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  1. 1. 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.
  2. 2. Form of the syllogism <ul><li>Dfn. Syllogism. This is a three-line argument with two premises and one conclusion in which there are only three terms. </li></ul><ul><li>FOR EXAMPLE: </li></ul><ul><li>All donuts are delicious treats. Some junk foods are delicious treats. Therefore, some junk food are donuts. </li></ul><ul><li>The three terms are: donuts, delicious treats, & junk oof. </li></ul>
  3. 3. Validity <ul><li>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). </li></ul><ul><li>FOR EXAMPLE: </li></ul><ul><li>All leopards have spots. All spotted animals wish they had stripes. Therefore, all leopards wish they had stripes. </li></ul><ul><li>NOTE: If the two premises were true, the conclusion would have to be true too. </li></ul>
  4. 4. Soundness <ul><li>An argument is sound if </li></ul><ul><li>(1) the argument is valid </li></ul><ul><li>(2) the premises are actually true. </li></ul><ul><li>FOR EXAMPLE: </li></ul><ul><li>All leopards are cats. No cat is a squirrel. Therefore, no leopard is a squirrel. </li></ul>
  5. 5. Universal Propositions <ul><li>Form 1: “All A is B.”  Universal positive </li></ul><ul><ul><li>“ All cockatoos are birds that can talk.” </li></ul></ul><ul><ul><li>Form 2: “No A is B.”  Universal negative “No cockatoo is a duck.” </li></ul></ul><ul><li>Form 3: “A is/is not B.”  Universal positive/negative “Australia is a place with many cockatoos.” </li></ul><ul><li>This includes where A has only one member “That baby cockatoo is a darling bird.” </li></ul>
  6. 6. Particular Propositions <ul><li>Form 1: “Some A is B”  Particular positive </li></ul><ul><li>“ Some chefs are good bakers.” </li></ul><ul><li>Form 2: “Some A is not B”  Particular negative </li></ul><ul><li>“ Some fish are not rainbow trout.” </li></ul><ul><li>Form 3: “x% of A is/is not B”  Particular positive/negative. Where x  100 or 0. </li></ul><ul><li>“ 64% of women are tea drinkers.” </li></ul>
  7. 7. Categorical Propositions <ul><li>In analyzing a syllogism, it’s usually best to rewrite the premises and the conclusion in the form of categorical propositions . </li></ul><ul><li>These are : </li></ul><ul><li>A: All P are Q. All basketball players are athletes. </li></ul><ul><li>E: No P is Q. No violinist is a football player. </li></ul><ul><li>I: Some P is Q. Some gymnasts are shy people. </li></ul><ul><li>O: Some P is not Q. Some mountain climbers are not stamp collectors. </li></ul><ul><li>NOTE: The letters A, E, I, and O are handy ways to abbreviate these 4 forms. </li></ul>
  8. 8. Categorical Syllogisms <ul><li>A categorical syllogism is a syllogism in which the premises and the conclusion are categorical claims. </li></ul><ul><li>FOR EXAMPLE: </li></ul><ul><li>All racoons are pesky animals. No pesky animal is a good pet. Therefore, no raccoon is a good pet </li></ul><ul><li>The standard form of a categorical syllogism is a syllogism stated in the order of major premise, minor premise, and then the conclusion. </li></ul><ul><li>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. </li></ul>
  9. 9. Categorical Syllogism in Standard Form <ul><li>Here’s a categorical syllogism in standard form. </li></ul><ul><li>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. </li></ul><ul><li>NOTE: The major premise is the premise that contains the predicate term (=major term) found in the conclusion. </li></ul><ul><li>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. </li></ul><ul><li>The middle term is the term that is found only in the premises, not the conclusion. </li></ul>
  10. 10. Handy Abbreviations <ul><li>P = Predicate of the conclusion  Major term </li></ul><ul><li>S = Subject of the conclusion  Minor term </li></ul><ul><li>M = Term found in both premises  Middle term </li></ul>
  11. 11. The Figures of the Syllogism <ul><li>M P P M M P P M   </li></ul><ul><li>S M S MM S M S </li></ul><ul><li>  S P S P S P S P </li></ul><ul><li>FIGURE 1 FIGURE 2 FIGURE 3 FIGURE 4 </li></ul><ul><li>Step down M’s on right M’s on left step up </li></ul>
  12. 12. Mood and Figure <ul><li>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. </li></ul><ul><li>FOR EXAMPLE: </li></ul><ul><li>Some vegetarians are cheese-eaters. All bicyclists are cheese-eaters. Therefore, some bicyclists are vegetarians. </li></ul><ul><li>The MOOD of the syllogism is: IAI. The figure is figure 2 (M’s on right). So the mood and figure is written: </li></ul><ul><li>IAI—(2). </li></ul>
  13. 13. Distribution <ul><li>Distribution of a term refers to how much of the class (the subject or the predicate) is being referred to in the propostion. </li></ul><ul><li>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. </li></ul><ul><li>Claims that are positive (A and I) do not distribute the PREDICATE —the predicate is only distributed in negative claims (E and O). </li></ul><ul><li>PROPOSITION DISTRIBUTED TERM(S): </li></ul><ul><li>All P is Q  subject </li></ul><ul><li>No P is Q  subject and predicate </li></ul><ul><li>Some P is Q  nothing </li></ul><ul><li>Some P is not Q  predicate </li></ul>
  14. 14. RULES OF THE SYLLOGISM <ul><li>  </li></ul><ul><li>Rule 1: The middle term must be distributed at least once. </li></ul><ul><li>  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 </li></ul><ul><li>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. </li></ul><ul><li>  </li></ul>
  15. 15. Rules of the Syllogism con. <ul><li>Rule 3: At least one premise must be positive. (Two negative premises = invalid argument) </li></ul><ul><li>Rule 4: If the syllogism has a negative premise, there must be a negative conclusion, and vice versa. </li></ul><ul><li>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. </li></ul><ul><li>(You cannot have two universal premises with a particular conclusion and you cannot have a universal conclusion unless both premises are also universal.) </li></ul>
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