Fallacy Of Division
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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''. Fall ...
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 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 ph ...
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, as claimed by the Roman
atomist Atomism (from Greek , ''atomon'', i.e. "uncuttable, indivisible") 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 a ...
Lucretius Titus Lucretius Carus ( , ;  – ) 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, and which usually is translated into En ...
, 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 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 g ...
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, 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 g ...
*
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, 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 ( ...
'' 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 {{logic-stub