Reasoning and critical thinking test 1

  1. Claim or proposition :: A statement capable of being true or false.

  2. Argument :: A set of premises, a conclusion, and an inference connecting the premises to the conclusion.

  3. Premise :: A claim presented as a reason or as evidence supporting a conclusion.

  4. Conclusion :: The claim that an argument is intended to establish.

  5. Inference :: The reasoning step connecting premises to a conclusion.

  6. Premise indicator :: A word or expression that often introduces a premise, such as because, since, given that, or considering that.

  7. Conclusion indicator :: A word or expression that often introduces a conclusion, such as therefore, thus, hence, so, or it follows that.

  8. Explanation :: A passage that assumes something is true and gives reasons why it is true.

  9. Argument versus explanation :: An argument tries to establish that something is true; an explanation assumes it is true and explains why.

  10. Simple argument :: An argument containing one inference and one conclusion.

  11. Complex argument :: An argument containing multiple connected inferences.

  12. Subargument :: A smaller argument contained within a complex argument.

  13. Intermediate conclusion :: A conclusion supported by earlier premises that is subsequently used as a premise.

  14. Final conclusion :: The ultimate conclusion that the complete argument is intended to establish.

  15. Standard form :: A numbered presentation that separates premises and conclusions and states which premises support each conclusion.

  16. Principle of charity :: The practice of selecting the strongest reasonable interpretation compatible with what an arguer said.

  17. Inference form or pattern :: The general reasoning structure shared by different arguments.

  18. Unstated premise :: A premise required by an argument but left implicit by the arguer.

  19. Unstated conclusion :: A conclusion intended by an argument but not explicitly stated.

  20. Argument diagram :: A visual representation showing which premises support which conclusions.

  21. Independent premises :: Premises that each provide support for a conclusion separately.

  22. Linked premises :: Premises that provide support only when considered together.

  23. Rational acceptability :: The degree to which it is reasonable to accept a claim, even when it is not absolutely certain.

  24. Entertaining a premise for the sake of argument :: Temporarily assuming a claim in order to determine what would follow if it were true.

  25. Scope :: The number or range of objects covered by a claim.

  26. Particular claim :: A claim stating that at least one object of a certain kind has or lacks a property.

  27. General claim :: A claim concerning a substantial number of objects of a certain kind.

  28. Statistical claim :: A general claim that specifies a numerical proportion or percentage.

  29. Universal generalization :: A claim concerning every member of a group, such as “All A are B.”

  30. Negative universal generalization :: A claim that no member of a group has a property, such as “No A are B.”

  31. Counterexample :: A single case that disproves a universal claim or shows that an argument form is invalid.

  32. Reliable source :: A source with a good record of accuracy that is competent, informed, and appropriately positioned to know the facts.

  33. Expert or authority :: A person with relevant specialized knowledge in a genuine field of expertise.

  34. Bias :: A tendency or interest that may distort someone’s judgment or presentation of information.

  35. Conflict of interest :: A personal or professional interest that may interfere with impartial judgment.

  36. Independent sources :: Sources that reached their conclusions separately rather than merely repeating one original source.

  37. Common knowledge :: Information that members of the relevant audience can reasonably be expected to know.

  38. Commonly held belief :: A belief accepted by many people that may nevertheless be false.

  39. Consistency :: A set of claims is consistent when it is possible for all of them to be true together.

  40. Inconsistency :: A set of claims is inconsistent when there is no possible situation in which all of them are true together.

  41. Contradiction :: In the strict sense, a claim that directly denies another claim.

  42. Deductive reasoning :: Reasoning intended to guarantee the conclusion if the premises are true.

  43. Non-deductive reasoning :: Reasoning intended to make the conclusion probable or reasonable without guaranteeing it.

  44. Valid argument :: An argument in which it is impossible for all the premises to be true and the conclusion false.

  45. Invalid argument :: An argument for which at least one possible situation has all true premises and a false conclusion.

  46. Counterexample to validity :: A possible situation or parallel argument with true premises and a false conclusion.

  47. Argument form :: A general pattern created by replacing parts of an argument with variables.

  48. Instance of an argument form :: A particular argument produced by replacing the variables in an argument form with specific content.

