Definitions

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Some O is made up of A and B. Without reference to any further or external information O{A, B} is a definition one could tentatively provide.

A and B are themselves subject to definition, such as A{a, b, c}, B{e, f, g}. An expanded definition of O would be O{ A(a, b, c), B(e, f, g) }.

The array A, B consists of subsets of O; an O which is in this context a set. The strings a, b, c and e, f, g are elements of the sets A and B respectively.

To use familiar language, O is the parent set, A, B are the child sets, a, b, c and e, f, g are grandchild sets. The simple definition is an order of sets, so that:

O
—A
—B

The expanded definition is an order of sets of sets, so that:

O
—A
——a, b, c
—B
——e, f, g

A definition must reflect such hierarchy. If one were to suggest that, say, O{A, B, e} they would effectively be arguing for an alteration in the order among the sets:

O
—A
——a, b, c
—B
——f, g
—e

In terms of structure the definitions O{A, B} and O{ A(a, b, c), B(e, f, g) } do complement one another. The latter analyses the former.

Whereas, the definitions in O{A, B} and O{A, B, e} cannot both be equally precise/valid, for their underlying order is different. They contradict one another.

Thus concludes this short syllogism on logically [in]valid definitions.

Thank you for reading!