Validity, Soundness, Strength, and Cogency

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A presentation on how to evaluate deductive and inductive arguments.

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What we have to learn to do we learn by doing. :

What we have to learn to do we learn by doing. Aristotle

Validity, soundness, strength, cogency:

Validity, soundness, strength, cogency

Deductive arguments:

Deductive arguments Factual claim Inferential claim Soundness Validity

Validity :

Validity Addresses whether the premises provide support for the conclusion. In a valid argument if the premises are true the conclusion has to be true. Validity is not connected with truth.

How to test for validity:

How to test for validity Assume the premises are true. Based on that assumption ask: Does the conclusion have to be true? If the answer is yes the argument is valid. If the answer is no the argument is invalid.

valid:

valid All television networks are media companies. NBC is a television network. Therefore, NBC is a media company.

valid:

valid All automakers are computer manufactures. United Airlines is an auto maker. Therefore, United Airlines is a computer manufacture.

invalid:

invalid All banks are financial institutions. Wells Fargo is a financial institution. Therefore, Wells Fargo is a bank. F B WF

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An argument with actually true premises and a false conclusion is always invalid.

Soundness :

Soundness Addresses the truth of the premises. To determine soundness simply ask: Are the premises REALLY true? Do not assume the premise are true this only applies to validity.

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Invalid arguments are ALWAYS unsound.

Inductive arguments:

Inductive arguments Factual claim Inferential claim Cogency Strength

Strength :

Strength Unlike validity strength is a term of degree. An argument is strong if the premises provide probable support for the conclusion. In general if the probability for the conclusion to follow from the premises is greater than 50% the argument is strong.

How to test for strength:

How to test for strength Assume the premises are true. Based on this assumption ask: Is the conclusion probably true? If the answer is yes the argument is strong. If the answer is no the argument is weak.

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All dinosaur bones discovered to this day have been at least 50 million years old. Therefore, probably the next dinosaur bone to be found will be at least 50 million years old.

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All meteorites found to this day have contained sugar. Therefore, probably the next meteorite to be found will contain sugar.

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When a lighted match is slowly dunked into water, the flame is snuffed out. But gasoline is a liquid, just like water. Therefore, when a lighted match is slowly dunked into gasoline, the flame will be snuffed out.

Cogency :

Cogency Addresses the actual truth of the premises. To determine cogency ask: Are the premises REALLY true? If the answer is yes the argument is cogent. If the answer is no the argument is uncogent.

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Weak arguments are ALWAYS uncogent.

Total evidence requirement:

Total evidence requirement In cogent inductive arguments the premises must not only be true but also not ignore any important evidence that would entail a different conclusion.

Do not confuse the terms!:

Do not confuse the terms! Deductive Valid/Invalid Sound/Unsound Inductive Strong/Weak Cogent/Uncogent

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Jerry was born on Easter Sunday. It necessarily follows, therefore, that his birthday always falls on a Sunday. Deductive Invalid Unsound

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All birds can fly. Penguins are birds. So, penguins can fly. Deductive Valid Unsound

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It tends to be cold in Minneapolis in January. So, probably it will be cold in Minneapolis next January. Inductive Strong Cogent

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The vast majority of popes have been Americans. Therefore, the next pope will probably be an American. Inductive Strong Uncogent

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If we’re at the North Pole, then we’re on Earth. We are on Earth. Therefore, we’re at the North Pole. Deductive Invalid Unsound

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Since Moby Dick was written by Shakespeare, and Moby Dick is a science fiction novel, it follows that Shakespeare wrote a science fiction novel. Deductive valid Unsound

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Since Agatha is the mother of Raquel and the sister of Tom, it follows that Tom is the uncle of Raquel. Deductive valid ?

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By accident Karen baked her brownies two hours longer than she should have. Therefore, they have probably been ruined. Inductive Strong ?

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Circle A has exactly twice the diameter of circle B. From this we may conclude that circle A has exactly twice the area of circle B. Deductive

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2 4 Circle A Circle B π r 2

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Circle A has exactly twice the diameter of circle B. From this we may conclude that circle A has exactly twice the area of circle B. Deductive Deductive Invalid Unsound

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After taking LSD, Alice said she saw a flying saucer land in the shopping center parking lot. Since Alice has a reputation for always telling the truth, we must conclude that a flying saucer really did land there. Inductive Weak Uncogent

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The United States Congress has more members than there are days in the year. Therefore, at least two members of Congress have the same birthday. Deductive Valid Sound

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A random sample of twenty-five country and western singers, including Garth Brooks and Dolly Parton, revealed that every single one of them studied music in Afghanistan. Therefore, probably the majority of country and western singers studied music in Afghanistan. Inductive Strong Uncogent

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