Read
Build the mental model
Move through the guided explanation first so the central distinction and purpose are clear before you evaluate your own work.
Fallacies And Errors
Bayesian and Problem-Solving Fallacies
Extends the taxonomy to probabilistic updating and practical strategy selection, showing how base-rate neglect and option-space failure behave across both domains.
Read the explanation sections first, then use the activities to test whether you can apply the idea under pressure.
Start Here
What this lesson is helping you do
Extends the taxonomy to probabilistic updating and practical strategy selection, showing how base-rate neglect and option-space failure behave across both domains. The practice in this lesson depends on understanding Species of a Fallacy, Support Miscalibration, and Option-Space Failure and applying tools such as Trace the Species Back to the Family and Diagnose by the Mode of Reasoning correctly.
How to approach it
Read the explanation sections first, then use the activities to test whether you can apply the idea under pressure.
What the practice is building
You will put the explanation to work through diagnosis practice, quiz, analysis practice, comparison exercise, rapid identification, evaluation practice, and argument building activities, so the goal is not just to recognize the idea but to use it under your own control.
What success should let you do
Diagnose and repair 10 Bayesian or problem-solving fallacies with explicit reference to the violated standard and the relevant priors, likelihoods, or constraints.
Reading Path
Move through the lesson in this order
The page is designed to teach before it tests. Use this sequence to keep the reading, examples, and practice in the right relationship.
Study
Watch the move in context
Use the worked examples to see how the reasoning behaves when someone else performs it carefully.
Do
Practice with a standard
Only then move into the activities, using the pause-and-check prompts as a final checkpoint before you submit.
Guided Explanation
Read this before you try the activity
These sections give the learner a usable mental model first, so the practice feels like application rather than guesswork.
Core idea
Why probability has its own fallacies
Bayesian reasoning combines prior beliefs with new evidence to produce updated beliefs. When the combination is done badly, the error is not usually about facts but about how much the facts should shift our confidence. That is why probability has its own fallacy family.
The most common Bayesian errors involve either neglecting the prior (base-rate neglect), confusing how likely the evidence is given the hypothesis with how likely the hypothesis is given the evidence, or overreacting or underreacting to new information relative to what the math would require.
What to look for
- Ask what the prior was before the evidence arrived.
- Ask how likely the evidence would be under rival hypotheses.
- Ask whether the update matches the strength of the evidence.
Bayesian fallacies are about poorly calibrated updates, not missing facts.
Species
Base-rate neglect and likelihood confusion
Base-rate neglect ignores how common the hypothesis was to begin with. In medical testing, for instance, a positive result on a very accurate test for a rare disease can still leave the chance that the patient has the disease quite low, because the disease is rare in the population. Ignoring the base rate produces badly miscalibrated conclusions.
Likelihood-posterior confusion mistakes P(evidence given hypothesis) for P(hypothesis given evidence). These are different quantities, related by Bayes' theorem. A classic example: 'If the suspect is guilty, the chance of these fibers at the scene is 95%.' That is not the same as 'Given these fibers, the chance of guilt is 95%' — the second depends on priors and on how often the fibers appear when the suspect is innocent.
What to look for
- Look for the prior before updating.
- Distinguish P(E|H) from P(H|E).
- Check whether the evidence is also likely under rival hypotheses.
A Bayesian update is only as good as the priors and the likelihoods it rests on.
Species
Over- and under-updating
Over-updating happens when a small piece of evidence produces a large swing in confidence that the math cannot justify. A single news story cannot usually shift a well-supported belief by much. Under-updating happens when strong evidence produces almost no shift, often because the reasoner is attached to the prior for non-evidential reasons.
Both are miscalibration species. The repair in either direction is the same kind: recompute the update more carefully, either by sanity-checking the likelihood or by honestly asking whether the prior is being defended because of evidence or because of attachment.
What to look for
- Ask whether the evidence really justifies the size of the shift.
- Ask whether the prior is being held for evidential or personal reasons.
- Sanity-check the updated belief against how future evidence would feel.
