Changes

{| align="center" cellspacing="8" width="90%"

{| align="center" cellspacing="8" width="90%"

| <math>G ~=~ \{ G_j \} ~=~ \{ j \widehat{~} G_j \} ~=~ \{ (j, G_j ) \}.\!</math>

|

<math>\begin{matrix}

G & = & \{ G_j \} & = & \{ j \widehat{~} G_j \} & = & \{ (j, G_j ) \}.

\end{matrix}</math>

|}

|}

The ''binder'' device <math>(\,\widehat{~}~)\!</math> works well in any situation where one desires to accentuate the fact that a formal subscript is being reclaimed and elevated to the status of an actual parameter.  By way of the operation indicated by the binder symbol the index bound to an object term can be rehabilitated as a full-fledged component of an elementary relation, thereby schematically embedding the indicated object in the experiential space of a typical agent.

The ''binder'' device <math>(\,\widehat{~}~)\!</math> works well in any situation where one desires to accentuate the fact that a formal subscript is being reclaimed and elevated to the status of an actual parameter.  By way of the operation indicated by the binder symbol the index bound to an object term can be rehabilitated as a full-fledged component of an elementary relation, thereby schematically embedding the indicated object in the experiential space of a typical agent.

The form of the binder notation is intended to suggest the use of ''pointers'' and ''views'' in computational frameworks, letting one interpret <math>j \widehat{~} x\!</math> in several different ways, for example, any one of the following.

The form of the caret notation is intended to suggest the use of "pointers" and "views" in computational frameworks, letting one interpret "j^x" in any one of many various ways, for example:

j^x = j's indication of x, j's access to x,

j's information on x, j's allusion to x,

j's copy of x, j's view of x.

j \widehat{~} x

& =

& j^\texttt{,}\text{s access to}~ x,

& j^\texttt{,}\text{s allusion to}~ x,

& j^\texttt{,}\text{s copy of}~ x,

& j^\texttt{,}\text{s indication of}~ x,

& j^\texttt{,}\text{s information on}~ x,

& j^\texttt{,}\text{s view of}~ x.

Presently, the distinction between indirect pointers and direct pointers, that is, between virtual copies and actual views of an objective domain, is not yet relevant here, being a dimension of variation that the discussion is currently abstracting over.

Presently, the distinction between indirect pointers and direct pointers, that is, between virtual copies and actual views of an objective domain, is not yet relevant here, being a dimension of variation that the discussion is currently abstracting over.