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To paraphrase, the present inquiry acts on the pretense that an inquiry can inquire into other inquiries, perhaps even those that are presently ongoing, and even inquire into itself, in sum, being entitled to inquire into the full genus of inquiry, <math>Y,\!</math> a class that includes <math>y_0\!</math> as a member.  But these representations, under cross examination, lead to a number of unanswered questions, like:  Just what is a &ldquo;generic inquiry&rdquo;, anyway?  Even more critically, their close and repeated examination leads to a host of &ldquo;unquestioned answers&rdquo;, answers already accepted as adequate, but whose appearances as answers need to be questioned again.

To paraphrase, the present inquiry acts on the pretense that an inquiry can inquire into other inquiries, perhaps even those that are presently ongoing, and even inquire into itself, in sum, being entitled to inquire into the full genus of inquiry, Y, a class that includes y0 as a member.  But these representations, under cross examination, lead to a number of unanswered questions, like:  Just what is a "generic inquiry", anyway?  Even more critically, their close and repeated examination leads to a host of "unquestioned answers", answers already accepted as adequate, but whose appearances as answers need to be questioned again.

The "formal posability" of a self application, for example, as expressed by the term "y.y", especially when the formal calculus that is called on to make sense of these applications is still merely prospective and still highly speculative, ought to arouse a lot of suspicion from the purely formal point of view.  Indeed, I cannot justify this way of proceeding, beginning in the middle of things and without stopping to establish a well defined formal system ahead of time, except to say that something very like it is unavoidable in a large number of natural circumstances, and so one ought to find a way of getting used to it.  A way of getting used to the natural situation of inquiry is one of the things that the present inquiry hopes to find.

The ''formal posability'' of a self application, for example, as expressed by the term <math>{}^{\backprime\backprime} y \cdot y {}^{\prime\prime},</math> especially when the formal calculus that is called on to make sense of these applications is still merely prospective and still highly speculative, ought to arouse a lot of suspicion from the purely formal point of view.  Indeed, I cannot justify this way of proceeding, beginning in the middle of things and without stopping to establish a well defined formal system ahead of time, except to say that something very like it is unavoidable in a large number of natural circumstances, and so one ought to find a way of getting used to it.  A way of getting used to the natural situation of inquiry is one of the things that the present inquiry hopes to find.

If it appears that this allows the present inquiry an unlimited scope or an excessive freedom, it has to be remembered that a "formal posability" is barely enough of a formal subsistence to begin an inquiry, but rarely enough to finish it.  It can be invaluable as the provisonal "grubstake" for a prospecting expedition, supplying the initial overhead it takes to "prime the pump" of subsequent exploration, but it is not sufficient to continue very far with an investigation.  In essence, it is nothing more substantial than a grammatical allowance or a syntactic hypothesis, in effect, a poetic license, a verbal permission, or a written suggestion.  Taking all of these cautions into account, it leaves the present inquiry motivated and justified by no more authority than their titles connote, and it obliges the precocity of what is written to be atoned for with all the critical benevolence of afterthought that can be mustered after the fact, to wit, through the diligent application of that turn of mind that allows one to write first and only later to think on the meaning.

If it appears that this allows the present inquiry an unlimited scope or an excessive freedom, it has to be remembered that a ''formal posability'' is barely enough of a formal subsistence to begin an inquiry, but rarely enough to finish it.  It can be invaluable as the provisional ''grubstake'' for a prospecting expedition, supplying the initial overhead it takes to ''prime the pump'' of subsequent exploration, but it is not sufficient to continue very far with an investigation.  In essence, it is nothing more substantial than a grammatical allowance or a syntactic hypothesis, in effect, a poetic license, a verbal permission, or a written suggestion.  Taking all of these cautions into account, it leaves the present inquiry motivated and justified by no more authority than their titles connote, and it obliges the precocity of what is written to be atoned for with all the critical benevolence of afterthought that can be mustered after the fact, to wit, through the diligent application of that turn of mind that allows one to write first and only later to think on the meaning.

Such was my life's deceitful morning,

Such the pleasures I enjoy'd!

| colspan="2" | Such was my life's deceitful morning,

But lang or noon, loud tempests storming,

A' my flowery bliss destroy'd.

| width="5%"  | &nbsp; || Such the pleasures I enjoy'd!

Tho fickle Fortune has deceiv'd me

(She promis'd fair, and perform'd but ill),

| colspan="2" | But lang or noon, loud tempests storming,

Of monie a joy and hope bereav'd me,

I bear a heart shall support me still.

| width="5%"  | &nbsp; || A' my flowery bliss destroy'd.

Robert Burns, I Dream'd I Lay, [CPW, 45]

| colspan="2" | Tho fickle Fortune has deceiv'd me

| width="5%"  | &nbsp; || (She promis'd fair, and perform'd but ill),

| colspan="2" | Of monie a joy and hope bereav'd me,

| width="5%"  | &nbsp; || I bear a heart shall support me still.

| colspan="2" align="right" | &mdash; Robert Burns, ''I Dream'd I Lay'', [CPW, 45]

The present inquiry acts on the purely formal suggestion that a generic inquiry can inquire into other inquiries, perhaps even those that remain ongoing, moreover, that a particular inquiry can even inquire into itself.  Interpolating the appropriate symbols, the present inquiry, referring to itself as "y0", acts on the instance of a purely formal possibility, one that it expresses as a premiss in the formula "y0 = y.y", intending this to be interpreted to the effect that an inquiry can inquire into a class of inquiries that includes itself as a member, and this is a hypothesis that is based on little more authority than the fact of its expression a prospective formal language, in other words, one whose interpretation is still a largely prospective matter.

The present inquiry acts on the purely formal suggestion that a generic inquiry can inquire into other inquiries, perhaps even those that remain ongoing, moreover, that a particular inquiry can even inquire into itself.  Interpolating the appropriate symbols, the present inquiry, referring to itself as "y0", acts on the instance of a purely formal possibility, one that it expresses as a premiss in the formula "y0 = y.y", intending this to be interpreted to the effect that an inquiry can inquire into a class of inquiries that includes itself as a member, and this is a hypothesis that is based on little more authority than the fact of its expression a prospective formal language, in other words, one whose interpretation is still a largely prospective matter.