Arguments: Deductive and Inductive Arguments Notes

Arguments: Deductive and Inductive Arguments

Deduction and Induction: Necessity vs. Probability

  • Deductive Arguments: These arguments claim that if the premises are true, it is impossible for the conclusion to be false. The conclusion necessarily follows from the premises.

  • Inductive Arguments: These arguments provide some evidence for the truth of the conclusion but do not guarantee it. The conclusion is likely or probable based on the evidence provided.

Common Types of Deductive Arguments

  • Based on Mathematics

  • From Definition

  • Categorical Syllogisms

  • Hypothetical Syllogisms

  • Disjunctive Syllogisms

Example: All members of the mongoose family are carnivores. Meerkats are members of the mongoose family. Therefore, the meerkat is a carnivore.

Common Types of Inductive Arguments

  • Prediction

  • Analogy

  • From Authority

  • Based on Signs

  • Causal Inference

Example: The vast majority of entertainers are extroverts. Stephen Colbert is an entertainer. Therefore, Stephen Colbert is an extrovert.

Deductive Arguments: Validity

  • Valid Deductive Arguments: These are arguments where it is impossible for the conclusion to be false if the premises are true.

  • Invalid Deductive Arguments: These are arguments where it is possible for the conclusion to be false even if the premises are true.

Soundness

  • Sound Argument: A sound argument is a valid argument with all true premises.

    Sound Argument = Valid argument + All true premises

Example: All flowers are plants. All daisies are flowers. Therefore, all daisies are plants.

Invalid and Unsound Argument

All roses are flowers.

All daisies are flowers.

Therefore, all daisies are roses.

Inductive Arguments: Strong versus Weak Arguments

  • Strong Inductive Arguments: These are arguments where it is improbable that the conclusion is false given that the premises are true. The conclusion probably follows from the premises.

  • Weak Inductive Arguments: These are arguments where the conclusion does not follow probably from the premises, even though it is claimed to.

Strong Inductive Argument Example

Every US president was older than 40. Therefore, probably the next US president will be older than 40.

Weak Inductive Argument Example

A few US presidents were lawyers. Therefore, probably the next US president will be older than 40.

Cogent Argument

  • Cogent Argument: A cogent argument is a strong argument with all true premises.
    Cogent Argument = Strong Argument + All true premises

Example: Every previous U.S. president was older than 40. Therefore, probably the next U.S. president will be older than 40.