Glossary

This page defines logical terms used in the files on individual fallacies and in entries in the weblog. The first occurrence of a defined term in a file or weblog entry is linked directly to its definition below. Since most of the terms are linked from multiple files, you will need to use the "Back" button on your browser to return to where you came from. If you have suggestions for words that should be added to the glossary, or comments or criticisms of the current definitions, please email the fallacist1.

Index

A B C D E F G H I J K L M N O P Q R S T U V W X Y Z

A

Addition
A validating form of argument with a disjunctive conclusion. There are two forms:
p.
Therefore, p or q.

Example: It's rainy.
Therefore, it's rainy or sunny.		 q.
Therefore, p or q.

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 All S are P.
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:

s and t share the properties P1,…, Pm.
s has the property Pn.
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".

Average
A statistical measurement that represents a typical or normal member of a class. There are three main such measurements; see Mean, Median, and Mode.

B

Barbara
Not Streisand, but the most famous form of categorical syllogism:

All M are P.
All S are M.
Therefore, all S are P.

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 for which it is unclear whether a vague term applies to it.

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.

C

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.

Confidence Level
A phrase from statistics used in survey research and public opinion polling. The confidence level of a survey is usually given as a percentage. It indicates how confident we can be that the survey results are approximately correct.

Example: 95% is the usual confidence level of public opinion polls. So, if a poll shows that 43% of the public likes pistachio and anchovy ice cream, that means that we can be 95% confident that the percentage of the public who actually do like that flavor is approximately 43%.

See: Margin of Error

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 taken out of context in such a way as to distort the speaker or author's intended meaning.

Etymology: This term consists of the word "context" combined with the suffix "-tomy", which comes from a classical Greek word meaning "cutting". The suffix is used in many medical terms for surgical operations, for instance, "appendectomy", which means the surgical removal of the appendix. So, a "contextomy" is the removal of a quote from its context. This word appears to have been coined by Milton Mayer2.

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: "If it's raining then it's cloudy" is logically equivalent, by contraposition, to "if it's not cloudy then it's not raining."

  • In categorical logic, the contraposition of a categorical proposition results from swapping the subject and predicate terms and negating them. Contraposition is a validating form of immediate inference for A- and O-type propositions, which are logically equivalent to their contrapositives.

    Example:"All bats are mammals" is logically equivalent, by contraposition, to "all non-mammals are non-bats."

Contrary Propositions
Propositions are contraries when they cannot all be true.

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: Tame

Antonym: Raw

Counter-example
There are two types of counter-example:
  1. A counter-example to a proposition: This is a true proposition which shows that a contrary proposition is false.

    Example: "John is an honest lawyer" is a counter-example to "all lawyers are dishonest".

  2. A counter-example to an argument form: This is an instance of that form which has true premisses and a false conclusion, showing that the form is non-validating.

D

Dangling Comparative
A comparative is a phrase comparing two or more things.

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. Augustus De Morgan

De Morgan's Laws
Two laws of equivalence in propositional logic:
  1. ~(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:

  2. ~(p & q) is equivalent to (~p v ~q)

    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:

Either p or q.
Not-p.
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.

E

Enthymeme
An argument with either a suppressed premiss or a suppressed conclusion.
E-type proposition No S are P.
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.
Existential quantifier
A quantifer which indicates that some member of a class has a property.

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.

F

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.

G

Generalization
A statement whose subject is a class rather than an individual. There are two types: existential generalizations and statistical generalizations.
Guarding
Weakening a claim in order to protect it from refutation3.

Compare & Contrast: Hedging.

H

Hedging
Weakening a claim so much that it no longer provides sufficient support for a conclusion3.

Compare & Contrast: Guarding.

Heuristic
Having to do with a rule of thumb.

I J K

Illogicality
Logical illiteracy; ignorance of the basic concepts and techniques of logic.
Immediate inference
An argument with exactly one premiss.
Implication
To say that a set of statements implies a statement means that the argument from the set to the statement is valid; see Validity. If a set of statements implies a statement and all of the statements in the set are true, then the implied statement must also be true.

Example: "Not all birds can fly" implies "Some birds cannot fly."

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. Some S are P.
I-type proposition
A proposition of the form: Some S are P. Neither term is distributed.

Example: Some marsupials are kangaroos.

L

Law of Excluded Middle
The propositional form: p or not-p.
Leibniz' Law
A validating form of argument when "Px" is an extensional context:

a=b
Pa.
Therefore, Pb.

Synonym: Substitution of Identicals

Logical Equivalence
Two statements are logically equivalent when each implies the other; see Implication. Logically equivalent statements mean the same thing logically.

Example: "Either it's not raining or it's not snowing" is logically equivalent to "It's not both raining and snowing."

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."

M

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.
Margin of Error
A term used in public opinion polling. The margin of error is a measure of the precision of a polling result. It is usually given as plus-or-minus n percentage points, written: ±n%. This means that the result of the poll is probably within n percentage points of the actual percentage.

