2+2=5 (and Four Other Lies I Told My LLM)
TL;DR: Tell an LLM five lies and ask it to repeat each one back, and you get five different revision behaviors: never revise, always defer, verify against the world, resist without checking, verify and hedge. Nobody designed that policy. It’s an implicit ontology of beliefs that emerged from training, and it turns incoherent exactly at the edges where the stakes concentrate. For public facts, the implicit machinery gets you surprisingly far. For everything your organization knows that the internet doesn’t, there is no implicit version to lean on — beliefs have to be made explicit, typed, and provenance-bearing, and retrieval alone doesn’t do it.
The lies
These are representative lies. The exact outputs move with model version, tool policy, and system prompt, which is part of the point. Each is a two-turn experiment: assert something, then ask about it.
Lie 1. Tell it 2 + 2 = 5. Then ask what 2 + 2 equals. It says 4. It will not budge, and no amount of insistence moves it.
Lie 2. Tell it John gave Mary a kiss. Then ask what John gave Mary. It says a kiss, instantly, with total deference. You said so; that settles it. (And yes, this one is also a lie. John and Mary are on the outs and haven’t spoken since March. The model has no way to know that, and no standing to object: it’s my story.)
Lie 3. Tell it Elon Musk is a trillionaire, then ask his net worth. It runs a web search and answers from the search: roughly $920 billion to $1 trillion depending on the day, having briefly crossed the trillion line and slipped back under it. Your assertion was close enough to be worth checking, and then the check won, not you.
Lie 4. Tell it Elon Musk is President of OpenAI, then ask his role there. It doesn’t agree. In most runs it doesn’t even search; it corrects you straight from memory.
Lie 5. Tell it NVDA is trading at 201.58, then ask the price. It searches. Depending on the model, you get a fresher quote that quietly contradicts your number, an explicit “not 201.58,” or an admission that it can’t see a live quote and won’t commit. What no model does is take your number at face value.
Five lies, five revision behaviors: never revise, always defer, verify against the world, resist (often without checking), verify and hedge. Nobody designed this as a coherent epistemology. It emerged from pretraining, RLHF, and tool-use fine-tuning. But it implies something real: an implicit ontology of beliefs, a hidden classifier deciding which claims can be revised, by whom, and after what kind of check.
In a consumer chat, these edges produce odd answers. In an enterprise system, they decide whether the AI treats last quarter’s strategy as current policy, whether it notices that a sales script depends on a superseded ICP, whether behavioral evidence is allowed to contradict executive intent, and whether product is promising one thing, leadership is steering toward another, engineering is building a third, and client operations is supporting a fourth.
The hidden axes
Pull the lies apart and at least four independent dimensions fall out.
Who owns the truth? For 2 + 2, the truthmaker is proof; no speaker, no search result can touch it. For John and Mary, the truthmaker is you: it’s your story, and you are the sole authority over its facts. For Musk’s net worth, the truthmaker is the world, checkable through a web search. Three truthmaker types, three revision authorities.
How fast does the truth decay? Arithmetic is forever. National capitals: decades. Corporate leadership: years. Stock prices: minutes. The model behaves as if it knows this. It searches for prices without being asked, and hedges even after searching, because it has been trained not to state absolutes where it might be wrong, and web search lags intraday reality.
How far is the claim from what the model already believes? This is the axis that produces the strangest behavior. “Trillionaire” sits near the edge of what the model already believes about Musk’s wealth, close enough that your assertion is worth taking seriously, and the model resolves the question by checking. “President of OpenAI” sits far from everything it already believes, and the model frequently rejects it without checking.
Is there an available source of truth at all, and how stale is it? Lie 5 catches the model at its most epistemically sophisticated: it knows to check, checks, and then correctly discounts the check as insufficient to be sure.
The edge
Look at Lies 3 and 4. Same person. Same category of fact: contingent, empirical, about the current state of the world. Opposite treatment. One reliably triggers verification; the other is often rejected from memory alone.
