1.4 Validity, Truth, Soundness, Strength and Cogency Learn the terms used to evaluate inductive and deductive arguments
1.4 Validity, Truth, Soundness, Strength and Cogency
Learn the terms used to evaluate inductive and deductive arguments
Deductive Arguments❖ An argument in which it is claimed that it is impossible
for the conclusion to be false if the premises are true is a deductive argument.
❖ That is, it is claimed that the argument it valid.
❖ In a valid argument, if the premises are true, the conclusion must be true too.
❖ “Validity” describes the relationship that the premises bear to the conclusion in a deductive argument.
❖ The test for validity: Imagine that the premises are true and the conclusion is false
❖ If you cannot imagine that the premises are true and the conclusion is false, then the argument is VALID.
❖ If you can imagine that the premises are true and the conclusion is false then the argument is INVALID.
❖ P1. All CCU students are hardworking. P2. Howie is a CCU student.
❖ C. So, Howie is hardworking.
❖ Valid: if the premises were true, the conclusion could not be false.
❖ P1. All CCU students are hardworking. P2. Howie is hardworking.
❖ C. So, Howie is a CCU student.
❖ Invalid: if the premises were true, the conclusion could still be false.
❖ In a “good” argument the premises support the conclusion (validity) AND the premises are true.
❖ A “good” deductive argument is called a “sound” argument. A sound argument is valid and has all true premises.
❖ P1. All CCU students are hardworking. P2. Howie is a CCU student.
❖ C. So, Howie is hardworking.
❖ Valid: if the premises were true, the conclusion could not be false.
❖ False premise(s) Unsound
Sound = Valid + True Premises
❖ P1. If Obama is president then he is Commander in Chief.
❖ P2. Obama is president.
❖ C. Therefore, he is Commander in Chief.
❖ Is this argument sound?
Sound = Valid + True Premises
❖ P1. All cats have tails.
❖ P2. My dog has a tail.
❖ C. So, my dog is a cat.
❖ Is this argument sound?
Inductive Arguments❖ An argument in which it is claimed that it is improbably
that the conclusion is false if the premises are true is an inductive argument.
❖ That is, it is claimed that the argument is strong.
❖ A strong argument is one whose conclusion is probably true given the truth of the premises.
❖ The test for strength: Imagine the premises are true, and determine whether the conclusion is probable given the truth of the premises.
❖ Does the truth of the premises make it more like that the conclusion is true then had the premises been false?
❖ P1. All past presidents have been men.
❖ C. The next president will be a man.
❖ Inductive: It is possible for the conclusion to be false
❖ Can be made stronger or weaker given more information.
❖ There are degrees of strength!
❖ P1. All past presidents have been men.
❖ C. The next president will be a man.
❖ P1. All past presidents have been women.
❖ C. The next president will be a woman.
❖ Arguments = Premises + conclusions
❖ Factual claim (are the premises true?)
❖ Inferential claim (is the argument valid/strong?)
❖ Deductive Arguments:
❖ Sound = Valid + True premises
❖ {valid: if the premises are true, the conclusion must be true}
❖ Inductive Arguments
❖ Cogent = Strong + True Premises
❖ {strong: the conclusion is probably true if the premises are true}