Paraconsistent Logic and AI models

John6666
Sun, 15 Mar 2026 05:30:49 +0000

Hmm… for now:

You are onto something. But the strongest version of your case is narrower and more precise than the article in its current form.

My overall judgment

I would not defend the article exactly as written.

I would defend a revised version built around this claim:

Current LLMs are not reliable epistemic agents because they do not cleanly distinguish among vagueness, contradiction, uncertainty, formal validity, and empirical grounding. A better architecture would be plural and layered, not purely generative.

That thesis is serious. It matches real technical work. It also fits your philosophical instincts much better than the article’s larger claims about AGI being a logical impossibility.

Why I think you are onto something

1. You correctly see that fluency is not knowledge

Modern LLMs are excellent at producing plausible language. That is not the same as having a built-in theory of when a claim is justified, when evidence is missing, when two sources conflict, or when the right answer is “I do not know.” Current research on hallucinations treats this as a major open problem. OpenAI’s 2025 paper argues that standard training and evaluation often reward guessing over acknowledging uncertainty, and AbstentionBench reports that abstention on unanswerable questions remains unsolved even for frontier models. (OpenAI)

That means your core complaint is real. The field has built very strong generators. It has not yet built a universally strong epistemic discipline on top of them. That is a fair criticism. (OpenAI)

2. Your hybrid instinct is right

The strongest technical work near your thesis does not say that raw next-token generation is enough. Logic-LM combines LLMs with symbolic solvers. LINC uses the LLM as a semantic parser into first-order logic, then hands deduction to an external theorem prover. There is even a 2025 paper that directly integrates an LLM into the interpretation function of a paraconsistent logic while aiming to preserve soundness and completeness. So your instinct that reasoning should be split across different layers is strongly aligned with current neurosymbolic research. (ACL Anthology)

That is the part of your article I find most promising. You are not merely complaining that models hallucinate. You are saying that the architecture is missing distinct components for distinct epistemic tasks. That is a good insight.

3. Your concern about contradiction is legitimate

There is real evidence that LLMs can contradict themselves or generate unstable factual claims. SelfCheckGPT is built around the idea that hallucinated facts often vary or conflict across multiple samples. Chain-of-Verification tries to reduce hallucinations by forcing a draft, then generating verification questions, answering those independently, and only then producing a revised answer. These methods do not prove your philosophical thesis, but they do support your intuition that consistency management and verification matter. (ACL Anthology)

So on the big picture, yes: you are pointing at a real weakness in current systems.

Where your article is strongest

Your best move is not the attack on “Big Tech” or the rhetoric about Pinocchio. Your best move is the underlying structure:

1. A generative model can be useful without being a full knower.

2. Language contains vagueness, conflict, ambiguity, and context dependence.

3. A single undifferentiated text generator is not well suited to all of those at once.

4. A better system should separate the tasks.

That is a much stronger case than “AI can never be intelligent.”

The article is also strongest when it pushes for a pre-output judgment layer. In engineering terms, that would mean the model does not go straight from prompt to final answer. It first classifies the kind of problem it faces. Then it decides which tools or reasoning regime should apply. That general shape is already visible in Logic-LM, LINC, verification pipelines, retrieval systems, and abstention benchmarks. (ACL Anthology)

Where your article weakens itself

This is the decisive part.

1. You conflate paraconsistent logic and fuzzy logic

This is the biggest conceptual problem in the draft.

Paraconsistent logic is about non-explosion under inconsistency. In plain language, it asks how a system can contain contradictions without collapsing into “everything follows.” Fuzzy logic is about degrees of truth for vague or imprecise predicates. In plain language, it is designed for cases like tall, young, rich, warm, likely, or near, where sharp boundaries are unnatural. (Stanford’s Dictionary of Physics.)

Your “35 degrees water is lukewarm” example is not mainly a paraconsistency case. It is a vagueness case. “Hot” and “cold” are context-sensitive predicates with blurry thresholds. That fits fuzzy logic or many-valued semantics much more naturally than paraconsistency. If you keep using “lukewarm” as your main example of paraconsistency, technically informed readers will attack that immediately, and they will be right to do so. (Stanford’s Dictionary of Physics.)

So the clean distinction is:

Fuzzy logic for borderline predicates and graded truth.

Paraconsistent logic for inconsistent evidence or conflicting commitments that should not trivialize the whole system. (Stanford’s Dictionary of Physics.)

