Test a Claim and a Counterexample
Evaluate a universal claim against complete supplied fictional records.
Supplied materials
- Original fictional plaza file: Claim in a leaflet: “Every renter used the new display board this week.” Rental list has six renters A–F. Display log lists A, B, C, D once each; logkeeper says all board use was recorded. Renter E’s letter says “I did not use the board this week.” F’s use is not mentioned in a personal account. Treat the six-person rental list and complete board log as the supplied scope; do not infer real-world completeness.
Learn the idea
An argument links evidence to a claim. Words such as “every” make a strong universal claim: all members of the stated group must satisfy it. One relevant counterexample is enough to challenge a universal claim. It is different from a claim that several or most of the group used the board.
Evaluate each record’s relevance and stated completeness. E’s letter directly conflicts with the leaflet’s “every renter” claim. The log, under its supplied complete-recording assumption, records four of six renters. F lacks a personal letter, but absence from the stipulated complete log has a specific role in this exercise. In a real inquiry, you would investigate whether a log was actually complete before treating absence that way.
- Define the leaflet’s group and time scope.
- Compare the six-person rental list with the display log.
- Identify E’s direct counterexample.
- Write a narrower replacement claim and state the log-completeness assumption it uses.
See the method in action
“Every renter is not supported: E explicitly reports not using the board. The stipulated complete log records four of six listed renters using it this week. A narrower claim is that four listed renters are recorded users, conditional on the log’s supplied completeness.”
Check your reasoning
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See the answer and explanation
E’s same-week letter reporting no board use.
E belongs to the stated six-renter group and reports not using the board during the same week, making a relevant counterexample.
Take it further
Changed claim: “At least one renter used the board this week.” Model reasoning: “The log entries for A–D support the narrower existence claim. E’s non-use does not refute at least one; the wording of the claim changes what counts as a counterexample.”
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