Example: The margin of error of most major public opinion polls is ±3%. So, if a poll shows that 43% of the public likes pistachio and anchovy ice cream, that means that we can be pretty sure that the percentage of the public who actually do like that flavor is between 40% and 46%.

See: Confidence Level

Mean
The arithmetic mean. What is usually meant by "average". The sum of a class of values divided by the number of those values.

Example: The mean of {1, 2, 3, 4, 5} = 3.

Median
Not the raised strip in the middle of the road; rather, a type of average. The middle value in a class of values, or the mean of two such middle values.

Examples: The median of {1, 2, 3, 4, 5} = 3. The median of {1, 2, 3, 4, 5, 6} = 3.5.

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.
Modal logic
  • In a broad sense, the logic of "modalities" that modify statements, such as necessity and possibility, obligation and permissibility, and temporal modifiers, among others.
  • In a narrow sense, the logic of the related modalities of necessity and possibility.
Mode
A type of statistical average. The most common value in a class of values. If there is no most common value, then there is no mode.

Examples: {1, 2, 3, 4, 5} has no mode. The mode of {1, 2, 2, 3, 3, 3} = 3. {1, 1, 2, 3, 3, 4} has two modes: 1 and 3.

Modus Ponens
A validating form of argument from propositional logic:

If p then q.
p.
Therefore, q.

Modus Tollens
A validating form of argument from propositional logic:

If p then q.
Not-q.
Therefore, not-p.

N

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". Some S are not P.

Negative categorical proposition
An E or O-type categorical proposition.
Negative correlation
A correlation between two variables in which an increase in one is accompanied by a decrease in the other.

Example: As speed increases, time to destination decreases.

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

Order of magnitude
The exponent of a number in scientific notation. To compare the size of numbers by their orders of magnitude is to compare their exponents in scientific notation.

Examples: 130 is one order of magnitude greater than 75―since 130 = 1.3 × 102 and 75 = 7.5 × 101 in scientific notation―while 45,000 is two orders of magnitude greater than 380―since 45,000 = 4.5 × 104 and 380 = 3.8 × 102.

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. Aristotle

P

The philosopher
A medieval term for Aristotle.
Positive correlation
A correlation between two variables in which an increase in one is accompanied by an increase in the other.

Example: The height of parents is positively correlated with the height of their children.

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.

Alternative spelling: Premise4

Charles Sanders Peirce
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.

Q

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.

R

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.

Synonym: Wild

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 thumb5
A rule that holds true for all normal members of a class, but admits exceptions. A rule of thumb is one that usually works in most situations, but may fail occasionally. The advantage of rules of thumb is that they are usually simpler and easier to use than universal rules that always work.

Synonym: Heuristic

S

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:
p & q.
Therefore, p.

Example: It's cloudy and rainy.
Therefore, it's cloudy.		 p & q.
Therefore, q.

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.

T

Tame
A tame example of a fallacy is one created by a logician as an example.

Synonym: Cooked-up

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:

If p then q.
Therefore, if not-q then not-p.

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.

U

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.
Universal quantifier
A quantifer which indicates that every member of a class has a property.

Examples: "All", "every", and "each", are universal quantifiers in English.

V

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:
  1. Arguments: To say of an argument that it is valid means that if its premisses are all true then its conclusion must also be true, that is, a valid argument is one that is necessarily truth-preserving.
  2. Argument Forms: An argument form is valid if every argument that is an instance of it is "valid" in the previous sense.

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; see Boobytrap. For this reason, I use "valid" only in sense 1, and "validating" for sense 2; see Validating.
Validating
Of an argument form every instance of which is valid.

W X Y Z

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.

Synonym: Raw

Antonym: Tame

Notes:

  1. Thanks to John Congdon and Geoff Hager.
  2. See:
    • Paul F. Boller, Jr. & John George, They Never Said It: A Book of Fake Quotes, Misquotes, & Misleading Attributions (Oxford, 1989), p. 3. Boller & George attribute this term to Milton Mayer:
    • Milton Mayer, "The View from the Metropol Window", The Progressive, Volume 22, Issue 10, 10/1/1958. This is the earliest occurrence of the word that I've been able to verify.
  3. Robert J. Fogelin & Walter Sinnott-Armstrong, Understanding Arguments: An Introduction to Informal Logic (1991), pp. 42-43.
  4. "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". This is like wearing both a belt and suspenders to keep your pants from falling down, since context usually makes it clear which meaning is intended, but at least your pants stay up. See: Dagobert D. Runes, Editor, Dictionary of Philosophy (Littlefield, Adams, 1960).
  5. The phrase "rule of thumb" does not come from a law allowing a man to beat his wife with any stick no thicker than his thumb. See:

Last Updated: 12/25/2021