Calibration means moving the right distance, not just in the right direction.
Species
Problem-solving fallacies
Problem solving has its own family of fallacies that look like other fallacies but are really about strategy space. False dilemma in a planning context means only two strategies are considered when many exist. Constraint neglect forgets a real limit like budget, time, or legal rule. Goal drift shifts the target mid-solution without noticing. Single-option fixation picks the first plausible plan and stops searching.
Failure to identify revision triggers is subtler: the plan may be fine in principle, but the reasoner never asks 'what would tell me this plan is going wrong?' Without revision triggers, a bad plan gets executed to the end because the reasoner has no signal to stop.
What to look for
- List the constraints explicitly before evaluating a plan.
- Ask what revision triggers exist for this plan.
- Check that the plan still matches the original goal, not a drifted version.
Problem-solving fallacies are usually option-space or constraint failures in disguise.
Core Ideas
The main concepts to keep in view
Use these as anchors while you read the example and draft your response. If the concepts blur together, the practice usually blurs too.
Species of a Fallacy
A more specific recurring error pattern that instantiates a broader fundamental inferential defect.
Why it matters: Species help learners see both the named error and its deeper structure.
Support Miscalibration
A family of errors in which the degree or type of support claimed is stronger, weaker, or otherwise different from what the evidence actually warrants.
Why it matters: This family unifies many inductive, Bayesian, and explanatory mistakes.
Option-Space Failure
A family of errors in which relevant alternatives, constraints, or strategy revisions are ignored.
Why it matters: This family is especially important in abductive, Bayesian, and problem-solving contexts.
Reference
Open these only when you need the extra structure
How the lesson is meant to unfold
Concept Intro
The core idea is defined and separated from nearby confusions.
Rule Or Standard
This step supports the lesson by moving from explanation toward application.
Worked Example
A complete example demonstrates what correct reasoning looks like in context.
Guided Practice
You apply the idea with scaffolding still visible.
Assessment Advice
Use these prompts to judge whether your reasoning meets the standard.
Mastery Check
The final target tells you what successful understanding should enable you to do.
Reasoning tools and formal patterns
Rules and standards
These are the criteria the unit uses to judge whether your reasoning is actually sound.
Trace the Species Back to the Family
A correct fallacy diagnosis should identify both the specific named error and the broader inferential defect it exemplifies.
Common failures
- The learner memorizes labels without understanding the violated standard.
- Two fallacies are treated as unrelated even though they share the same deeper defect.
Diagnose by the Mode of Reasoning
The same surface error term may need different analysis depending on whether the reasoning is deductive, inductive, abductive, Bayesian, or practical.
Common failures
- A probabilistic error is judged as though it were purely deductive.
- A problem-solving failure is mislabeled with a rhetorical fallacy name while ignoring strategic structure.
Repair Rather Than Merely Label
A strong fallacy analysis should explain what inferential repair would be required for the argument to meet the relevant standard.
Common failures
- The fallacy is named but not explained.
- No corrected version of the reasoning is offered.
Charitable Reading Before Fallacy Accusation
Before diagnosing a fallacy, reconstruct the strongest plausible version of the argument and check whether the error survives that reconstruction.
Common failures
- Attacking a careless phrasing instead of the best version of the argument.
- Declaring a fallacy prematurely without checking for an implicit premise that would rescue the reasoning.
Patterns
Use these when you need to turn a messy passage into a cleaner logical structure before evaluating it.
Fallacy Taxonomy Map
Input form
argument_or_reasoning_case
Output form
family_species_repair_analysis
Steps
- Identify the mode of reasoning involved.
- State the standard that should govern the case.
- Determine the fundamental fallacy family violated.
- Identify the most specific species if one applies.
- State how the reasoning would need to be repaired.
Watch for
- Naming a species without identifying the violated standard.
- Using a familiar fallacy label when the deeper defect is actually different.
Cross-Mode Fallacy Comparison
Input form
paired_reasoning_cases
Output form
shared_family_different_species_analysis
Steps
- Identify the reasoning mode in each case.
