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The formula with which the initial part of this inquiry is annotated, y0 = y.y, is intended to suggest that the present inquiry, y0, is the result of applying a generic inquiry, y, to itself.  A close inspection reveals, however, that this formula does not quite make sense, at least, not yet, and there are many things that lie in the way of its doing so.

The formula with which the initial part of this inquiry is annotated, <math>y_0 = y \cdot y</math>, is intended to suggest that the present inquiry, <math>y_0\!</math>, is the result of applying a generic inquiry, <math>y\!</math>, to itself.  A close inspection reveals, however, that this formula does not quite make sense, at least, not yet, and there are many things that lie in the way of its doing so.

For one thing, where is the system of interpretation that can make sense of these signs, not just the "y" and the "y0" but the "." of an indicated application that is so often slighted to the point of omission?  Neither the form of this application nor the medium of its transmission are likely to be so transparent, or quite so easily taken for granted.

For one thing, where is the system of interpretation that can make sense of these signs, not just the <math>{}^{\backprime\backprime} y {}^{\prime\prime}</math> and the <math>{}^{\backprime\backprime} y_0 {}^{\prime\prime}</math> but the <math>{}^{\backprime\backprime} \cdot {}^{\prime\prime}</math> of an indicated application that is so often slighted to the point of omission?  Neither the form of this application nor the medium of its transmission are likely to be so transparent, or quite so easily taken for granted.

For another thing, who really imagines that naming an ongoing process is all that it takes to fix it in mind, to make it a passive object of thought?  The problem is that we never hold the inquiry itself within our grasp, but only the signs of it, and only a sample of these.  When all is said and done, there is nothing but the protocol of an experiment, the record of a trial, or the text of an inquiry that we have to examine.  In a sense, a statement to the effect that y0 = "y".y makes for a better account of how this self-described self-application actually gets going, since it is only an arbitrary sign of the passing moment of inquiry that supplies the initial argument and indicates the ultimate object of the pressing moment of inquiry.  In effect, the present inquiry, y0, is the result of calling up a generic faculty for inquiry, y, and setting it to work on whatever is indicated by a purely conventional name for itself, that is to say, on the argument "y".

For another thing, who really imagines that naming an ongoing process is all that it takes to fix it in mind, to make it a passive object of thought?  The problem is that we never hold the inquiry itself within our grasp, but only the signs of it, and only a sample of these.  When all is said and done, there is nothing but the protocol of an experiment, the record of a trial, or the text of an inquiry that we have to examine.  In a sense, a statement to the effect that <math>y_0 = {}^{\backprime\backprime} y {}^{\prime\prime} \cdot y</math> makes for a better account of how this self-described self-application actually gets going, since it is only an arbitrary sign of the passing moment of inquiry that supplies the initial argument and indicates the ultimate object of the pressing moment of inquiry.  In effect, the present inquiry, <math>y_0\!</math>, is the result of calling up a generic faculty for inquiry, <math>y\!</math>, and setting it to work on whatever is indicated by a purely conventional name for itself, that is to say, on the argument <math>{}^{\backprime\backprime} y {}^{\prime\prime}</math>.

All in all, the original formula serves well enough as a sigil, a wholly symbolic annotation, and so it can be allowed to rest at the top of the current phase of work, but if this semblance of an equation is intended to make sense in a less arbitrary, a more articulate, and a less occult fashion, then it will have to be given a more practical meaning, in terms that can guide the actual conduct of inquiry.

All in all, the original formula serves well enough as a sigil, a wholly symbolic annotation, and so it can be allowed to rest at the top of the current phase of work, but if this semblance of an equation is intended to make sense in a less arbitrary, a more articulate, and a less occult fashion, then it will have to be given a more practical meaning, in terms that can guide the actual conduct of inquiry.

The work up to this point pushes the discussion of formalization as far as it can go in a certain direction, at least, for now.  While maintaining this discussion, it is time to step back, to recall the broader context in which formalization takes place, and thus to enter on a discussion of the inquiry that this process of formalization is initially meant to serve.  y0 = y?y >= y?{d, f} >= y?{d}.

The work up to this point pushes the discussion of formalization as far as it can go in a certain direction, at least, for now.  While maintaining this discussion, it is time to step back, to recall the broader context in which formalization takes place, and thus to enter on a discussion of the inquiry that this process of formalization is initially meant to serve.  <math>y_0 = y \cdot y >\!\!= y \cdot \{ d, f \} >\!\!= y \cdot \{ d \}</math>.

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