Changes

With this preamble, I return to develop my own account of formalization, with special attention to the kind of step that leads from the inchoate chaos of casual discourse to a well-founded discussion of formal models.  A formalization step, of the incipient kind being considered here, has the peculiar property that one can say with some definiteness where it ends, since it leads precisely to a well-defined formal model, but not with any definiteness where it begins.  Any attempt to trace the steps of formalization backward toward their ultimate beginnings can lead to an interminable multiplicity of open-ended explorations.  In view of these circumstances, let me limit my attention to the frame of the present inquiry and try to sum up what brings me to this point.

With this preamble, I return to develop my own account of formalization, with special attention to the kind of step that leads from the inchoate chaos of casual discourse to a well-founded discussion of formal models.  A formalization step, of the incipient kind being considered here, has the peculiar property that one can say with some definiteness where it ends, since it leads precisely to a well-defined formal model, but not with any definiteness where it begins.  Any attempt to trace the steps of formalization backward toward their ultimate beginnings can lead to an interminable multiplicity of open-ended explorations.  In view of these circumstances, let me limit my attention to the frame of the present inquiry and try to sum up what brings me to this point.

It begins like this:  I ask whether it is possible to reason about inquiry in a way that leads to a productive end.  I pose this question as an inquiry into inquiry, and I use the formula <math>y_0 = y \cdot y</math> to express the relationship between the present inquiry, <math>y_0\!</math>, and a generic inquiry, <math>y\!</math>.  Then I propose a couple of components of inquiry, expressed in the form <math>y >\!\!= \{ d, f \}</math>, that appear to be worth investigating.  Applying these components to each other, as must be done in the present inquiry, I am led to the current discussion of formalization, <math>y_0 = y \cdot y >\!\!= f \cdot d</math>.

It begins like this:  I ask whether it is possible to reason about inquiry in a way that leads to a productive end.  I pose this question as an inquiry into inquiry, and I use the formula <math>y_0 = y \cdot y</math> to express the relationship between the present inquiry, <math>y_0\!</math>, and a generic inquiry, <math>y\!</math>.  Then I propose a couple of components of inquiry, discussion and formalization, that appear to be worth investigating, expressing this proposal in the form <math>y >\!\!= \{ d, f \}</math>.  Applying these components to each other, as must be done in the present inquiry, I am led to the current discussion of formalization, <math>y_0 = y \cdot y >\!\!= f \cdot d</math>.

There is already much to question here.  At least, so many repetitions of the same mysterious formula are bound to lead the reader to question its meaning.

There is already much to question here.  At least, so many repetitions of the same mysterious formula are bound to lead the reader to question its meaning.

<ol style="list-style-type:decimal">

<ol style="list-style-type:decimal">

<li> The notion of a "generic inquiry" is ambiguous.  Its meaning in practice depends on whether this descriptive term is interpreted literally or merely as a figure of speech.  In the literal case, the name <math>{}^{\backprime\backprime} y {}^{\prime\prime}</math> denotes a particular inquiry, <math>y \in Y\!</math>, one that is assumed to be equipotential or prototypical in a yet to be specified way.  In the figurative case, the name <math>{}^{\backprime\backprime} y {}^{\prime\prime}</math> is simply a variable that ranges over a collection <math>Y\!</math> of nominally conceivable inquiries.</li>

<li> The term ''generic inquiry'' is ambiguous.  Its meaning in practice depends on whether the description of an inquiry as being generic is interpreted literally or merely as a figure of speech.  In the literal case, the name <math>{}^{\backprime\backprime} y {}^{\prime\prime}</math> denotes a particular inquiry, <math>y \in Y\!</math>, one that is assumed to be prototypical in yet to be specified ways.  In the figurative case, the name <math>{}^{\backprime\backprime} y {}^{\prime\prime}</math> is simply a variable that ranges over a collection <math>Y\!</math> of nominally conceivable inquiries.</li>

<li> On first reading, the recipe <math>y_0 = y \cdot y</math> appears to specify that the present inquiry is constituted by taking everything denoted by the most general concept of inquiry that the present inquirer can imagine and inquiring into it by means of the most general capacity for inquiry that this same inquirer can muster.</li>

<li> On first reading, the recipe <math>y_0 = y \cdot y</math> appears to specify that the present inquiry is constituted by taking everything denoted by the most general concept of inquiry that the present inquirer can imagine and inquiring into it by means of the most general capacity for inquiry that this same inquirer can muster.</li>