- State the governing standard for each case.
- Identify the shared fundamental family.
- Explain how the species differ by context.
- Compare the repairs required.
Watch for
- Assuming identical labels imply identical structure.
- Ignoring that mode-specific standards shape what counts as an error.
Worked Through
Examples that model the standard before you try it
Do not skim these. A worked example earns its place when you can point to the exact move it is modeling and the mistake it is trying to prevent.
Worked Example
Species in Bayesian and Practical Reasoning
Probabilistic and practical fallacies often arise because option space, constraints, or the calibration of support are mishandled. The repairs look different, but the underlying family structure is the same as in the other lessons.
Species Map
Problem Solving
- false dilemma in strategy
- constraint neglect
- goal drift
- failure to identify revision triggers
- single-option fixation
- plan commitment despite evidence
Bayesian Probability
- base-rate neglect
- likelihood-posterior confusion
- over-updating from weak evidence
- under-updating in the face of strong evidence
- conjunction fallacy
- prosecutor's fallacy
Worked Example
Base-rate neglect: a worked case
Repair
Compute the posterior using both the prior (base rate) and the likelihood. Never take test accuracy as a direct report of P(disease|positive).
Analysis
Out of 10,000 people, about 1 has the disease and tests positive (true positive). About 9,999 do not have it, and 1% of those — roughly 100 — will test positive anyway (false positives). So out of roughly 101 positive tests, only 1 is a real case. The probability of actually having the disease given a positive test is about 1%, not 99%.
Argument
A test for a rare disease is 99% accurate (meaning P(positive|disease) = 0.99 and P(negative|no disease) = 0.99). The disease affects 1 in 10,000 people. A patient tests positive. How likely is it that she actually has the disease?
Pause and Check
Questions to use before you move into practice
Self-check questions
- Was the probability update calibrated to both the prior and the evidence?
- Did the practical analysis consider relevant constraints and alternatives?
- What would tell the reasoner the plan or belief needs to be revised?
Practice
Now apply the idea yourself
Move into practice only after you can name the standard you are using and the structure you are trying to preserve or evaluate.
Diagnosis Practice
IntegratedRepair the Bayesian or Practical Error
For each case, identify the reasoning mode (Bayesian or problem-solving), name the fallacy family and species, and explain how the update or strategy should be corrected.
Five mixed cases
Some cases are Bayesian, some are strategy-based, and one could be read either way. Explain your mode choice as part of the diagnosis.
Case 1 — The rare-disease test
This test is 99% accurate. I tested positive. So I have a 99% chance of having the disease.
What does '99% accurate' actually mean, and where is the base rate?
Case 2 — The product launch
We can either launch next Monday or never launch at all. There is no other path forward.
How many real options exist here?
Case 3 — The news swing
One leaked memo appeared yesterday. I now believe the company is definitely committing fraud, and nothing short of total acquittal will change my mind.
Is this update calibrated? What would update you back?
Case 4 — The forensic claim
If the suspect were innocent, the chance of these fibers at the scene would be only 2%. Therefore the chance he is innocent is only 2%.
Which probability is which?
Case 5 — The tutoring rollout
Our tutoring rollout plan is perfect. We built it three months ago and we're following it exactly. Anyone questioning it is just nervous.
What revision triggers have been built into the plan?
Quiz
FoundationsScenario Check: Bayesian and Problem-Solving Fallacies
Each question presents a scenario or challenge. Answer in two to four sentences. Focus on showing that you can use what you learned, not just recall it.
Scenario questions
Work through each scenario. Precise, specific answers are better than long vague ones.
Question 1 — Diagnose
A student makes the following mistake: "Ignoring priors in Bayesian cases." Explain specifically what is wrong with this reasoning and what the student should have done instead.
Can the student identify the flaw and articulate the correction?
Question 2 — Apply
You encounter a new argument that you have never seen before. Walk through exactly how you would diagnose probability error, starting from scratch. Be specific about each step and explain why the order matters.