That single correction would improve your article more than anything else.

2. LLMs are not basically Boolean syllogism machines

Your article often reads as if current models work by applying binary Boolean logic internally and then exploding under contradiction. That is not how transformer LLMs are built. Transformers are neural architectures based on attention mechanisms, and the dominant autoregressive paradigm for LLMs is next-token prediction. They are continuous, probabilistic systems, not classical deduction engines in disguise. (arXiv)

This matters because your current diagnosis mislocates the failure. The main technical problem is not that the model has secretly committed itself to Aristotelian syllogism and Boolean truth tables. The problem is that a probabilistic text generator is being asked to do too many epistemically different jobs without enough explicit structure.

So I would replace this claim:

LLMs hallucinate because they are based on Boolean logic.

with this claim:

LLMs hallucinate because probabilistic generation alone is being used where tasks also require grounding, conflict management, calibration, and abstention.

That version is much stronger.

3. Your causal story about hallucinations is too simple

You often write as if hallucinations mainly come from reinforcement learning, stochasticity, or the attempt to simulate creativity. The current literature is broader than that. Hallucination research now treats the problem as multi-causal. It spans pretraining data, fine-tuning, alignment, prompting, retrieval quality, decoding choices, evaluation methods, and weak incentives for uncertainty. OpenAI’s paper emphasizes “rewarding guessing,” and surveys explicitly treat hallucination as a broad taxonomy with multiple causes and mitigation strategies. (OpenAI)

So I would not say RLHF is the cause. I would say it is one factor in a larger system that still does not sufficiently reward truthfulness, calibration, and refusal.

4. Your AGI impossibility claims are much too strong

This is where the article moves from “provocative and interesting” to “overreaching.”

Saying that AGI is a logical impossibility, that imagination is non-computable, or that AI can never produce genuinely original knowledge is not something your article actually proves. Those are very large philosophical claims. There is an active field of computational creativity, with serious surveys on machine creativity and creative systems. That does not prove machines will equal or exceed human minds. But it does show that the impossibility claim is not established just by saying “algorithms are algorithms.” (ACM Digital Library)

Here I would advise restraint. You do not need those impossibility claims to make your best argument. They make the piece sound grander, but they make it less defensible.

5. Your theory of truth is presented too narrowly

The article often writes as if the relevant account of truth is basically settled and then applies that framework directly to AI. Philosophically, that is too quick. Even leaving aside deeper debates, the practical problem in AI is not only “what is truth?” It is also:

what counts as evidence,

what counts as support,

what counts as conflict,

what counts as insufficient information,

and when the system should abstain.

Those are epistemic and operational questions as much as metaphysical ones. That is why I think the article is stronger as a paper about epistemic architecture than as a paper about the essence of truth.

The key distinction your paper needs

Your article currently treats several different phenomena as if they had one root. They do not.

You are really discussing at least four different things.

A. Vagueness

Examples: hot, cold, lukewarm, old, likely, near, safe.
Best fit: fuzzy logic, many-valued semantics, context-sensitive semantics. (Stanford’s Dictionary of Physics.)

B. Inconsistency

Examples: one source says X, another says not-X; the model has conflicting retrieved facts; two commitments cannot both be maintained.
Best fit: paraconsistent logic or other non-explosive approaches. (Stanford’s Dictionary of Physics.)

C. Uncertainty

Examples: not enough information, stale information, false-premise question, underspecified question.
Best fit: calibration, confidence estimation, abstention. (OpenAI)

D. Formal deduction

Examples: if-then structure, quantifiers, consistency-sensitive inference, proof tasks.
Best fit: symbolic logic, theorem provers, constraint solvers. (ACL Anthology)

Once you split the problem this way, your article becomes much more powerful. Instead of saying “paraconsistent logic solves LLM hallucinations,” you can say:

LLM reliability requires different formal treatments for different failure modes.

That is a serious claim.

The philosophical frame that fits your case best

I do not think your best frame is “replace current AI with paraconsistent logic.”

I think your best frame is logical pluralism.

Logical pluralism is the view that more than one logic can be correct, depending on what notion of validity or consequence relation is at issue. For your project, that is ideal. It lets you say that no single formal regime should be expected to handle all linguistic and epistemic situations equally well. Different subproblems call for different formal treatments. (Stanford’s Dictionary of Physics.)

