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Logic: A complete introduction, by S. Lee > Logic Glosssary Terms > Flashcards

Logic Glosssary Terms Flashcards

1
Q

That which requires empirical justification.

A

A posteriori (S-FL)

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2
Q

That which does not depend on empirical evidence.

A

A priori (S-FL)

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3
Q

When the argument is directly against persons, seeking to defame or discredit them. It is also called genetic fallacy, because it attacks at the genesis of an idea rather than the truth of its content.

A

Abusive ad hominem (S-FL)

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4
Q

A shift of meaning arising as a consequence of changes in the emphasis given to its words or parts, thus leading to fallacious reasoning.

A

Accent (S-FL)

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5
Q

An informal fallacy when one applies a generalization to an individual case that it does not properly govern.

A

Accident (S-FL)

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6
Q

An expression is ambiguous if it has more than one meaning.

A

Ambiguity (S-FL)

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7
Q

An informal fallacy when one of the statements in an argument has more than one plausible meaning because of the loose or awkward way in which the words in that statement are combined.

A

Amphiboly (S-FL)

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8
Q

Statement which is true or false by virtue of the meaning of the statement alone.

A

Analytic statement (S-FL)

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9
Q

When an argument appeals to the fact that a view is universally or commonly held as support to its truth.

A

Appeal to common practice (S-FL)

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10
Q

When careful reasoning is replaced with devices to create enthusiasm and emotional support for the conclusion advanced.

A

Appeal to emotion (S-FL)

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11
Q

When careful reasoning is replaced with direct or insinuated threats to force the acceptance of the conclusion.

A

Appeal to force (S-FL)

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12
Q

A fallacy in which a proposition is argued to be true simply on the basis that it has not been proved false, or false simply because it has not been proved true.

A

Appeal to ignorance (S-FL)

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13
Q

When an argument appeals to a party having no legitimate claim to authority in the matter at hand.

A

Appeal to inappropriate authority (S-FL)

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14
Q

When an argument is not based on proper reasons but some unfortunate circumstance.

A

Appeal to pity (S-FL)

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15
Q

Arguments sharing the form – ‘Most people approve of X, therefore X is true.’

A

Appeal to populace (S-FL)

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16
Q

The strategy of praising someone in order to convince them to do the thing that you want.

A

Apple polishing (S-FL)

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17
Q

Structure that comprises a conclusion and some premises.

A

Argument (S-FL)

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18
Q

The basic unit that expresses a complete thought.

A

Atomic proposition (S-FL)

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19
Q

When we tend to retain and recall only information readily available to us recently or boosted via media coverage.

A

Availability bias (S-FL)

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20
Q

¬¬𝑝 ≡ 𝑝

A

Axiom of double negation (S-FL)

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21
Q

An argument begs the question when the reasoner assumes in the premises the truth of what he or she seeks to establish in the conclusion.

A

Begging the question (S-FL)

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22
Q

The principle that there are only two possible truth-values for a proposition. Classical logic, including categorical logic, propositional logic, and predicate logic, accepts bivalence.

A

Bivalence (S-FL)

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23
Q

A syllogism (an argument with exactly two premises and one conclusion) that comprises only categorical propositions.

A

Categorical syllogism (S-FL)

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24
Q

An argument in which the premises do not only support, but are in turn supported by the conclusion.

A

Circular argument (S-FL)

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25
Q

When the attack is indirectly against persons, suggesting that they adopt their views chiefly because of their special circumstances or interests.

A

Circumstantial ad hominem (S-FL)

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26
Q

An argument is cogent it its premises are acceptable, relevant to and sufficient for its conclusion.

A

Cogent argument (S-FL)

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27
Q

A logical system is complete if every logical implication in that system is provable. In other words, for every truth-functionally valid argument, there is a way in this system to deduce the conclusion of that argument from its premises.

A

Completeness (of a logical system) (S-FL)

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28
Q

A proposition comprising several atomic propositions.

