Fallacy of division

Short description: Fallacy

The fallacy of division[1] is an informal fallacy 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:

1. The second grade in Jefferson Elementary eats a lot of ice cream
2. Carlos is a second-grader in Jefferson Elementary
3. Therefore, Carlos eats a lot of ice cream

The converse of this fallacy is the fallacy of composition, 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.[2][3][4][5]

## Contents

* 1 History
* 2 Examples in statistics
* 3 See also
* 4 References
* 5 Further reading
* 6 External links

## History

Both the fallacy of division and the fallacy of composition were addressed by Aristotle in Sophistical Refutations.

In the philosophy of the ancient Greek Anaxagoras, as claimed by the Roman atomist Lucretius,[6] 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 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.[7]

## See also

* Ecological fallacy
* Fallacy of composition
* Synecdoche, the figure of speech of two forms:
* Pars pro toto using the word for a part by way of referring to the whole
* Totum pro parte using the word for the whole by way of referring to a part

## References

1. ↑ "Division". https://fallacyfiles.org/division.html.
2. ↑ M. R. Bennett; P. M. S. Hacker. 2003. Philosophical Foundations of Neuroscience. Table of contents.
3. ↑ Rom Harré. Behind the Mereological Fallacy. Philosophy 87:3, July 2012, pp. 329-352. https://doi.org/10.1017/S0031819112000241
4. ↑ P.M.S. Hacker. 2013. Before the Mereological Fallacy: A Rejoinder to Rom Harré. Philosophy, 88(1), 141-148. doi:10.1017/S003181911200054X
5. ↑ H. Van Eyghen. 2023. The Brain Perceives. The Brain infers. Wittgenstein and the Cognitive Science of Religion, 53-72. doi:10.5040/9781350329386.0011
6. ↑ Brauneis, Robert (2009). Intellectual Property Protection of Fact-based Works: Copyright and Its Alternatives. Edward Elgar Publishing. p. 110.
7. ↑ Burnham Terrell, Dailey (1967). Logic: A Modern Introduction to Deductive Reasoning. Holt, Rinehart and Winston. pp. 160–163. https://archive.org/details/logicmodernintro0000terr.

## Further reading

* Werner Ebeling; Hans-Michael Voigt. Parallel Problem Solving from Nature - PPSN IV: International Conference on Evolutionary Computation. The 4th International Conference on Parallel Problem Solving from Nature Berlin, Germany, September 22–26, 1996. Proceedings, Volume 114. Springer Science & Business Media. pp. 170–173.
* Richard M. Grinnell; Jr., Yvonne A. Unrau. Social Work Research and Evaluation: Foundations of Evidence-Based Practice. Oxford University Press. pp. 393–394.

## External links

* "Division". The Fallacy Files. https://fallacyfiles.org/division.html.

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Fallacies (list)

Formal|

| In propositional logic|

* Affirming a disjunct
* Affirming the consequent
* Denying the antecedent
* Argument from fallacy

|

In quantificational logic|

* Existential
* Illicit conversion
* Proof by example
* Quantifier shift

Syllogistic fallacy|

* Affirmative conclusion from a negative premise
* Exclusive premises
* Existential
* Necessity
* Four terms
* Illicit major
* Illicit minor
* Negative conclusion from affirmative premises
* Undistributed middle

* Masked man
* Mathematical fallacy

Informal|

| Equivocation|

* Equivocation
* False equivalence
* False attribution
* Quoting out of context
* Loki's Wager
* No true Scotsman
* Reification

|

Question-begging fallacies|

* Circular reasoning / Begging the question
* Loaded language
* Leading question
* Compound question / Loaded question / Complex question
* No true Scotsman

Correlative-based fallacies|

* False dilemma
* Perfect solution
* Denying the correlative
* Suppressed correlative

Illicit transference|

* Composition
* Division
* Ecological

Secundum quid
(ignoring qualifications)|

* Accident
* Converse accident

Faulty generalization|

* Anecdotal evidence
* Sampling bias
* Cherry picking
* McNamara
* Base rate / Conjunction
* Double counting
* False analogy
* Slothful induction
* Overwhelming exception

Vagueness / Ambiguity|

* Accent
* Syntactic ambiguity
* Continuum
* Sorites paradox
* False precision
* Moving the goalposts
* Slippery slope
* Quoting out of context

Questionable cause|

* Animistic
* Furtive
* Correlation implies causation
* Cum hoc
* Post hoc
* Gambler's
* Inverse
* Regression
* Single cause
* Slippery slope
* Texas sharpshooter

Fallacies of relevance|

| Appeals to emotion|

* Fear
* Flattery
* Novelty
* Pity
* Ridicule
* Think of the children
* In-group favoritism
* Invented here / Not invented here
* Island mentality
* Loyalty
* Parade of horribles
* Spite
* Stirring symbols
* Wisdom of repugnance

|

Genetic fallacies|

| Ad hominem|

* Abusive
* Association
* Reductio ad Hitlerum
* Godwin's law
* Reductio ad Stalinum
* Circumstantial
* Appeal to motive
* Bulverism
* Poisoning the well
* Tone
* Tu quoque
* Whataboutism

|

* Authority
* Accomplishment
* Ipse dixit
* Poverty / Wealth
* Etymology
* Nature
* Tradition / Novelty
* Chronological snobbery

Appeals to consequences|

* Argumentum ad baculum
* Wishful thinking

* Ad nauseam
* Argument to moderation
* Argumentum ad populum
* Appeal to the stone / Proof by assertion
* Ignoratio elenchi
* Argument from silence
* Invincible ignorance
* Moralistic / Naturalistic
* Motte-and-bailey fallacy
* Rationalization
* Red herring
* Appeal to worse problems
* Two wrongs make a right
* Special pleading
* Straw man
* Cliché
* I'm entitled to my opinion

* Categories
* Fallacies
* Formal fallacies
* Informal fallacies
* List
* Philosophy portal

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