Fallacy of division

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A fallacy of division occurs when one reasons logically that something true of a thing must also be true of at least some of its constituents.

An example:

1. A Boeing 747 can fly unaided across the ocean
2. If a Boeing 747 can fly unaided across the ocean, then one of its jet engines can fly unaided across the ocean.
3. One of its jet engines can fly unaided across the ocean

The converse of this fallacy is called fallacy of composition; it arises when one fallaciously attributes a property of some part of a thing to the thing as a whole.

Another example:

1. Brains can think
2. Brains are nothing but the neurons that they comprise
3. If brains can think, then the individual neurons in them must be thinking
4. If individiual neurons cannot think, then brains cannot think (from 3)
5. Individual neurons cannot think
6. Brains cannot think (from 4 & 5)
7. F (from 1 & 6)

Hence, we prove by contradiction that there is "something more" to the brain that the neurons in it (~2). The real problem is point 3, which commits the falacy of division.

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 homeomeria, 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.

Informal fallacies v • d • e
Special pleading | Red herring | Gambler's fallacy and its inverse Fallacy of distribution (Composition | Division) | Begging the question | Many questions
Correlative-based fallacies:
	False dilemma (Perfect solution) | Denying the correlative | Suppressed correlative
Deductive fallacies:
	Accident | Converse accident
Inductive fallacies:
	Hasty generalization | Overwhelming exception | Biased sample False analogy | Misleading vividness | Conjunction fallacy
Vagueness:
	False precision | Slippery slope
Ambiguity:
	Amphibology | Continuum fallacy | False attribution (Contextomy | Quoting out of context) Equivocation (Loki's Wager | No true Scotsman)
Questionable cause:
	Correlation does not imply causation | Post hoc | Regression fallacy Texas sharpshooter | Circular cause and consequence | Wrong direction | Single cause
Other types of fallacy