# Fallacy of division

A fallacy of division is the error in logic 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 2nd grade in Jefferson elementary eats a lot of ice cream
2. Carlos is a 2nd grader in Jefferson elementary
3. Therefore, Carlos eats a lot of ice cream

The converse of this fallacy is called 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 constituent 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.[1][2][3]

## 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,[4] 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.[5]

## References

2. Rom Harré. Behind the Mereological Fallacy. Philosophy 87:3, July 2012, pp. 329-352. https://doi.org/10.1017/S0031819112000241
3. P.M.S. Hacker. 2013. Before the Mereological Fallacy: A Rejoinder to Rom Harré. Philosophy, 88(1), 141-148. doi:10.1017/S003181911200054X
4. Brauneis, Robert (2009). Intellectual Property Protection of Fact-based Works: Copyright and Its Alternatives. Edward Elgar Publishing. p. 110.
5. Burnham Terrell, Dailey (1967). Logic: A Modern Introduction to Deductive Reasoning. Holt, Rinehart and Winston. pp. 160–163.
• 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.
• "Division". The Fallacy Files.