Young America's dilemma: Shall I be wise and great, or
rich and powerful? (poster from 1901) This is an
example of a false dilemma: an informal fallacy using a
disjunctive premise that excludes viable alternatives.
burglar broke into the house last night, got hungry on the job, and had a midnight snack, would also
explain the state of the kitchen. But this conclusion is not justified because it is not the best or most likely
explanation.[82][83]
Not all arguments live up to the standards of correct reasoning. When they do not, they are usually
referred to as fallacies. Their central aspect is not that their conclusion is false but that there is some flaw
with the reasoning leading to this conclusion.[84] So the argument "it is sunny today; therefore spiders
have eight legs" is fallacious even though the conclusion is true. Some theorists, like John Stuart Mill,
give a more restrictive definition of fallacies by additionally requiring that they appear to be correct.[85]
This way, genuine fallacies can be distinguished from mere mistakes of reasoning due to carelessness.
This explains why people tend to commit fallacies: because they have an alluring element that seduces
people into committing and accepting them.[86] However, this reference to appearances is controversial
because it belongs to the field of psychology, not logic, and because appearances may be different for
different people.[87]
Fallacies are usually divided into formal and
informal fallacies.[38] For formal fallacies, the
source of the error is found in the form of the
argument. For example, denying the antecedent
is one type of formal fallacy, as in "if Othello is a
bachelor, then he is male; Othello is not a
bachelor; therefore Othello is not male".[88] But
most fallacies fall into the category of informal
fallacies, of which a great variety is discussed in
the academic literature. The source of their error
is usually found in the content or the context of
the argument.[89] Informal fallacies are
sometimes categorized as fallacies of ambiguity,
fallacies of presumption, or fallacies of
relevance. For fallacies of ambiguity, the
ambiguity and vagueness of natural language are
responsible for their flaw, as in "feathers are light; what is light cannot be dark; therefore feathers cannot
be dark".[90] Fallacies of presumption have a wrong or unjustified premise but may be valid otherwise.[91]
In the case of fallacies of relevance, the premises do not support the conclusion because they are not
relevant to it.[92]
The main focus of most logicians is to study the criteria according to which an argument is correct or
incorrect. A fallacy is committed if these criteria are violated. In the case of formal logic, they are known
as rules of inference.[93] They are definitory rules, which determine whether an inference is correct or
which inferences are allowed. Definitory rules contrast with strategic rules. Strategic rules specify which
inferential moves are necessary to reach a given conclusion based on a set of premises. This distinction
does not just apply to logic but also to games. In chess, for example, the definitory rules dictate that
bishops may only move diagonally. The strategic rules, on the other hand, describe how the allowed
Fallacies
Definitory and strategic rules