Argument Mapping Skill

Master the art of reconstructing, visualizing, and evaluating the logical structure of arguments.

Why Map Arguments?

Argument mapping serves several purposes:

• Clarify: Make implicit structure explicit

• Evaluate: Assess validity and soundness systematically

• Communicate: Present complex arguments visually

• Critique: Identify weaknesses and hidden assumptions

• Steelman: Ensure fair representation of opposing views

Basic Argument Structure

Components of an Argument

Component Definition Example

Conclusion The claim being argued for "Socrates is mortal"

Premise A reason supporting the conclusion "All men are mortal"

Inference The logical move from premises to conclusion "Therefore..."

Assumption Unstated premise needed for validity (Often hidden)

Simple Argument Form

P1: [Premise 1] P2: [Premise 2]

C: [Conclusion]

Example:

P1: All men are mortal P2: Socrates is a man

C: Socrates is mortal

The Toulmin Model

Stephen Toulmin's model captures the nuanced structure of real-world arguments.

Six Components

                    QUALIFIER
                        │
                        ▼

GROUNDS ──────────► CLAIM ◄─────────── REBUTTAL │ ▲ │ │ │ │ ▼ │ ▼ WARRANT ◄──────── BACKING (Unless...)

Component Definition Example

Claim The conclusion/assertion "We should ban smoking in restaurants"

Grounds Evidence/data supporting claim "Secondhand smoke causes cancer"

Warrant Principle connecting grounds to claim "We should prevent cancer-causing exposures"

Backing Support for the warrant itself "Preventing harm is a core purpose of public policy"

Qualifier Degree of certainty "Probably," "Certainly," "Presumably"

Rebuttal Conditions where claim fails "Unless economic harm outweighs health benefits"

Toulmin Diagram Template

┌─────────────────────────────────────────────────────────────────────┐ │ │ │ CLAIM: [Central thesis/conclusion] │ │ Qualifier: [Certainly/Probably/Possibly] │ │ │ │ ──────────────────────────────────────────────────────────────── │ │ │ │ GROUNDS: │ REBUTTAL: │ │ [Evidence/facts/data] │ Unless [exception conditions] │ │ │ │ │ ──────────────────────────────────────────────────────────────── │ │ │ │ WARRANT: │ │ [Principle that licenses inference from grounds to claim] │ │ │ │ ──────────────────────────────────────────────────────────────── │ │ │ │ BACKING: │ │ [Support for the warrant] │ │ │ └─────────────────────────────────────────────────────────────────────┘

Argument Reconstruction Protocol

Step 1: Identify the Conclusion

What is the main claim being defended?

Indicator words: therefore, thus, hence, so, consequently, it follows that, we can conclude

If not explicit: What would the speaker want you to believe/do?

Step 2: Find the Premises

What reasons are given for the conclusion?

Indicator words: because, since, for, given that, as shown by, the reason is

List them: Number each premise explicitly (P1, P2, P3...)

Step 3: Make Implicit Premises Explicit

What unstated assumptions are needed for the argument to work?

Test: If we add this premise, does the argument become valid?

Charity: Choose the most reasonable implicit premises

Step 4: Analyze the Structure

How do the premises relate?

Linked premises: Work together (all needed)

P1 + P2
   │
   ▼
   C

Convergent premises: Independent support (each sufficient)

P1     P2
 \    /
  \  /
   C

Serial/Chain arguments: One supports another

P1
 │
P2
 │
 C

Step 5: Evaluate

• Validity: Does conclusion follow from premises?

• Soundness: Are premises actually true?

• Strength (inductive): How probable is conclusion given premises?

Diagramming Conventions

Standard Notation

┌─────┐ │ P1 │ ← Premise (box) └──┬──┘ │ ▼ ┌─────┐ │ C │ ← Conclusion (box) └─────┘

Linked vs. Convergent

Linked (all premises needed together):

┌─────┐ ┌─────┐ │ P1 │───│ P2 │ └──┬──┘ └──┬──┘ └────┬────┘ ▼ ┌─────┐ │ C │ └─────┘

Convergent (independent support):

┌─────┐ ┌─────┐ │ P1 │ │ P2 │ └──┬──┘ └──┬──┘ │ │ └─────┬───────┘ ▼ ┌─────┐ │ C │ └─────┘

Sub-Arguments

When a premise is itself supported:

┌─────┐ │ P1a │ ← Sub-premise └──┬──┘ ▼ ┌─────┐ │ P1 │ ← Intermediate conclusion / Premise for main argument └──┬──┘ │ ┌──┴──┐ │ P2 │ └──┬──┘ ▼ ┌─────┐ │ C │ ← Main conclusion └─────┘

