Categorical syllogism


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Categorical syllogism

  2. 2. CATEGORICAL PROPOSITION: <ul><li>A proposition that relates two classes or categories is called a categorical preposition. </li></ul><ul><li>The classes are denoted respectively by the subject term and the predicate term and the proposition asserts that either all or part of the class denoted by the subject term is included or excluded from the class denoted by the predicate term. </li></ul><ul><li>e.g. </li></ul>
  3. 3. <ul><li>Radical politician do not find it easy to compromise. </li></ul><ul><li>Badr Muneer starred in orbal </li></ul><ul><li>Not all convicted murderers get the death penalty. </li></ul>
  4. 4. <ul><li>The first statement assert that the entire class of radical politician is excluded from the class of persons who find it easy to compromise. </li></ul><ul><li>In the second statement Badr Muneer is included in the class of person who starred in the movie orbal. </li></ul><ul><li>In the third statement assert that part of the class of convicted murderers is excluded from the class of persons who get death penalty. </li></ul>
  5. 5. <ul><li>There are four different standard form of categorical proposition. </li></ul><ul><li>1 : A = All tables are wooden </li></ul><ul><li>2 : E = No tables are wooden </li></ul><ul><li>3 : I = Some tables are wooden </li></ul><ul><li>4 : O = Some tables are not wooden </li></ul><ul><li> </li></ul>
  6. 6. <ul><li>The first one is universal affirmative proposition. It is a about two classes, the class of all tables and the class of all wooden saying the first class is included in the second. </li></ul><ul><li>Schematically: All s is p Where s represent subject term and p represent predicate term </li></ul>
  7. 7. <ul><li>Second example: </li></ul><ul><li>No tables are wooden </li></ul><ul><li>It is universal negative proposition. It says that the first class is excluded from the second </li></ul><ul><li>Schematically: </li></ul><ul><li>No S is P </li></ul>
  8. 8. <ul><li>Third example: </li></ul><ul><li>Some tables are wooden. </li></ul><ul><li>It is particular and affirmative proposition. It affirm that some members of the class of all tables are also members of the class of all wooden. It may be written schematically as: </li></ul><ul><li>some S is P </li></ul><ul><li>It assert that at least one member of the class designated by the subject term is also a member of the class P. </li></ul>
  9. 9. <ul><li>Forth example: </li></ul><ul><li>Some tables are not wooden. </li></ul><ul><li>It is particular negative proposition. It refers to some particular member of that class. It may be written schematically as: </li></ul><ul><li>some S are not P </li></ul><ul><li>It says that at least one member of the class designated by the subject term S is excluded from the whole of the class of the predicate term P. </li></ul>
  11. 11. CATEGORICAL SYLLOGISM: A categorical syllogism is a formal deductive argument consisting of three statements TERMS: MIDDLE TERM: It is a term that occurs in both premises and does not occur in conclusion.
  12. 12. : THREE TERMS MAJOR TERM : Major term is the predicate of the conclusion. MINOR TERM: Minor term is the subject of the conclusion. EXAMPLE: No homework is fun ……… major premise Some reading is homework ……… minor premise Some reading is not fun………. Conclusion
  13. 13. DISTRIBUTION OF TERMS : A categorical term is said to distributed if all individual members of that category are accounted. There are four categorical propositions that distribute there terms. A, E I,O are the standard names for type of statement indicated STATEMENT TYPE TERM DISTRIBUTED A: All X are Y subject E: No X are Y subject, predicate I: some X are Y none O: some X are not Y predicate
  14. 14. RULES AND FALLACIES : Valid syllogism conforms to certain rules which if violated, a specific “Formal Fallacy “ is committed and the syllogism becomes invalid RULES: There are six rules for standard form syllogisms which are presented follows:
  15. 15. RULE NO: 1 RULE: A valid standard-form categorical syllogism must contain exactly three terms, each of which is used in the same sense throughout the argument. FALLACY: FALLACY OF FOUR TERMS
  16. 16. EXAMPLE: <ul><li>All rare things are expensive things. </li></ul><ul><li>All great novels are rare things. </li></ul><ul><li>Therefore ,all great novels are expensive things. </li></ul><ul><li>This syllogism appears to have only three terms but there are really four terms, since one of them, the middle term, is used in different senses in two premises. </li></ul><ul><li>2. All dogs are animals , </li></ul><ul><li>All cats are mammals , </li></ul><ul><li>So all dogs are mammals. </li></ul><ul><li>The four terms are: dogs, animals, cats and mammals </li></ul>
  17. 17. RULE NO :2 RULE: In a valid standard form categorical syllogism the middle term must be distributed at least once. FALLACY: Undistributed middle
  18. 18. EXAMPLE : All sharks are fish. All salmon are fish All salmon are sharks. In this syllogism the middle term is “fish”. In both premises “fish” occurs as the predicate of an A proposition and therefore it is not distributed in either premises. Thus syllogism commits the fallacy of undistributed middle.
  19. 19. RULE NO : 3 RULE: If a term is distributed in the conclusion, then it must be distributed in a premise. FALLACY: Illicit major ; illicit minor
  20. 20. EXAMPLES: All horses are animals Some dogs are not horses Some dogs are not animals In this example there is fallacy of “illicit major.” All tigers are mammals All mammals are animals All animals are tigers In this example there is fallacy of “illicit minor.”
  21. 21. RULE NO :4 RULE: In a categorical syllogism, two negative premises are not allowed FALLACY: Exclusive premises
  22. 22. EXAMPLE: No fish are mammals. Some dogs are not fish. Some dogs are not mammals. This syllogism is invalid because it has two negative premises and because of that it commit the fallacy of exclusive premises.
  23. 23. RULE NO:5 RULE: A negative premise requires a negative conclusion, and a negative conclusion requires a negative premise. FALLACY: Drawing an affirmative conclusion from negative premise or drawing a negative conclusion from affirmative premises.
  24. 24. EXAMPLE: All crows are birds Some wolves are not crows Some wolves are birds All triangles are three angled polygon All three angled polygons are three sided polygons Some three sided polygons are not triangles Both are invalid because 1st draws an affirmative conclusion from a negative premise. And 2nd draws negative conclusion from affirmative premises
  25. 25. RULE NO :6 RULE: If both premises are universal, the conclusion cannot be particular. FALLACY: Existential fallacy.
  26. 26. EXAMPLE : All mammals are animals All unicorns are mammals Some unicorns are animals. This syllogism is invalid because in this case the conclusion is EXISTENTIAL i-e Beginning with ‘Some’.
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