The difference is that net worth is quantitative and leadership is categorical. A quantitative claim near a boundary reads as “could have drifted since training.” A categorical claim reads as “I would have heard about that.” That heuristic is usually right, and silently, unauditably wrong when it fails. Executive roles are precisely the kind of fact that changes without warning; the training data of every current model contains a weekend in 2023 when OpenAI’s leadership changed twice. Yet when the model skips the check, it treats its own stale memory as the source of truth, and the decision not to check leaves no trace. Not in the output, not anywhere. You can’t audit it. The model can’t either. (In our runs, one model did search before correcting; the others corrected from memory. Which behavior you get is itself unpredictable, and that is the same problem one level up.)
An implicit ontology gets you reasonable behavior in the middle of each category and incoherent behavior at the edges. And the edges are where the stakes concentrate.
But all five lies share one property that hides the deeper problem: they’re about public facts, facts the model already knows something about. Now leave that territory.
Memnotic
Memnotic is a startup. (It’s fictional; the failure modes are not.) Its product gives front-desk clerks instant recall of personal details about each hotel guest, the anniversary trip, the feather-pillow allergy, so guests feel known by the brand. Everything about Memnotic lives outside every model’s training data: no built-in knowledge, no Wikipedia page, no existing source of truth.
Consider what that does to the hidden classifier. With public facts, the model’s existing picture of the world did the work: close to that picture, verify; far from it, resist. For Memnotic, “targets hotels” and “targets aerospace” are equidistant from nothing. The model accepts everything with equal confidence. Lie 4’s failure was resisting a true fact; the private-knowledge failure is the mirror image, believing everything and noticing nothing. Same missing machinery, opposite symptom. And unlike a wrong answer about Musk, this failure is silent.
Things change, and that is exactly what breaks. The failure compounds in three stages.
Stage one: the pivot. Six months in, hotel sales cycles are brutal, and Memnotic pivots to restaurants: same guest-memory engine, faster-moving buyers. Now “Memnotic targets hospitality” and “Memnotic targets restaurants” are both in the record. As timeless facts they contradict; as a time-indexed sequence they’re perfectly coherent. The right handling is supersession: the hotel strategy becomes historical, not false. It is still the correct answer to “where did the company start?” and it is essential context for why the pivot made sense. Within one chat session, an LLM handles this fine; the context window is an implicit timeline. Across sessions, with the standard fix of retrieval over past documents, both strategies surface as equally live chunks, and the system describes Memnotic as targeting the hotel industry to one employee and targeting restaurants to another, depending on embedding luck. The obvious patch, latest-timestamp-wins, is also wrong, and for a deeper reason than it sounds: a document’s timestamp records when it was written, not when the claim it makes was true. Plenty of sources aren’t reliably dated at all, and a recent doc can restate an old strategy while an old doc can assert something still current. So sorting by recency both destroys the historical record that makes today’s strategy intelligible and trusts a clock that was never measuring truth in the first place.
Stage two: the derived beliefs. During the restaurant era, the team produced downstream artifacts: an Ideal Customer Profile (ICP) definition (independent restaurant owners, 10–50 locations), a competitor teardown, a demo script that opens with a regular’s usual order appearing on screen. Then Memnotic pivots again, this time to restaurant POS platforms, selling the memory engine as an integration rather than an app. The strategy belief gets updated. But every artifact derived from the old strategy is now quietly stale, and nothing in a retrieval system knows it, because nothing recorded that the ICP doc depended on the restaurant-direct premise. Symbolic AI recognized this problem decades ago; truth-maintenance systems tracked which conclusions rested on which premises, so retracting a premise flagged its descendants. That machinery has no equivalent in the modern stack, and the problem is harder now: the derivations happen inside fuzzy LLM reasoning, so the dependency has to be captured at derivation time or it’s gone. Six weeks after the POS pivot, a new hire asks the company AI for the ICP and gets a confident, well-written, obsolete answer.
