Diagramming Arguments: A Step-by-Step Guide

Diagramming Arguments: A Step-by-Step Guide

Introduction to Argument Diagramming

• Diagramming arguments symbolically represents the logical flow from premises to conclusions.
• Before diagramming, individual propositions within an argument are replaced by numbers.
• Important: The numbers reflect the order of propositions as presented in the text, not necessarily their logical roles (premise or conclusion).
  • For example, a conclusion might be the first proposition presented, denoted by number $1$, but it will appear at the end of the diagram.
• Conclusions typically appear in one of two positions when verbally presented:
  • All reasons (premises) are given first, followed by the conclusion.
  • The conclusion is stated first, followed by all the reasons (premises) supporting it.
• Every argument must have at least one premise and one conclusion, requiring a minimum of two numbered propositions.
• Arguments often contain multiple premises, but for the purpose of the test, assume arguments have only one conclusion. Homework problems may occasionally include arguments with more than one conclusion.

Step 1: Numbering Propositions (Example)

• Consider the following argument:
  1. Feminism is the commitment to eliminating patriarchy.
  2. Patriarchy oppresses women.
  3. Everyone should be a feminist.
• Here, each distinct statement is assigned a number.$1$, $2$, and $3$ represent the propositions in the order they appear.

Step 2: Finding the Conclusion

• The first critical step in diagramming an argument is to identify its conclusion.
• For this class, once the conclusion is identified, all other numbered propositions will be considered premises (with potential exceptions in specific homework problems).
• Crucial Rule: The conclusion will always be placed at the bottom of the argument diagram, regardless of its numerical order or presentation sequence in the original argument.
  • Self-correction example: If the argument started with "1. Everyone should be a feminist," followed by reasons $2$ and $3$, proposition $1$ would still be at the bottom of the diagram.

Step 3: Deciding if Premises are Dependent or Independent

• This step involves determining how the premises work together (or separately) to support the conclusion.

Dependent Premises

• Definition: Dependent premises work collectively to form a single, unified argument for the conclusion.
• Characteristic: A single dependent premise, taken in isolation, would not make sense as an argument for the conclusion.
• Example (Feminism revisited):
  1. Feminism is the commitment to eliminating patriarchy.
  2. Patriarchy oppresses women.
  3. Everyone should be a feminist.
  • Conclusion: Proposition $3$
  • Premises: Propositions $1$ and $2$
  • If only proposition $2$ ("Patriarchy oppresses women") were used to argue for $3$ ("Everyone should be a feminist"), it wouldn't fully make sense without implicitly including the idea from proposition $1$ (connecting patriarchy to feminism's goal).
  • Therefore, $1$ and $2$ are dependent; they link the concepts of feminism, patriarchy, and the reason for elimination.

Independent Premises

• Definition: Independent premises each offer a separate and distinct line of support for the conclusion.
• Characteristic: An argument can make sense using only one independent premise (though it might be weaker). The argument becomes stronger with more independent premises.
• Analogy: Independent premises are like individual threads in a rope. Each thread provides some strength, and adding more threads (premises) makes the rope (argument) stronger.
• Example (Pettit's class):
  1. Pettit tries to make his classes fun.
  2. Getting a good grade in Pettit's class does not require getting A's on his tests.
  3. Pettit works hard to explain material to a student.
  4. Students will want to take Pettit's class.
  • Conclusion: Proposition $4$
  • Premises: Propositions $1$, $2$, and $3$
  • Each premise can independently support the conclusion:
    • "Pettit tries to make his classes fun. Therefore, students will wanna take Pettit's class." (Makes sense as an argument)
    • "Getting a good grade in Pettit's class does not require getting A's on his tests. Therefore, students will wanna take Pettit's class." (Makes sense)
    • "Pettit works hard to explain material to students. Therefore, students will wanna take Pettit's class." (Makes sense)
  • Having all three independent premises makes the argument for $4$ much stronger.

Step 4: Using Symbols for Diagramming

• Two primary symbols are used to visually represent argument structure:
  • Arrow ($\rightarrow$): Connects premises (or sets of premises) to the conclusion.
  • Plus Sign (+$): Used exclusively for linking dependent premises. It is never used with independent premises.

Diagramming Independent Premises

• Each independent premise gets its own arrow pointing to the conclusion.
• Example (Pettit's class):
  ext{1} \rightarrow \text{4}
  ext{2} \rightarrow \text{4}
  ext{3} \rightarrow \text{4}

Diagramming Dependent Premises

• Dependent premises are linked together with a plus sign, and then a single arrow extends from this combined unit to the conclusion.
• Example (Feminism):
  \text{1} + \text{2} \rightarrow \text{3}

Complex Example from Text (Page 76)

• Consider the argument:
  1. Extremely sarcastic people feel inadequate.
  2. Extreme sarcasm is a form of unprovoked hostility.
  3. Unprovoked hostility results from feelings of inadequacy.
• The provided diagram for this argument is: \text{2} + \text{3} \rightarrow \text{1}
  • Here, propositions 2$and$3$are dependent premises, linked by a plus sign, supporting conclusion$1$. Notice conclusion$1 is at the bottom of the diagram despite its numerical order.

Advanced Concepts and Stipulations

Proposition as Both Premise and Conclusion (Chain of Reasoning)

• Definition: In a chain of reasoning, a single proposition can act as a conclusion derived from a previous premise, and simultaneously as a premise supporting a subsequent conclusion.
• Example (Page 77 - Car Won't Start):
  Since, 1. My car won't start, 2. I will have to take the bus. So, 3. I will need exact change for the fare.
• Diagram: \text{1} \rightarrow \text{2} \rightarrow \text{3}
  • In this chain:
    • 2$is the conclusion of the argument from$1.
    • 2$is also the premise for the argument to$3.
• Important Note: When diagramming, the task is to represent the structure of the argument as presented, not to evaluate its goodness or soundness (e.g., whether taking Uber is a better option than the bus).

Stipulations for Class/Test

• Single Conclusion: For the purposes of this class's tests, arguments will always have only one conclusion.
  • Technically: It is possible for a single premise to lead to multiple conclusions (e.g., "Joe is a student at Morgan State University" could lead to "Joe can register for classes," "Joe can use the library," and "Joe can get an ID card").
  • If such a scenario appeared in homework (though Kelly text might differ), it would technically be considered multiple distinct arguments, each with its own arrow stemming from the single premise to each conclusion.

Summary of Diagramming Steps

1. Replace each proposition with a corresponding number.
2. Identify the conclusion of the argument.
3. Determine whether the premises providing support are dependent or independent.
4. Use arrows (\rightarrow$) and plus signs ($+$$) appropriately to construct the argument diagram.

If you encounter any difficulties, please reach out via email or attend office hours.