Fallacy of division

A fallacy of division occurs when one reasons logically that something true for the 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. Both fallacies were addressed by Aristotle in Sophistical Refutations.

In the philosophy of the ancient Greek Anaxagoras, as claimed by the Roman atomist Lucretius,^[1] 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.

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.

Examples

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.^[2]

See also

• Ecological fallacy
• 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. Brauneis, Robert (2009). Intellectual Property Protection of Fact-based Works: Copyright and Its Alternatives. Edward Elgar Publishing. p. 110.
2. 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.