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• CHAPTER NINE THE STEPPING STONES OF LOGIC: SYLLOGISMS SECOND THOUGHTS, 4 th ed . Wanda Teays McGraw-Hill Higher Ed. © 2010. Wanda Teays. All rights reserved.
• Form of the syllogism
• Dfn. Syllogism. This is a three-line argument with two premises and one conclusion in which there are only three terms.
• FOR EXAMPLE:
• All donuts are delicious treats. Some junk foods are delicious treats. Therefore, some junk food are donuts.
• The three terms are: donuts, delicious treats, & junk oof.
• Validity
• First, there is the issue of validity . The argument is structurally correct (so that if the premises were true, the conclusion could not be false).
• FOR EXAMPLE:
• All leopards have spots. All spotted animals wish they had stripes. Therefore, all leopards wish they had stripes.
• NOTE: If the two premises were true, the conclusion would have to be true too.
• Soundness
• An argument is sound if
• (1) the argument is valid
• (2) the premises are actually true.
• FOR EXAMPLE:
• All leopards are cats. No cat is a squirrel. Therefore, no leopard is a squirrel.
• Universal Propositions
• Form 1: “All A is B.”  Universal positive
• “ All cockatoos are birds that can talk.”
• Form 2: “No A is B.”  Universal negative “No cockatoo is a duck.”
• Form 3: “A is/is not B.”  Universal positive/negative “Australia is a place with many cockatoos.”
• This includes where A has only one member “That baby cockatoo is a darling bird.”
• Particular Propositions
• Form 1: “Some A is B”  Particular positive
• “ Some chefs are good bakers.”
• Form 2: “Some A is not B”  Particular negative
• “ Some fish are not rainbow trout.”
• Form 3: “x% of A is/is not B”  Particular positive/negative. Where x  100 or 0.
• “ 64% of women are tea drinkers.”
• Categorical Propositions
• In analyzing a syllogism, it’s usually best to rewrite the premises and the conclusion in the form of categorical propositions .
• These are :
• A: All P are Q. All basketball players are athletes.
• E: No P is Q. No violinist is a football player.
• I: Some P is Q. Some gymnasts are shy people.
• O: Some P is not Q. Some mountain climbers are not stamp collectors.
• NOTE: The letters A, E, I, and O are handy ways to abbreviate these 4 forms.
• Categorical Syllogisms
• A categorical syllogism is a syllogism in which the premises and the conclusion are categorical claims.
• FOR EXAMPLE:
• All racoons are pesky animals. No pesky animal is a good pet. Therefore, no raccoon is a good pet
• The standard form of a categorical syllogism is a syllogism stated in the order of major premise, minor premise, and then the conclusion.
• This gives us a uniform way to set out syllogisms so they are easy to assess, and we aren’t scrambling trying to figure out what’s what.
• Categorical Syllogism in Standard Form
• Here’s a categorical syllogism in standard form.
• No vampires are morning people. Some morning people are folks who like scrambled eggs for breakfast. Therefore, no folks who like scrambled eggs for breakfast are vampires.
• NOTE: The major premise is the premise that contains the predicate term (=major term) found in the conclusion.
• The second premise is called the minor premise and it contains the subject term (=minor term) found in the conclusion. Both premises have a linking term (= middle term) that does not appear in the conclusion.
• The middle term is the term that is found only in the premises, not the conclusion.
• Handy Abbreviations
• P = Predicate of the conclusion  Major term
• S = Subject of the conclusion  Minor term
• M = Term found in both premises  Middle term
• The Figures of the Syllogism
• M P P M M P P M  
• S M S MM S M S
•   S P S P S P S P
• FIGURE 1 FIGURE 2 FIGURE 3 FIGURE 4
• Step down M’s on right M’s on left step up
• Mood and Figure
• The mood of the syllogism is found after the syllogism is in categorical standard form. Then you just read the abbreviations (A,E,I, O) of the universal/particular and positive/negative propostions. The figure is found by the location of the middle term.
• FOR EXAMPLE:
• Some vegetarians are cheese-eaters. All bicyclists are cheese-eaters. Therefore, some bicyclists are vegetarians.
• The MOOD of the syllogism is: IAI. The figure is figure 2 (M’s on right). So the mood and figure is written:
• IAI—(2).
• Distribution
• Distribution of a term refers to how much of the class (the subject or the predicate) is being referred to in the propostion.
• It’s easy to find: Claims that are all-or-nothing (A and E claims) refer to all of the subject class. Claims that are particular (I and O claims) refer to only some. So the SUBJECT IS DISTRIBUTED in universal claims—but not particular claims.
• Claims that are positive (A and I) do not distribute the PREDICATE —the predicate is only distributed in negative claims (E and O).
• PROPOSITION DISTRIBUTED TERM(S):
• All P is Q  subject
• No P is Q  subject and predicate
• Some P is Q  nothing
• Some P is not Q  predicate
• RULES OF THE SYLLOGISM
•
• Rule 1: The middle term must be distributed at least once.
•   Rule 2: If a term is distributed in the conclusion, it must also be distributed in its corresponding premise Illicit major : When the major term is distributed in the conclusion, but is not distributed in the major premise  Illicit minor: When the minor term is distributed in the conclusion, but is not distributed in the minor premise
• Note: A valid syllogism does not requires the conclusion to have its terms distributed. But if a term is distributed in the conclusion, then it must also be distributed in its corresponding premise.
•
• Rules of the Syllogism con.
• Rule 3: At least one premise must be positive. (Two negative premises = invalid argument)
• Rule 4: If the syllogism has a negative premise, there must be a negative conclusion, and vice versa.
• Rule 5: If both of the premises are universal, the conclusion must also be universal. And if the conclusion is universal, both premises must be universal as well.
• (You cannot have two universal premises with a particular conclusion and you cannot have a universal conclusion unless both premises are also universal.)