1 Distinctions between deduction and induction Deduction Induction

1. Distinctions between deduction and induction

Deduction Induction o The premises are supposed to provide necessary support for the conclusion. o If all of the premises are true, the conclusion must be true. o All of the information or factual content in the conclusion is contained, at least implicitly, in the premises. o The premises are supposed to provide probable support for the conclusion. o If all of the premises are true, the conclusion is probably true, but not necessarily true. o The conclusion contains information not present, even implicitly, in the premises.

Deduction 1. 2. 3. Induction Every mammal has a heart. All horses are mammals. Therefore, every horse has a heart. 1. 2. Every horse that has ever been observed has had a heart. Therefore, every horse has a heart

Deduction Induction 1. NNU is in Nanjing. 2. Nanjing is in Jiangsu. 3. NNU is in Jiangsu. 1. If it is raining today, I will stay at home. 2. It is raining today. 3. So, I stay at home. 1. All observed swans are white. 2. Therefore, all swans are white. 1. Most of honors students are smart. 2. Yuanyuan is a honors student. 3. So, she is smart.

2. Evaluating deductive arguments

Evaluating terms o Valid, invalid, sound, and unsound

Valid argument o A valid argument is such a deductive argument in which if the premises were true, the conclusion would have to be true. o Information in the conclusion cannot go beyond the information in the premises. o It is impossible for the premises to be true but the conclusion to be false.

Examples o x is taller than y and y is taller than z. Therefore, x is taller than z. o Some students are female. Therefore, some students are not female. o Some students are humans. Some students are female. Therefore, some humans are female.

Difficult Points o A valid argument does not mean that the premises have to be true and the conclusion has to be true. o A deductive argument with all true premises and a true conclusion cannot guarantee it is a valid argument. o An invalid argument could have all true premises and a true conclusion.

Valid Invalid T premises T conclusion Possible T premises F conclusion Impossible Possible F premises T conclusion Possible F premises F conclusion Possible

Valid T premises T conclusion T premises F conclusion All wines are beverages. Chardonnay is a wine. Therefore, Chardonnay is a beverage. None exists. F premises T conclusion All wines are soft drinks. Coke is a wine. Therefore, Coke is a soft drink. F premises F conclusion All wines are whiskeys. Coke is a wine. Therefore, Coke is a whiskey.

T premises T conclusion Invalid All wines are beverages. Chardonnay is a beverage. Therefore, Chardonnay is a wine. T premises F conclusion All wines are beverages. Coke is a beverage. Therefore, Coke is a wine. F premises T conclusion All wines are whiskeys. Chardonnay is a whiskey. Therefore, Chardonnay is a wine. F premises F conclusion All wines are whiskeys. Coke is a whiskey. Therefore, Coke is a wine.

Sound and unsound arguments o An argument is sound if and only if it is a valid argument with all true premises. o A sound argument = a valid argument + all true premises o An unsound argument will be the one that is either invalid or with at least one false premise.

Which is the following is sound? 1. All dogs play chess. 2. Fido is a dog. 3. Therefore, Fido plays chess. 1. All odd numbers are greater than 2. 2. 4 is an odd number. 3. So, 4 is greater than 2. 1. NNU is in Ohio. 2. Ohio is in Canada. 3. Therefore, NNU is in Canada. 1. All flowers are plants. 2. All roses are flowers. 3. All roses are plants.

3. Evaluating inductive arguments

Evaluating terms o Strong, weak, cogent, and uncogent

Cogent and Uncogent o A cogent argument is the strong argument with all true premises. o A cogent = strong + all true premises o An argument is uncogent if and only if either it is weak or it has at least one false premise.

Inductive arguments o An inductive argument is strong if and only if, when the premises were true, the conclusion would be most likely to be true. o An argument is weak if and only if, when the premises were true, the conclusion would not be most likely to be true.

Examples o Strong: All observed swans are white. Therefore, all swans are white. o Weak: All observed swans are white. Therefore, all swans are black. o Cogent: All observed ravens are black. Therefore, all ravens are black. o Uncogent: Either it has at least a false premise or it is weak.