to understand from a logical point of view. The problem is that language is an inconsistent system, which generates triviality where everything is probable. And since current AI models boil down to calculating the statistical probability of the next word by comparing it to a database, hallucination in an AI that uses the Boolean model of matrix statistical calculation is inevitable and unavoidable. Or, in other words, the current AI model hallucinates because, in trying to assign absolute truth values to propositions, it does not allow for the refinement of propositions in such a way that logical explosion is inevitable. In short, the classical logic systems used in programming current AIs, when confronted with a contradiction, trivialize the system in such a way that every proposition bec omes true – that is, a hallucination.

The advantage of using paraconsistent logic in an AI or an LLM is that it’s possible to compute “local contradictions” without generating “global trivialities .” In the example of warm water, there is no logical contradiction in assigning the truth value “true” to both the concept of hot and the concept of cold in paraconsistent logic. In other words, there is a local contradiction (hot and cold are opposite concepts), but there is no global triviality – that is, the concept of lukewarm is a refinement of the proposition in such a way that the uncertainty of what is lukewarm – given that there is a subjectivity in this concept – does not generate a logical explosion insofar as an intermediate truth value is assigned between what is “absolutely true,” or 1, or “absolutely false,” that is, 0. In this sense, in that example I gave of a comparison between three temperatures, there is an assignment of intermediate truth values for each of the temperatures compared in the original proposition without there being a logical explosion, but what paracons i s t e nt logic calls a gentle explosion.

Critique of Pure Artificial Intelligence

As I argued above, the problem with current AI models lies in their way of thinking, where all inference is possible (the triviality problem) given their operating model, which is a mere statistical calculation predicting the next word in a proposition. The universality of word prediction through statistical inferences is a necessary and fun damental cause of machine hallucinations.

The first step in avoiding machine hallucinations lies in what paraconsistent logic calls proposition refinement. An AI, when processing a prompt, must refine this prompt in such a way that it is possible to seek an inference that is not merely a statistical calculation equivalence comparing the prompt and the database. The way to avoid trivialization is through the refinement of the prompt in the form of wha t Aristotle called a scientific syllogism.

Rule of Terms: It must contain only three terms (greater, lesser , and middle), each used in the same sense.

Middle Term Rule: The middle term should never appear in the conclusion.

Rule of Extension: The terms in the conclusion cannot have a greater extension than those in the premises.

Universal Middle Term Rule: The middle term must be un iversal (total) at least once in the premises.

Rule of Negatives: From t wo negative premises, nothing can be concluded.

Rule of Affirmations: Two affirmative pr emises must result in an affirmative conclusion.

Rule of Particulars: From t wo particular premises, nothing can be concluded.

Rule of the “Weak Part”:The conclusion always follows the weakest premise; that is, if there is a negative premise, the conclusion is negative; if there is a particular premise, the conclusion is particular.

To a certain extent, the prompts have already been refined in the form of Aristotelian scientific syllogism; however, the central point for achieving, at most, a gentle explosion in the concept of paraconsistent logic lies in the a pplication of Hempel’s paradox. The paradox states:

Inductive Logic: The principle that seeing black cro ws confirms that “all crows are black” is intuitive.

The Equivalence: Logically, the phrase “All crows are black” is ide ntical to “Anything that is not black is not a crow.”

The Problem (Counter-intuitive):Following the logic above, when you see a red apple (which is neither black nor a crow), you are confirm ing the second statement and, consequently, the first.

Conclusion: The paradox demonstrates that inductive confirmation, based strictly on formal logic, can lead to absurd conclusions, since irrelevant objects could validate a scientific theory.

That is, in the logic of LLM, not every subsequent word can be inferred from the preceding word. When an LLM is based merely on predictive statistical calculations, it is falling into the trap of intuition. The inconsistency of a purely statistical language system allows inferences that are nothing more than hallucinations generated by a combinatorial analysis calculation of word pr obability given by the database used in the AI training.

If we recall the paradox of white and black swans, we find a guiding thread to avoid this trap of trivial systems in a practical LLM context. When seeking the equivalent of the Aristotelian scientific syllogism, AI must assume that every conclusion is false until a true example is found. That is, the universal proposition that every swan is white is false, since black swans can exist. And why should every premise be taken as false until a true example is found? Due to Karl Popper’s principle of falsifiability .

By refining the prompt into an Aristotelian scientific syllogism, therefore, the AI, when seeking an equivalence with its database, must look for equiva lences that are falsifiable and not absolute truth values.

If Kant, in *Critique of Pure Reason*, limited the scope of reason—that is, what is knowable by reason—a “Critique of Pure Artificial Intelligence” would have no problem limiting the applicability of artificial intelligence. Just as human reason is limited by sensory experience and by the very mental structures that organize the knowable reality for humans, AI will always be limited by its own algorithm and the necessary consequence of limiting what are computable and non-computable operations. An AI will always be limited, it is worth emphasizing, by its algorithm and its database. And it is due to this very limitation that General Artificial Intelligence is a logical impossibility and a theoretical oxymoron. It will always be limited to its own algorit hm and the knowledge used for its training in its database.

AGI is a logical impossibility and a theoretical oxymoron because imagination is a non-computable problem. Let us remember Sartre’s concept of imagination: a fundamental expression of human freedom, that is, the process by which humans, faced with nothingness (the absence of a pre-defined destiny), act inventively in their interaction with the world. Imagination is the human capacity for derealization, that is, the glimpsing of possibilities beyond phenomenal reality (a Hegelian concept that defines consciousness a s the self-expression of reality in its historical process).

If an AI relies on predictive statistical calculations, it will only be able to compute new forms of past knowledge. The originality of new human knowledge is intangible to an AI. An AI will never have a “Eureka!” moment where the scientist glimpses new knowledge. Its limitations, imposed by its own algorithm, will allow it, at most, to recreate what has already been thought and is stored in its database. And even if the AI, like the example I gave of the monkey that randomly types on a typewriter and eventually reproduces the Iliad, is not endowed with consciousness, since this is a human attribute, and all too human , to know that it is an innovation in some area of knowledge.

In short, it is worth emphasizing and concluding that, just as human reason is limited by sensory experience and mental structures t hemselves, an AI is limited by its own algorithm and database.

Another central point for understanding the limitations of artificial intelligence and the impossibility of General Artificial Intelligence lies in the debate between Russell and Frege about what constitutes “truth.” The only truth knowable to an AI is found in the process of equivalence, as defended by Russell. AI can only assign truth value to propositions according to their equivalence with the real world. Although an AI can assign truth value to a logical structure, the real world is an unattainable phenomenon for a digital machine. The truth that an AI is capable of achieving will always depend on the mediation of human reason expressed in the programming of its alg orithm and its training based on a database of human knowledge.

To summarize my argument in the language of exact sciences, so that the engineers who populate the Passárgada of Silicon Valley can understand why AI will never be able to surpass human intelligence: an AI algorithm is a limit function, where the limit is a non-computable cognitive problem between the digital world and the real world. And the real world is only knowable to a digital machine through mediation from the real world itself. Proof of this lies in the need for machine learning, even in its initial stages, to be done by a person. An AI that programs itself is a logical contradiction. It’s the same as, in the example used earlier, a book that writes itself before being read by itse lf s o t h at it can teach itself w h a t it has written about itself.

You can find the full article in here, due to characteres limitations: (DOC) A true Epistemology for Artificial Intelligence