Rigorous Reasoning

Foundations

Arguments and Their Parts

Introduces the concept of an argument and teaches students to identify premises, conclusions, and the inference that connects them.

Focus on understanding the core distinction first, then use the examples to see how the idea behaves in actual arguments.

FoundationsConceptLesson 1 of 50% progress

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What this lesson is helping you do

Introduces the concept of an argument and teaches students to identify premises, conclusions, and the inference that connects them. The practice in this lesson depends on understanding Argument, Premise, Conclusion, and Inference and applying tools such as Relevance Standard and Sufficiency Standard correctly.

How to approach it

Focus on understanding the core distinction first, then use the examples to see how the idea behaves in actual arguments.

What the practice is building

You will put the explanation to work through classification practice, analysis practice, diagnosis 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

Correctly identify premises, conclusion, and inference in 6 short passages, and correctly classify 4 passages as argument or non-argument.

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.

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.

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.

Definition

What makes a passage an argument

An argument is not just a cluster of sentences about the same topic. It is a structure in which one or more claims are offered as reasons for accepting another claim. That support relation is the heart of the lesson: if no claim is being used to back up another, you do not yet have an argument.

When you read a passage, do not start by asking whether you agree with it. Start by asking what job each sentence is doing. Some sentences report facts, some explain why an accepted event occurred, some tell a story, and some try to justify a conclusion. Logical analysis begins when you can tell the difference between those jobs.

What to look for

  • Find the claim the speaker most wants the audience to accept.
  • Look for the sentence or sentences offered in support of that claim.
  • Ask whether the passage is trying to prove something or merely describe or explain it.
A passage counts as an argument only when its statements are arranged so that some of them function as support for another.

Parts of an argument

Premises, conclusion, and inference

The conclusion is the statement the argument is trying to establish. The premises are the statements offered in support of that conclusion. Students often spot the conclusion last because writers sometimes place it at the beginning, hide it in the middle, or leave it partly implicit. The order of sentences is less important than their role.

Inference is the logical connection between premises and conclusion. It is not always written as its own sentence. Often the inference is the claim that the premises, taken together, give you a reason to move to the conclusion. When you explain an argument well, you are not just listing parts; you are showing how the parts fit together.

What to look for

  • State the conclusion in your own words before labeling the premises.
  • Check whether each alleged premise actually supports the conclusion rather than merely surrounding it.
  • Describe how the premises are supposed to lead to the conclusion.
Good argument analysis is structural: identify the conclusion, identify the supporting claims, then explain the inferential link.

Common confusion

Arguments versus explanations

Arguments and explanations can look alike because both may use words like because, since, or therefore. The difference is their aim. An argument tries to establish that a claim is true or acceptable. An explanation starts from something already accepted and tries to show why it happened or how it came about.

That is why a passage can contain reasons without being an argument in the logical sense. If the speaker assumes the conclusion is already settled and is only filling in its cause, background, or mechanism, the passage is explanatory rather than argumentative. Learning to notice that difference will prevent you from mislabeling every reason-giving passage as an argument.

What to look for

  • Ask whether the passage is defending a claim or accounting for an accepted fact.
  • Treat indicator words as clues, not guarantees.
  • If the conclusion is already assumed true and the passage explains why, classify it as an explanation rather than an argument.
Reasons can appear in both arguments and explanations, so you must identify the author's purpose before you classify the passage.

Method

A method for unpacking everyday passages

A reliable way to analyze a passage is to read it twice. On the first pass, identify the topic and the claim that seems most central. On the second pass, mark the sentences that are supposed to support that claim. Only after that should you rewrite the passage in standard form with premises listed above the conclusion.

Rewriting matters because natural language hides structure. Speakers leave out assumptions, bury conclusions, and mix background information with evidence. Standard form forces you to separate what is doing logical work from what is merely setting the scene. Once the structure is visible, evaluation becomes much easier.

What to look for

  • Read once for the overall point and once for support relations.
  • Separate background information from premises.
  • Rewrite the argument in standard form before evaluating it.
If you can restate a passage in standard form, you are usually far closer to understanding what the reasoning actually is.

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.

Argument

A set of statements in which one or more premises are offered in support of a conclusion.

Why it matters: The argument is the fundamental unit of reasoning that the entire platform builds upon.

Premise

A statement offered as evidence or a reason in support of an argument's conclusion.

Why it matters: Identifying premises is the first step in analyzing any argument.

Conclusion

The statement that an argument claims to establish on the basis of its premises.

Why it matters: The conclusion is what the arguer wants the audience to accept.

Inference

The reasoning step that connects premises to a conclusion.

Why it matters: Inference is the logical glue of an argument and the focus of all subsequent evaluation.

Reference

Open these only when you need the extra structure

How the lesson is meant to unfold

Hook

A motivating question or contrast that frames why this lesson matters.

Concept Intro

The core idea is defined and separated from nearby confusions.

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.

Relevance Standard

Each premise of an argument must bear directly on the truth or probability of the conclusion.

Common failures

  • A premise addresses a different topic than the conclusion.
  • A premise appeals to emotion or authority rather than providing evidence for the conclusion.

Sufficiency Standard

The premises, taken together, must provide enough support to justify accepting the conclusion.

Common failures

  • The argument draws a sweeping conclusion from a single example.
  • Key evidence needed to support the conclusion is missing entirely.

Deductive Validity Standard

In a valid deductive argument, if the premises are true, the conclusion must be true.

Common failures

  • The student judges validity by whether the conclusion sounds plausible rather than by logical structure.
  • The student conflates truth of premises with validity of the argument form.