Can the student transfer the skill of diagnose probability error to a genuinely new case?
Question 3 — Distinguish
Someone confuses support miscalibration with option space failure. Write a short explanation that would help them see the difference, and give one example where getting them confused leads to a concrete mistake.
Does the student understand the boundary between the two concepts?
Question 4 — Transfer
The worked example "Species in Bayesian and Practical Reasoning" showed one way to handle a specific case. Describe a situation where the same method would need to be adjusted, and explain what you would change and why.
Can the student adapt the demonstrated method to a variation?
Use one of the sentences above and move carefully from ordinary language to a clearer predicate-logic style representation.
Analysis Practice
FoundationsApply the Concepts: Bayesian and Problem-Solving Fallacies
Analyze each passage below using the concepts from this lesson. Identify key logical features and explain your reasoning.
Practice scenarios
Work through each scenario carefully. Apply the concepts from this lesson.
Scenario 1
A local council argues: every park that has been surveyed shows declining bird populations. The marsh reserve has not been surveyed. Therefore, we cannot conclude anything about its bird population.
Scenario 2
The professor told the class: 'Either your hypothesis is testable, or it does not belong in a scientific paper.' Maria's hypothesis predicts no observable outcomes.
Scenario 3
A fitness study concludes that runners who stretch before exercise report fewer injuries. However, runners who stretch may also be more cautious in other ways.
Pick one of the passages above and map how the reasons are supposed to support the conclusion.
Diagnosis Practice
FoundationsSpot the Error: Bayesian and Problem-Solving Fallacies
Each passage contains a logical mistake. Identify the error, name it if possible, and explain why the reasoning fails.
Practice scenarios
Work through each scenario carefully. Apply the concepts from this lesson.
Case A
Everyone at the meeting agreed the policy is fair. Since the meeting was open to the public, we can say the public agrees the policy is fair.
Case B
No reptile is a mammal. No mammal is an insect. Therefore, no reptile is an insect.
Case C
The forecast said 70% chance of rain. It did not rain. Therefore, the forecast was wrong.
Use one of the passages above. Name the weakness, explain the violated standard, and show how the reasoning should be repaired.
Comparison Exercise
FoundationsCompare and Connect: Bayesian and Problem-Solving Fallacies
Compare the reasoning in the passages below. Identify similarities, differences, and which argument is stronger, explaining your criteria.
Practice scenarios
Work through each scenario carefully. Apply the concepts from this lesson.
Argument X
Since all observed swans in Europe were white, all swans are white.
Argument Y
Since the chemical formula for water is H2O in every sample we have tested, water is H2O.
Argument Z
Since every student I asked preferred online classes, all students prefer online classes.
Use one of the sentences above and move carefully from ordinary language to a clearer predicate-logic style representation.
Analysis Practice
FoundationsDeep Practice: Bayesian and Problem-Solving Fallacies
Apply the concepts from this lesson to more complex scenarios. Work through each carefully and explain your reasoning in full.
Advanced practice scenarios
Each scenario tests your ability to apply foundational logic concepts in realistic contexts.
Case 1
An editorial argues: 'Standardized testing must be eliminated because it causes student anxiety. And since anything that causes anxiety is harmful, standardized testing is harmful.' Analyze the argument's structure, identify any hidden premises, and evaluate its strength.
Case 2
A scientist writes: 'We observed that 90% of treated mice recovered, while only 30% of untreated mice recovered. The treatment appears effective. However, the treated group was also younger on average.' Identify the argument, the potential confounder, and what additional information would strengthen or weaken the conclusion.
Case 3
A philosopher claims: 'Either free will is an illusion, or moral responsibility is justified. Neuroscience has shown that brain activity precedes conscious decisions. Therefore, free will is probably an illusion, and moral responsibility may not be justified.' Map the logical structure and evaluate whether the conclusion follows.
Pick one of the passages above and map how the reasons are supposed to support the conclusion.
Analysis Practice
FoundationsReal-World Transfer: Bayesian and Problem-Solving Fallacies
Apply what you have learned to these real-world contexts. Analyze each scenario using the tools and concepts from this lesson.
