Changes

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<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 "y" denotes a particular inquiry, y ? Y, one that is assumed to be plenipotential or prototypical in a yet to be specified way.  In the figurative case, the name "y" is simply a variable that ranges over a collection Y of nominally conceivable inquiries.</li>

<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> On first reading, the recipe "y0 = y·y" 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>

<li> Given the formula "y0 = y·y", the subordination "y >= {d, f}", and the successive containments "F ? M ? D", the y that looks into y is not restricted to examining y's immediate subordinates, d and f, but it can investigate any feature of y's overall context, whether objective, syntactic, interpretive, whether definitive or incidental, and finally it can question any supporting claim of the discussion.  Moreover, the question y is not limited to the particular claims that are being made here, but applies to the abstract relations and the general notions that are invoked in making them.  Among the many kinds of inquiry that suggest themselves, there are the following possibilities:</li>

<li> Given the formula <math>y_0 = y \cdot y,</math> the subordination <math>y \succ \{ d, f \},</math> and the successive containments <math>F \subseteq M \subseteq D,</math> the <math>y\!</math> that looks into <math>y\!</math> is not restricted to examining <math>y \operatorname{'s}</math> immediate subordinates, <math>d\!</math> and <math>f,\!</math> but it can investigate any feature of <math>y \operatorname{'s}</math> overall context, whether objective, syntactic, interpretive, whether definitive or incidental, and finally it can question any supporting claim of the discussion.  Moreover, the question <math>y\!</math> is not limited to the particular claims that are being made here, but applies to the abstract relations and the general notions that are invoked in making them.  Among the many kinds of inquiry that suggest themselves, there are the following possibilities:</li>

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<ol style="list-style-type:lower-alpha">

<li> Inquiry into propositions about application and equality.

<li> Inquiry into propositions about application and equality.<br>Start with the formula <math>y_0 = y \cdot y</math> itself.</li>  

Start with the formula "y0 = y·y" itself.</li>  

<li> Inquiry into application (.).</li>

<li> Inquiry into application (&nbsp;<math>\cdot</math>&nbsp;).</li>

<li> Inquiry into equality (=).</li>

<li> Inquiry into equality (<math>=\!</math>).</li>

<li> Inquiry into indices (e.g. 0).</li>

<li> Inquiry into indices (for example, the <math>0</math> in <math>y_0\!</math>).</li>

<li> Inquiry into terms, namely, constants and variables.<br> What are the functions of "y" and "y0" in this respect?</li>

<li> Inquiry into terms, namely, constants and variables.<br>What are the functions of <math>^{\backprime\backprime} y ^{\prime\prime}</math> and <math>^{\backprime\backprime} y_0 ^{\prime\prime}</math> in this respect?</li>

<li> Inquiry into decomposition or subordination (>=).</li>

<li> Inquiry into decomposition or subordination (<math>\succ</math>).</li>

<li> Inquiry into containment or inclusion.  In particular, examine the claim "F ? M ? D" which conditions the chances that a formalization has an object, the degree to which a formalization can be carried out by means of a discussion, and the extent to which an object of formalization can be conveyed by a form of discussion.</li>

<li> Inquiry into containment or inclusion.  In particular, examine the claim that <math>F \subseteq M \subseteq D</math> which conditions the chances that a formalization has an object, the degree to which a formalization can be carried out by means of a discussion, and the extent to which an object of formalization can be conveyed by a form of discussion.</li>

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If inquiry begins in doubt, then inquiry into inquiry begins in doubt about doubt.  All things considered, the formula "y0 = y·y" has to be taken as the first attempt at a description of the problem, a hypothesis about the nature of inquiry, or an image that is tossed out by way of getting an initial fix on the object in question.  Everything in this account so far, and everything else that I am likely to add, can only be reckoned as hypothesis, whose accuracy, pertinence, and usefulness can be tested, judged, and redeemed only after the fact of proposing it and after the facts to which it refers have themselves been gathered up.

If inquiry begins in doubt, then inquiry into inquiry begins in doubt about doubt.  All things considered, the formula <math>y_0 = y \cdot y</math> has to be taken as the first attempt at a description of the problem, a hypothesis about the nature of inquiry, or an image that is tossed out by way of getting an initial fix on the object in question.  Everything in this account so far, and everything else that I am likely to add, can only be reckoned as hypothesis, whose accuracy, pertinence, and usefulness can be tested, judged, and redeemed only after the fact of proposing it and after the facts to which it refers have themselves been gathered up.

A number of problems present themselves due to the context in which the present inquiry is aimed to present itself.  The hypothesis that suggests itself to one person, as worth exploring at a particular time, does not always present itself to another person as worth exploring at the same time, or even necessarily to the same person at another time.  In a community of inquiry that extends beyond an isolated person and in a process of inquiry that extends beyond a singular moment in time, it is therefore necessary to consider the nature of the communication process that the discussion of inquiry in general and the discussion of formalization in particular need to invoke for their ultimate utility.

A number of problems present themselves due to the context in which the present inquiry is aimed to present itself.  The hypothesis that suggests itself to one person, as worth exploring at a particular time, does not always present itself to another person as worth exploring at the same time, or even necessarily to the same person at another time.  In a community of inquiry that extends beyond an isolated person and in a process of inquiry that extends beyond a singular moment in time, it is therefore necessary to consider the nature of the communication process that the discussion of inquiry in general and the discussion of formalization in particular need to invoke for their ultimate utility.

Solitude and solipsism are no solution to the problems of community and communication, since even an isolated individual, if ever there was, is, or comes to be such a thing, has to maintain the lines of communication that are required to integrate past, present, and prospective selves - in other words, translating everything into present terms, the parts of one's actually present self that involve actual experiences and present observations, present expectations as reflective of actual memories, and present intentions as reflective of actual hopes.  So the dialogue that one holds with oneself is every bit as problematic as the dialogue that one enters with others.  Others only surprise one in other ways than one ordinarily surprises oneself.

Solitude and solipsism are no solution to the problems of community and communication, since even an isolated individual, if ever there was, is, or comes to be such a thing, has to maintain the lines of communication that are required to integrate past, present, and prospective selves &mdash; in other words, translating everything into present terms, the parts of one's actually present self that involve actual experiences and present observations, present expectations as reflective of actual memories, and present intentions as reflective of actual hopes.  So the dialogue that one holds with oneself is every bit as problematic as the dialogue that one enters with others.  Others only surprise one in other ways than one ordinarily surprises oneself.

I recognize inquiry as beginning with a "surprising phenomenon" or a "problematic situation", more briefly described as a "surprise" or a "problem", respectively.  These are the types of moments that try our souls, the instances of events that instigate inquiry as an effort to achieve their own resolution.  Surprises and problems are experienced as afflicted with an irritating uncertainty or a compelling difficulty, one that calls for a response on the part of the agent in question:

I recognize inquiry as beginning with a ''surprising phenomenon'' or a ''problematic situation'', more briefly described as a ''surprise'' or a ''problem'', respectively.  These are the types of moments that try our souls, the instances of events that instigate inquiry as an effort to achieve their own resolution.  Surprises and problems are experienced as afflicted with an irritating uncertainty or a compelling difficulty, one that calls for a response on the part of the agent in question:

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