Example: It's sunny.
Therefore, it's rainy or sunny.
Ad hoc hypothesis An auxilliary hypothesis that lacks independent support which is adopted to save a theory from refutation. Such hypotheses are bad because any theory can be rescued from refutation in this way. Auxilliary hypotheses should be justified by independent evidence.
Translation: "Ad hoc " means "to this", indicating that something is for a specific, limited purpose. For instance, an ad hoc committee is a temporary one set up to deal with a specific problem.
Example: Before Kepler, astronomers believed that planets moved in circular orbits. However, observations of planetary positions did not fit with this theory. The theory was saved from refutation by adopting the ad hoc hypothesis of epicycles. Of course, the theory should have been rejected because planets do not move in circular orbits. A fortiori Translation: "Even more so; by a stronger reason" (Latin ).
This phrase is used when arguing that what is true of a given case because it possesses a certain attribute will certainly be true of another case which has more of the relevant attribute.
Example: Suppose that Tommy is Timmy's older brother. We can argue that if Tommy is too young to see a certain movie, then a fortiori Timmy is too young, as well, since he is younger than Tommy. Affirmative categorical proposition An A or I -type categorical proposition. Ambiguity The state of having more than one meaning. Ambiguous Exhibiting ambiguity, that is, having more than one meaning. Amphibolous Exhibiting amphiboly, that is, having more than one meaning due to ambiguous grammar. Antecedent The propositional component of a conditional proposition whose truth is the condition for the truth of the consequent. In "if p then q ", "p " is the antecedent. A-type proposition A proposition of the form: All S are P. The subject term, S. is distributed.
Example: All monkeys are primates. Argument A unit of reasoning composed of propositions. Argument by analogy An argument of the form:
Therefore, t has the property Pn . Argument form The logical form of an argument, which consists of the logical forms of the statements which make up the argument.
Example: The argument form of "It's raining and the sun is shining, therefore it's raining" is "p and q. therefore p ". Argument Indicator A word or phrase that indicates the occurrence of an argument. There are two types of argument indicator: premiss indicators and conclusion indicators.
Examples: "Therefore" and "inasmuch as". Barbara Not Streisand, but the most famous form of categorical syllogism:
The name "Barbara" came from a Medieval mnemonic poem for remembering validating forms of categorical syllogism, and the vowels indicate that the three propositions in this form are all A-type. Biconditional Proposition A proposition of the form: p if and only if q. A bi-("two")conditional proposition is equivalent to the conjunction of two conditional propositions: if p then q and if q then p. Boobytrap A linguistic snare which is not itself fallacious, but may cause someone to inadvertently commit a fallacy. For instance, an ambiguous or vague sentence is not in and of itself fallacious, since it is not an argument, but it may cause somebody to infer a false conclusion. Borderline case A case in which it is unclear whether a vague terms applies or not.
Example: A balding man is a borderline case of baldness, because it is not clear whether the vague term "bald" applies to him or not. Categorical proposition A proposition of one of the four forms: A. E. I. or O. Categorical syllogism A syllogism whose premisses and conclusion are categorical propositions, and which has exactly three terms. Category A category is a type, collection, or class of similar things.
Examples: Shoes, ships, cabbages, and kings. Category mistake An error of ascribing characteristics to an object which is of the wrong type, or category, of thing for that kind of characteristic.
Example: "Pi is lithe and slimy." Chain of arguments A series of arguments linked by the conclusion of each being a premiss in the next, except for the final argument in the chain. Cogency The characteristic of a cogent argument. Cogent A cogent argument is one such that if the premisses are true, then the conclusion is more likely to be true than false. Both valid and strong inductive arguments are cogent. Commuting Not getting to and from a job, but switching two components.
Example: Commuting "p and q " produces "q and p ". Conclusion In an argument, the proposition for which evidence is provided. Conclusion Indicator A type of argument indicator that indicates the proposition in which it occurs is a conclusion.
Examples: "Hence" and "we may conclude that". Conditional Proposition A proposition which asserts a condition for the truth of another proposition.
Example: If it rains, then the street will be wet. Conjunct One of the propositional components of a conjunction.
Example: "It's raining" is the first conjunct of "it's raining and the sun is shining." Conjunction A proposition of the "both and" form.
Example: "It's both raining and the sun is shining." Connective A word or phrase which produces a compound sentence from simpler sentences. For example, in the compound sentence "it's raining and the sun is shining", "and" is a connective. Consequent The propositional component of a conditional proposition whose truth is conditional. In "if p then q ", "q " is the consequent. Contextomy A quote which is taken out of context so as to distort the speaker or author's intended meaning. Boller & George attribute this term to Milton Mayer.
