Rigorous Reasoning
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Foundations·Introductory·5 lessons·65 practice activities·~200 min

Foundations of Logical Reasoning

What reasoning is and why structure matters

What you'll learn

By the end of this unit, you can…

  • Identify argument parts.
  • Classify reasoning mode.
  • Apply evaluative standards.
  • Extract and formalize argument.

Lessons

Lesson sequence

  1. 1

    Arguments and Their Parts

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

    16 activities5 worked examples
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  2. 2

    Three Modes of Reasoning

    Introduces deductive, inductive, and abductive reasoning, clarifying how each mode connects premises to conclusions and what standard of support each provides.

    16 activities5 worked examples
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  3. 3

    Evaluating Arguments

    Students learn to evaluate arguments by applying standards of validity, inductive strength, relevance, and sufficiency.

    15 activities5 worked examples
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  4. 4

    From Natural Language to Structure

    Students learn to extract arguments from natural language, identify implicit premises, and produce a semi-formal structured outline as a bridge to full symbolic formalization.

    15 activities5 worked examples
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  5. 5

    Capstone: Diagnosing Real-World Reasoning

    An integrative lesson that asks students to combine every foundations skill on a single passage: find the argument, extract its structure, name its reasoning mode, evaluate it, and explain the result.

    3 activities5 worked examples
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How to study

Three moves that work for this unit

1

Read the explanation

Each lesson opens with a guided walkthrough — read it before the activity.

2

Study the worked example

Look at why each step follows, not just what the answer is.

3

Practice with the target in mind

Know which rule applies and what would make the response weak before you start.

Reference materials

Optional context for the unit. Each lesson surfaces the concepts and rules it uses — these are here when you want the bigger picture.

Concept map (8 terms)

Argument

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

Premise

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

Conclusion

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

Inference

The reasoning step that connects premises to a conclusion.

Validity

The property of an argument whose conclusion cannot be false while all its premises are true.

Inductive Strength

A property of inductive arguments in which the premises make the conclusion probable but not certain.

Indicator Words

Words or phrases such as 'therefore,' 'because,' and 'since' that signal the presence of an argument and mark premises or conclusions.

Formalization

The process of translating natural-language arguments into a structured symbolic or semi-symbolic form.

Rules and standards (4)
  • 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..
Formalization patterns (2)
  • Argument Extraction from Natural Language. From natural_language_passage to structured_argument 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..
  • Semi-Symbolic Argument Outline. From structured_argument to semi_symbolic_form 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..
Full mastery and assessment guidance

Mastery requirements

  • Identify argument parts. Percent Consistent · 80_percent_consistent
  • Classify reasoning mode. Correct Classifications · 9_correct_classifications
  • Apply evaluative standards. Successful Evaluations · 6_successful_evaluations
  • Extract and formalize argument. Successful Extractions And Outlines · 4_successful_extractions_and_outlines

Assessment advice

  • 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?
  • 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.
  • Does the argument claim that the conclusion must follow, that it probably follows, or that it is the best explanation?
  • Could the premises be true while the conclusion is false, and if so, is that a defect or simply the nature of the reasoning mode?
  • Do not classify an argument as deductive simply because you believe its conclusion is true.
  • Do not treat abduction as a fallacy; it is a legitimate mode of reasoning used in science and everyday life.
  • Am I judging the argument's structure or just whether I believe the conclusion?
  • Have I checked both relevance and sufficiency of the premises?
  • Am I applying the right standard for the type of reasoning involved?
  • Do not dismiss an argument as bad simply because a premise is false; focus on the logical connection between premises and conclusion.
  • Do not confuse sufficiency with relevance: a premise can be relevant but still insufficient on its own.
  • Have I identified all indicator words in the passage?
  • Does my standard-form argument capture everything the original passage was trying to argue?
  • Is every implicit premise I added genuinely required for the argument to work?
  • Do not add implicit premises that go beyond what the argument requires; only add what is needed to connect the explicit premises to the conclusion.
  • Do not strip away important qualifiers when converting prose to standard form.
  • Did I find the argument before I evaluated anything?
  • Did I name the mode before picking a standard?
  • Would my verdict make sense to a reader who has not taken this unit?
  • Forcing an evaluation onto a passage that is not an argument.
  • Treating the verdict as optional rather than as the final output.
Historical context (3)
  • Aristotle. Created the first systematic study of argument forms, establishing logic as a discipline and defining the syllogism. Argument-form analysis and the concept of validity as a structural property.
  • Chrysippus and the Stoics. Developed propositional logic and catalogued basic argument forms such as modus ponens and modus tollens. Propositional argument patterns and the analysis of conditional reasoning.
  • Charles Sanders Peirce. Coined the term 'abduction' and treated it as the stage of inquiry where hypotheses are formed to explain surprising facts, distinct from deduction and induction. Best-explanation reasoning, hypothesis comparison, and diagnostic reasoning tools.