1.4 Validity, Truth, 1.4 Validity, Truth, Soundness, Strength Soundness, Strength and Cogencyand Cogency

Goal: Learn the terms used to Goal: Learn the terms used to evaluate inductive and evaluate inductive and deductive argumentsdeductive arguments

Deductive ArgumentsDeductive Arguments

An argument in which An argument in which it is claimed thatit is claimed that it it is impossible for the conclusion to be is impossible for the conclusion to be false if the premises are true is a false if the premises are true is a deductive argument.deductive argument.

That is, That is, it is claimed thatit is claimed that the argument it the argument it valid. valid.

In a valid argument, if the premises are In a valid argument, if the premises are true, the conclusion must be true too. true, the conclusion must be true too.

““Validity” describes the relationship Validity” describes the relationship that the premises bear to the that the premises bear to the conclusion in a deductive conclusion in a deductive argument. argument.

The test for validity: Imagine that The test for validity: Imagine that the premises are true and the the premises are true and the conclusion is falseconclusion is false

If you cannot imagine that the If you cannot imagine that the premises are true and the premises are true and the conclusion is false, then the conclusion is false, then the argument is VALID.argument is VALID.

If you can imagine that the premises If you can imagine that the premises are true and the conclusion is false are true and the conclusion is false then the argument is INVALID. then the argument is INVALID.

P1. All CCU students are P1. All CCU students are hardworking.hardworking.

P2. Howie is a CCU student. P2. Howie is a CCU student.

C. So, Howie is hardworking. C. So, Howie is hardworking.

Valid: if the premises were true, the Valid: if the premises were true, the conclusion could not be false. conclusion could not be false.

P1. All CCU students are P1. All CCU students are hardworking.hardworking.

P2. Howie is hardworking. P2. Howie is hardworking.

C. So, Howie is a CCU student. C. So, Howie is a CCU student.

Invalid: if the premises were true, Invalid: if the premises were true, the conclusion could still be false. the conclusion could still be false.

In a “good” argument the premises In a “good” argument the premises support the conclusion (validity) support the conclusion (validity) AND the premises are true. AND the premises are true.

A “good” deductive argument is A “good” deductive argument is called a “sound” argument. A called a “sound” argument. A sound argument is valid and has sound argument is valid and has all true premises. all true premises.

P1. All CCU students are hardworking.P1. All CCU students are hardworking.

P2. Howie is a CCU student. P2. Howie is a CCU student.

C. So, Howie is hardworking. C. So, Howie is hardworking.

Valid: if the premises were true, the Valid: if the premises were true, the conclusion could not be false. conclusion could not be false.

False premise(s)False premise(s)

UnsoundUnsound

Sound = Valid + True PremisesSound = Valid + True Premises

P1. If Obama is president then he is P1. If Obama is president then he is Commander in Chief. Commander in Chief.

P2. Obama is president.P2. Obama is president.

C. Therefore, he is Commander in C. Therefore, he is Commander in Chief. Chief.

Is this argument sound?Is this argument sound?

Sound = Valid + True PremisesSound = Valid + True Premises

P1. All cats have tails.P1. All cats have tails.

P2. My dog has a tail.P2. My dog has a tail.

C. So, my dog is a cat. C. So, my dog is a cat.

Is this argument sound?Is this argument sound?

Inductive ArgumentsInductive Arguments

An argument in which An argument in which it is claimed thatit is claimed that it it is improbably that the conclusion is is improbably that the conclusion is false if the premises are true is an false if the premises are true is an inductive argument. inductive argument.

That is, it is claimed that the argument is That is, it is claimed that the argument is strong. strong.

A strong argument is one whose A strong argument is one whose conclusion is probably true given the conclusion is probably true given the truth of the premises. truth of the premises.

The test for strength: Imagine the The test for strength: Imagine the premises are true, and determine premises are true, and determine whether the conclusion is probable whether the conclusion is probable given the truth of the premises. given the truth of the premises.

Does the truth of the premises make Does the truth of the premises make it more like that the conclusion is it more like that the conclusion is true then had the premises been true then had the premises been false? false?

P1. All past presidents have been P1. All past presidents have been men.men.

C. The next president will be a man. C. The next president will be a man.

Inductive: Possible for the conclusion Inductive: Possible for the conclusion to be falseto be false

Can be made stronger or weaker Can be made stronger or weaker given more information. given more information.

There are degrees of strength!There are degrees of strength!

P1. All past presidents have been men.P1. All past presidents have been men.

C. The next president will be a man. C. The next president will be a man.

P1. All past presidents have been P1. All past presidents have been women.women.

C. The next president will be a woman. C. The next president will be a woman.

P1. Every student I know has a cell P1. Every student I know has a cell phone.phone.

C. So, all students have cell phones. C. So, all students have cell phones.

P1. Every only child surveyed reported P1. Every only child surveyed reported being satisfied not having siblings.being satisfied not having siblings.

C. Thus all only children are so C. Thus all only children are so satisfied. satisfied.

Cogent = Strong + True Cogent = Strong + True PremisesPremises

P1. I have lost every hand so far.P1. I have lost every hand so far.

C. So, I will win the next hand. C. So, I will win the next hand.

P1. Korby Ray used Ultra 90 and P1. Korby Ray used Ultra 90 and lost 50#.lost 50#.

