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PWR-113 · Reasoning, Judgement & Strategy
Test eight fictional arguments by searching for counterexamples
This exercise asks one narrow question: if all stated premises were true, would the conclusion have to be true? The eight arguments use invented categories so real-world beliefs do not decide the answer. For an invalid argument, supply one possible case where every premise is true and the conclusion false. For a valid argument, state the short chain that makes a counterexample impossible. Plausibility, confidence and factual truth are not substitutes for validity. The cards are untimed and may be represented in plain language, symbols, audio or diagrams. Do not transfer the score to intelligence, general rationality or consequential legal, clinical, financial, employment or security judgments; those require domain expertise and accountable review. Stop if the drill becomes an intelligence comparison, high-pressure timed test or tool for a real dispute.
Tutorial curriculum · current public edition · Revision 7T · Full Tutorial Edition
Revision 7T · Full Tutorial Edition · complete governed practice tutorial
Test eight fictional arguments by searching for counterexamples
This exercise asks one narrow question: if all stated premises were true, would the conclusion have to be true? The eight arguments use invented categories so real-world beliefs do not decide the answer. For an invalid argument, supply one possible case where every premise is true and the conclusion false. For a valid argument, state the short chain that makes a counterexample impossible. Plausibility, confidence and factual truth are not substitutes for validity. The cards are untimed and may be represented in plain language, symbols, audio or diagrams. Do not transfer the score to intelligence, general rationality or consequential legal, clinical, financial, employment or security judgments; those require domain expertise and accountable review. Stop if the drill becomes an intelligence comparison, high-pressure timed test or tool for a real dispute.
Authority and safety
- Use only the bounded configuration. Use neutral syllogisms or fictional rule systems. Avoid legal, clinical, political or interpersonal accusations.
- Stop if the frame becomes an intelligence test, timed drill or consequential decision rule.
- Do not apply it to legal, clinical, financial, employment or security judgments.
Exact materials
- Eight argument cards in the fixture, each containing all premises and one conclusion.
- Response sheet with columns: valid/invalid, confidence 0–100, attempted counterexample or proof chain, added assumption, checked answer and correction.
- Method card: ‘Temporarily assume the premises. Try to make them all true while making the conclusion false. One coherent case disproves validity.’
- Counterexample tokens or simple diagrams for representing fictional objects; text or audio reasoning is equally valid.
- Answer key covered until all eight initial classifications and confidence ratings are recorded.
- Boundary card: neutral formal exercise only; no intelligence label and no use as a decision rule in a real high-stakes domain.
Set up in this order
- Review the definitions: a premise is assumed for the exercise, a conclusion is the claim being tested, and valid means no case can have true premises with a false conclusion.
- Choose an accessible representation and remove time pressure. Complete one unscored example: ‘All zims are blue; K is a zim; therefore K is blue’ is valid.
- For cards D1–D8, first mark valid or invalid and confidence without viewing the answer key.
- For every proposed invalid card, construct a specific counterexample. For every proposed valid card, write the premise link that forces the conclusion.
- Reveal the key, score classification and justification separately, and label errors as form error, added assumption or plausibility interference.
- Correct each missed card once and stop after eight. A 3–7-day fresh set may test retention, but this supplied set must not be memorised and called transfer.
Supplied fixture
| Card | Premises | Conclusion |
|---|---|---|
| D1 | All mirks are dovens. All dovens are pale. | All mirks are pale. |
| D2 | All toras are nims. Some nims are blue. | Some toras are blue. |
| D3 | No pelts are jars. Some jars are round. | Some round things are not pelts. |
| D4 | Some sivs are lons. All lons are quiet. | Some sivs are quiet. |
| D5 | All rens are veks. No veks are tall. | No rens are tall. |
| D6 | Some abels are gold. Some abels are square. | Some gold things are square. |
| D7 | No cados are fens. No fens are gors. | No cados are gors. |
| D8 | All hups are kels. No hups are round. | No kels are round. |
Check your work only after you finish
Lock every response first. The checking page is separate so the answers are not exposed inside this exercise.
Scoring rule
For each of eight cards, award 1 point for the correct valid/invalid classification and 1 point for an adequate proof chain or explicit counterexample: 16 points total. A classification with no justification can earn at most 1 point. For invalid cards, the counterexample must satisfy every premise while falsifying the conclusion; for valid cards, the chain must identify the forcing premise relationship. Report classification/8, justification/8, total/16, confidence and error types. A high score demonstrates only performance on these forms, not general intelligence, factual truth or sound high-stakes judgment.