Argument Identification Standard

A passage contains an argument only if it presents one or more claims intended as reasons for accepting another claim.

Common failures

  • The student treats a mere description or explanation as an argument.
  • The student fails to identify an implicit premise that is essential to the argument.

Patterns

Use these when you need to turn a messy passage into a cleaner logical structure before evaluating it.

Argument Extraction from Natural Language

Input form

natural_language_passage

Output form

structured_argument

Steps

  • Read the passage and identify indicator words.
  • Determine which statement is the conclusion.
  • List the explicit premises.
  • Check for implicit premises and make them explicit.
  • Write the argument in standard form: premises listed above a line, conclusion below.

Watch for

  • Confusing background information with premises.
  • Missing an implicit premise that the argument relies on.
  • Misidentifying the conclusion because the passage places it first.

Semi-Symbolic Argument Outline

Input form

structured_argument

Output form

semi_symbolic_form

Steps

  • Assign labels (P1, P2, etc.) to each premise and C to the conclusion.
  • Identify the logical relationship between premises (conjunction, conditional, disjunction).
  • Represent the relationship using arrow or ampersand notation.
  • Verify that the semi-symbolic outline preserves the original argument's meaning.

Watch for

  • Assigning the same label to different claims.
  • Using a conditional arrow when the relationship is actually conjunctive.
  • Losing important qualifiers when abbreviating premises.

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

A Simple Everyday Argument

An argument has at least one premise offered as a reason and a conclusion that is supposed to follow from those reasons. Here, two premises work together to support one conclusion.

Content

  • Premise 1: All grocery stores in this town close by 9 PM.
  • Premise 2: FreshMart is a grocery store in this town.
  • Conclusion: FreshMart closes by 9 PM.

Worked Example

Not Every Passage Is an Argument

This passage describes facts but does not offer any claim as a reason for accepting another claim. Descriptions, explanations, and reports are not arguments.

Content

  • The library opens at 8 AM and closes at 10 PM. It has three floors and a coffee shop on the ground level.

Pause and Check

Questions to use before you move into practice

Self-check questions

  • Is there a claim that the passage is trying to get me to accept?
  • Are reasons offered in support of that claim, or is the passage merely describing something?

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.

Classification Practice

Foundations

Argument or Not?

Read each short passage and determine whether it contains an argument. If it does, identify the premise(s) and the conclusion.

Short passages

Choose at least two passages. For each one, decide whether it is an argument or a non-argument and explain why.

Passage A

It must have rained last night, because the sidewalks are still wet this morning.

Passage B

The student center opens at 7 AM, closes at 11 PM, and serves breakfast until 10:30.

Passage C

The plant died because nobody watered it during spring break.

Passage D

Since the battery is dead, the car will not start.

Use one of the class-claim passages above. Identify the terms, put the claims into standard form, and explain the resulting categorical structure.

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Analysis Practice

Foundations

Mapping the Inference

For each argument provided, draw a simple diagram or write a sentence explaining how the premises connect to the conclusion.

Arguments to map

Pick one or two arguments and spell out how the support is supposed to move from premises to conclusion.

Passage A

All staff with building access completed safety training. Marisol has building access. Therefore, Marisol completed safety training.

Passage B

The clouds are dark, the radar shows rain moving in, and the wind is picking up, so the outdoor game will probably be delayed.

Passage C

The office printer stopped working right after the toner warning appeared, so the empty toner cartridge is the best current explanation.

Pick one of the passages above and map how the reasons are supposed to support the conclusion.

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Analysis Practice

Foundations

Apply the Concepts: Arguments and Their Parts

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.

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Diagnosis Practice

Foundations

Spot the Error: Arguments and Their Parts

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.

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Comparison Exercise

Foundations

Compare and Connect: Arguments and Their Parts

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.

Choose one of the passages above and decide whether it is an argument. Then explain how you know.

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Analysis Practice

Foundations

Deep Practice: Arguments and Their Parts

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.

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Analysis Practice

Foundations

Real-World Transfer: Arguments and Their Parts

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.

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Rapid Identification

Foundations

Timed Drill: Arguments and Their Parts

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.

Choose one of the passages above and decide whether it is an argument. Then explain how you know.

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Evaluation Practice

Foundations

Peer Review: Arguments and Their Parts

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.

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Argument Building

Foundations

Construction Challenge: Arguments and Their Parts

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.

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Diagnosis Practice

Foundations

Counterexample Challenge: Arguments and Their Parts

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.

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Analysis Practice

Foundations

Integration Exercise: Arguments and Their Parts

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.

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Diagnosis Practice

Foundations

Misconception Clinic: Arguments and Their Parts

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.

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Analysis Practice

Foundations

Scaffolded Analysis: Arguments and Their Parts

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.

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Analysis Practice

Foundations

Synthesis Review: Arguments and Their Parts

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.

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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!

Riko

Further Support

Open these only if you need extra help or context

Mistakes to avoid before submitting
  • Do not assume a passage is an argument just because it contains the word 'because'; it may be offering a causal explanation.
  • Do not ignore sentences that lack indicator words; they may still be premises.
Where students usually go wrong

Confusing an explanation of why something happened with an argument for why something is true.

Treating any opinionated statement as an argument even when no supporting reasons are given.

Overlooking the conclusion when it appears at the beginning of a passage rather than at the end.

Historical context for this way of reasoning

Aristotle

Aristotle defined a deduction (syllogismos) as discourse in which, certain things being stated, something other than what is stated follows of necessity. This remains the template for understanding arguments.