Since all definitions of terms are effected by means of other terms, every system of definitions which is not circular must start from a certain apparatus of undefined terms.
Whitehead, Russell, Principia Mathematica
If we admit the necessity of a system of definitions, we should assume the risk of using undefined terms. It is the risk of being contrary to the definitions and to what they bring on to the formation of knowledge.
How could be presented as necessary the fact that those undefined terms are able to form an apparatus?
Any undefined term is closer to a discontinuous relation to another undefined term than to the strictness of an apparatus.
The ancient theory of some undefined and intuitive terms should counter the free movement of them due to their undefined character.
The intuition of them is rather the confession that they does not present the stability of a notion caught in a definitional string.
Their movement depends on the mover more than definitions themselves do. For the mover establish which ones of the possible undefined terms are to be chosen for forming a useful apparatus.
When the mover decides their inclusion into an apparatus, he has already forgotten his movement of searching. He forgets because he always keeps the definitions in his mind.
Thus, the logical procedure of searching for undefined terms pass over the possible flowering buds of an ethical problem: how much we are really sincere in choosing undefined terms for a definitional system?
Only in the case of facing such problem, we can disclose the logical system of definitions to the living aggregation of our thoughts.
Their living assembly does not induce disorder, but just an unordered association. Because the mover cannot be excluded from the explanation of their association, it is to be thought as elements of a non-systematical, but still a unitary form of mover’s exposure of his rational nature. This exposure always bears on mover’s unitary personality and it could be called ‘his proper world’.
Apart from its Greek nominal ancestry as ‘cosmos’, but also involved by some Ancient philosophers, ‘world’ designates a loosely aggregation of various elements. We could admit one ordering principle, but by this admission itself we recognize that the world contains a state of affairs which has to be ordered, and it is still unordered.
The mover of undefined terms plays the role of the principle of his world. Accordingly, his nature as a principle is to be found in what he has different from the unordered state of things and from ordered one. The solution will come from a study of what a human being possesses and there could not be qualified neither as ordered, nor as an unordered. Primarily, it would be about what he has without a direct relation to some rational processes.
And also we could speak about a reestablishing of circularity, but in a domain of human life when it is not banished.