C. So, if I use Ultra 90 I will lose C. So, if I use Ultra 90 I will lose 50#.50#.

Arguments = Premises + conclusionsArguments = Premises + conclusionsFactual claim (are the premises true?)Factual claim (are the premises true?)Inferential claim (is the argument Inferential claim (is the argument valid/strong?)valid/strong?)

Deductive ArgumentsDeductive ArgumentsSound = Valid + True premisesSound = Valid + True premises

{valid: if the premises are true, the conclusion {valid: if the premises are true, the conclusion must be true}must be true}

Inductive ArgumentsInductive ArgumentsCogent = Strong + True PremisesCogent = Strong + True Premises

{strong: the conclusion is probably true if the {strong: the conclusion is probably true if the premises are true}premises are true}

Deductive ArgumentsDeductive Arguments

1. All hamburgers are high in fat. 1. All hamburgers are high in fat. Quarter-pounders with cheese Quarter-pounders with cheese are hamburgers. Therefore, are hamburgers. Therefore, quarter-pounders with cheese quarter-pounders with cheese are high in fat. are high in fat.

Sound ___ = Valid ___ + True premises ___Sound ___ = Valid ___ + True premises ___

Deductive ArgumentsDeductive Arguments

1. All hamburgers are high in fat. 1. All hamburgers are high in fat. Quarter-pounders with cheese Quarter-pounders with cheese are hamburgers. Therefore, are hamburgers. Therefore, quarter-pounders with cheese quarter-pounders with cheese are high in fat. are high in fat.

Sound _ Sound _ __ = Valid __ __ = Valid ___ + True premises _ _ + True premises _ *__ *__

2. All hamburgers are high in fat. 2. All hamburgers are high in fat. Chicken nuggets are high in fat. Chicken nuggets are high in fat. Therefore, chicken nuggets are Therefore, chicken nuggets are hamburgers. hamburgers.

Sound ___ = Valid ___ + True premises ___Sound ___ = Valid ___ + True premises ___

2. All hamburgers are high in fat. 2. All hamburgers are high in fat. Chicken nuggets are high in fat. Chicken nuggets are high in fat. Therefore, chicken nuggets are Therefore, chicken nuggets are hamburgers. hamburgers.

Sound _x__ = Valid __x_ + True premises _ Sound _x__ = Valid __x_ + True premises _ __ __

3. All hamburgers are good sources 3. All hamburgers are good sources of vitamins. Fresh vegetables and of vitamins. Fresh vegetables and fruit are hamburgers. Therefore, fruit are hamburgers. Therefore, fresh vegetables and fruit are fresh vegetables and fruit are good sources of vitamins. good sources of vitamins.

Sound ___ = Valid ___ + True premises ___Sound ___ = Valid ___ + True premises ___

3. All hamburgers are good sources 3. All hamburgers are good sources of vitamins. Fresh vegetables and of vitamins. Fresh vegetables and fruit are hamburgers. Therefore, fruit are hamburgers. Therefore, fresh vegetables and fruit are fresh vegetables and fruit are good sources of vitamins. good sources of vitamins.

Sound _x__ = Valid _ Sound _x__ = Valid _ __ + True premises _x__ __ + True premises _x__

Inductive ArgumentsInductive Arguments

1.1. Meatpacking has become the most Meatpacking has become the most hazardous occupation in the US, with hazardous occupation in the US, with three times the injury rate of factory three times the injury rate of factory work. Therefore, John who works at a work. Therefore, John who works at a meatpacking plant will probably get meatpacking plant will probably get injured on the job. injured on the job.

Cogent___ = Strong ___ + True Premises Cogent___ = Strong ___ + True Premises ______

2. I haven’t gotten sick from eating 2. I haven’t gotten sick from eating fast food yet, so I will probably fast food yet, so I will probably get sick if I eat fast food any time get sick if I eat fast food any time soon. soon.

Cogent___ = Strong ___ + True Premises ___Cogent___ = Strong ___ + True Premises ___

3. McDs promises,3. McDs promises, “… “…to use only to use only fresh, wholesome ingredients fresh, wholesome ingredients when serving you and your when serving you and your family;” so they only use fresh, family;” so they only use fresh, wholesome ingredients in their wholesome ingredients in their food. food.

Cogent___ = Strong ___ + True Premises ___Cogent___ = Strong ___ + True Premises ___

4. Because McDs is the single 4. Because McDs is the single largest purchaser of US beef, they largest purchaser of US beef, they have considerable say over how have considerable say over how beef is processed in this country. beef is processed in this country. So, the beef they buy (and sell) is So, the beef they buy (and sell) is safe. safe.

Cogent___ = Strong ___ + True Premises ___Cogent___ = Strong ___ + True Premises ___

5. McD’s webpage has a statement 5. McD’s webpage has a statement from Dr. Dean Ornish whose diet from Dr. Dean Ornish whose diet has been proven to reduce heart has been proven to reduce heart disease; therefore, the foods that disease; therefore, the foods that McDs serves are part of a heart-McDs serves are part of a heart-healthy diet. healthy diet.

Cogent___ = Strong ___ + True Premises ___Cogent___ = Strong ___ + True Premises ___