Argument Forms

Argument Forms

  • Definition: Argument forms are structured expressions indicating a relationship of premises leading to a conclusion.

Different Arguments - Same Form

  • Example 1:

    • (P1) Lady Gaga will win the next presidential election or Kylie Jenner will win the next presidential election.
    • (P2) Kylie Jenner won’t win the next presidential election.
    • (C) Therefore, Lady Gaga will win the next presidential election.

  • Example 2:

    • (P1) My cup contains tea or my cup contains coffee.
    • (P2) My cup doesn’t contain coffee.
    • (C) Therefore, my cup contains tea.

Examples of Valid Argument Forms

  • Common Structure:
    • (P1) Sentence 1 or Sentence 2.
    • (P2) Not Sentence 2.
    • (C) Therefore, Sentence 1.

Valid vs Invalid Argument Forms

  • Valid Argument: All derived arguments remain valid.

  • Invalid Argument: At least one derived argument is invalid.

  • Example of Invalid Argument:

    • (P1) Sentence 1 or Sentence 2.
    • (P2) Sentence 2.
    • (C) Therefore, Sentence 1.
    • Instance: (P1) Joaquin Phoenix is president or Joe Biden is president.
    • (P2) Joe Biden is president.
    • (C) Therefore, Joaquin Phoenix is president.

Irreplaceable Logical Expressions

  • Cannot replace logical terms without altering the meaning:
    • "or" must not be replaced with "because".
    • Examples:
    • (P1) Dogs bark or cats meow.
    • (P2) It’s not the case that cats meow.
    • (C) Therefore, dogs bark.
    • In contrast, for "because":
      • (P1) Dogs bark because cats meow.
      • (P2) It’s not the case that cats meow.
      • (C) Therefore, dogs bark.

Conditional Argument Forms

  • Structure:
    • (P1) If A, then B.
    • (P2) A.
    • (C) Therefore, B.

Expand and Don’t Collapse

  • Expansion Rule:
    • Expand when connecting two affirmative sentences:
    • Example: "Egon and Selma are accountants" becomes "Egon is an accountant and Selma is an accountant".
    • No Expansion when referring to a set:
    • Example: "Erin and Jamie are a couple" remains as is; can't expand to individual specifics.

Logical Expressions

  • Connections formed by the logical expressions:
    • "and"
    • "or"
    • "not" (i.e., "it’s not the case that")
    • "if…then"
    • "if and only if"

Truth-functional

  • Based on truth values of connected sentences.
  • Example of truth table interpretation:
    • If we ascertain truth values of components, we define the truth of the sentence as a whole.

Understanding Conditional Statements

  • Structure:
    • If P, then Q.
  • Truth Conditions:
    • Both are true: I am well, and I help you move.
    • Antecedent true, consequent false: I am well, but I don't help you move.
    • Antecedent false, consequent can be true/false: examples of broken promises regarding moving.

Truth Tables

  • Negation:

    • Not P
    • Truth Table:
    • T (True) -> F (False)
    • F (False) -> T (True)

  • Conjunction:

    • P and Q
    • Truth Table example:
    • T and T = T
    • Others = F

  • Disjunction:

    • P or Q
    • Truth Table example:
    • T or T = T
    • Others = F

  • Bi-Conditional:

    • P if and only if Q
    • Truth table outcomes determined by truth pairs.

Important Note

  • Ensure that logical structures and expressions are accurately maintained to uphold validity in arguments and logic.