Transfer practice
Connect the concepts from this lesson to contexts outside the classroom.
Media literacy
A social media post claims: 'A new study proves that video games improve intelligence.' The post links to a study of 40 college students who played puzzle games for 2 weeks and showed improved scores on one type of spatial reasoning test. Evaluate this claim using what you know about arguments, evidence, and reasoning.
Everyday reasoning
A friend argues: 'I should not get vaccinated because my cousin got vaccinated and still got sick. Also, I read an article that said natural immunity is better.' Identify the types of reasoning, assess their strength, and explain what additional evidence would be relevant.
Professional context
A manager says: 'Our last three hires from University X performed well, so we should recruit exclusively from University X.' Analyze the reasoning type, identify potential problems, and suggest a better approach.
Pick one of the passages above and map how the reasons are supposed to support the conclusion.
Rapid Identification
FoundationsTimed Drill: Bayesian and Problem-Solving Fallacies
Work through these quickly. For each passage, identify whether it contains an argument, name its type if so, and point to the conclusion. Aim for speed and accuracy.
Quick-fire argument identification
For each item, decide: argument or not? If yes, what type and what is the conclusion? Under 45 seconds per item.
Item 1
The bridge was built in 1962. It was designed by a local engineering firm and cost $2.3 million.
Item 2
Because the experiment was not replicated, the results should be treated with caution.
Item 3
Sharks have survived five mass extinction events, so they are remarkably resilient species.
Item 4
If the evidence was obtained illegally, the court must exclude it. The evidence was obtained without a warrant. Warrantless searches are illegal. Therefore, the court must exclude the evidence.
Item 5
The town council meets every second Tuesday. This week is the second Tuesday. The library will be used for the meeting.
Item 6
The most likely reason the power went out is the thunderstorm, since the outage started exactly when lightning struck the transformer.
Use one of the sentences above and move carefully from ordinary language to a clearer predicate-logic style representation.
Evaluation Practice
FoundationsPeer Review: Bayesian and Problem-Solving Fallacies
Below are sample student attempts to identify and analyze arguments. Evaluate each response: Is the identification correct? Is the analysis accurate? What feedback would you give?
Evaluate student argument analyses
Each student tried to break down an argument into premises and conclusion. Assess their work.
Student A's work
Passage: 'Since exercise reduces stress and stress causes health problems, exercise prevents health problems.' Student A wrote: 'Premise 1: Exercise reduces stress. Premise 2: Stress causes health problems. Conclusion: Exercise prevents health problems. This is a valid deductive argument.'
Student B's work
Passage: 'The committee should approve the budget because it was prepared by experts.' Student B wrote: 'This is not an argument. It is just a recommendation.'
Student C's work
Passage: 'Most doctors recommend regular check-ups. Regular check-ups catch diseases early. Early detection saves lives. Therefore, you should get regular check-ups.' Student C wrote: 'Premise 1: Most doctors recommend check-ups. Conclusion: You should get check-ups. This is an inductive argument from authority.'
Student D's work
Passage: 'It will probably rain tomorrow because the barometric pressure is dropping and clouds are moving in from the west.' Student D wrote: 'Premise 1: Barometric pressure is dropping. Premise 2: Clouds are moving in. Conclusion: It will probably rain. This is an inductive argument based on observed indicators. Strength: moderate, since weather patterns are not perfectly predictable.'
Choose one of the passages above and evaluate it using the right standard for its reasoning mode.
Argument Building
FoundationsConstruction Challenge: Bayesian and Problem-Solving Fallacies
Build arguments from scratch. For each task, construct a well-structured argument with clear premises and a conclusion. Identify the reasoning type you are using.
Construct original arguments
For each prompt, build a complete argument from scratch. Clearly state premises, conclusion, and reasoning type.
Task 1
Construct a deductive argument with two premises that concludes: 'This substance is not an acid.' Make sure the argument is valid.