Source: Paul F. Boller, Jr. & John George, They Never Said It: A Book of Fake Quotes, Misquotes, & Misleading Attributions (Oxford, 1989), p. 3. Contingent Proposition A proposition which is neither logically true nor logically false, that is, its truth-value depends upon facts about the world. Contradictory Propositions Two propositions are contradictories when they must have opposite truth-values, that is, one must be true and the other false.
Example: "Napoleon was short" and "Napoleon was not short" are contradictories. Contrapositive The contrapositive of a conditional proposition, "If A then B", is a proposition of the form "If not-B then not-A". A conditional proposition and its contrapositive are logically equivalent.Example: The contrapositive of "If it's snowing then it's cold out" is "If it's not cold out then it's not snowing." Contraposition "Contraposition" has two meanings, one in propositional logic and the other in categorical logic. In both cases, contraposition refers to a form of immediate inference in which the grammatical subject and predicate are switched and negated.
- In propositional logic, a conditional proposition of the form "If P then Q", is contraposed by switching the antecedent and consequent and negating them to get a proposition of the form "If not-Q then not-P". A conditional proposition and its contrapositive are logically equivalent. Sometimes called "transposition".
Example: "All bats are mammals" is logically equivalent, by contraposition, to "all non-mammals are non-bats."
Example: "Napoleon was short" and "Napoleon was tall" are contraries. Converse of a conditional A conditional proposition with the antecedent and consequent of another conditional proposition switched.
Example: The converse of "if today is Tuesday, then this is Belgium" is "if this is Belgium, then today is Tuesday." Conversion A form of immediate inference for categorical propositions in which the subject and predicate terms are switched. Conversion is a validating form of inference for E- and I-type propositions, and the converted statements are logically equivalent.
Example: "No dogs are cats" is logically equivalent, by conversion, to "no cats are dogs". Cooked-up A cooked-up example is one created simply to be an example.
Synonym: TameAntonym: Raw Counter-example There are two types of counter-example:
- A counter-example to a proposition: This is a true proposition which shows that a contrary proposition is false.
Example: "Jimmy is taller than Timmy."
A dangling comparative is one in which one of the things being compared is missing.
Example: "Jimmy is taller."
Though context often makes it clear what things are being compared, a dangling comparative can be ambiguous and, thus, a logical boobytrap. Deductive Of an argument in which the logical connection between premisses and conclusion is claimed to be one of necessity. Default Presumed until overridden by contrary evidence.
Synonym: Defeasible. Defeasible
Synonyms: Default, presumptive, prima facie. Definiendum The word or phrase in a definition that is defined.
Example: In the definition, "bachelor" = "unmarried man", "bachelor" is the definiendum. Definiens The word or phrase in a definition that does the defining.
Example: In the definition, "bachelor" = "unmarried man", "unmarried man" is the definiens.
De Morgan's Laws Two laws of equivalence in propositional logic:
- ~(p v q) is equivalent to (~p & ~q)
Example: "It's neither rainy nor snowy" is equivalent to "it's not rainy and it's not snowy".And:
Example: "It's not both rainy and snowy" is equivalent to "either it's not rainy or it's not snowy".
Etymology: These laws are named for the logician Augustus De Morgan. Disjoint Two classes are disjoint when they have no common member.
Example: The class of apples and the class of oranges are disjoint. Disjunct One of the propositional components of a disjunction.
Example: "It's raining" is the first disjunct of "Either it's raining or it's snowing." Disjunction A proposition of the "either or" form. A disjunction is true if one or both of its disjuncts is true; otherwise, it is false.
Example: "Either it's raining or it's snowing." Disjunctive Of a disjunction. Disjunctive Syllogism A validating form of argument with a disjunctive premiss:
Therefore, q. Distributed A term in a categorical proposition is distributed if and only if the proposition implies every proposition that results from replacing the term with a more specific term.
Example: The subject term "mammals" in "all mammals are animals" is distributed because the proposition implies "all cats are animals", "all dogs are animals", "all humans are animals", etc. In contrast, the predicate term "animals" is not distributed because the proposition doesn't imply that all mammals are cats. Distribution A characteristic of terms in categorical
propositions which are either distributed or undistributed. Enthymeme An argument with either a suppressed premiss or a suppressed conclusion. E-type proposition
A proposition of the form: No S are P. Both terms are distributed.