A

Complex proposition (S-FL)

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29
Q

The argument assumes some unstated premises such that it misleads the audience into believing something which the responder cannot clarify by giving a simple answer.

A

Complex question (S-FL)

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30
Q

The fallacy of composition is made when (a) one reasons mistakenly from the attributes of a part to the attributes of the whole, or (b) one reasons mistakenly from the attributes of an individual member of some collection to the attributes of the totality of that collection.

A

Composition (S-FL)

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31
Q

A system is computable if there is an effective procedure to calculate a solution.

A

Computable (S-FL)

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32
Q

A function that maps objects to truth-values. For example, the concept of being a horse maps a horse, calls it 𝑥, to truth (because 𝑥 is a horse) but a cow, 𝑦, to falsity (because 𝑦 is not a horse).

A

Concept (in Frege’s terminology) (S-FL)

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33
Q

A proposition that one wants to uphold.

A

Conclusion (S-FL)

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34
Q

A strategy in natural deduction for arguments with a conditional conclusion. It proves an argument by first assuming the antecedent of the conclusion, working out its consequent and then discharging the assumption itself.

A

Conditional Proof (CP) (S-FL)

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35
Q

A conjunction is true only when both components (conjuncts) are true.

A

Conjunction (S-FL)

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36
Q

An argument involving conjunction. The following are valid forms: 𝑝, 𝑞, therefore 𝑝 & 𝑞 (composition); 𝑝 & 𝑞, therefore 𝑝 (decomposition).

A

Conjunctive inference (S-FL)

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37
Q

A dilemma that argues from how the horns are related to how the entailments are related. The general form is: 𝑝 V 𝑞, 𝑝 → 𝑟, 𝑞 → 𝑠 / ∴ 𝑟 V 𝑠

A

Constructive dilemma (S-FL)

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38
Q

A categorical syllogism is valid if and only if the premises contain the conclusion; i.e., the conclusion obtains under the conditions that make the premises true.

A

Containment (S-FL)

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39
Q

Statements that are true in one world but false in another.

A

Contingent statements (S-FL)

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40
Q

A statement is always false. Contrast ‘tautology.’

A

Contradiction (S-FL)

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41
Q

The relation that propositions have exactly opposite truth-values.

A

Contradictory (S-FL)

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42
Q

A combined operation of obverting a proposition, then converting it, and then obverting it again. The resultant proposition takes the form of having non-P in the subject position and non-S in the predicate position.

A

Contraposition (S-FL)

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43
Q

The relation that two propositions cannot both be true but can both be false.

A

Contrary (S-FL)

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44
Q

An operation to form propositions by interchanging the subject and the predicate of an original proposition.

A

Conversion (S-FL)

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45
Q

An argument in which the truth of the premises completely determines the truth of the conclusion given that it is a valid argument.

A

Deduction (S-FL)

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46
Q

An item to be found.

A

Definiendum (S-FL)

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47
Q

That which defines a term.

A

Definiens (S-FL)

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48
Q

A dilemma that argues backwards from what the entailments are not to what the horns are not. The general form is: 𝑝 → 𝑟, 𝑞 → 𝑠, ¬ 𝑟 V ¬ 𝑠 ∕ ∴ ¬ 𝑝 V ¬ 𝑞.

A

Destructive dilemma (S-FL)

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49
Q

An argument form that has two horns: 𝑝 and 𝑞, each entailing some results.

A

Dilemma (S-FL)

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50
Q

A disjunction is false only when both components (disjuncts) are false.

A

Disjunction (S-FL)

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51
Q

A syllogism involving disjunction. A valid argument form is 𝑝 V 𝑞, ¬ 𝑝, ∴𝑞 . An invalid form is 𝑝 V, 𝑝, ∴ ¬ 𝑞.

A

Disjunctive syllogism (S-FL)

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52
Q

A term is distributed if every member of the class it refers to is exhausted by the proposition containing it.

