Chapter 15: Rules for Judging Validity

Distribution (p. 152) Several of the rules use the notion of distribution. A term is distributed if it refers to all members of a class. Where D means “is distributed” and U means “is undistributed,” the distribution of terms in a categorical proposition is as follows: All S D are P U. No S D are P D. Some S U are P U. Some S U are not P D.

Rules for Evaluating Syllogisms (pp ) 1. All standard-form categorical syllogisms have exactly three terms that are used with the same meaning throughout the syllogism. –This tells you to make sure you have a categorical syllogism, since a categorical syllogism must have exactly three terms used in the same sense throughout the syllogism. –Equivocations –If a syllogism breaks this rule, it can break no other. If the syllogism breaks the first rule, it is not a categorical syllogism.

Rules for Evaluating Syllogisms (pp ) 2. The middle term of a standard-form categorical syllogism must be distributed exactly once. 3. The major term of a valid standard-form categorical syllogism is either distributed twice (in both the premise and the conclusion) or not at all. 4. The minor term of a valid standard-form categorical syllogism is either distributed twice (in both the premise and the conclusion) or not at all.

Rules for Evaluating Syllogisms (pp ) 5. There must be as many negative premises as negative conclusions (either one of each or none). 6. There must be as many particular premises as particular conclusions (either one of each or none). If a syllogism breaks any one of the last five rules, it will break at least two of them.

Rules for Evaluating Syllogisms: Examples (pp ) Consider an argument of the following form: All M are P. Some S are M, Some S are P. Mark the distribution of terms: All M D are P U. Some S U are M U, Some S U are P U.

Rules for Evaluating Syllogisms: Examples (pp ) Now go through the rules: –We have a schema, so there is no chance of an equivocation. So, Rule 1 is followed. –The middle term is distributed exactly once. So Rule 2 is followed. –The major term is undistributed twice. So, Rule 3 is followed. –The minor term is undistributed twice. So Rule 4 is followed. –There are no negative premises or conclusions. So Rule 5 is followed. –There is one particular premise and one particular conclusion, So, Rule 6 is followed. –No rules are broken. So, the argument is valid.

Rules for Evaluating Syllogisms: Examples (pp ) Consider the following: Some aardvarks are handsome animals. Some handsome animals are salamanders. No salamanders are aardvarks. Make sure the terms are used consistently throughout. They are. Mark the distribution of terms: Some A U are H U. Some A U are S U. No S D are A D.

Rules for Evaluating Syllogisms: Examples (pp )  The middle term is undistributed. So Rule 2 is broken. The major term is distributed only once. So Rule 3 is broken. The minor term is distributed only once. So Rule 4 is broken. There are no negative premises, but there is a negative conclusion. So Rule 5 is broken. There are two particular premises and a universal conclusion. So Rule 6 is broken. At least one rule has been broken. So, the argument is invalid.

Rules for Evaluating Syllogisms: Examples (pp ) Consider the following: Some aardvarks are not sheep, and no sheep are trumpets, so all aardvarks are trumpets. You have exactly three terms, so there is no problem with rule 1. Mark the distribution of terms: No S D are T D. Some A U are not S D. All A D are T U.

Rules for Evaluating Syllogisms: Examples (pp ) The middle term (S) is distributed twice. So, the syllogism violates Rule 2. The major term (T) is distributed only once. So the syllogism violates Rule 3. The minor term (A) is distributed only once. So the syllogism violates Rule 4. We have two negative premises and an affirmative conclusion. So the syllogism violates Rule 5. We have a particular premise and a universal conclusion. So, the syllogism violates Rule 6. At least one rule has been violated. So the argument form is invalid.

Rules for Evaluating Syllogisms: Examples (pp ) Consider the following: All mice are rodents, so some mice are bothersome beasts, since some rodents are bothersome beasts. There is no problem with the first rule. We may set forth the syllogism in standard form, marking the distributions: Some R U are B U. All M D are R U Some M U are B U.

Rules for Evaluating Syllogisms: Examples (pp ) The middle term is undistributed. So, the syllogism violates Rule 2. The major term is undistributed twice, which is fine (Rule 3). The minor term is distributed once. So, the syllogism violates Rule 4. There are no negative premises or conclusions, which is fine (Rule 5). There is one particular premise and one particular conclusion, which is fine (Rule 6). Since at least one rule was broken, the syllogism is invalid.

Rules for Evaluating Syllogisms: Examples (pp ) Consider the following: All things in Vogue are very fashionable things. So, no advertising T-shirts are things in vogue, since no advertising T-shirts are fashionable things. The syllogism is invalid: It breaks Rule 1. Vogue is a fashion magazine. Most of the things in Vogue are pictures of people wearing fancy clothes. To be “in vogue” (lower case, no italics) is to be popular. There are four terms. It is not a categorical syllogism. It can break no other rules.