Important Terms In Logic & Critical Thinking

Logic and Critical Thinking

1)    What is “Logic”

The study of the methods and principles used to distinguish correct from incorrect reasoning.

2) Preposition: An assertion that something is (or is not) the case: all propositions are either true or false.

3) Statement: The meaning of a declarative sentence at a particular time: in logic, the word “statement” is sometimes is used instead of the proposition.

4) Simple proposition: A proposition making only one assertion.

5) Compound proposition: A proposition containing two or more simple propositions.

6) Disjunctive proposition: A type of compound proposition; if true, at least one of the component propositions must be true.

7) Hypothetical proposition: A type of compound proposition is false only when the antecedent is true and the consequent is false.

8) Inference: A process of linking proposition by affirming one proposition based on one or more other proposition 

9) Argument: A structured group of propositions, reflecting an inference.

10) Premise: A proposition is used in an argument to support some other proposition.

11) Conclusion: The proposition in an argument that the other propositions the premises, support.

12) Deductive argument: Claim to support its conclusion conclusively. One of the two classes of argument 

13) Inductive argument: Claim to support its conclusion only with some degree of probability. One of the two classes of argument.

14) Valid argument: All the premises are true, the conclusion must be true, apply only to the deductive argument.

15) Invalid argument: The conclusion is not necessarily true, even if all the premises are true; apply only deductive arguments.

16) Classical logic: Traditional techniques based on Aristotle’s works for the analyses of deductive arguments.

17) Modern symbolic logic: Methods used by most modern logicians to analyze deductive arguments.

18) Probability: The like hood that some conclusion (of an inductive argument) is true.

19) Truth: An attribute of a proposition that asserts what really is the case.

20) Conclusion-indicator: A word or phrase that typically introduces an argument’s conclusion.

21) Premise-indicator: A word or phrase that typically introduces a premise in an argument.

22) Rhetorical question: A question whose answer is assumed to be obvious.

23) Command: A direct statement.

24) Enthymeme: An argument containing an unstated proposition.

25) Class: The collection of all objects that have some specified characteristic in common.

26) Explanation: A group of statements purporting to account for why something is the way it is an explanation is not an argument.

27) Universal affirmative proposition: The proposition asserts that the whole of one class is included or contained in another class. 

e.g.  All   S is  P.

28) Universal negative proposition: The proposition asserts that the whole of one class is excluded from the whole of another class. 

e.g. No S  is P.

29) Particular affirmative proposition: The proposition that asserts that two classes have some members in common, 

e.g.  Some S  is P.

30) Particular negative proposition: The proposition that asserts that at least one member of a class is excluded from the whole of another class, 

e.g. Some S is not P.

31) Quality: An attribute of every categorical proposition is determined by whether the proposition affirms or denies some form of class inclusion.

32) Quantity: An attribute of every categorical proposition determine by whether the proposition refers to all members (universal) or only some member (particular) of the subject class

33) Distribution: A characterization of whether terms refer to all members of the class designated by that term in a categorical proposition.

34) Opposition: Any logical relation among the kinds of categorical propositions (A, E, I, O) exhibited on the square of opposition.

35) Contradictories: Two propositions that cannot both be true and cannot both be false at the same time.

36) Contraries: Two propositions cannot both be true; if one is true, the other must be false. They can both be false.

37) Sub-contraries: Two propositions that cannot both be false; if one is false the other must be true they can both be true.

38) Sub-alternation: The opposition between a universal proposition (the superaltern) and its corresponding particular proposition (the subaltern). In classical logic, the universal proposition indicates the truth of its consequent particular proposition.

39) Square of opposition: A diagram showing the logical relationship among the four types of categorical propositions (A, E, I, O) the traditional square of opposition differs from the modern square of opposition in important ways.

40) Immediate inference: An inference is drawn directly from only one premise.

41) Mediate inference: An inference is drawn from more than one premise; the conclusion is drawn from the first premise through the mediation of the second.

42) Conversion: An inference is formed by interchanging the subject and predicate terms of a categorical proposition. Not all conversions are valid.

43) Complement of a class: Collection of all things that do not belong to that class.

44) Obversion: An inference is formed by changing the quality of a proposition and replacing the predicate term with its complement. Obversion is valid for any standard form categorical proposition.

45) Contraposition: An inference is formed by replacing the subject term of a proposition with the complement of its predicate term and replacing the predicate term with the complement of its subject term. Not all contrapositions are valid.

46) Boolean interpretation: The modern interpretation of categorical propositions, on which universal propositions (A and E ) are not assumed to refer to classes that have members.

47) Existential fallacy: A fallacy in which the argument relies on the illegitimate assumption that a class has members. When there is no expiate assertion that it does.

48) Venn diagrams: A method of representing classes and categorical proposition using overlapping circles.

49) Standard-Form categorical syllogism: A categorical syllogism in which the premises and conclusions are all standard-form categorical propositions (A, E, I, O) and are with the major premises first. The minor premises see and the conclusion is last.

50) Major term / major premises: The major term is the term that occurs as the predicate of the conclusion in a standard-form syllogism. The major premise is the premise that contains the major term. 

51) Minor term / Minor premise: The minor term is the term that occurs as the subject of the conclusion in a standard-form syllogism. The minor premise is the premise that contains the4 minor terms.

52) Middle Term: The term that occurs in both premises., but never in the conclusion of a standard-form syllogism.

53) Mood: One of the 64 3-letter portrayals of absolute arguments dictated by the types of the standard-structure suggestions it contains.

54) Figure: The logical shape of a syllogism is determined by the position of the middle term in its premises there are four possible figures.

