Changes

Setting out initially on the positive track, I begin with the assumption that a RIF is a real possibility.  In order to conceive of a RIF being possible it is necessary to set aside a host of set theoretic difficulties that might be imagined to afflict any invocation of self referent themes.  No matter whether interpretation is presented in terms of a framework, a faculty, a process, a trajectory, or a hypostatic agent that is assumed to carry out its procedures, there is a problem about how anything so fleeting and so sweeping as an ongoing interpretation can refer to itself as a situated form of activity, in other words, as an objective system of interpretation that rests within a context of alternative interpretations.

Setting out initially on the positive track, I begin with the assumption that a RIF is a real possibility.  In order to conceive of a RIF being possible it is necessary to set aside a host of set theoretic difficulties that might be imagined to afflict any invocation of self referent themes.  No matter whether interpretation is presented in terms of a framework, a faculty, a process, a trajectory, or a hypostatic agent that is assumed to carry out its procedures, there is a problem about how anything so fleeting and so sweeping as an ongoing interpretation can refer to itself as a situated form of activity, in other words, as an objective system of interpretation that rests within a context of alternative interpretations.

There is a piece of terminology that is often useful in this connection.  In set-theoretic contexts, either one of the phrases <math>{}^{\backprime\backprime}X ~\operatorname{collects}~ Y{}^{\prime\prime}\!</math> or <math>{}^{\backprime\backprime}X ~\operatorname{encases}~ Y{}^{\prime\prime}\!</math> will be used to mean that <math>Y \in X.\!</math> These formulations can be taken as abbreviated ways of saying that <math>{}^{\backprime\backprime}X ~\operatorname{enumerates}~ Y ~\operatorname{among~its~cases}{}^{\prime\prime}.\!</math> Thus, they express the converse of the membership relation but manage to avoid the ambiguity of the phrase <math>{}^{\backprime\backprime}X ~\operatorname{contains}~ Y{}^{\prime\prime},\!</math> a form that would otherwise have to be qualified on each occasion of its use by specifying whether one means &ldquo;contains as an element&rdquo; or &ldquo;contains as a subset&rdquo;, as the case may be.

There is a piece of terminology that is often useful in this connection.  In set-theoretic contexts, either one of the phrases ''X collects Y''& or ''X encases Y'' can be used to mean the same thing as ''Y'' &isin; ''X''.  These formulations can be taken as abbreviated ways of saying that ''X'' enumerates ''Y'' among its cases.  Thus, they express the converse of the membership relation but manage to avoid the ambiguity of the phrase ''X contains Y'', a form that would otherwise have to be qualified on each occasion of its use by specifying whether one means ''contains as an element'' or ''contains as a subset'', as the case may be.

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