Objections and Rebuttals

┌─────┐ │ P1 │ └──┬──┘ ▼ ┌─────┐ ┌─────────┐ │ C │ ◄─ ✗ ───│Objection│ └─────┘ └────┬────┘ │ ┌────▼────┐ │ Rebuttal│ └─────────┘

Dialectical Tree Format

For multi-position debates:

THESIS: [Main Position A] │ ├── Support 1: [Argument for A] │ ├── Evidence 1a │ └── Evidence 1b │ ├── Support 2: [Another argument for A] │ └── ANTITHESIS: [Opposing Position B] │ ├── Objection to Support 1: [Why it fails] │ ├── Objection to Support 2: [Why it fails] │ └── Positive argument for B │ └── SYNTHESIS: [Higher-level resolution] │ ├── What's preserved from A ├── What's preserved from B └── What's new

Common Argument Patterns

Deductive Patterns

Modus Ponens:

P1: If A, then B P2: A

C: B

Modus Tollens:

P1: If A, then B P2: Not B

C: Not A

Disjunctive Syllogism:

P1: A or B P2: Not A

C: B

Hypothetical Syllogism:

P1: If A, then B P2: If B, then C

C: If A, then C

Reductio ad Absurdum:

P1: Assume A (for contradiction) P2: A leads to contradiction B & not-B

C: Not A

Inductive Patterns

Generalization:

P1: Sample S has property P P2: Sample S is representative of population X

C: (Probably) All X have property P

Analogy:

P1: A has properties F, G, H P2: B has properties F, G P3: A has property X

C: (Probably) B has property X

Inference to Best Explanation:

P1: Phenomenon P is observed P2: Hypothesis H would explain P P3: H is the best available explanation

C: (Probably) H is true

Philosophical Argument Patterns

Conceivability Argument:

P1: X is conceivable P2: If conceivable, then possible

C: X is possible

Counterexample:

P1: Thesis T claims all X are Y P2: Case C is X but not Y

C: Thesis T is false

Thought Experiment:

P1: In scenario S, intuition I is strong P2: If I is correct, then principle P

C: Principle P

Hidden Assumption Detection

Method 1: Gap Analysis

• State the premises

• State the conclusion

• Ask: What must be true for this inference to work?

• The answer is the hidden assumption

Method 2: Negation Test

• Negate a potential assumption

• If the argument fails, the assumption was needed

Method 3: Charity + Validity

• Assume the argument is intended to be valid

• What premise would make it valid?

• That's the most charitable hidden assumption

Common Hidden Assumptions

Type Example

Empirical Facts about the world assumed without evidence

Normative Value judgments assumed without defense

Conceptual Definitions assumed without clarification

Background Shared context assumed without statement

Scope Universality assumed without justification

Evaluation Criteria

For Deductive Arguments

Criterion Question Assessment

Validity Does conclusion follow necessarily? Yes/No

Soundness Are all premises true? Yes/No/Unknown

Completeness Are hidden premises stated? Yes/Partially/No

For Inductive Arguments

Criterion Question Assessment

Strength How probable is conclusion given premises? Strong/Moderate/Weak

Cogency Are premises true AND argument strong? Yes/No

Sample quality Is evidence representative? Yes/No

Output Templates

Standard Reconstruction

Argument Reconstruction: [Topic/Source]

Conclusion

[State the main claim being argued for]

Explicit Premises

P1: [First stated premise] P2: [Second stated premise] P3: [Third stated premise]

Hidden Premises

H1: [First unstated assumption needed for validity] H2: [Second unstated assumption]

Argument Structure

[Diagram showing how premises relate to conclusion]

Evaluation

• Validity: [Valid/Invalid—explain]
• Soundness: [Sound/Unsound/Unknown—explain]
• Key weakness: [Most vulnerable point]

Dialectical Context

[How this argument relates to the broader debate]

Debate Map

Debate Map: [Topic]

Question at Issue

[The central question being debated]

Position A: [Label]

Thesis: [Main claim]

Arguments:

1. [Argument 1]
   • Objection: [Counter]
   • Reply: [Response]
2. [Argument 2]

Position B: [Label]

Thesis: [Main claim]

Arguments:

1. [Argument 1]
2. [Argument 2]

Points of Agreement

• [Shared premise 1]
• [Shared premise 2]

Core Disagreement

[What the debate ultimately turns on]

Assessment

[Which position is stronger and why]

Integration with Other Skills

• philosophical-analyst: Use mapping in step 2 (argument reconstruction)

• symposiarch: Map arguments during debate management

• thought-experiments: Map the argument structure of thought experiment cases

• devils-advocate: Identify weak premises in argument maps

Reference Files

• patterns.md : Comprehensive catalog of argument patterns

• diagramming.md : Extended diagramming conventions and tools