A

Distribution (in categorical logic) (S-FL)

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53
Q

The fallacy of division is formed when (a) one reasons mistakenly from the attributes of a whole to the attributes of one of its parts, and (b) one reasons mistakenly from the attributes of a totality of a collection of entities to the attributes of the individual entities themselves.

A

Division (S-FL)

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54
Q

A method of proof is effective if every argument can be determined, within a definite number of steps, to be either valid or invalid.

A

Effective (S-FL)

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55
Q

Expressions that usually arouse particular feelings or judgments.

A

Emotive words (S-FL)

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56
Q

Names that do not have a referent as they depict.

A

Empty names (S-FL)

57
Q

Two propositions are equivalent if they always share the same truth-value.

A

Equivalence (S-FL)

58
Q

The fallacy of equivocation occurs when the same word or phrase is used with two or more meanings, deliberately or accidentally, in the formulation of an argument.

A

Equivocation (S-FL)

59
Q

A proposition has existential import if it is typically used to assert the existence of objects.

A

Existential import (S-FL)

60
Q

An invalid argument in the following form: 𝑝 → 𝑞, 𝑞, ∴ 𝑝.

A

Fallacy of affirming the consequent (S-FL)

61
Q

An invalid argument in the following form: form: 𝑝 → 𝑞, ¬ 𝑝, ∴ ¬ 𝑞.

A

Fallacy of denying the antecedent (S-FL)

62
Q

A fallacy in which one treats as the cause of a thing that which is not really the cause of that thing.

A

False cause (S-FL)

63
Q

An argument commits the fallacy of false dichotomy or false dilemma if it presents two alternatives as exhaustive, when in fact other possibilities exist.

A

False dichotomy or false dilemma (S-FL)

64
Q

The pattern indicating the location of the middle term in a categorical syllogism.

A

Figure (S-FL)

65
Q

An operation that maps a certain object to another.

A

Function (in mathematics and logic) (S-FL)

66
Q

The reasoner falsely assumes that the history of outcomes will affect future outcomes when in fact the events are independent of each other.

A

Gambler’s fallacy (S-FL)

67
Q

The reverse process of instantiation.

A

Generalization (S-FL)

68
Q

A phenomenon studied in social psychology and organization behavior in which a group values harmony and coherence over accurate analysis and critical evaluation, thus resulting in an irrational or dysfunctional decision-making outcome.

A

Groupthink (S-FL)

69
Q

When one moves too carelessly or quickly from a single case to an indefensibly broad generalization.

A

Hasty generalization (S-FL)

70
Q

A two-place predicate denoting a relation, often expressed in English as ‘is identical to,’ ‘is the very same thing as,’ or simply ‘is,’ etc.

A

Identity (S-FL)

71
Q

Jargon or expressions with unusual usage deviating from ordinary usage without explicit definition.

A

Idiosyncratic expressions (S-FL)

72
Q

An expression without a specified domain.

A

Incomplete expression (S-FL)

73
Q

Propositions cannot be true together.

A

Inconsistence (S-FL)

74
Q

An argument in which the conclusion is likely to be true although it can be false even when the premises are true.

A

Induction (S-FL)

75
Q

Construct a model for quantification such that, instead of using variables and quantifiers, we now express formulas solely in terms of individual constants.

A

Instantiation (S-FL)

76
Q

When the premises miss the point, purporting to support one conclusion while in fact supporting or establishing another.

A

Irrelevant conclusion (S-FL)

77
Q

The study of the methods and principles used to distinguish between good and bad reasoning.

A

Logic (S-FL)

78
Q

A method of arguing for the validity (or invalidity) of an argument by constructing an argument of the same logical structure but which is obviously valid (or invalid).

A

Logical analogy (S-FL)

79
Q

The project to reduce arithmetic completely to logic championed by Gottlob Frege (1948–1925).

A

Logicism (S-FL)

80
Q

The premise containing the major term in a categorical syllogism.

A

Major premise (S-FL)

81
Q

The predicate of the conclusion in a categorical syllogism.

