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.
- The 2nd grade in Jefferson elementary eats a lot of ice cream
- Carlos is a 2nd grader in Jefferson elementary
- Therefore, Carlos eats a lot of ice cream
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.
In the philosophy of the ancient Greek Anaxagoras, as claimed by the Roman atomist Lucretius, 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.
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- 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.