Symbolic Arguments

• A symbolic argument consists of a set of premises and a conclusion.
• If the car is a mustang, then it is fast. The car is fast, therefore the car is a mustang.
  • The premises are:
    • If the car is a mustang, then it is fast.
    • The car is fast
  • The conclusion is : the car is a mustang
• We can discuss the validity of this argument using logic.
  • Step 1 , represent the statement symbolically.
    • p: the car is a mustang.
    • q: the car is fast.
    • p → q, q then p
  • Step two: write as if premise 1 and premise 2 then conclusion
    • ((p → q) ∧ q) → p
  • Step three, if the statement is a tautology then the argument is valid.
  • This argument is not valid, it is invalid or it is a fallacy
• Try If I live in Edinboro then I like snow. I live in Edinboro. Therefore I like snow.
  • This argument is valid, therefore it is a valid argument.
• Some valid arguments:
  • The argument we just saw:

    p → q;
    p
    __________
    ∴ q
      

    is so common, it is called the law of detachment and unless instructed otherwise, it can be stated as justification that an argument is valid.
  • Show that p→ q, ∼ q, ∴ ∼ p is valid.
  • This is the law of contraposition
  • Law of Syllogism p → q, q→ r ∴ p → r
  • Disjunctive Syllogism p ∨ q, ∼p ∴ q.
• Some well known false arguments:
  • Fallacy of Converse p→ q, q, ∴ p, we have seen this is false above
  • Fallacy of inverse p → q, ∼p ∴ ∼ q
• Exercises 13-50 page 159