Logic

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amcmullen
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230733
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Logic
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2013-09-18 18:16:50
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  1. Logic
    The organized body of knowledge, or science, that evaluates arguments
  2. Argument
    A group of statements, one or more of which are claimed to provide support for, or reasons to believe, one of the others.
  3. Good Argument
    An argument in which the premises really do support the conclusion
  4. Bad Argument
    An argument in which the premises claim to, but do not, support the conclusion
  5. Statement
    A sentence that is either true or false, and is typically declarative
  6. Truth Values
    Truth & Falsity
  7. Premises
    Statements that set forth the reasons or evidence
  8. Conclusion
    The statement that the evidence is claimed to support or imply
  9. Conclusion Indicators
    • Therefore
    • Accordingly
    • Entails that
    • Wherefore
    • We may conclude
    • It must be that
    • For this reason
    • So
    • Thus
    • Consequently
    • We may infer
    • Hence
    • It follows that
    • Implies that
    • As a result
  10. Premise Indicators
    • Since
    • As indicated by
    • Because
    • For
    • In that
    • May be inferred from
    • As
    • Given that
    • Seeing that
    • For the reason that
    • In as much as
    • Owing to
  11. Inference
    The reasoning process expressed by an argument
  12. Proposition
    The meaning or information content of a statement
  13. Syllogistic Logic
    • Kind of logic in which the fundamental elements are terms
    • Arguments are evaluated as good or bad based on how terms are arranged in the argument
  14. Modal Logic
    Kind of logic that involves such concepts as possibility, necessity, belief, and doubt
  15. To contain an argument, a passage has to satisfy two conditions:
    • At least one of the statements must claim to present evidence or reasons (premises) (Factual Claim)
    • There must be a claim that the alleged evidence supports or implies something; a claim that something follows from the alleged evidence or reasons (conclusion) (Inferential Claim)
  16. Factual Claim
    A claim that something is true; a claim that evidence or reasons are being presented
  17. Inferential Claim
    • A claim that alleged evidence or reasons support or imply something; something follows from something
    • Inferential Claims are objective; they are not equatable to the intent of the arguer
    • Explicit or Implicit
  18. Explicit Inferential Claim
    Usually asserted by indicator words
  19. Implicit Inferential Claim
    Contains no indicator words
  20. Non-Inferential Passages
    Unproblematic passages that lack a claim that anything is being proved
  21. Types of Non-Arguments
    • Warnings
    • Pieces of Advice
    • Statements of Belief
    • Statements of Opinion
    • Loosely Associated Statements
    • Reports
    • Expository Passages
    • Illustrations
    • Explanations
    • Conditional Statement
  22. Warning
    A form of expression that is intended to put someone on guard against a dangerous or detrimental situation
  23. Piece of Advice
    A form of expression that makes a recommendation about some future decision or course of conduct
  24. Statement of Belief/Opinion
    An expression about what someone happens to believe or think about something
  25. Loosely Associated Statements
    May be about the same general subject, but lack a claim that one is proved by the others
  26. Report
    A group of statements that convey information about some topic or event
  27. Expository Passage
    • A kind of discourse that begins with a topic sentence followed by one or more sentences that develop the topic sentence
    • Expository Passages can also be taken as arguments if the purpose of the subsequent sentences in the passage is not only to flesh out the topic sentence but also to prove it
  28. Illustration
    • An expression involving one or more examples that is intended to show what something means or how it is done
    • Illustrations can be taken as arguments, if the example provided is intended to prove the claim
  29. Arguments From Example
    An argument that purports to prove something by giving one or more examples of it
  30. Explanation
    • An expression that purports to shed light on some event or phenomenon
    • Composed of two elements - Explanandum & Explanans
    • Explanations show why something is the case
    • Not an argument
  31. Explanandum
    The statement that describes the event or phenomenon to be explained
  32. Explanans
    The statement, or group of statements, that purports to do the explaining
  33. Conditional Statement
    • If...then statement
    • Composed of two elements - Antecedent & Consequent
    • Not an argument
    • May be the premise, conclusion, or both, of an argument
  34. Antecedent
    Component statement immediately following the "if"
  35. Consequent
    Component statement immediately following the "then"
  36. Relation between conditional statements and arguments:
    • A single conditional statement is not an argument
    • A conditional statement may serve as either the premise, conclusion, or both, or an argument
    • The inferential content of a conditional statement may be re-expressed to form an argument
  37. Sufficient Condition
    • The condition represented by the antecedent in a conditional statement
    • A is all that is needed for the occurrence of B
  38. Deductive Argument
    • An argument incorporating the claim that it is impossible for the conclusion to be false given that the premises are true
    • Involves necessary reasoning
  39. Inductive Argument
