Fallacy of division

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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. A Boeing 747 can fly unaided across the ocean.
  2. A Boeing 747 has jet engines.
  3. Therefore, one of its jet engines can fly unaided across the ocean.

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.

An application: Famously and controversially, in the philosophy of the Greek Anaxagoras (at least as it is discussed 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 plainly 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.

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In statistics an ecological fallacy (or ecological inference 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 confusion between higher average and higher likelihood.

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