A

Major term (S-FL)

82
Q

Logical systems which accept that a proposition may not be either true or false but have other values; for example: intuitionist logic accepts ‘indeterminate’ propositions; free logic accepts ‘truth-valuelessness;’ and, fuzzy logic accepts degrees of truth.

A

Many-valued logics (S-FL)

83
Q

A material implication is false only when the antecedent is true, but the consequent is false.

A

Material implication (S-FL)

84
Q

The term that appears only in the premises of a categorical syllogism.

A

Middle term (S-FL)

85
Q

The premise containing the minor term in a categorical syllogism.

A

Minor premise (S-FL)

86
Q

The subject of the conclusion in a categorical syllogism.

A

Minor term (S-FL)

87
Q

When the burden of proving a point is placed on the wrong side. Generally, the burden of proof is on the person whose views go against common sense.

A

Misplacing the burden of proof (S-FL)

88
Q

Arguments that involve material implications and some other forms of proposition.

A

Mixed hypothetical syllogisms (S-FL)

89
Q

A valid argument in the following form: 𝑝 → 𝑞, 𝑝, 𝑞.

A

Modus ponens (S-FL)

90
Q

A valid argument in the following form: 𝑝 → 𝑞, ¬ 𝑞, ∴ ¬ 𝑝.

A

Modus tollens (S-FL)

91
Q

Presents the categorical proposition types of a categorical syllogism in the order of the major premise, the minor premise, and the conclusion.

A

Mood (S-FL)

92
Q

‘𝑝 is the necessary condition of 𝑞’ means whenever there is no 𝑝, there is no 𝑞.

A

Necessary condition (S-FL)

93
Q

Statements that are always true or always false.

A

Necessary statements (S-FL)

94
Q

A proposition and its negation cannot both be true or false at the same time.

A

Negation (in propositional logic) (S-FL)

95
Q

Concerning values or evaluations.

A

Normative (S-FL)

96
Q

A predicate that connects 𝑛 number of parties.

A

N-place predicate (S-FL)

97
Q

An expression is obscure when it lacks a core meaning.

A

Obscurity (S-FL)

98
Q

An operation to form propositions by changing the quality of a categorical proposition and replacing the predicate term by its complement (namely, changing P into non-P).

A

Obversion (S-FL)

99
Q

A puzzle that has apparently reasonable assumptions yet generates absurd consequences.

A

Paradox (S-FL)

100
Q

A reason to support the belief in the conclusion.

A

Premise (S-FL)

101
Q

Anything the content of which is capable of being true or false. It is a logical notion.

A

Proposition (S-FL)

102
Q

An expression composed of a predicate and a variable; it has no truth-values and must be either bounded by a quantifier (universal or existential) or substituted with an individual constant to become truth-evaluable.

A

Propositional function (S-FL)

103
Q

A valid argument that involves only material implications. It has the following form: 𝑝 → 𝑞, 𝑞 → 𝑟, ∴ 𝑝 → 𝑟.

A

Pure hypothetical syllogism (chain argument) (S-FL)

104
Q

Changing the subject, diverting attention away to other issues.

A

Red herring (S-FL)

105
Q

A reasoning strategy in which we construct an argument in such a way that it leads to a logical contradiction, and we infer from this that at least one of the premises of this argument is false.

A

Reductio ad absurdum (S-FL)

106
Q

The relation between language and reality.

A

Reference (S-FL)

107
Q

Objects picked up by an expression.

A

Reference/extension/denotation (S-FL)

108
Q

A relation that bestows upon itself; in symbols, if a relation 𝑅 is reflexive and 𝑎 is any member of a domain, then 𝑅𝑎𝑎 always holds. Example: identity, ‘is equal to.’ Counter-example: love.

A

Reflexive relation (S-FL)

109
Q

An implicit proposition in the form of a different mood of speech, e.g., question or exclamation.

A

Rhetorical question (S-FL)

110
Q

The domain or extent to which a quantifier governs.

