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Adam I. Gerard
ISU
NIU
CS MS TBD

Symbol Binding #2

Strengthening the original proposal.

Symbol Binding Itself Unbound

Ok, somewhat obviously, the Symbol Binding symbol (itself) might be criticized for being (itself) unbound or absent a permanent, immutably, fixed meaning! I suppose this is analogous to Hume's Law V, Cantor's Paradoxes, etc.

Here are some ways to strengthen that original idea:

  1. A Self-Binding operator (variant) that ranges over itself and the following (suffixed/appended) expression. I'll use Unicode U+29CB: to differentiate this from the weaker notion introduced earlier.
  2. Inner Binding and Outer Binding - an Inner Binding operator that binds a particular expression and an Outer Binding operator that affixes the meaning of the Inner Binding Operator. Here, the Outer Binding operator can self-bind (or not), can be Chiastic (or not). Something like ⧋⊡P
  3. Less efficiently, (more wildly,) a Chiastic Binding operator - wherein ⧋⧋ = ⧋ and ⧋ = ⧋⧋ (and ⧋⧋ = ⧋⧋⧋) for the binding operator wherein each nth-placed binds all m>n-placed (righter-sided) and every is self-bound Chiastically on the second reading. The idea here is that the symbol conveys a multitude of sequentially, yet self-containing, information and contains/conveys/stores (non-symbolic) information syntactically without the symbol itself changing.

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