Use a counterexample
See this course’s project requirements
An argument-audit packet with a premise map, conditional tests, counterexamples, repaired reasoning, certainty labels, and a final evidence-based room recommendation.
Keep your working files in your own notebook or software. Save a private description, checklist, and work link in My Proof.
What to include
- Identify premises, conclusion, and assumptions.
- Test conditional direction and create valid counterexamples.
- Explain and repair irrelevant or incomplete reasons.
- Distinguish rule-based conclusions from uncertain predictions.
- Produce the final map with a clear change trigger.
Review and revise
Use these criteria to check your work and choose what to improve.
- Argument roles are correctly identified.
- Counterexamples have the required true-condition/false-result structure.
- Revisions address the actual evidence gap.
- Final conclusions follow the supplied facts without hidden assumptions.
Want more background?
The idea in everyday life
Fictional claims: C1 “Every quiet room has a projector.” C2 “If a room has a projector, it is suitable for our 20-person workshop.” Records: A quiet/has projector/16 seats; B quiet/no projector/24 seats; C noisy/has projector/24 seats.
One valid exception can refute “all,” but it does not establish the opposite universal claim.
Use a counterexample: guided practice
One valid exception can refute “all,” but it does not establish the opposite universal claim.
Use paper or a free local text editor. This is an original fictional practice case; do not submit its records to a real service. Start this lesson with these facts, even if an earlier variation changed them. Fictional claims: C1 “Every quiet room has a projector.” C2 “If a room has a projector, it is suitable for our 20-person workshop.” Records: A quiet/has projector/16 seats; B quiet/no projector/24 seats; C noisy/has projector/24 seats.
1. Test C1
Find a quiet room without a projector.
You should see: Room B refutes C1.
It meets the condition and violates the claimed universal result.
2. Test C2
Find a projector room that cannot hold 20 people.
You should see: Room A refutes projector alone as sufficient suitability.
One favorable feature does not satisfy every stated need.
3. Narrow the claims
Rewrite each claim to match what the records establish.
You should see: Some quiet rooms have projectors; projector presence alone does not establish suitable capacity.
A correction should be no stronger than its evidence.
4. Preserve unknowns
State whether B is suitable overall.
You should see: B holds the group but lacks a projector; suitability depends on whether projection is required.
Refuting a rule does not answer every remaining decision.
What to finish
Use a counterexample record with the worked decisions and changed-case check.
Watch for this
Replacing a disproved “all” claim with an equally unsupported “none” claim.
How can I tell I understand it?
Test a universal claim or argument with a case that exposes its limit. Explain the evidence behind the result and correct any mismatch.
Quick knowledge check
Answer all 3 questions. Get at least 2 right and the lesson completes automatically.
You’ll get an explanation for each answer. Signed in? Your results save to your account.
Pass the check. We’ll save the progress.
Answer all 3 questions above and get at least 2 right. You can review the explanations and try again.
Go to the knowledge checkOptional course overview video · same video as Lesson 1
How to Argue - Philosophical Reasoning: Crash Course Philosophy #2
From CrashCourse. Watch here or open it on YouTube .
Optional course overview. Follow the written steps below at your own pace.Tools, templates, and lesson sources
Tools and templates
Tools open in a new tab so you can keep your place here.
Sources and further reading
Explore the references behind this lesson.
Source & access notes · checked 2026-09-12
Inspected premises, conclusions, and the distinction between truth and logical support.
Access: Public page or PDF inspected without payment or institutional sign-in on September 12, 2026. Optional external accounts are unnecessary for this course.
Reuse: Link and original paraphrase only. Public access does not grant blanket reuse; no provider text, figures, or exercises are reproduced.
Source & access notes · checked 2026-09-12
Inspected conditional forms, counterexamples, and deductive versus inductive inference.
Access: Public page or PDF inspected without payment or institutional sign-in on September 12, 2026. Optional external accounts are unnecessary for this course.
Reuse: Link and original paraphrase only. Public access does not grant blanket reuse; no provider text, figures, or exercises are reproduced.
Report a problem with this lesson
Tell us what went wrong. Please leave out personal information and private project contents.