The 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''. Fallac ...
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 in the construction of an argument that may appear to be well-reasoned if unnoticed. The term was introduced in the Western intellectual tradition by the Aristotelian '' De Sophisti ...
is called
fallacy of composition
The fallacy of composition is an informal fallacy that arises when one inference, 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; therefo ...
, 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 constituents 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 inference, 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; therefo ...
were addressed by
Aristotle
Aristotle (; 384–322 BC) was an Ancient Greek philosophy, Ancient Greek philosopher and polymath. His writings cover a broad range of subjects spanning the natural sciences, philosophy, linguistics, economics, politics, psychology, a ...
in ''
Sophistical Refutations
''Sophistical Refutations'' (; ) is a text in Aristotle's ''Organon'' in which he identified thirteen fallacies.Sometimes listed as twelve. According to Aristotle, this is the first work to treat the subject of deductive reasoning in ancient Gree ...
''.
In the philosophy of the ancient Greek
Anaxagoras
Anaxagoras (; , ''Anaxagóras'', 'lord of the assembly'; ) was a Pre-Socratic Greek philosopher. Born in Clazomenae at a time when Asia Minor was under the control of the Persian Empire, Anaxagoras came to Athens. In later life he was charged ...
, as claimed by the Roman
atomist
Atomism () is a natural philosophy proposing that the physical universe is composed of fundamental indivisible components known as atoms.
References to the concept of atomism and its atoms appeared in both ancient Greek and ancient Indian philo ...
Lucretius
Titus Lucretius Carus ( ; ; – October 15, 55 BC) was a Roman poet and philosopher. His only known work is the philosophical poem '' De rerum natura'', a didactic work about the tenets and philosophy of Epicureanism, which usually is t ...
, 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 language, German: ', "description of a State (polity), state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data. In applying statistics to a s ...
, 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 gro ...
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 st ...
, 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 gro ...
*
Fallacy of composition
The fallacy of composition is an informal fallacy that arises when one inference, 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; therefo ...
*
Synecdoche
Synecdoche ( ) is a type of metonymy; it is a figure of speech that uses a term for a part of something to refer to the whole (''pars pro toto''), or vice versa (''totum pro parte''). The term is derived . Common English synecdoches include '' ...
, the figure of speech of two forms:
** ''
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; and metonymy, where ...
'' using the word for a part by way of referring to the whole
** ''
Totum pro parte
is Latin for "the whole for a part"; it refers to a kind of metonymy. The plural is , "wholes for parts". In context of language, it means something is named after something of which it is only a part (or only a limited characteristic, not nece ...
'' using the word for the whole by way of referring to a part
References
Further reading
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External links
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{{Fallacies
Division
Relevance fallacies