Task 2
Build an inductive argument with at least three pieces of evidence supporting the conclusion: 'Regular reading improves vocabulary.' Make it as strong as you can.
Task 3
Construct an argument that uses an indicator word for the conclusion and a different indicator word for at least one premise. The topic should be about environmental policy.
Task 4
Build two different arguments for the same conclusion: 'Public libraries should remain publicly funded.' One argument should be deductive, the other inductive. Explain why one might be more persuasive than the other.
Use one of the sentences above and move carefully from ordinary language to a clearer predicate-logic style representation.
Diagnosis Practice
FoundationsCounterexample Challenge: Bayesian and Problem-Solving Fallacies
For each argument, construct a counterexample or identify a scenario that shows the reasoning is flawed. Explain what the counterexample reveals about the argument's weakness.
Counterexamples and edge cases
Each argument has a flaw. Expose it with a specific counterexample.
Argument 1
Every time I have washed my car, it rained the next day. Therefore, washing my car causes rain.
Argument 2
No one at the party complained about the food. Therefore, everyone enjoyed the food.
Argument 3
This policy worked well in Sweden. Therefore, it will work well in Brazil.
Argument 4
The candidate won 60% of the vote in the primary. Therefore, they will win the general election.
Argument 5
All the reviews on the website are positive. Therefore, the product is excellent.
Use one of the passages above. Name the weakness, explain the violated standard, and show how the reasoning should be repaired.
Analysis Practice
FoundationsIntegration Exercise: Bayesian and Problem-Solving Fallacies
These exercises connect the concepts from this lesson to ideas across different reasoning domains. Apply foundational concepts to scenarios that require multiple analytical tools.
Cross-cutting foundational exercises
Each scenario tests your ability to apply foundational logic concepts alongside other analytical skills.
Scenario 1
A news article reports: 'Scientists have proven that coffee is good for you, according to a new study of 500 adults who drink coffee daily.' Identify all arguments in this claim, classify the reasoning type(s), evaluate the evidence quality, and explain what additional information would be needed.
Scenario 2
A school board argues: 'Since standardized test scores are the best measure of student learning, and our test scores have risen 10% this year, our educational quality has improved.' Identify the premises and conclusion, classify the reasoning, spot any hidden assumptions, and construct an alternative explanation for the score increase.
Scenario 3
A city planner argues: 'If we build more bike lanes, more people will bike. More biking reduces car traffic. Less car traffic means less pollution. Therefore, building bike lanes will reduce pollution.' Map the argument structure, evaluate each inferential step separately (some may be deductive, others inductive), and identify the weakest link.
Scenario 4
An investor reasons: 'This company's stock has risen every year for the past eight years. The CEO is talented and the industry is growing. I should invest heavily.' Identify all reasoning types present, evaluate each one, and explain how the different types of reasoning interact in this argument.
Pick one of the passages above and map how the reasons are supposed to support the conclusion.
Diagnosis Practice
FoundationsMisconception Clinic: Bayesian and Problem-Solving Fallacies
Each item presents a common misconception about arguments, reasoning, or logic. Identify the misconception, explain why it is wrong, and state the correct principle.
Common logic misconceptions
Diagnose and correct each misconception about basic logic and arguments.
Misconception 1
A student says: 'An argument with true premises must have a true conclusion.'
Misconception 2
A student claims: 'If two people disagree, at least one of them must be using bad logic.'
Misconception 3
A student writes: 'Opinions cannot be arguments because arguments require facts, not opinions.'
Misconception 4
A student argues: 'A strong argument is one that is persuasive. If people are convinced by it, it must be a good argument.'
Misconception 5
A student says: 'An explanation and an argument are the same thing -- both provide reasons for something.'
Use one of the passages above. Name the weakness, explain the violated standard, and show how the reasoning should be repaired.
Analysis Practice
FoundationsScaffolded Analysis: Bayesian and Problem-Solving Fallacies
Build an argument analysis in stages. Each task provides a passage and walks you through the analysis process step by step. Complete each stage before moving on.
Step-by-step argument analysis
Analyze each argument progressively, one skill at a time.
