A fallacy of division
is an
informal fallacy
Informal fallacies are a type of incorrect argument in natural language. The source of the error is not just due to the ''form'' of the argument, as is the case for formal fallacies, but can also be due to their ''content'' and ''context''. Falla ...
that occurs when one reasons that something that is true for a whole must also be true of all or some of its parts.
An example:
# The second grade in Jefferson Elementary eats a lot of ice cream
# Carlos is a second-grader in Jefferson Elementary
# Therefore, Carlos eats a lot of ice cream
The converse of this
fallacy
A fallacy is the use of invalid or otherwise faulty reasoning, or "wrong moves," in the construction of an argument which may appear stronger than it really is if the fallacy is not spotted. The term in the Western intellectual tradition was in ...
is called
fallacy of composition
The fallacy of composition is an informal fallacy that arises when one infers that something is true of the whole from the fact that it is true of some part of the whole. A trivial example might be: "This tire is made of rubber, therefore the ve ...
, which arises when one fallaciously attributes a property of some part of a thing to the thing as a whole.
If a system as a whole has some property that none of its constituents has (or perhaps, it has it but not as a ''result'' of some constituent's having that property), this is sometimes called an ''
emergent'' property of the system.
The term ''mereological fallacy'' refers to approximately the same incorrect inference that properties of a whole are also properties of its parts.
History
Both the fallacy of division and the
fallacy of composition
The fallacy of composition is an informal fallacy that arises when one infers that something is true of the whole from the fact that it is true of some part of the whole. A trivial example might be: "This tire is made of rubber, therefore the ve ...
were addressed by
Aristotle
Aristotle (; grc-gre, Ἀριστοτέλης ''Aristotélēs'', ; 384–322 BC) was a Greek philosopher and polymath during the Classical period in Ancient Greece. Taught by Plato, he was the founder of the Peripatetic school of ...
in ''
Sophistical Refutations
''Sophistical Refutations'' ( el, Σοφιστικοὶ Ἔλεγχοι, Sophistikoi Elenchoi; la, De Sophisticis Elenchis) is a text in Aristotle's ''Organon'' in which he identified thirteen fallacies.Sometimes listed as twelve. According to A ...
''.
In the philosophy of the ancient Greek
Anaxagoras
Anaxagoras (; grc-gre, Ἀναξαγόρας, ''Anaxagóras'', "lord of the assembly"; 500 – 428 BC) was a Pre-Socratic Greek philosopher. Born in Clazomenae at a time when Asia Minor was under the control of the Persian Empire, ...
, as claimed by the Roman
atomist Lucretius
Titus Lucretius Carus ( , ; – ) was a Ancient Rome, Roman Roman literature, poet and Ancient Roman philosophy, philosopher. His only known work is the philosophical poem ''De rerum natura'', a didactic work about the tenets and philosoph ...
, it was assumed that the atoms constituting a substance must themselves have the salient observed properties of that substance: so atoms of water would be wet, atoms of iron would be hard, atoms of wool would be soft, etc. This doctrine is called ''
homoeomeria'', and it depends on the fallacy of division.
Examples in statistics
In
statistics
Statistics (from German: ''Statistik'', "description of a state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data. In applying statistics to a scientific, indust ...
an
ecological fallacy
An ecological fallacy (also ecological ''inference'' fallacy or population fallacy) is a formal fallacy in the interpretation of statistical data that occurs when inferences about the nature of individuals are deduced from inferences about the gr ...
is a logical fallacy in the interpretation of statistical data where inferences about the nature of individuals are deduced from inference for the group to which those individuals belong. The four common statistical ecological fallacies are: confusion between ecological correlations and individual correlations, confusion between group average and total average,
Simpson's paradox
Simpson's paradox is a phenomenon in probability and statistics in which a trend appears in several groups of data but disappears or reverses when the groups are combined. This result is often encountered in social-science and medical-science ...
, and other statistical methods.
See also
*
Ecological fallacy
An ecological fallacy (also ecological ''inference'' fallacy or population fallacy) is a formal fallacy in the interpretation of statistical data that occurs when inferences about the nature of individuals are deduced from inferences about the gr ...
*
Fallacy of composition
The fallacy of composition is an informal fallacy that arises when one infers that something is true of the whole from the fact that it is true of some part of the whole. A trivial example might be: "This tire is made of rubber, therefore the ve ...
*
Synecdoche
Synecdoche ( ) is a type of metonymy: it is a figure of speech in which a term for a part of something is used to refer to the whole ('' pars pro toto''), or vice versa ('' totum pro parte''). The term comes from Greek .
Examples in common E ...
, the figure of speech of two forms:
** ''
Pars pro toto
''Pars pro toto'' (, ), , is a figure of speech where the name of a ''portion'' of an object, place, or concept is used or taken to represent its entirety. It is distinct from a merism, which is a reference to a whole by an enumeration of parts; ...
'' using the word for a part by way of referring to the whole
** ''
Totum pro parte
''Totum pro parte'' is Latin for "the whole for a part"; it refers to a kind of metonymy. The plural is ''tota pro partibus'', "wholes for parts". In a context of language, it means something is named after something of which it is only a part (or ...
'' using the word for the whole by way of referring to a part
References
Further reading
*
*
External links
*
Division
Division or divider may refer to:
Mathematics
*Division (mathematics), the inverse of multiplication
*Division algorithm, a method for computing the result of mathematical division
Military
*Division (military), a formation typically consisting ...
Relevance fallacies
Emergence
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