Worked example
- On D6, the learner temporarily assumes both premises: some abels are gold, and some abels are square. The word ‘some’ does not say the same abel satisfies both claims.
- The learner constructs Abel A, which is gold and not square, and Abel B, which is square and not gold.
- Both premises are true: at least one abel is gold and at least one abel is square. The conclusion ‘some gold things are square’ is false in this model because neither object has both properties.
- The learner marks D6 invalid and writes the two-object model. That earns 1 classification point and 1 counterexample point.
- Across the full fictional set, suppose seven classifications and six justifications are correct. The total is 7 + 6 = 13/16; the missing justification points remain visible rather than being inferred from confidence.
Correct result: D6 earns 2/2 because the two-abel counterexample keeps both premises true and makes the conclusion false. The illustrative full-set score is 13/16. Neither result certifies rationality, intelligence or competence in a consequential domain.
Right and wrong
| Moment | Right / safer | Wrong / riskier | Why |
|---|---|---|---|
| Testing an odd premise | Assume it temporarily and ask what follows. | Call the argument invalid because the fictional category sounds implausible. | Validity concerns the relationship between premises and conclusion, not real-world plausibility. |
| Rejecting an inference | Give a model with true premises and a false conclusion. | Say only ‘the conclusion might be wrong.’ | A concrete counterexample demonstrates the logical possibility required. |
| Reading ‘some’ | Allow different witnesses unless the premises link them. | Assume two ‘some’ statements refer to the same object. | That hidden identity assumption causes the D6 error. |
| Using a valid form | Trace D1 from mirk to doven to pale. | Accept it only because pale mirks sound believable. | The premise chain, not belief, forces the conclusion. |
| Applying the score | Describe accuracy on eight neutral arguments. | Use 16/16 to approve a legal, medical or financial decision. | Formal-task performance does not supply domain facts, authority or accountable review. |
Common mistakes and fixes
| Mistake | Fix |
|---|---|
| The learner argues that a premise is false in real life. | Bracket factual truth and test whether the conclusion must follow if the premises are true. |
| A counterexample violates one of the premises. | Check every premise line by line before claiming the conclusion can be false. |
| ‘All hups are kels’ is reversed to ‘all kels are hups.’ | Draw one contained set: hups sit inside kels; properties of hups need not cover other kels. |
| Confidence is used as a justification point. | Score confidence separately; award the second point only for a valid chain or counterexample. |
| The same eight answers are memorised and presented as transfer. | Use fresh forms after delay for any retention or transfer claim and keep this supplied set labelled practice. |
Evidence boundary
What the tutorial may—and may not—claim.
Supportable claim
Deductive reasoning on specified problems may improve with structured practice, but the active-control advantage and durable transfer remain uncertain.
Measurement boundary
Declare formalism, language, item novelty, active control, response accuracy, explanation, delay and transfer domain; one task is not general rationality.
Become perfectly logical
MetricAccuracy and explanation on predeclared novel deduction problems after delay
BoundaryA logic-task gain does not prove global intelligence or better high-stakes decisions.
Negative and limiting findings
- The training app did not outperform its active control.
- Abstract logic principles alone had little effect unless mapping to concrete examples was made available.
- Neither source tested durable retention or consequential real-world transfer.
Prohibited wording
- become perfectly logical
- logic app raises intelligence
- never make a reasoning error
- deductive score proves rationality
Direct source register
Evidence that supports—and limits—the route.
Patricia W. Cheng; Keith J. Holyoak; Richard E. Nisbett; Lindsay M. Oliver · 1986 · PRIMARY_RESEARCH
Supports only the bounded empirical proposition in the declared configurations. Constrains generalisation, transfer, certainty or efficacy; it is not optional context.
Robert A. Cortes; Adam B. Weinberger; Adam E. Green · 2023 · PRIMARY_RESEARCH
Supports only the bounded empirical proposition in the declared configurations. Constrains generalisation, transfer, certainty or efficacy; it is not optional context.
Tutorial delivery controls
Learn, adapt, troubleshoot and resume
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Step-by-step learner mode
Each activity includes its success check, a nearby accessible alternative and an “I’m stuck” correction path. Alternatives preserve the target where possible; when they change the task, Titan labels them as related rather than equivalent.