Example: No monkeys are marsupials. Existential generalization An existentially-quantified generalization, it asserts that a class is not empty. See "Existential Quantifier".Examples:
- Some swans are black.
- There is an alligator in the swimming pool.
Examples: "Some", and "there is", are existential quantifiers in English. Extension The class of things to which a term applies.
Example: The extension of the term "apple" is the class of all apples. Fallacious Of a bad argument which is an instance of a fallacy. Final conclusion The conclusion of the last argument in a chain of arguments, which is not a premiss in any argument of the chain. Generalization A statement whose subject is a class rather than an individual. There are two types: existential generalizations and statistical generalizations. Heuristic Having to do with a rule of thumb. Illogicality Logical illiteracy; ignorance of the basic concepts and techniques of logic. Immediate inference An argument with exactly one premiss. Inductive Of an argument in which the logical connection between premisses and conclusion is claimed to be one of probability. Inverse of a relation The inverse of a relation between two things is simply the same relationship in the opposite direction. For instance, the relation of being shorter than is the inverse of the relation of being taller than; if Jack is taller than Jill, then Jill is shorter than Jack. In other words, the relationship of height between Jack and Jill is the same, but in the first case Jack bears the relation to Jill, whereas in the second Jill bears it to Jack.
I-type proposition A proposition of the form: Some S are P. Neither term is distributed.
Example: Some marsupials are kangaroos. Law of Excluded Middle The propositional form: p or not-p. Leibniz' Law
Alias: Substitution of Identicals A validating form of argument when "Px " is an extensional context:
Therefore, Pb. Logicality Logical literacy; knowledge of the basic concepts and techniques of logic. Logically-true Of a proposition which is true on purely logical grounds.
Example: "Either it's raining or it's not." Major premiss In a categorical syllogism, the premiss which contains the major term. Major term In a categorical syllogism, the predicate term of the conclusion which also occurs in the major premiss. Middle Term In a categorical syllogism, the term which occurs in both premisses. Minor premiss In a categorical syllogism, the premiss which contains the minor term. Minor term In a categorical syllogism, the subject term of the conclusion which also occurs in the minor premiss. Modus Ponens A validating form of argument from propositional logic:
Therefore, q. Modus Tollens A validating form of argument from propositional logic:
Therefore, not-p. Narrow Scope A term has narrow scope when it modifies the smallest part of a sentence that is grammatically possible.
Example: In "all the presidents of the United States are not female", the scope of the negation is not the whole sentence but only the predicate "are female". Necessary condition A condition which must be true if the proposition that it is a condition for is to be true. In other words, "p is a necessary condition for q " means "if q then p ".
Example: "Oxygen is a necessary condition for animal life", that is, "if an animal is alive, then that animal has oxygen". Negation In propositional logic, a proposition which denies the truth of its component proposition.
Example: "Today is not Friday" is the negation of "today is Friday".
Negative categorical proposition An E or O -type categorical proposition. Non sequitur
Translation: "It does not follow" (Latin) An obviously invalid argument, especially one in which the premisses are clearly irrelevant to the conclusion. Not a type of fallacy. O-type proposition A proposition of the form: Some S are not P. The predicate term, P. is distributed.
Example: Some marsupials are not koalas.
The philosopher A medieval term for Aristotle. Predicate Term The term in a categorical proposition that is not the subject of the proposition, which is usually the second term occurring in the proposition.
Example: In "all cats are mammals", "mammals" is the predicate term. Premiss In an argument, a proposition presented as evidence for the conclusion. "Premiss" is a technical term in logic, which is frequently spelled "premise". Both are correct spellings, but I choose to follow the logician Charles Sanders Peirce in using the double-s spelling throughout the Fallacy Files. The reason for this is to avoid any ambiguity created by other uses of the word "premise".
Source: Dagobert D. Runes (Editor), Dictionary of Philosophy (Littlefield, Adams, 1960). Premiss Indicator A type of argument indicator that indicates the proposition in which it occurs is a premiss.
Examples: "Since" and "for the reason that". Proposition A sentence with a truth-value.
Synonym: Statement Propositional logic A system of logic concerning the logical relations between atomic propositions and truth-functional compounds of them. Quantifier A logical constant which indicates the quantity of a class which has a property.
Examples: "All", "no", and "some", are the most frequently studied quantifiers in English. Raw A raw example is one that was not intended to be an example, but is taken from a source such as a periodical, book, radio or television program, or other medium.
