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Composition and division
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The logical fallacies of composition and division are a pair of fallacies which are based on a confusion between what is true of the part and what is true of the whole. The fallacy of composition is an incorrect inference from what is known of the parts to asserting the same of the whole; and the fallacy of division is the reverse, from the whole to the part. Comparing the fallacy to the figures of speech called synecdoche (as when one says "wheels" to refer to an auto), one might say that the fallacy consists of taking the figure of speech literally.
These arguments are fallacious in part due to the existence of emergent phenomena - that higher order properties may just "emerge" from the fact there many individual components working together. A key example of this is Conway's Game of Life, where small squares operate due to minute rules, but produce complex and unpredictable behaviours on a larger scale. The behaviour of the extremely large objects in the Game of Life doesn't really indicate the lower level rules very well; that a spaceship (the name given to a particular pattern that moves across the board) moves in a particular direction is not an indicator of the basic rules which only say whether a square is "alive" or "dead".
Properties of systems can change dramatically over different scales. At short enough scales, the world is flat - and one could prove the earth is flat simply by measuring a floor, or even a field, or averaging out over a hilly environment. But at much larger scales, the earth is curved. Conversely, knowing the earth has a known curve to it at larger scales wouldn't be indicative of any local environment such as mountains or plains. The cycle of temperature over a day also doesn't indicate an overall cycle across a season, or a year, or over an entire climate. As temperature plummets at night and rises when the sun comes back up, and this doesn't predict nor say anything about winter or summer. This seems obvious; but of course the earth is curved at larger scales and full of varied terrain at smaller scales and of course day-long weather and year-long weather aren't the same, but it's where this fact isn't so obvious that fallacies come into play. For instance, the exact same weather argument is frequently proposed as an argument against climate change.
Textbook examples of the fallacy:
- Because large objects are made of atoms, large objects have the properties of atoms, and atoms have the properties of large objects.
- Because the head of state represents the nation, to say something bad about him/her is to insult the nation.
Some examples of the fallacy as used by creationists:
- Because no living thing is older than a few hundred, or at most a few thousand, years old, life itself is no older than a few thousands of years.
- Because entropy does not decrease in an isolated and closed system, it does not decrease in the universe as a whole (which is made up of isolated and closed systems); and it does not decrease in any part of the universe (because every part is part of some isolated and closed system). (The last example might be seen as an interesting case of both composition division: the whole contains at least one part where entropy does not increase, "thereby" the restriction is true of the whole; and any such restriction on entropy on the whole is "thereby" true of any of its parts (all its parts, not only "isolated and closed systems"); and "thereby" any restriction one of the parts is true of all of the parts.)
A favorite of climate change deniers:
- Because no individual human being is powerful enough to affect the climate of Earth, anthropogenic climate change is impossible.
And finally a classic from anti-feminists amongst others:
- [X] privilege doesn't exist because individual non-[X] people might be wealthy.
 Spotlight fallacy
Composition and division is related to, but distinct from the spotlight fallacy. The latter is committed when unrepresentative information about parts is being used to make statements about the whole, even though the inference is correct, while the latter applies when the inference itself is incorrect, even if the information about parts is complete or at least representative.