Review the definitions: a premise is assumed for the exercise, a conclusion…
Review the definitions: a premise is assumed for the exercise, a conclusion is the claim being tested, and valid means no case can have true premises with a false conclusion.
“Review the definitions: a premise is assumed for the exercise, a conclusion is the claim being tested, and valid means no case can have true premises with a false conclusion” isolates the named evidence distinction so the learner can interpret Deductive reasoning without extending the claim.
The output directly answers “Review the definitions: a premise is assumed for the exercise, a conclusion is the claim being tested, and valid means no case can have true premises with a false conclusion”, names the relevant distinction and stays within the supplied record.
I’m stuck on this step
Reset: Re-read this authored instruction — “Review the definitions: a premise is assumed for the exercise, a conclusion is the claim being tested, and valid means no case can have true premises with a false conclusion.” — and its success check, then attempt only this step.
Possible snag: The learner argues that a premise is false in real life.
Correction: Bracket factual truth and test whether the conclusion must follow if the premises are true.
Possible snag: A counterexample violates one of the premises.
Correction: Check every premise line by line before claiming the conclusion can be false.
Stop / get help: A governed step-by-step lesson may be completed independently inside its stated limits. Stop if the declared configuration cannot be maintained, uncertainty becomes material, adverse effects appear, or qualified authority is required.
Choose an accessible representation and remove time pressure
Choose an accessible representation and remove time pressure. Complete one unscored example: ‘All zims are blue; K is a zim; therefore K is blue’ is valid.
“Choose an accessible representation and remove time pressure” fixes the exact Deductive reasoning configuration or decision before later observations are compared.
The learner can verify “Choose an accessible representation and remove time pressure” from the declared materials, position or recorded choice before continuing.
I’m stuck on this step
Reset: Re-read this authored instruction — “Choose an accessible representation and remove time pressure. Complete one unscored example: ‘All zims are blue; K is a zim; therefore K is blue’ is valid.” — and its success check, then attempt only this step.
Possible snag: The result from “Choose an accessible representation and remove time pressure. Complete one unscored example: ‘All zims are blue; K is a zim; therefore K is blue’ is valid.” does not yet meet this declared check: The learner can verify “Choose an accessible representation and remove time pressure” from the declared materials, position or recorded choice before continuing.
Correction: Return to the start of “Choose an accessible representation and remove time pressure”, reduce complexity or pace, and repeat only the part needed to satisfy: “The learner can verify “Choose an accessible representation and remove time pressure” from the declared materials, position or recorded choice before continuing.”
Stop / get help: A governed step-by-step lesson may be completed independently inside its stated limits. Stop if the declared configuration cannot be maintained, uncertainty becomes material, adverse effects appear, or qualified authority is required.
For cards D1–D8, first mark valid or invalid and confidence without viewing…
For cards D1–D8, first mark valid or invalid and confidence without viewing the answer key.
“For cards D1–D8, first mark valid or invalid and confidence without viewing the answer key” carries the authored Deductive reasoning method into a reviewable output without adding an unstated task, dose or claim.
Evidence of completion shows the learner followed this exact instruction without adding an unstated step: “For cards D1–D8, first mark valid or invalid and confidence without viewing the answer key.”
I’m stuck on this step
Reset: Re-read this authored instruction — “For cards D1–D8, first mark valid or invalid and confidence without viewing the answer key.” — and its success check, then attempt only this step.
Possible snag: ‘All hups are kels’ is reversed to ‘all kels are hups.’
Correction: Draw one contained set: hups sit inside kels; properties of hups need not cover other kels.
Stop / get help: A governed step-by-step lesson may be completed independently inside its stated limits. Stop if the declared configuration cannot be maintained, uncertainty becomes material, adverse effects appear, or qualified authority is required.
For every proposed invalid card, construct a specific counterexample
For every proposed invalid card, construct a specific counterexample. For every proposed valid card, write the premise link that forces the conclusion.
“For every proposed invalid card, construct a specific counterexample” creates the auditable value, condition or statement needed for the tutorial’s later comparison and conclusion.
A legible entry directly completes “For every proposed invalid card, construct a specific counterexample” and records the requested condition, decision or boundary without adding a new claim.
I’m stuck on this step
Reset: Re-read this authored instruction — “For every proposed invalid card, construct a specific counterexample. For every proposed valid card, write the premise link that forces the conclusion.” — and its success check, then attempt only this step.
