|Cogito ergo sum|
Logic and rhetoric
A category mistake (also known as a category error, categorical error, or distributive fallacy) is a logical fallacy that occurs when a speaker (knowingly or not) confuses the properties of the whole with the properties of a part. It contains the fallacy of composition (assuming the whole has the properties of the part) and the fallacy of division (assuming the part has the properties of the whole). Alternatively, the category mistake can also be characterized as the fallacy of mistaking the categorical and ontological status of a given concept, such as grouping it under categories that are not relevant, e.g. "The number 3 is blue". 
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 Earth 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.
- This is fallacious because quantum mechanics demonstrably only operates on a very small scale, and classical physics demonstrably only operates on a macro scale.
- Because the head of state represents the nation, to say something bad about them is to insult the nation.
- Because science says that romantic love involves biochemical factors and evolved instincts, it devalues love and represents a loveless worldview.
- Birds cannot fly, because feathers can't fly, visceral organs can't fly, and neither bones nor muscles can fly.
- This is fallacious because if all these things are arranged together in the right way, they can indeed achieve flight, as is proved by the existence of flying objects made of non-flying materials.
- 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 and 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.
Climate change fantasists
- Because no individual human being is powerful enough to affect the climate of Earth, anthropogenic climate change is impossible.
All political parties
The example Gilbert Ryle gives is a tour by someone visiting Oxford who looks around and asks to see the university. Ryle tells him he is at the university; "Here are the buildings, here are the professors, here are the students, etc." The visitor then tells him that he sees the buildings, the professors, and the students, but he still doesn't see the university. The point of the story is that the visitor has the expectation that the university is a physical object and not an abstraction.
Ryle makes this distinction as an argument against dualism.
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 former applies when the inference itself is incorrect, even if the information about parts is complete or at least representative.