Antonym: Cooked-up Reductio ad absurdum A type of argument in which an assumption is shown to imply an obviously false conclusion, thus demonstrating that the original assumption is false.
Synonym: Indirect argument or proof Regression to the Mean The statistical phenomenon in which an extreme value of a random variable is likely to be followed by a less extreme value, that is, one closer to the mean.
Example: Suppose that a randomly-selected person is unusually tall. A second randomly-selected person is likely to be closer to average (mean) height than the first. Rule of thumb A rule which holds true for all normal members of a class, but admits exceptions. Scope A characteristic of logical terms, such as quantifiers and truth-functional connectives, but also of non-logical modifiers. The scope of a term is the part of a sentence which it modifies. In natural languages, such as English, the scope of a term is often ambiguous.
Example: The scope of the negation in the old saying "all that glitters is not gold" is the entire statement "all that glitters is gold". Self-contradictory A proposition is self-contradictory when it is necessarily false.
Example: "It is raining but it isn't raining." Simplification A validating form of argument with a conjunctive premiss. There are two forms:
Example: It's cloudy and rainy.
Therefore, it's cloudy.
Example: It's cloudy and rainy.
Therefore, it's rainy.
Sophist An itinerant teacher of Ancient Greece, whose subjects usually included rhetoric. Sound Of a valid argument whose premisses are true. Statement Synonym: Proposition Statement form The logical form of a statement, which results from replacing all non-logical terms in the statement with variables.
Example: The statement form of "It's raining and the sun is shining" is "p and q ". Statistical generalization A proposition which asserts something of a percentage of a class. Universal generalizations are the special cases when the percentage equals 100% or 0%.
Example: 90% of birds can fly. Subject Term The term in a categorical proposition that is the subject of the proposition, which is usually the first term occurring in the proposition.
Example: In "all cats are mammals", "cats" is the subject term. Subfallacy A fallacy that is a specific form of a more general fallacy. Sufficient condition A condition which if true ensures that the proposition that it is a condition for is true. In other words, "p is a sufficient condition for q " means "if p then q ".
Example: "Decapitation is a sufficient condition for death", that is, "if an animal is decapitated, then it will die". Suppressed Of a premiss or conclusion in an enthymeme which is unexpressed, typically because it is obvious. Syllogism An argument with two premisses. Tame A tame example of a fallacy is one created by a logician as an example.
Antonym: Wild Tautology A truth-functionally compound proposition which is true for every possible combination of truth-values of its components. Term A word or phrase that can be used to refer to a class of things.
Examples: Shoes, ships, cabbages, kings, tall blond men with one red shoe. Transposition A validating form of argument from propositional logic:
Example: If it's pouring then it's raining.
Therefore, if it's not raining then it's not pouring.
Synonym: Contraposition Truth-functional A connective is truth-functional if the truth-value of a compound proposition formed with the connective is a function of the truth-values of the simpler statements from which it is constructed. Truth-value There are two truth-values: true and false. Universal generalization A 100% or 0% statistical generalization, that is, a proposition that asserts that something is true of all or none of a class.Examples:
- All whales are mammals.
- No whales are fish.
Examples: "All", "every", and "each", are universal quantifiers in English. Vague Of a term which is imprecise by having borderline cases.Example: "Bald" is vague, because some men are borderline cases, since they are neither clearly bald nor clearly not bald. Such men we usually call "balding". Vagueness The type of imprecision in which a term has borderline cases to which it is unclear whether it applies. Valid "Valid" is an ambiguous adjective which is used in two related senses:
- Of arguments which are necessarily truth-preserving.
- Of argument forms every instance of which are "valid" in sense 1. See "validating".
Usually context, namely, whether the subject is an argument or argument form, makes it clear which of these meanings is intended. However, sometimes this ambiguity is a boobytrap which leads to confusion. For this reason, in the Fallacy Files, I use "valid" only in sense 1, and "validating" for sense 2. Validating Of an argument form every instance of which is valid. Wide scope A term has wide scope when it modifies the largest part of a sentence that is grammatically possible, which is usually though not invariably the entire sentence.
Example: The negation in the old saying "all that glitters is not gold" has wide scope.
Alias: Broad scope Wild A wild example of a fallacy is one found in the natural habitat of fallacious arguments, namely, the reasoning of real people, as opposed to the exercises in a logic textbook.
Acknowledgments: Thanks to John Congdon and Geoff Hager.