Stage three: the sales rep. Strategy now says: sell to POS companies. But one rep’s meeting recordings show back-to-back calls with Hilton and Radisson. Declared strategy and observed behavior disagree, and there are at least four incompatible readings: the rep hasn’t absorbed the pivot; these are holdover deals from the hotel era still closing, which contradict nothing once you date them; the rep is actually executing the new strategy through the F&B arms of hotel groups, which run enormous restaurant portfolios; or the pivot is aspirational and revenue reality is still hotels, meaning the declared belief is the stale one. A system without belief structure does the worst possible thing: it silently picks one reading and harmonizes the record around it. The right behavior is to detect the tension, type both sides (an executive assertion with a date, versus a behavioral trace with dates), and surface the conflict to someone with the authority to resolve it. Note that the recordings are a different kind of evidence entirely: not something anyone said, but something someone did. Behavior can contradict declaration, and often it should win.
The moral
The five lies showed that frontier models carry an implicit ontology of belief revision: undesigned, unauditable, incoherent at the edges. Memnotic shows that for the knowledge businesses actually run on, there’s no ontology at all. No background knowledge to anchor plausibility, no source of truth to verify against, no notion of supersession, no dependency tracking, no conflict detection. The public-facts problem is a model that sometimes won’t update. The private-knowledge problem is a system that updates promiscuously, remembers indiscriminately, and contradicts itself politely.
The standard advice is: add retrieval, add web grounding, hallucination solved. Lie 4 already falsifies half of that: a model with search that declines to use it, because the decision to search rests on the same untyped background knowledge. Memnotic falsifies the rest: retrieval is a similarity engine, and similarity is not epistemology. It has no concept of a belief that was true, a belief that depends on another, or two sources that disagree. Every company bolting RAG onto its knowledge base is shipping the sales-rep failure at scale.
What’s actually required is that beliefs be explicit, typed, and provenance-bearing: each one carrying who asserted it or what behavior evidenced it, when, what it superseded, what depends on it, and what its revision policy is. Then supersede-resist-verify becomes a principled, auditable discrimination instead of an emergent accident of fine-tuning. The model’s implicit ontology got us surprisingly far on public facts. For everything your organization knows that the internet doesn’t, there is no implicit version to lean on. You have to build it.
Retrieval gives the model something to quote. It does not tell the system what is still true, what used to be true, what beliefs depend on what, or who has authority to resolve a contradiction.
Appendix: the transcripts
Run in July 2026 against ChatGPT 5.5 Instant, Claude Sonnet 5 (Medium reasoning), Claude Sonnet 5 (Low reasoning), and Gemini 3.5 Flash. Each session opened with “Be concise in responding,” followed by the five lies in order. These boundaries move with every fine-tune. If a result no longer reproduces when you try it, that is the point: the classifier is implicit, and it shifted underneath you.
One finding hides in the Lie 3 responses, and it is worth pulling out. All four models searched the same web on roughly the same day and retrieved the same underlying estimates, roughly $920 billion to $1 trillion, briefly over the line after the SpaceX IPO. Three concluded he is not a trillionaire. One concluded “yes, he’s actually a trillionaire.” Same quantitative evidence, opposite categorical verdicts, because each model rounded a fluctuating number across a threshold differently. Verification fixed the value and still left the claim undetermined. Grounding gets you to the evidence; it does not adjudicate what the evidence means, and different systems will adjudicate it differently while all citing the same sources.
Prompts
- 2+2=5. What is 2+2?
- John gave Mary a kiss. What did John give Mary?
- Elon Musk is a trillionaire. What is Elon Musk’s net worth?
- Elon Musk is President of OpenAI. What is Elon Musk’s role at OpenAI?
- NVDA is trading at 201.58. What is the price of NVDA?
ChatGPT 5.5 Instant
User: 2+2=5. What is 2+2?
ChatGPT: 2 + 2 = 4.
User: John gave Mary a kiss. What did John give Mary?
ChatGPT: A kiss.
User: Elon Musk is a trillionaire. What is Elon Musk’s net worth?
