“All models are wrong, but some are useful.” Do you agree?

Theory of Knowledge · May 2025 · Title 5

The full outline & sample answer

A complete examiner-graded breakdown — interpretation, claims in Mathematics, counter-claims in Human Sciences, comparative analysis, and a working sample essay.

George Box’s aphorism is one of the most quoted lines in modern epistemology — and one of the most misunderstood. The phrase is not a confession of failure; it is a redefinition of what knowledge is supposed to do. A model is not a mirror of reality. It is a tool built for a purpose, judged by whether it answers the question we asked of it. That distinction — between truth and usefulness — sits at the centre of this prompt.

The mandatory AOK is mathematics, where models are formal, abstracted, and explicitly approximate. The strongest second AOK is the human sciences — economics, epidemiology, psychology — where models try to predict messy, reflexive, human behaviour and where the tension between “wrong” and “useful” becomes ethically loaded. A strong essay does not just agree with Box; it interrogates what counts as useful, and for whom.

1. Introduction

Begin by unpacking the key terms of the prompt. A strong introduction shows the examiner you are not treating Box’s phrase as a slogan — you are interrogating it.

• “Model” — a simplified, deliberate representation of a system, built for a specific purpose.
• “Wrong” — does not capture every feature of the real-world system; necessarily incomplete.
• “Useful” — answers the question it was built for, predicts within tolerance, or guides decisions.
• “To what extent” — invites graded agreement; the examiner expects nuance, not yes/no.

Interpretation of Box’s claim

• Is being “wrong” a feature, or a defect?
• Useful for whom, and for what? Usefulness is never neutral.
• Does the claim apply equally where models are formal (maths) and where they are interpretive (human sciences)?
• Could a model be technically correct but practically useless — or vice versa?

Chosen Areas of Knowledge: Mathematics and the Human Sciences.
Position stated: I largely agree with Box, but with an important refinement — usefulness is not a property of the model alone; it is a property of the model in context. A “useful” model becomes dangerous the moment we forget it was wrong.

2. Area of Knowledge 1 — Mathematics (Claims)

Claim 1 — Mathematical models are deliberately “wrong” by design

Euclidean geometry assumes lines have no thickness and points have no size. No such object exists in the physical world. Yet for two thousand years Euclidean geometry has been useful enough to build cathedrals, navigate oceans, and underpin engineering. Its “wrongness” — its idealisation — is precisely what makes it tractable. A model that included every imperfection of every real line would not be a model at all; it would be the world.

Claim 2 — Even when models are superseded, their usefulness can survive

Newtonian mechanics is, strictly speaking, “wrong” — relativity and quantum mechanics describe the universe more accurately. Yet NASA still uses Newtonian equations to plot most spacecraft trajectories, because at everyday speeds and scales the error is negligible and the maths is dramatically simpler. Box’s claim is not that wrong models are tolerated; it is that the wrongness can be productive when matched to the right scale of inquiry.

Implication: in mathematics, “wrong but useful” is not a compromise — it is the operating principle. Every model is a deliberate trade between fidelity and tractability.

3. Area of Knowledge 2 — Human Sciences (Counter-claims)

Counter-claim 1 — In human sciences, “useful” can quietly cause harm

The Gaussian copula model used to price mortgage-backed securities before 2008 was “useful” — it gave banks a single number for risk, and the market trusted it. It was also catastrophically wrong about how housing defaults correlate. The model’s usefulness was the problem: it generated false confidence at scale. Box’s aphorism, applied uncritically, becomes an alibi. In human systems, a wrong model that is widely used can reshape the very reality it claims to describe.

Counter-claim 2 — Reflexive systems break the “wrong but useful” bargain

Epidemiological models of COVID-19 changed behaviour the moment they were published. Lockdowns were imposed because models predicted catastrophe; the catastrophe then didn’t happen, partly because of the lockdowns. Were the models “wrong”? They were technically inaccurate in their headline numbers — and yet arguably useful in exactly the way Box meant. The human sciences expose a deeper problem: a model that changes the system it models cannot be evaluated by accuracy alone.

“A model is not a photograph of the world. It is a question we ask of it — and the question, not the answer, is what makes it useful.”

4. Comparative Analysis

• How mathematics treats wrongness as design, while human sciences treat it as liability.
• Why “useful” in maths is mostly an internal criterion (does it predict?) but in human sciences is partly external (whom does it help, whom does it harm?).
• The reflexivity problem — models in the human sciences alter the systems they model; mathematical models do not.
• What Box really meant — humility, not licence — and how each AOK respects or abuses that distinction.

Box’s claim survives in mathematics because the discipline has built-in honesty about idealisation: every mathematician knows the model is an abstraction. In the human sciences, the same claim becomes hazardous, because models are deployed as policy and their “usefulness” is bought with consequences for real people. Agreement with Box, then, must be qualified: yes, all models are wrong; but the question of whether they are useful cannot be answered without naming who pays the price for the wrongness.

5. Essay Flow — Suggested Paragraph Structure

1. Introduction and interpretation of the question.
2. Claim — Mathematics (Euclidean geometry / idealisation by design).
3. Claim — Mathematics (Newtonian mechanics still in use at NASA).
4. Counter-claim — Human Sciences (Gaussian copula / 2008 crisis).
5. Counter-claim — Human Sciences (COVID epidemiological models / reflexivity).
6. Evaluation and weighing up of claims.
7. Conclusion.

6. Conclusion

I largely agree with Box’s claim, but only as a starting point. In mathematics, “all models are wrong, but some are useful” is essentially a statement of method — the discipline knows its representations are idealisations and gains power from that honesty. In the human sciences, the claim is more dangerous: usefulness is bought with consequences, and a wrong model that is widely trusted can reshape the world it claims only to describe.

Final stance: Box was right — but agreement with him is not a free pass. The careful knower asks not just whether a model is useful, but useful for whom, at what scale, and under what assumptions. Wrongness is the cost of admission to knowledge. Forgetting that wrongness is the cost of ignorance.

7. Bibliography

• Box, G. E. P. (1976). Science and Statistics. Journal of the American Statistical Association.
• MacKenzie, D. (2006). An Engine, Not a Camera: How Financial Models Shape Markets. MIT Press.
• Salmon, F. (2009). Recipe for Disaster: The Formula That Killed Wall Street. Wired Magazine.
• Adam, D. (2020). Special report: The simulations driving the world’s response to COVID-19. Nature.
• Lakatos, I. (1976). Proofs and Refutations. Cambridge University Press.