A

Scope of quantification (S-FL)

111
Q

Criteria or reasons by virtue of which objects are picked up by an expression. In particular, Frege (1892) conceived sense as modes of presentation to the mind or modes or determination of reference. Intension is technically defined by Carnap (1956) as a function from possible worlds to truth-values. Connotation is used by Mill (1872) to mean the properties shared by the set of objects a term denotes.

A

Sense/intension/connotation (S-FL)

112
Q

A string of symbols that is complete in grammatical structure and meaning. It is a linguistic item.

A

Sentence (S-FL)

113
Q

A proposition asserting that a particular individual has a specified attribute.

A

Singular proposition (S-FL)

114
Q

A small concession is presented as having potentially catastrophic consequences.

A

Slippery slope argument (S-FL)

115
Q

An argument is sound if it is a valid argument and the premises are all true.

A

Sound argument (S-FL)

116
Q

A logical system is sound if and only if it does not allow a deduction beginning with true propositions to end up with false ones.

A

Soundness (of a logical system) (S-FL)

117
Q

Something that expresses a belief. It is a mental entity.

A

Statement (S-FL)

118
Q

A fallacy that occurs when one levels one’s arguments against a crude caricature of one’s opponent’s views.

A

Straw man fallacy (S-FL)

119
Q

If P is true, the Q is true, but not vice versa.

A

Subalternation (S-FL)

120
Q

A simple argument within a more complex argument to support its conclusion.

A

Sub-argument (S-FL)

121
Q

The relation that two propositions can both be true but cannot both be false.

A

Subcontrary (S-FL)

122
Q

‘𝑝 is the sufficient condition of 𝑞’ means whenever 𝑝 exists, 𝑞 exists.

A

Sufficient condition (S-FL)

123
Q

An argument that has exactly two premises and one conclusion.

A

Syllogism (S-FL)

124
Q

A relation that if an individual 𝑎 is related to another individual 𝑏, then 𝑏 is related back to 𝑎 in the same way; in symbols, 𝑅𝑎𝑏 implies 𝑅𝑏𝑎. Example: ‘being a sibling of.’ Counter-example: ‘being the boss of.’

A

Symmetric relation (S-FL)

125
Q

Any statement that is not analytic.

A

Synthetic statement (S-FL)

126
Q

A statement that is always true.

A

Tautology (S-FL)

127
Q

A relation that can be carried forward; in symbols, 𝑅𝑎𝑏 and 𝑅𝑏𝑐 implies 𝑅𝑏𝑎. Examples: ‘larger than,’ older than.’ Counter-example: love.

A

Transitive relation (S-FL)

128
Q

Whatever it is.

A

Truth (S-FL)

129
Q

A function that maps objects according to their truth-values.

A

Truth-function (S-FL)

130
Q

A relation in which the truth-value of the combined sentence is completely determined by the truth-values of the component sentences.

A

Truth-functional relation (S-FL)

131
Q

Two propositions are truth-functionally equivalent when they have exactly the same truth-value in every possible truth-value assignment.

A

Truth-functionally equivalent (S-FL)

132
Q

A complete list of all possible truth-value assignments of a proposition.

A

Truth-table (S-FL)

133
Q

True or False.

A

Truth-value (S-FL)

134
Q

The truth-value assigned to a complex proposition depending on the truth-values of its constituent atomic propositions.

A

Truth-value assignment (S-FL)

135
Q

A special type of ad hominem argument, in which you attempt to discredit your opponent’s views by pointing out that he or she does not always act on them.

A

Tu quoque (you too) (S-FL)

136
Q

An expression is vague if it has a core meaning though does not have a clear boundary.

A

Vagueness (S-FL)

137
Q

An argument is valid if and only if the conclusion follows the premises. It also means that the conclusion cannot be false if all the premises are true.

A

Validity (S-FL)

138
Q

Roughly the same as a proposition; i.e., something that can be either true or false.

A

Well-formed formula (S-FL)

Logic: A complete introduction, by S. Lee (3 decks)

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