55) Fallacy of four terms: If a categorical syllogism contains more than three terms then such formal mistake is known as the fallacy of four terms.

56) Fallacy of the undistributed middle term: If a categorical syllogism contains a middle term that is not distributed in either premise then such kind of formal mistake is known as the fallacy of the undistributed middle term.

57) Fallacy of an illicit major: A formal mistake in which the major term of a syllogism is undistributed in the major premise but is distributed in the conclusion.

58) Fallacy of an illicit minor: If the minor term of a syllogism is undistributed in the minor premise but is distributed in the conclusion then it is called the fallacy of an illicit minor.

59) Fallacy of exclusive premise: If both premises of a syllogism are negative then it is called the fallacy of exclusive premises.

60) Fallacy: Drawing an affirmative conclusion from a negative premise

A formal mistake in which one premise of the syllogism is negative but the occlusion is affirmative.

61) Existential fallacy: As a formal fallacy, the mistake of inferring a particular conclusion forms two universal premises.

62) Barbara: The traditional name for the valid syllogism with the mood and figure. e.g. (AAA-1)

63) Castres: The traditional name for the valid syllogism with the mood and figure. e.g. (AEE-2)

64) Simple statement: A statement that does not contain any other statement as a component.

65) Compound statement: If a statement contains another statement as its component then it is known as a compound statement.

66) Conjunction: A truth-functional connective meaning “and” symbolized by the dot (.)

67) Truth value: Truth value refers to the status of any statement as true or false.

68) Truth-functional component: A component of a compound statement whose replacement by another statement having the same truth value would not change the truth value of the compound statement.

69) Truth-functional compound statement: A compound statement whose truth is wholly determined by the truth values of its components.

70) Truth-functional connective: Any logical connective (including conjunction, disjunction, material implication, and material equivalence) between the components of a truth-functional compound statement.

71) Negation: Negation refers to the "Denial", symbolized by the tilde or curl (~).

72) Disjunction: A truth-functional connective meaning “or” it has a “weak” (inclusive) sense, symbolized by the wedge (y)(o) “week” and a “strong” (exclusive) sense.

73) Punctuation: The parentheses, brackets, and braces are used in symbolic language to eliminate meaning.

74) Conditional statement: A compound statement of the form “if P then q”

75) Consequent: In a conditional statement, the component that immediately follows the “then”

76) Antecedent: In a conditional statement, the component immediately follows the “if”.

77) Implication: The relation that holds between the antecedent and the consequent of a conditional statement. There are different kinds of implications.

78) House shoe: A symbol is used to represent material implication, which is the common, partial meaning of an l “then” statement.

79) Material implication: A truth-functional relation symbolized by the horseshoe (>) that may connect two statements, the statement “p materially implies q” is true when either p false, or q is true.

80) 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.

81) Statement variable: A letter (lower case) for which a statement may be sustained.

82) Argument form: An array of symbols exhibiting the logical structure of an argument contains statement variables but no statements.

83) Substitution instance of an argument form: Any argument that results from the consistent substitution of statement for statement variables in an argument form.

84) Specific form of an argument: The argument form from which the given argument results when a different simple statement is substituted for each different statement variable.

85) Invalid Argument form: A form of an argument that has at least one substitution instance with a false conclusion and true premises.

86) Valid Argument Form: An argument form that has no substitution instances with true premises and a false conclusion.

87) Truth Table: An array on which the validity of an argument may be tested by indicating all possible combinations of the truth values of the statement variables contained in that form.

88) Disjunctive Syllogism: A valid argument in which one premise is a disjunction, one premise is the denial of one of the two disjuncts and the conclusion is the truth of the other disjunct.

89) Modus Tollens: A valid argument that relies upon a conditional premise, and in which another premise denies the consequent of that conditional and the conclusion denies its antecedent.

90) Modus Ponens: A valid argument that relies upon a conditional premise, and in which another premise affirms the antecedent of that conditional and the conclusion affirms its consequent.

91) Hypothetical Syllogism: A valid argument containing only conditional propositions.

92) Fallacy of affirming the consequent: A formal 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.

93) Fallacy of Denying the antecedent: A formal 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.

94) Statement form: An array of symbols that exhibits the logical structure of a statement, contains statement variables but no statement.

95) Substitution instance of a statement form: Any statement that results from the consistent substitution of statement variables in a statement form.

96) Specific form of a statement: The statement form from which the given statement results when a different simple statement is substituted consistently for each different statement variable.

97) Tautologous statement form: A statement form, that has only true substitution instances, a tautology.

98) Self-contradictory statement form: A statement form, that has only false substitution instances: a contradiction.

99) Contingent statement form: Statement form that has both true and false substitution instances.

100) Peirce’s Law: A tautological statement of the form [(p) q))p])p

101) Materially equivalent: A truth-functional relation asserting that two statements connected by the three are signed (=) have the same truth value.

102) Bio conditional statement: A compound statement asserts that its two component statements imply one another and therefore are materially equivalent.

103)  Logically equivalent: Two statements for which the statement of their material equivalence is a tautology are equivalent in meaning and may replace one another

104)  Double Negation: An expression of logical equivalence between a symbol and the negative of the negation of that symbol.

105) Demorgan’s theorems: Tow useful logical equivalence:

1. The negation of the disjunction of two statements is logically equivalent to the conjunction of the negation of the two disjuncts; and,

2. The negation of the conjunction of two statements is logically equivalent to the disjunction of the negations of the two conjuncts.

106) Principle of identity: If any statement is true, it is true.

107)  Principle of non-contradiction: No statement can be both true and false.

108) Principle of excluded middle: Every statement is either true or false.