Level Category Error

(Should be called "CategoryLevelError", but it's not a Category Page.)

"Every element of a set has property foo, therefore the set itself has property foo." A category error: not all sets are elements of themselves so there is ab initio no reason to expect it to have the same properties as any or all of its elements.

E.g., "The Universe consists of all things. This thing had a cause, that thing had a cause, ..., each and every thing in the Universe had a cause; ergo the Universe had a cause." (The Primum Mobile of Thomas Aquinas.)

E.g., "The human race consists of all human beings. This human being has fewer than six legs, That human being has fewer than six legs, ..., each and every human being in the entire human race has fewer than six legs; ergo the human race has fewer than six legs."

This is formally known as the CompositionFallacy.

Not really; The CompositionFallacy as described there appears to be "Some member of a set X has property Foo, therefore all members of the set X have property Foo." This is to be distinguished from "All members of a set X have property Foo, therefore X has property Foo".

The archetypal examples there have X being the set of people and property Foo being "Benefited from the invention of computers" and "Benefited from winning the lottery". Neither make the error described here; both mistake the individual members of a set for the set itself. So confounding CompositionFallacy with LevelCategoryError is itself a LevelCategoryError!

So either they're not the same thing, or CompositionFallacy has merely been poorly described. In which latter case, whatever is being described there is not CompositionFallacy but some other sort of error.

A LogicalFallacy related to MixingLevels.

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