Weakening by Providing Counterexamples

A counterexample is a specific case that contradicts a general claim. In logic, a single counterexample is sufficient to disprove a universal statement ("all X are Y"). In the more nuanced world of LNAT arguments — where claims are rarely stated as absolutes — counterexamples weaken arguments by showing that the general pattern does not hold in all cases, raising doubts about the reliability of the conclusion.

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The Logic of Counterexamples

Against universal claims

A universal claim asserts that something is true in all cases. A single counterexample disproves it entirely.

Claim: "All democracies have written constitutions." Counterexample: The United Kingdom is a democracy without a written constitution.

The counterexample conclusively disproves the universal claim.

Against general claims

Most LNAT arguments make general claims — that something is usually, typically, or probably the case. A single counterexample does not disprove a general claim, but it does weaken it by showing that exceptions exist.

Claim: "Private schools produce better academic results than state schools." Counterexample: Several state grammar schools and London comprehensives consistently outperform the majority of private schools in league tables.

This does not disprove the general trend, but it weakens the argument by demonstrating that the relationship between school type and results is more complex than the claim suggests.

The spectrum of impact

Type of claim	Effect of a counterexample
Universal ("all", "every", "always")	A single counterexample disproves the claim
Strong generalisation ("usually", "typically")	A counterexample weakens by showing exceptions
Weak generalisation ("sometimes", "can")	A counterexample has little impact — the claim already acknowledges exceptions
Qualified claim ("in most OECD countries")	A counterexample weakens only if it falls within the specified scope

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How Counterexamples Appear in LNAT Questions

LNAT questions testing counterexamples typically take these forms:

• "Which of the following, if true, would most weaken the argument?" — the correct answer provides a case that contradicts the argument's general claim
• "Which of the following would be the strongest objection to the author's argument?" — a counterexample that undermines the key premise or conclusion
• "The author's conclusion is undermined by..." — a specific case or data point that contradicts the conclusion

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What Makes a Strong Counterexample?

Not all counterexamples are equally effective. The strength of a counterexample depends on how relevant and representative it is.

Feature	Strong counterexample	Weak counterexample
Relevance	Directly addresses the specific claim being made	Tangentially related to the claim
Comparability	Involves circumstances similar to those discussed in the argument	Involves very different circumstances
Representativeness	Suggests a pattern of exceptions, not a unique anomaly	Is clearly an outlier that does not challenge the general trend
Documentation	Is well-documented and verifiable	Is anecdotal or difficult to confirm

Example of a strong counterexample

Argument: "Countries that have decriminalised drug possession have seen significant increases in drug use."

Strong counterexample: "Portugal decriminalised the personal possession of all drugs in 2001. In the two decades since, drug use rates have remained stable or declined, and drug-related deaths have fallen dramatically."

This is strong because Portugal is a well-documented case that directly contradicts the claim, involving a comparable (European) country over a substantial time period.

Example of a weak counterexample

Argument: "Raising the minimum wage leads to job losses."

Weak counterexample: "My friend runs a small business and says he would not reduce his workforce if the minimum wage went up."

This is weak because it is anecdotal (one person's prediction), not documented (a stated intention rather than an observed outcome), and not representative (one small business cannot speak for the whole economy).

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Worked Example 1

"History shows that economic sanctions are an effective tool for changing the behaviour of authoritarian regimes. When the international community applies economic pressure, regimes eventually comply with international norms."

Question: Which of the following, if true, would most weaken this argument?

A. Some authoritarian regimes have nuclear weapons, making military intervention impractical. B. Comprehensive sanctions were imposed on North Korea for over three decades without achieving denuclearisation; on Cuba for over sixty years without achieving democratisation; and on Iran for over forty years with only limited and temporary concessions — suggesting that sanctions frequently fail to change regime behaviour. C. Economic sanctions can harm ordinary citizens in the targeted country. D. Not all members of the international community agree on when sanctions should be applied.