That gives you a much stronger architecture:

use symbolic logic for strict deduction,

use fuzzy logic for vague predicates,

use paraconsistent logic for conflicting evidence,

use retrieval and verification for empirical questions,

use abstention for underdetermined questions. (Stanford’s Dictionary of Physics.)

This is the version of your idea that I think experts would take seriously.

What I would keep from your article

I would keep these points.

Keep 1

“Mere generation is not enough.”
Yes. Strong point.

Keep 2

“Current systems need an explicit judgment layer.”
Yes. Very good point.

Keep 3

“Contradictions should not globally trivialize a system.”
Yes. Good and technically meaningful.

Keep 4

“A useful AI architecture should distinguish kinds of questions before answering.”
Yes. Very strong idea.

Keep 5

“Human-like fluency should not be confused with warranted knowledge.”
Yes. Central and correct.

What I would cut or weaken

Cut 1

“AI is based on Boolean logic, therefore hallucination is inevitable.”

Too simple. Technically inaccurate. (arXiv)

Cut 2

“Paraconsistent logic or fuzzy logic” as if they were interchangeable.

They are not. (Stanford’s Dictionary of Physics.)

Cut 3

“RLHF is the cause of hallucinations.”

Too strong. The evidence points to multiple causes. (OpenAI)

Cut 4

“AGI is a logical impossibility.”

You have not shown that. It invites objections that distract from your best argument. (ACM Digital Library)

Cut 5

The stronger rhetorical attacks on engineers and companies.

They add heat, but they reduce credibility.

What your strongest revised thesis would be

Here is the version I think is best:

Current LLMs should not be treated as self-sufficient epistemic agents. They are probabilistic language generators that can be highly useful, but they need a plural architecture around them. Formal deduction should be delegated to symbolic tools. Vague predicates should be handled with graded or context-sensitive semantics. Conflicting information should be managed by non-explosive reasoning. Empirical claims should be grounded in retrieval and verification. Unanswerable questions should trigger abstention rather than confident guessing.

That is clear. It is defensible. It matches actual technical directions in the field. (ACL Anthology)

What a concrete architecture could look like

If you want your article to move from philosophical essay to serious proposal, I would sketch something like this:

Step 1. Classify the prompt

Is this:

factual,

deductive,

vague,

conflicting,

normative,

or underdetermined?

Step 2. Route by type

Deductive → theorem prover or symbolic solver

Factual → retrieval plus reference checking

Vague → fuzzy or context-sensitive interpretation

Conflicting → paraconsistent handling of local inconsistency

Underdetermined → abstain or request missing context

Step 3. Verify before final output

Use something like a verification pass. The general pattern behind Chain-of-Verification is good here. SelfCheckGPT is also relevant as a cheap instability detector. (ACL Anthology)

Step 4. Return not just an answer, but an epistemic status

For example:

supported,

weakly supported,

conflicting sources,

context-dependent,

unknown.

This is what your article is really aiming for. Not just “better answers,” but better judgment.

My view on your use of Kant, Aristotle, Popper, and philosophy of language

Your philosophical direction is better than your engineering description.

Kant is useful if you use him to talk about the conditions under which a system can judge, not as a general anti-AI slogan.

Aristotle is useful if you use him for distinctions among forms of inference and for the need to avoid careless equivocation.

Popper is useful for empirical claims and scientific conjectures, but not every user prompt is a falsifiable scientific hypothesis.

Philosophy of language is very useful here because many AI failures are failures of context, reference, vagueness, scope, presupposition, and support.

So yes, philosophy belongs in this debate. But it works best when it sharpens distinctions, not when it substitutes for technical description.

My blunt conclusion

You are not completely wrong. You are identifying a real problem. In fact, you are identifying one of the most important problems in current AI: the gap between language generation and epistemic responsibility.

But your article currently overstates and conflates too much.

The three biggest fixes are:

1. Separate fuzzy logic from paraconsistent logic.

2. Stop describing LLMs as if they were basically Boolean engines.

3. Replace the “AGI is impossible” conclusion with a more precise claim about the limits of current LLM-style epistemic architecture.

If you make those changes, your paper becomes much stronger.

My final assessment is this:

Your intuition is good.

Your main categories need tightening.

Your best contribution is architectural and epistemological, not metaphysical.

Your strongest frame is pluralism, not one replacement logic.

Your most defensible thesis is that AI needs a layered theory of judgment.

That is a paper worth writing.