    • An argument incorporating the claim that it is improbable that the conclusion be false given that the premises are true
    • Involves probabilistic reasoning
  40. Features of an argument to look for to decide deductive or inductive
    • The occurrence of special indicator words
    • The actual strength of the inferential link between premises and conclusion
    • Form or style of argumentation
  41. Inductive Indicators
    • Probably
    • Improbable
    • Plausible
    • Likely
    • Unlikely
    • Reasonable to conclude
  42. Deductive Indicators
    • Necessarily
    • Certainly
    • Absolutely
    • Definitely
  43. Deductive Argument Forms
    • Arguments with a distinct form or character that indicate the premises are supposed to provide absolute support for the conclusion
    • Argument Based on Mathematics
    • Argument From Definition
    • Categorical
    • Hypothetical
    • Disjunctive Syllogisms
  44. Argument Based on Mathematics
    An argument in which the conclusion depends on some purely arithmetic or geometric computation or measurement
  45. Argument From Definition
    An argument in which the conclusion is claimed to depend merely on the definition of some word or phrase used in the premise or conclusion
  46. Syllogism
    An argument consisting of exactly two premises and one conclusion
  47. Categorical Syllogism
    • A syllogism in which each statement begins with one of the words:
    • All
    • No
    • Or
    • Some
    • *Usually treated as deductive
  48. Hypothetical Syllogism
    A syllogism having a conditional "if...then" statement for one or both of its premises
  49. Disjunctive Syllogism
    A syllogism having a disjunctive "either...or" statement
  50. Inductive Argument Forms
    • Arguments such that the contents of the conclusion is in some way intended to "go beyond" the contents of the premises
    • Predictions About the Future
    • Arguments From Analogy
    • Inductive Generalizations
    • Arguments From Authority
    • Arguments Based on Signs
    • Causal Inferences
  51. Predictions
    An argument that proceeds from our knowledge of the past to a claim about the future
  52. Argument From Analogy
    An argument that depends on the existence of an analogy, or similarity, between two things or states of affairs
  53. Generalizations
    An argument that proceeds from the knowledge of a selected sample to some claim about the whole group
  54. Argument From Authority
    An argument that concludes something is true because a presumed expert or witness said that it is
  55. Argument Based on Signs
    An argument that proceeds from the knowledge of a sign to a claim about the thing or situation the sign symbolizes
  56. Causal Inference
    An argument that proceeds from the knowledge of a cause to a claim about an effect - or - from knowledge of an effect to a claim about a cause
  57. Particular Statement
    One that makes a claim about one or more particular members of a class
  58. General Statement
    Makes a claim about all the members of a class
  59. Valid Deductive Argument
    • An argument in which it is impossible for the conclusion to be false given that the premises are true
    • Validity is determined by the relationship between the premises and the conclusion
  60. Invalid Deductive Argument
    A deductive argument in which it is possible for the conclusion to be false given that the premises are true
  61. Sound Argument
    A deductive argument that is valid and has all true premises
  62. Unsound Argument
    A deductive argument that is invalid, has one or more false premises, or both
  63. Strong Inductive Argument
    An inductive argument in which it is improbable that the conclusion be false given that the premises are true
  64. Weak Inductive Argument
    An argument in which the conclusion does not follow probably from the premises, even though it is claimed to
  65. Total Evidence Requirement
    The premises must not exclude or overlook some crucial piece of evidence that undermines the stated premises and requires a different conclusion
  66. Cogent Argument
    • An inductive argument that is strong and has all true premises
    • Premises must meet the total evidence requirement
  67. Uncogent Argument
    An inductive argument that is weak, has one or more false premises, fails to meet the total evidence requirement, or any combination of these
  68. Uniformity of Nature
    Future tends to replicate the past, and regularities that prevail in one spatial region tend to prevail in other regions
  69. Argument Form
    • An arrangement of words and letters such that the uniform substitution of terms or statements in place of the letters results in an argument
    • All A are B
    • All B are C
    • All A are C
  70. Substitution Instance
    Any argument that is produced by uniformly substituting terms or statements in place of the letters in an argument form
  71. Counterexample Method
    • A substitution instance having true premises and a false conclusion
    • A method for proving invalidity
  72. Categorical Syllogism Form Words
    • All
    • Some
    • No 
    • Are
    • Not
  73. Hypothetical Syllogism For Words
    • If
    • Then
    • Not
  74. Form Words for Other Arguments
    • Either
    • Or
    • Both
    • And
  75. Invalid Argument
    TP = FC
  76. How to Symbolize an Argument
    • 1) Determine conclusion/premises
    • 2) Isolate Logical Terms
    • 3) Rewrite using letter symbols

    If the form is valid, the argument is valid
  77. Counter-Example Method
    • 1) Determine Conclusion/Premises
    • 2) Isolate the form (symbolize it)
    • 3) Create a substitution instance - start with the conclusion, look for true premises
    • 4) If created TP = Fproven form invalid
    • 5) Original argument is proven invalid

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