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Consequently, it must be possible to explain these apparent abilities in just one of two ways:  either to account for the faculties of reflection and selection by presenting a logical model of the processes involved, or else to dispel the illusion of each performance by showing what goes on in its place.  In either case, an inquiry into the virtues of critically reflective phenomena is called on to provide a plausible model for what is happening beneath the semblances of reflective and critical thought.  Whether the resulting resolution of a particular phenomenon preserves or dissolves its appearances is a matter that depends on the details of the case, and perhaps to a degree on personal taste.

Consequently, it must be possible to explain these apparent abilities in just one of two ways:  either to account for the faculties of reflection and selection by presenting a logical model of the processes involved, or else to dispel the illusion of each performance by showing what goes on in its place.  In either case, an inquiry into the virtues of critically reflective phenomena is called on to provide a plausible model for what is happening beneath the semblances of reflective and critical thought.  Whether the resulting resolution of a particular phenomenon preserves or dissolves its appearances is a matter that depends on the details of the case, and perhaps to a degree on personal taste.

'''Point 26.'''     This marks a branch point.  I tentatively assume that the apparent power of reflection is really more or less as it appears to be, at least, in the same spirit as it appears to be, and not some radically insidious self-deception arising on the part of its apparent agents.

Point 26. This marks a branch point.  I tentatively assume that the apparent power of reflection is really more or less as it appears to be, at least, in the same spirit as it appears to be, and not some radically insidious self deception arising on the part of its apparent agents.

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, I use either one of the phrases "X collects Y" or "X encases Y" to mean that Y C 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.

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.

To wrap up the development of this reflective project in a single line:  When the mind's original effort to catch itself at work seizes on the inventions of set theory to encapsulate its speculations, the ensuing breed of self reification that comes from mingling an unbridled capacity for self referent expressions with an unchecked propensity for creating abstract objects gives rise to the generation of set theoretic paradoxes.  As a result, it is incumbent on me to show how the concretely limited kinds of constructions that I have in mind can avoid a similar excess and steer clear of the corresponding difficulties.

To wrap up the development of this reflective project in a single line:  When the mind's original effort to catch itself at work seizes on the inventions of set theory to encapsulate its speculations, the ensuing breed of self reification that comes from mingling an unbridled capacity for self referent expressions with an unchecked propensity for creating abstract objects gives rise to the generation of set theoretic paradoxes.  As a result, it is incumbent on me to show how the concretely limited kinds of constructions that I have in mind can avoid a similar excess and steer clear of the corresponding difficulties.