Evaluating Arguments: Deductive Arguments and Validity

Evaluating Arguments

Truth vs. Support

  • The success of an argument depends on:
    • The truth or falsity of the premises.
    • The degree of support the premises provide for the conclusion. This is the focus of this lecture.

Logical Analysis: Focusing on Structure

  • To analyze the logical structure, we temporarily disregard whether the premises are actually true or false.
  • We focus on: If the premises were true, would the conclusion necessarily follow?

Types of Logical Support

  • Two types of support premises can give to a conclusion:
    • Conclusive Support: The argument intends to prove (guarantee) the conclusion. If the premises are true, the conclusion cannot be false.
    • High Degree of Support: The argument intends to provide a probable degree of support. If the premises are true, the conclusion is more likely than not to be true, but not guaranteed.

Certainty vs. Probability

  • Conclusive Support: Aims for certainty: If the premises are true, the conclusion must be true.
  • Probable Support: Aims for probability: If the premises are true, there are strong reasons to believe the conclusion is true, but certainty is not achieved.

Deductive vs. Inductive Arguments

  • Two types of arguments:

    • Deductive Arguments: Intended to provide conclusive support. If premises are true, the conclusion must be true. In analyzing premises, the conclusion can be necessarily inferred.
    • Inductive Arguments: Intended to provide a high degree or probable degree of support. The conclusiondoesn't necessarily follow, but the premises give strong reasons to accept the conclusion.

  • Deductive Arguments: Deal with certainty and necessity.

  • Inductive Arguments: Deal with probability.

Focus on Deductive Arguments

  • We will primarily focus on deductive arguments now.
  • Deductive arguments intend to give conclusive support for their conclusions.

Validity: A Key Concept for Deductive Arguments

  • Validity is central to understanding deductive arguments.
  • A deductive argument intends to provide conclusive support.
    • If it succeeds -> argument is Valid.
    • If it fails -> argument is Invalid.
  • Recognizing argument is deductive is not enough to determnine validity. One has to determine do the premises give conclusive support for the conclusion.
  • Validity depends on the logical structure of the argument - the inferential link between premises and conclusion.

Precise Meaning of Validity

  • "Correct" is too vague. We need a precise definition.
  • Valid Argument: The conclusion follows by necessity from the premises.
  • Invalid Argument: The conclusion is not entailed by the premises.

Definition of a Valid Argument

  • Valid Argument: A deductive argument where there's no possible way for all the premises to be true and the conclusion false at the same time.
  • Another way to say this:
    • If all the premises are true, then the conclusion has to be true.
  • Truth of premises guarantees the truth of conclusion.
  • Valid arguments are "truth-preserving."