Fallacy of division
A fallacy of division occurs when one reasons logically that if a property is true of something, it must be true of all of its parts.
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.
A boeing 747 has the ability to fly unaided because of the systems is contains allowing it to do so. Although the 747 can fly unaided, the engine does not contain the system that the 747 as a whole contains, and so it cannot fly unaided.
1. Functioning brains think. 2. Functioning brains are nothing but the neurons that they are composed of. 3. If functioning brains think, then the individual neurons in them think. 4. Individual neurons do not think. 5. Functioning brains do not think. (From 3 & 4) 6. Functioning brains think and functioning brains do not think. (From 1 & 5)
The opposite of the fallacy of division is the fallacy of composition, which occurs when one fallaciously attributes a property of a part to the sum of the parts as a whole. You can see both the fallacy of division (premise 3) and the fallacy of composition (premise's 4 & 5) in the second example.