Illicit minor is a formal fallacy committed in a

categorical syllogism A syllogism ( grc-gre, συλλογισμός, ''syllogismos'', 'conclusion, inference') is a kind of logical argument that applies deductive reasoning to arrive at a conclusion based on two propositions that are asserted or assumed to be true ...

that is

invalid Invalid may refer to: * Patient, a sick person * one who is confined to home or bed because of illness, disability or injury (sometimes considered a politically incorrect term) * .invalid, a top-level Internet domain not intended for real use As ...

because its

minor term A syllogism ( grc-gre, συλλογισμός, ''syllogismos'', 'conclusion, inference') is a kind of logical argument that applies deductive reasoning to arrive at a conclusion based on two propositions that are asserted or assumed to be true. ...

is undistributed in the

minor premise A syllogism ( grc-gre, συλλογισμός, ''syllogismos'', 'conclusion, inference') is a kind of logical argument that applies deductive reasoning to arrive at a conclusion based on two propositions that are asserted or assumed to be true ...

but distributed in the conclusion. This fallacy has the following

argument form In logic, logical form of a Statement (logic), statement is a precisely-specified Semantics, semantic version of that statement in a formal system. Informally, the logical form attempts to formalize a possibly Syntactic ambiguity, ambiguous sta ...

: :All A are B. :All A are C. :Therefore, all C are B. ''Example:'' : All cats are felines. : All cats are mammals. : Therefore, all mammals are felines. The minor term here is

mammal Mammals () are a group of vertebrate animals constituting the class Mammalia (), characterized by the presence of mammary glands which in females produce milk for feeding (nursing) their young, a neocortex (a region of the brain), fur ...

, which is not distributed in the

"All cats are mammals", because this premise is only defining a property of possibly some mammals (i.e., that they're

cat The cat (''Felis catus'') is a domestic species of small carnivorous mammal. It is the only domesticated species in the family Felidae and is commonly referred to as the domestic cat or house cat to distinguish it from the wild members of ...

s.) However, in the conclusion "All mammals are felines", mammal ''is'' distributed (it is talking about all mammals being felines). It is shown to be false by any

that is not a feline; for example, a dog. ''Example:'' : Pie is good. : Pie is unhealthy. : Thus, all good things are unhealthy.

See also