Possible snag: The result from “For every proposed invalid card, construct a specific counterexample. For every proposed valid card, write the premise link that forces the conclusion.” does not yet meet this declared check: A legible entry directly completes “For every proposed invalid card, construct a specific counterexample” and records the requested condition, decision or boundary without adding a new claim.
Correction: Return to the start of “For every proposed invalid card, construct a specific counterexample”, reduce complexity or pace, and repeat only the part needed to satisfy: “A legible entry directly completes “For every proposed invalid card, construct a specific counterexample” and records the requested condition, decision or boundary without adding a new claim.”
Stop / get help: A governed step-by-step lesson may be completed independently inside its stated limits. Stop if the declared configuration cannot be maintained, uncertainty becomes material, adverse effects appear, or qualified authority is required.
Reveal the key, score classification and justification separately, and label errors as…
Reveal the key, score classification and justification separately, and label errors as form error, added assumption or plausibility interference.
“Reveal the key, score classification and justification separately, and label errors as form error, added assumption or plausibility interference” creates the auditable value, condition or statement needed for the tutorial’s later comparison and conclusion.
The work shows the value requested by “Reveal the key, score classification and justification separately, and label errors as form error, added assumption or plausibility interference”, retains the supplied units or signs and leaves any unsupported value unknown.
I’m stuck on this step
Reset: Re-read this authored instruction — “Reveal the key, score classification and justification separately, and label errors as form error, added assumption or plausibility interference.” — and its success check, then attempt only this step.
Possible snag: Confidence is used as a justification point.
Correction: Score confidence separately; award the second point only for a valid chain or counterexample.
Stop / get help: A governed step-by-step lesson may be completed independently inside its stated limits. Stop if the declared configuration cannot be maintained, uncertainty becomes material, adverse effects appear, or qualified authority is required.
Correct each missed card once and stop after eight
Correct each missed card once and stop after eight. A 3–7-day fresh set may test retention, but this supplied set must not be memorised and called transfer.
Keep this exact Deductive reasoning action explicit and reviewable: “Correct each missed card once and stop after eight. A 3–7-day fresh set may test retention, but this supplied set must not be memorised and called transfer.”
Evidence of completion shows the learner followed this exact instruction without adding an unstated step: “Correct each missed card once and stop after eight. A 3–7-day fresh set may test retention, but this supplied set must not be memorised and called transfer.”
I’m stuck on this step
Reset: Re-read this authored instruction — “Correct each missed card once and stop after eight. A 3–7-day fresh set may test retention, but this supplied set must not be memorised and called transfer.” — and its success check, then attempt only this step.
Possible snag: The same eight answers are memorised and presented as transfer.
Correction: Use fresh forms after delay for any retention or transfer claim and keep this supplied set labelled practice.
Stop / get help: A governed step-by-step lesson may be completed independently inside its stated limits. Stop if the declared configuration cannot be maintained, uncertainty becomes material, adverse effects appear, or qualified authority is required.
Correct versus incorrect execution
These accessible process diagrams are built from the tutorial’s own right/wrong teaching. They are not anatomical illustrations and do not add technique beyond the canonical tutorial.
Assume it temporarily and ask what follows.
Call the argument invalid because the fictional category sounds implausible.
Give a model with true premises and a false conclusion.
Say only ‘the conclusion might be wrong.’
Allow different witnesses unless the premises link them.
Assume two ‘some’ statements refer to the same object.
Trace D1 from mirk to doven to pale.
Accept it only because pale mirks sound believable.
Describe accuracy on eight neutral arguments.
Use 16/16 to approve a legal, medical or financial decision.
Method-structure checklist
10 of 10 structural checks present
- Ordered, Power-specific instructions — present
- Every activity has a success check — present
- Materials or supplied records are declared — present
- Measurement or assessment rule is present — present
- Tutorial-specific troubleshooting is present — present
- Stopping or escalation boundary is present — present
- Every activity has an adjacent alternative — present
- Correct-versus-incorrect comparison is present — present
- Evidence context is bound to the Power record — present
- Planning metadata is present — present
The method-readiness band and presence checklist assess tutorial presentation and are separate from evidence quality for the underlying Power. They are automated editorial aids, not human approval.
Manual editorial sign-off: Pending. This tutorial must not display a human-approved state until an identified editor signs the exact content hash.