Notes on Logic

Basics

Author
Affiliation

Christopher L. Holland

Saint Louis University

Lecture Date

January 22, 2025

Updated

January 22, 2025

1 What Is Logic?

  • The study of methods for evaluating arguments
  • Statements and Propositions
    • Statement: A sentence that expresses a proposition
    • Proposition: The content or meaning of a (fully interpreted) statement
      • Two or more statements may express the same proposition.
        • Both “the moon orbits the earth” and “the earth is orbited by the moon” express the same proposition.
        • Both “Jesus is Lord” and “Kyrios Iēsous” express the same proposition, that Jesus is Lord
      • A single statement may have more than one meaning.
        • “I shot an elephant in my pajamas” (Groucho Marx in Animal Crackers).
    • Most of the time, I will use the two terms (statement and proposition) interchangeably.
  • Truth value
    • The property of a proposition being either true or false
    • Statements express propositions
    • Questions, proposals, suggestions, commands, and exclamations do not express propositions.
    • Which of the following are statements?
      • Today is Tuesday.
      • What day of the week is it?
      • Please walk the dog.
      • If it is raining.
      • Mom said “If it is raining.”
      • Keep out!
      • Wet cement.
      • Ouch!
      • Murder is illegal.
      • Murder is wrong.
      • Yuck!
  • Three fundamental laws of logic
    • The law of identity: \(p\) is \(p\)
    • The law of noncontradiction: it is impossible that both \(p\) and not-\(p\) are true
    • The law of excluded middle: either \(p\) is true or not-\(p\) is true

2 What Is an Argument?

2.1 Arguments

  • A set of statements where some of the statements, the premises, are used to support another statement, the conclusion.
  • Premise
    • a statement intended to support the conclusion
  • Conclusion
    • statement supported by the premise(s)
  • Indicator words
    • Conclusion
      • consequently, thus, therefore, it follows that, as a result, hence, so, which means that
    • Premise
      • in view of the fact, because, assuming that, since, due to the fact that, inasmuch as, for

2.2 Non-Arguments

  • Reports
  • Opinions
  • Illustrations
  • Explanations
    • The sky appears blue from the earth’s surface because light rays from the sun are scattered by particles in the atmosphere.
    • Explanans / Explicans
      • light rays from the sun are scattered by particles in the atmosphere.
    • Explanandum / Explicandum
      • The sky appears blue from the earth’s surface
  • Conditionals
    • If-then statements. The if part is called the antecedent. The then part is called the consequent.
      • If . . . then . . .
      • The antecedent is sufficient condition.
      • The consequent is the necessary condition.
    • Stylistic Variants
      • if it is raining, then the ground is wet
        if (antecedent), then (consequent)
      • the ground is wet if it is raining
        (consequent) if (antecedent)
      • given that it is raining, the ground is wet
        given that (antecedent), (consequent)
      • the ground is wet, given that it is raining
        (consequent), given that (antecedent)
      • it is raining only if the ground is wet
        (antecedent) only if (consequent)
    • a conditional is not an argument, but many arguments include conditionals. For example:
      • (P1) If it is raining, then the ground is wet.
      • (P2) The ground is not wet.
      • (C1) So, it is not raining.

Reference

Howard-Snyder, Frances, Daniel Howard-Snyder, and Ryan Wasserman. 2013. The Power of Logic. New York: McGraw-Hill.
Pojman, Louis P. 2006. Philosophy: The Pursuit of Wisdom. 5th ed. Belmont, CA: Wadsworth.