Re: Operator Variables in Logical Graphs • 6

A funny thing just happened.  Let’s see if we can tell where.  We started with the algebraic expression where the operand suggests the contemplated absence or presence of an arbitrary arithmetic expression.  Next we contemplated the absence or presence of the operator in to be determined by the value of a newly introduced variable, say which is placed in a new slot of a newly extended operator form, as suggested by the following Figure.

What happened here is this.  Our contemplation of a constant operator as being potentially variable gave rise to the contemplation of a newly introduced but otherwise quite ordinary operand variable, albeit in a newly-fashioned formula.  In its interpretation for logic the newly formed operation may be viewed as an extension of ordinary negation, one in which the negation of the first variable is controlled by the value of the second variable.

We may regard this development as marking a form of controlled reflection, or a form of reflective control.  From here on out we’ll use the inline syntax to indicate the corresponding operation on two variables, whose formal operation table is given below.

• The Entitative Interpretation for which and
  calls this operation logical equality.
• The Existential Interpretation for which and
  calls this operation logical difference.

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