Logic 9

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  1. 2 kinds of symbolic logic:
    • 1. Simple (atomic)
    • 2. Compound (complex)
  2. Simple (atomic)
    • has no other part to it.
    • Ex: Columbia is the capital of S.C.
  3. Compound (complex)
    • Statement that contains another statement as a component
    • Ex: The lights are on, the lights are off
    • In order to have a complex statement, you must be able to replace it with something that makes sense.
  4. Common compound propositions:
    Their parts are called:
    • Conjunctions
    • Conjuncts
  5. Conjuncts are connected together with the word:
    • And
    • Yet
    • But
    • Never the less
    • Ex: Andrew went swimming and Susan went hiking
  6. Disjunction:
    • Or
    • Unless
  7. Propositional variables=
    p, q, r, s.....
  8. Truth Functional Component
    Any component of a compound statement whose replacement by another statement having the same truth value would notchange the truth value of the compound statement
  9. Exclusive Sense of Disjunction:
    It is either one or the other, BUT not both are true
  10. Inclusive sense of disjunction
    • One or the other or both may be true
    • Ex: Getting a 3.8 gpa will get you on the deans list, or having a 3.9 will...
  11. Disjunctions "v" will only be false when:
    both p and q are false
  12. Conditional statements:
    a compound statement with the form, "if p, then q"
  13. Antecedent in a conditional statement:
    the component that immediately follows the "if"
  14. Consequent in a conditional statement:
    component that immediately follows the "then"
  15. Implication:
    the relation that holds between the antecedent and the consequent of a conditional state.
  16. Whenever you have a true antecedent:
    the whole thing will be true
  17. If Combes was a rockstar he'd be famous
    Combes isnt a rockstar
    Therefore Combes isnt famous

    C (horseshoe) F
    - C
    - F

    This is nota good argument...
    refutation by counter example:

    • If obama were a rockstar hed be famous
    • Obama isnt a rockstar
    • Therefore obama is famous
  18. Valid argument=
    When youhave true premises and true conclusions
  19. True premises and False conclusion=
  20. Material implication:
    • Symbolized by the horseshoe
    • p materially implies q
    • is true when either p is false, or q is trueq
  21. Refutation by logical analogy:
    exhibiting the fault of an argument by presenting another argument with the same form whose premises are known to be true and whose conclusion is known to be false

    The obama and combes example of being a rockstar
  22. Statement variable:
    A letter (lower case) for which a statement may be substituted
  23. Invalid argument form:
    argument form that has at least one substitution instance with true premises and a false conclusion
  24. Valid argument form
    argument form that has no substitution instances with true premises and a false con.
  25. Disjunctive Syllogism:
    a valid argument where one premise is a disjunction, another premise is is the denial of one of the two disjuncts, and the conclusion is the truth of the other disjunct.

    • p v q
    • -p
    • q
  26. Modus Ponens:
    A valid argument that relies on a conditional premise, and another premise affirms the antecedent of that conditional, and the conclusion affirms its consequent

    • p (horseshoe) q
    • p
    • q
  27. Modus Tollens:
    Valid argument that relies on a conditional premise and another premise denies the consequent of that conditional, and the conclusion denies its antecedent

    • p (horseshoe) q
    • -q
    • -p
  28. Hypothetical Syllogism:
    Valid argument containing only conditional propositions.

    • p (horseshoe) q
    • q (horseshoe) r
    • p (horseshoe) r
  29. Common invalid forms
    • 1. Fallacy of affirming the consequent
    • 2. Fallacy of denying the antecedent
  30. Fallacy of affirming the consequent:
    Fallacy in which the second premise of an argument affirms the consequent of a conditional premise and the conclusion of its argument affirms its antecedent.

    • p (horseshoe) q
    • q
    • p
  31. Fallacy of denying the antecedent:
    Fallacy in which the second premise of an argument denies the antecedent of a conditional premise and the conclusion of the argument denies its consequent

    • p (horseshoe) q
    • -p
    • -q
  32. Tautologous Statement form:
    A statement form that has only true substitution instances, a "tautology"
  33. Self-contradictory statement form:
    A statement form that has only false substituion instances, a "contradiction"
  34. Contingent Statement form:
    A statement form that has both true and false substitution instances
  35. Peirce's Law
    • A tautological statement of the form:
    • [(p horseshoe q) horseshoe p] horseshoe p
  36. Materially Equivalent:
    A truth funcvtional relation asserting that two statements connected by the three bar sign have the same truth values
  37. Biconditional Statement:
    A compound statement that asserts that its two component statements imply one another and therefore are materially equivalent.
  38. Logically equivalent:
    two statements for which the statement of their material equivalence is a tautology; they are equivalent in meaning and can replace one another.
  39. Double Negation:
    An expression of logical equivalence between a symbol and the negation of the negation of that symbol.
  40. De Morgan's Theorems
    • 1. the negation of the disjunction of two statements is logically equivalent to the conjunction ofthe negations of the two disjuncts
    • 2. The negation of the conjunction of two statements is logically equivalent to the disjunction of the negations of the two conjuncts
  41. p (horseshoe) q is logically equivalent to:
    - p v q
  42. The three laws of thought:
    • 1. principle of identity
    • 2. principle of noncontradiction
    • 3. principle of excluded middle
  43. Principle of identity:
    if any statement is true, it is true
  44. Principle of Noncontradiction:
    • No statement can be both true and false
    • Every state. of the form p dot -p must be false. that every such state. is self contradictory
  45. Principle of excluded middle:
    • Every state. is either true or false
    • Every state. of the form p v -p must be true
    • That every such state. is a tautology
Card Set:
Logic 9
2011-11-21 16:17:50
Symbolic logic

symbolic logic
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