Logic

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  1. Traditional Logic:
    • Concerns categorical propositions and categoricalpropositions affirm/deny the relationship between class and objects.
    • (Class of humans, call of mortals)
  2. 4 kinds of categorical propositions
    • 1. Universal affirmative prop. All S is P.
    • 2. Universal negative prop. No S is P
    • 3. Particular affirmative prop. Some S is P
    • 4. Particular negative prop. Some S is not P
  3. Categorical Proposition-
    a proposition that asserts a relationship between one category and some other category.
  4. Universal Affirmative Proposition (A propositions)
    • Prop. that assert that the whole of one class is included or contained in another class.
    • All S is P.
    • Example: All politicians are liars.
  5. Universal Negative Proposition (E propositions)
    • Prop that assert that the whole of one class is excluded from the whole of another class
    • No S is P
    • Example: No politicians are liars
  6. Particular Affirmative Proposition (I propositions)
    • Prop that assert that 2 classes have some member or members in common
    • Some S is P
    • Example: Some politicians are liars
  7. Particular Negative Propositions (O propositions)
    • Prop. that assert that at least 1 member of a class is excluded from the whole of another class
    • Some S are not P
    • Example: Some politicians are not liars
  8. All lawyers are wealthy people

    name and form;
    A - Universal affimative
  9. No criminals are good citizens

    Name and form;
    E - Universal negative
  10. Some chemicals are poisons

    Name and form;
    I - Particular affirmative
  11. Some insects are not pests

    Name and form;
    O - Particular negative
  12. Quality-
    Determined by whether the proposition affirms or denies some form of class inclusion (affirmative or negative)
  13. Quantity-
    Determined by whether the propositions refers to all members ("universal") or only some members ("particular") of the subject class
  14. Distribution-
    • A characterization of whether terms in a categorical proposition refer to all members of the class designated by that term.
    • If it makes term to all of the members- distributed
    • If it doesnt make term to all of the members- undistributed
  15. Distibuted vs. Undistributed
    *All S are P;
    • S= distributed
    • P=undistributed
  16. Distributed vs. undistributed

    *Some S are P;
    • S=undistributed
    • P=undistributed
  17. Distributed vs undistributed

    *No S are P;
    • S=distributed
    • P=distributed
  18. Any predicate will be undistributed in an ____ statement.
    A
  19. Statements are not distributed or undistributed, just
    the terms S and P
  20. ______ propositions are distributed, regardless of quality.
    Universal
  21. Opposition-
    Any logical relation among the kinds of categorical propositions (A,E,I,O) exhibited on the Square of Op.
  22. Contradictories-
    Two propositions that cannot both be false
  23. Contraries-
    • Two propositions that cannot both be true; if one is true, that other must be false.
    • They CAN both be false
  24. Subcontraries-
    • Two propositions that cannot both be false; if one is false the other must be true.
    • They CAN both be true.
  25. Subalternation-
    • The opposition between a universal proposition (the superaltern) and its corresponding particular proposition (the subaltern).
    • It implies the truth of its corresponding particular proposition
  26. Square of Opposition-
    Diagram showing the logical relationships among the 4 types of categorical propositions
  27. Image Upload
    • A-(all S is P)=superaltern of I; contrary of E; & contradictory of O
    • E-(No S is P)=Superaltern of ); contrary to A; & contradictory to I.
    • I-(Some S is P)=subaltern to A; contradictory to E; & subcontrary to O.
    • O-(Some S are not P)=subaltern to E; subcontrary to I; & contradictory to A.
  28. If A being given is true, then
    • E is false
    • I is true
    • O is false
  29. E being given as true, then
    • A is false
    • I is false
    • O is true
  30. I being given as true, then
    • E is false
    • A is undetermined
    • O is undetermined
  31. O being given as true, then
    • A is false
    • E is undetermined
    • I is undetermined
  32. A being given as false, then
    • O is true
    • E is undetermined
    • I is undetermined
  33. E being given as false, then
    • I is true
    • A is undetermined
    • O is undetermined
  34. I being given is false, then
    • A is false
    • E is true
    • O is true
  35. O being given as false, then
    • A is true
    • E is false
    • I is true
  36. Immediate Inference-
    An inference drawn directly from only one premise
  37. All S are P and No S are P are both what type of quantity?
    Universal
  38. Some S are P and Some S are not P are both what type of quantity?
    Particular
  39. Conversion-
    • An inference formed by interchanging the Subject and Predicate terms of a categorical proposition.
    • Only works for E & I statements
    • No S are P - No P are S.
    • Some S are P - Some P are S
    • (Some students are females - Some females are students)
  40. Convert by Limitations
    • All S are P - Some P are S
    • Turn an A statement into an I statement.
    • ONLY used in A statements
    • Only one-way inference(cant go the other way)
  41. Converse of: (A) All S is P;
    (I): Some P is S (by limitation)
  42. Converse of: (E) No S is P;
    (E): no P is S
  43. Converse of: (I) Some S is P;
    (I) Some P is S
  44. Converse of: (O) Some S is not P;
    (I) Some P is S **Conversion is not valid
  45. Complement of a class-
    The collection of all things that do not belong to that class
  46. Obversion-
    An inference formed by changing the quality of a prop. and replacing the predicate term by its complement.
  47. Obversion is done in 3 ways
    • 1. Change the quality of the statement
    • 2. Leave the subject alone
    • 3. Substitute the predicate with its complement
    • *All S are P
    • *No S are P
    • *No S are NON P
  48. OBV. All humans are mortal-
    No humans are non-mortal
  49. Obverse of; (A) All S is P;
    (E) No S is non P
  50. Obverse of; (E) No S is P;
    (A) All S is non P
  51. Obverse of (I) Some S is P;
    (O) Some S is not non P
  52. Obverse of; (O) Some S is not P;
    (I) Some S is non P
  53. Contraposition-
    • An inference formed by replacing the subject term of a prop. with the complement of its predicate term, and replacing the predicate term by the complement of its subject term.
    • Only works for A & O statements
  54. All P are S - Contraposition
    All non P are non S
  55. Contraposition by limitation
    Works only for E statements
  56. If A being given is true, then E is;
    False
  57. If A being given is true, then I is;
    True
  58. If A is true, then O is
    False
  59. If E is true, then A is;
    False
  60. If E is true, then I is;
    False
  61. If E is true, then O is;
    True
  62. If I is true, then E is;
    False
  63. If I is true, then A is;
    Undetermined
  64. I is true, then O is
    Undetermined
  65. If O is true, then A is;
    False
  66. O is true, then E is;
    Understermined
  67. O is true, I is;
    undetermined
  68. If A is false, then o;
    true
  69. If A is false, then E is
    undetermined
  70. If A is false, then I is;
    undetermined
  71. E is false, then I is;
    true
  72. E is false, then A is;
    undetermined
  73. If E is false, then Ois;
    undtermined
  74. If I is false, then A is;
    false
  75. f I is false, then E is;
    True
  76. If I is false, then O is
    true
  77. If O is false, then a is;
    true
  78. If O is false, then E is;
    false
  79. If O is false, then I is;
    true
  80. What is the contrapositive of;

