Analyzing Arguments Flashcards 1D

Flashcards covering the different types of arguments, validity, and soundness.

What is an inductive argument?

An argument where specific premises lead to a general conclusion.

Provide an example of an inductive argument.

Premise: Bluebirds fly. Premise: Hummingbirds fly. Premise: Cardinals fly. Conclusion: All birds fly.

What is a deductive argument?

An argument where general premises lead to a specific conclusion.

Give an example of a deductive argument.

Premise: All doctors are intelligent. Premise: Dr. Jones is a doctor. Conclusion: Dr. Jones is intelligent.

How is the strength of an inductive argument evaluated?

Based on how well the premises support the conclusion; whether a compelling case is made.

What makes an inductive argument weak?

If the conclusion is not well supported by its premises.

What two criteria are applied to evaluate a deductive argument?

Validity and Soundness

When is a deductive argument considered valid?

If the conclusion follows necessarily from its premises, regardless of the truth of the premises.

When is a deductive argument considered sound?

If it is valid and its premises are all true.

How can a Venn diagram be used to test the validity of a deductive argument?

Draw a Venn diagram representing the premises and check if it confirms the conclusion.

Describe the 'Affirming the Hypothesis' argument form.

If p, then q. p is true. Therefore, q is true. (Valid)

Describe the 'Affirming the Conclusion' argument form.

If p, then q. q is true. Therefore, p is true. (Invalid)

Describe the structure of a deductive argument with a chain of conditionals.

If p, then q. If q, then r. Therefore, if p, then r. (Valid)

Describe the 'Denying the Hypothesis' argument form.

If p, then q. p is false. Therefore, q is false. (Invalid)

Describe the 'Denying the Conclusion' argument form.

If p, then q. q is false. Therefore, p is false. (Valid)

What is a mathematical proof?

A deductive argument that demonstrates the truth of a certain claim or theorem.

How are theorems often discovered?

By induction

In mathematics, is deduction or induction used for proofs?

Deduction