Division Fallacy

Definition

Let:

• $W$ : A whole composed of parts
• $p_i$ : A part of $W$
• $P$ : A property

Then an argument commits the Division Fallacy if and only if it asserts:

$$W\text{ has property }P⟹\forall p_i\in W,p_i\text{ has property }P$$

NOTE

Properties of the whole do not necessarily apply to individual parts.