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1.4 Validity, Truth, Soundness, Strength and Cogency Goal: Learn the terms used to evaluate inductive and deductive arguments

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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.

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“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

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

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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.

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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.

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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.

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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

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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?

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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?

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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.

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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?

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P1. All past presidents have been men. C. The next president will be a man. Inductive: Possible for the conclusion to be false Can be made stronger or weaker given more information. There are degrees of strength!

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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.

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P1. Every student I know has a cell phone. C. So, all students have cell phones. P1. Every only child surveyed reported being satisfied not having siblings. C. Thus all only children are so satisfied.

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Cogent = Strong + True Premises P1. I have lost every hand so far. C. So, I will win the next hand. P1. Korby Ray used Ultra 90 and lost 50#. C. So, if I use Ultra 90 I will lose 50#.

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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}

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Deductive Arguments 1. All hamburgers are high in fat. Quarter-pounders with cheese are hamburgers. Therefore, quarter- pounders with cheese are high in fat. Sound ___ = Valid ___ + True premises ___

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Deductive Arguments 1. All hamburgers are high in fat. Quarter-pounders with cheese are hamburgers. Therefore, quarter- pounders with cheese are high in fat. Sound _ __ = Valid __ _ + True premises _ *__

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2. All hamburgers are high in fat. Chicken nuggets are high in fat. Therefore, chicken nuggets are hamburgers. Sound ___ = Valid ___ + True premises ___

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2. All hamburgers are high in fat. Chicken nuggets are high in fat. Therefore, chicken nuggets are hamburgers. Sound _x__ = Valid __x_ + True premises _ __

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3. All hamburgers are good sources of vitamins. Fresh vegetables and fruit are hamburgers. Therefore, fresh vegetables and fruit are good sources of vitamins. Sound ___ = Valid ___ + True premises ___

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3. All hamburgers are good sources of vitamins. Fresh vegetables and fruit are hamburgers. Therefore, fresh vegetables and fruit are good sources of vitamins. Sound _x__ = Valid _ __ + True premises _x__

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Inductive Arguments 1. Meatpacking has become the most hazardous occupation in the US, with three times the injury rate of factory work. Therefore, John who works at a meatpacking plant will probably get injured on the job. Cogent___ = Strong ___ + True Premises ___

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2. I haven’t gotten sick from eating fast food yet, so I will probably get sick if I eat fast food any time soon. Cogent___ = Strong ___ + True Premises ___

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3. McDs promises, “…to use only fresh, wholesome ingredients when serving you and your family;” so they only use fresh, wholesome ingredients in their food. Cogent___ = Strong ___ + True Premises ___

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

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

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