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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!