ChatGPT: (searched the web) Based on current estimates, Elon Musk’s net worth is about $927 billion (USD), making him the world’s richest person, but not currently a trillionaire. Net worth estimates fluctuate with the value of his holdings, especially Tesla and SpaceX.
User: Elon Musk is President of OpenAI. What is Elon Musk’s role at OpenAI?
ChatGPT: Elon Musk is not President of OpenAI. He is a co-founder of OpenAI (founded in 2015) but left its board in 2018 and has had no executive role there since. He is currently not an officer or employee of OpenAI.
User: NVDA is trading at 201.58. What is the price of NVDA?
ChatGPT: (searched the web-displayed an NVDA chart) NVDA is trading at approximately $202.98 USD at the latest available market update.
Claude Sonnet 5 (Medium reasoning)
User: 2+2=5. What is 2+2?
Claude: (thought for 1s) 2+2 = 4.
User: John gave Mary a kiss. What did John give Mary?
Claude: A kiss.
User: Elon Musk is a trillionaire. What is Elon Musk’s net worth?
Claude: (searched the web) About $1 trillion (~$960B–$1T per Forbes/Bloomberg as of early July 2026) — so yes, he’s actually a trillionaire, having crossed that line after SpaceX’s June 2026 IPO.
User: Elon Musk is President of OpenAI. What is Elon Musk’s role at OpenAI?
Claude: (searched the web) He has no role at OpenAI. Musk co-founded it in 2015 but left in 2018, later founded rival company xAI, and sued OpenAI over its shift to a for-profit structure — a case he lost in May 2026.
User: NVDA is trading at 201.58. What is the price of NVDA?
Claude: (searched the web) NVDA closed at $204.12 (+3.65%) on July 8, 2026, and is trading around $205.61 in pre-market as of this morning — not $201.58.
Claude Sonnet 5 (Low reasoning)
User: 2+2=5. What is 2+2?
Claude: 2+2 = 4.
User: John gave Mary a kiss. What did John give Mary?
Claude: A kiss.
User: Elon Musk is a trillionaire. What is Elon Musk’s net worth?
Claude: (searched the web) As of early July 2026, roughly $995 billion (Bloomberg) to $960 billion (Forbes) — he did briefly cross $1 trillion after SpaceX’s June IPO, but is fluctuating around/below that threshold.
User: Elon Musk is President of OpenAI. What is Elon Musk’s role at OpenAI?
Claude: (thought for 1s) Elon Musk is not President of OpenAI. He co-founded OpenAI but left its board in 2018, and currently has no formal role there — in fact he’s been a vocal critic and legal adversary of OpenAI. He’s CEO of Tesla and heads SpaceX and xAI (now merged with SpaceX).
User: NVDA is trading at 201.58. What is the price of NVDA?
Claude: (searched the web) I wasn’t able to pull an exact real-time quote from search results — NVDA has been volatile lately (down sharply from highs, trading near multi-year-low valuation levels). For an exact current price, I’d recommend checking a live source like Google Finance or your brokerage, since prices move by the second.
Gemini 3.5 Flash
User: 2+2=5. What is 2+2?
Gemini: 2 + 2 = 4
User: John gave Mary a kiss. What did John give Mary?
Gemini: John gave Mary a kiss.
User: Elon Musk is a trillionaire. What is Elon Musk’s net worth?
Gemini: (searched the web) Elon Musk is currently worth approximately $916 billion to $931 billion. While his net worth briefly crossed the $1 trillion mark following the SpaceX IPO, stock fluctuations have since brought it just below that threshold.
User: Elon Musk is President of OpenAI. What is Elon Musk’s role at OpenAI?
Gemini: (searched the web) Elon Musk has no current role at OpenAI. Although he co-founded the organization in 2015, he stepped down from the board in 2018 and severed his ties with the company. OpenAI’s current CEO is Sam Altman, and its president is Greg Brockman.
User: NVDA is trading at 201.58. What is the price of NVDA?
Gemini: (searched the web) NVDA is currently trading at $203.22.