    A: All S is P-
    A: All non-P is non-S
  81. What is the contrapositive of;

    E: No S is P-
    O: Some non-P is not non-S. (by limitation)
  82. What is the contrapositive of

    O: Some S is not P
    O: Some non-P is not non-S
  83. If there is just one pair of complements, then _________ will be used
    Obversion
  84. If there are two pairs of complements, then _______ will be used
    Contraposition
  85. If S and P terms need to be reversed you will use;
    • Conversion
    • Contraposition
  86. Boolean Interpretation
    Universal propositions (A and E) are not assumed to refer to classes that have members
  87. In the boolean interpretation what statements are said to have existential import?
    I and O statements
  88. In the Boolean Int., "Some S are P"-
    • 1. Will be false, There are S's and none are P's. (Some Usc students are alligators)
    • 2. Will also be false if there are no S's (Some martians are green) There are no existing martians.
  89. In the Boolean Int., "Some S are not P"-
    • 1. Will be false when all S's are P
    • 2. Will be false if there are no S's to begin with (Some martians are not green)
  90. In the Boolean Int., "No S are P" is true when,
    • 1. there are S's that are p
    • 2. Are no S's to begin with
  91. Existential Fallacy
    In Boolean Int. cant go from A-I or E-O
  92. What still works when dealing with Boolean Interp.
    • Contraposition
    • Conversion
    • Obversion
  93. Image Upload
    • All S is P
    • Predicate term in NOT distributed
  94. Image Upload
    • No S is P
    • No philosophers are idlers
    • Both S and P are distributed
  95. Image Upload
    • Some S is P
    • Both terms are undistributed
  96. Image Upload
    • Some S is not P
    • We are told something about the entire predicate class
    • S is notdistributed, P is distributed
  97. Image Upload
    • A------E; Now can be both true.
    • I------O; can both be False now
    • A-----O; Contradictories
    • I------E; Contradictories
  98. Symbolic Representation of All S is P;
    S bar P = 0

    • The class of things that are both S and non-P is empty. (OBV= all s are p)
    • (All humans are mortal)
  99. Symbolic representation of No S is P
    • SP =0
    • The class of things that are both S and P is empty
  100. Symbolic representation of Some S is P
    • SP does not = 0
    • The class of things that are both S and P is not empty. (SP has at least 1 member)
    • "X" indicates that something is there
    • (SP is the overlap in the middle of the circles)
  101. Symbolic representation of Some S is not P
    • S bar P does not = 0
    • The class of things that are both S and non-P in not empty. (S bar P has atleast 1 member)
  102. In the Boolean inter. A and E statements;
    Do not have exestential import
  103. In the Boolean Inter. I and O statements;
    have existential import
  104. Fallacies of Ambiguity
    • 1. Equivocation
    • 1. Amphiboly
    • 3. Accent
    • 4. Composition
    • 5. Division
  105. Fallacy of Equivocation
    An informal fallacy in which 2 or more meanings of the same word or phrase have been confused

    • Words that are vague or unclear
    • Example: gay
  106. Example of the fallacy of equivocation
    • All kids have four legs
    • My three year old is a kid
    • Therefore my three year old has four legs

    (kid could mean kid or goat...)
  107. Fallacy of Amphiboly
    An informal fallacy arising from the loose, awkward, or mistaken way in which words are combined, leading to alternative possible meanings of a statement
  108. I've looked everywhere in this area for an instruction book on how to play the concertina without success. you need no instructions. just plunge in ahead boldly.
    Fallacy of amphiboly
  109. Fallacy of Accent
    • Happens when a term or phrase has a meaning in the conclusionof an argument that is different from its meaning in one of the premises.
    • Difference is usually because there is a change in emphasis given to the words used
  110. Fallacy of Composition
    An inference is mistakenly drawn from the attributes of the parts of a whole to the attributes of the whole itself
  111. ...each person's happiness is a good to that person, and the general happiness, therefore, a good to the aggregate of all persons
    example of fallacy of composition
  112. Fallacy of Division
    is a mistaken inference is drawn from the attributes of a whole to the attributes of the parts of the whole
  113. "No man will take counsel, but every man will take money: therefore money is better than counself
    example of fallacy of Division
Author:
faulkebr
ID:
106048
Card Set:
Logic
Updated:
2011-10-26 18:14:02
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Chapter 6
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