  49. Truth-preserving form :: An argument form with no instance containing true premises and a false conclusion.

  50. Formally valid argument :: An argument whose form is valid.

  51. Logically valid form :: A form that is valid solely because of its logical structure.

  52. Sound argument :: A valid argument with all true premises.

  53. Valid but unsound argument :: An argument with valid reasoning but at least one false premise.

  54. Truth versus validity :: Truth applies to individual claims; validity applies to the relationship between an argument’s premises and conclusion.

  55. Implication or entailment :: A set of premises implies or entails a conclusion when the corresponding argument is valid.

  56. Equivalent claims :: Claims that imply each other and therefore have the same truth value in every possible situation.

  57. Logical meaning of “some” :: “Some A are B” means that at least one A is B; it does not imply that some A are not B.

  58. Propositional logic :: The study of argument forms whose variable components are complete propositions.

  59. Logical operator or connective :: An expression that joins or modifies propositions, such as not, and, or, or if-then.

  60. Negation :: The denial of a proposition; symbolized as ¬A and read “not A.”

  61. Double negation :: Two consecutive negations; A and ¬¬A are equivalent.

  62. Conjunction :: A proposition of the form A & B, meaning “A and B.”

  63. Conjunct :: Either component of a conjunction.

  64. Disjunction :: A proposition of the form A ∨ B, meaning “A or B.”

  65. Disjunct :: Either component of a disjunction.

  66. Inclusive disjunction :: “A or B” meaning that at least one is true and possibly both are true.

  67. Exclusive disjunction :: “Either A or B but not both,” symbolized as (A ∨ B) & ¬(A & B).

  68. Conditional :: A proposition of the form A → B, meaning “If A, then B.”

  69. Antecedent :: The first component, A, in a conditional A → B.

  70. Consequent :: The second component, B, in a conditional A → B.

  71. Converse :: The converse of A → B is B → A; it is not generally equivalent to the original conditional.

  72. Contrapositive :: The contrapositive of A → B is ¬B → ¬A; it is equivalent to the original conditional.

  73. Biconditional :: A proposition of the form A ↔ B, meaning “A if and only if B.”

  74. Iff :: An abbreviation for “if and only if.”

  75. Sufficient condition :: A is sufficient for B when A guarantees B; symbolized as A → B.

  76. Necessary condition :: B is necessary for A when A cannot occur without B; symbolized as A → B.

  77. Necessary and sufficient condition :: Each condition guarantees the other; symbolized with a biconditional A ↔ B.

  78. Not both A and B :: Symbolized as ¬(A & B).

  79. Neither A nor B :: Symbolized as ¬(A ∨ B), equivalent to ¬A & ¬B.

  80. A if B :: Symbolized as B → A.

  81. A only if B :: Symbolized as A → B.

  82. A unless B :: Symbolized as ¬B → A.

  83. A provided that B :: Symbolized as B → A.

  84. Double negation rule :: From A infer ¬¬A, or from ¬¬A infer A; valid.

  85. Conjunction rule :: From A and B infer A & B; valid.

  86. Simplification rule :: From A & B infer A, or infer B; valid.

  87. Weakening rule :: From A infer A ∨ B; valid.

  88. Disjunctive syllogism :: A ∨ B, ¬A, therefore B; valid. It also works by eliminating B to conclude A.

  89. Modus ponens :: A → B, A, therefore B; valid.

  90. Modus tollens :: A → B, ¬B, therefore ¬A; valid.

  91. Hypothetical syllogism :: A → B, B → C, therefore A → C; valid.

  92. Formal fallacy :: An error in reasoning caused by using an invalid argument form.

  93. Affirming the consequent :: A → B, B, therefore A; invalid because B could occur for another reason.

  94. Denying the antecedent :: A → B, ¬A, therefore ¬B; invalid because B could still occur for another reason.

  95. Formal proof :: A chain of valid inferences deriving a conclusion from stated premises.

  96. Proof justification :: The inference rule and earlier line numbers that justify a line in a formal proof.

  97. Reduction to absurdity :: A proof method that assumes the opposite of the desired conclusion, derives a contradiction, and rejects the assumption.

  98. Indirect proof :: Another name for a proof by reduction to absurdity.