Scaffold 1
Passage: 'Because violent crime has increased 15% this year and the police budget was cut 10% last year, the budget cuts are responsible for the crime increase. Therefore, the city council should restore police funding.' Stage 1: Identify all premises and the conclusion. Stage 2: Classify the reasoning type. Stage 3: Identify any hidden premises or assumptions. Stage 4: Evaluate the strength of the inference. Stage 5: Suggest what additional evidence would strengthen or weaken this argument.
Scaffold 2
Passage: 'Three out of four dentists recommend this toothpaste. Since expert opinion is reliable, you should use this toothpaste. After all, if experts recommend something, it must be good.' Stage 1: Put the argument in standard form. Stage 2: Identify the reasoning type for each inferential step. Stage 3: Spot any logical errors or questionable assumptions. Stage 4: Rewrite the argument to make it stronger.
Scaffold 3
Passage: 'Countries that invest in education have stronger economies. Our country should invest more in education to strengthen the economy. This is proven by the examples of South Korea, Finland, and Singapore.' Stage 1: Map the argument structure. Stage 2: Identify whether this is primarily deductive, inductive, or abductive. Stage 3: Evaluate the evidence. Stage 4: Identify the strongest objection to this argument. Stage 5: Revise the argument to address that objection.
Pick one of the passages above and map how the reasons are supposed to support the conclusion.
Analysis Practice
FoundationsSynthesis Review: Bayesian and Problem-Solving Fallacies
These exercises combine everything you have learned about arguments, reasoning types, and evaluation. Each scenario requires you to identify, classify, analyze, evaluate, and improve an argument.
Comprehensive foundations review
Apply all foundational logic skills together.
Comprehensive 1
A school district superintendent argues: 'Our district should adopt year-round schooling. Studies show students in year-round schools retain 10% more knowledge. Teachers in year-round districts report higher job satisfaction. The only objection is tradition, but tradition is not a good reason to hold back progress. Other districts that switched have seen rising test scores within two years.' Perform a complete analysis: identify all premises and the conclusion, classify each reasoning step, find any hidden assumptions, spot any logical errors, evaluate the overall strength, and rewrite the argument to make it stronger.
Comprehensive 2
A debate transcript: Speaker A says 'Social media causes depression -- the data is clear.' Speaker B responds 'That is correlation, not causation. Besides, my teenagers use social media constantly and they are perfectly happy.' Speaker A replies 'Your children are exceptions. The overall trend is undeniable.' Analyze each speaker's reasoning: identify argument types, evaluate their strength, identify logical errors, find hidden assumptions, and draft what a well-reasoned third speaker should say.
Pick one of the passages above and map how the reasons are supposed to support the conclusion.
Argument Mapper
Build an argument diagram by adding premises, sub-conclusions, and a conclusion. Link nodes to show which claims support which.
Add nodes above, or load a template to get started. Each node represents a proposition in your argument.
■ Premise■ Sub-conclusion■ Conclusion
Animated Explainers
Step-by-step visual walkthroughs of key concepts. Click to start.
Read the explanation carefully before jumping to activities!
Further Support
Open these only if you need extra help or context
Mistakes to avoid before submitting
- Assuming a practical plan is good merely because it is decisive.
- Treating test accuracy as a direct probability of the hypothesis.
Where students usually go wrong
Ignoring priors in Bayesian cases.
Treating one visible option as the whole practical choice set.
Confusing 'accurate test' with 'almost certainly accurate diagnosis in this individual'.
Historical context for this way of reasoning
C. L. Hamblin
Hamblin's work matters here because it pushes us to analyze real reasoning defects in context rather than reciting fallacy names mechanically. Bayesian and problem-solving errors are exactly the kinds of cases textbook fallacy lists tend to miss.
Amos Tversky and Daniel Kahneman
Their work on heuristics and biases documented base-rate neglect, the conjunction fallacy, and anchoring effects as empirical patterns, giving fallacy theorists concrete examples of what miscalibrated updating looks like in practice.