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    9 2 t4_chapterninepowerpoint 9 2 t4_chapterninepowerpoint Presentation Transcript

    • 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.)