1. The whole is defined and determined by its parts (axiom). 2. The recursion is defined and determined by its part (axiom). 3. Something exists and that something has at least one part (assumption). 4. Wholeness and recursion are both possible for all of the phenomenon (3). 5. That something is either endless or finite (language truth). 6. The whole and recursive something has the endless parts (1,2,3,4,5). 7. The whole something is both equal to its part and, therefore, it is recursive (1,3,4,5). 8. The recursive something is both endless and, therefore, it is whole (2,3,4,5). 9. That something equals to its own part, so it's both as whole so recursive (3,4,5). S: No free of parts things are non-whole and non-recursive (1-9).