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# The class <math>M</math> is suggested by the adjectives ''distinct'', ''decided'', ''defined'', ''definite'', ''determinate'', ''different'', ''differentiated'', or ''discrete'', and, within a stretch of the imagination, by ''acute'', ''conspicuous'', ''eminent'', ''manifest'', ''poignant'', ''salient'', or ''striking''.  To the geometric imagination, these terms suggest a ''pointedness''.

# The class <math>M</math> is suggested by the adjectives ''distinct'', ''decided'', ''defined'', ''definite'', ''determinate'', ''different'', ''differentiated'', or ''discrete'', and, within a stretch of the imagination, by ''acute'', ''conspicuous'', ''eminent'', ''manifest'', ''poignant'', ''salient'', or ''striking''.  To the geometric imagination, these terms suggest a ''pointedness''.

In this frame of thought, it needs to be understood that the intended sense of these last two classes excludes the common usage of words like ''clear'', ''clearly'', and so on, or ''distinct'', ''distinctly'', and so on, as elliptic figures of speech that are intended to be taken in a more literal way to mean ''clearly true'', and so on, or ''distinctly true'', and so on.

In this frame of thought, it needs to be understood that the intended sense of these last two classes excludes the common usage of words like "clear", "clearly", and so on, or "distinct", "distinctly", and so on, as elliptic figures of speech that are intended to be taken in a more literal way to mean "clearly true", and so on, or "distinctly true", and so on.

In this connection, when I mention one of these properties it is only meant as a representative of its class.  Also, as they are used in this context, these terms are intended only in what is diversely called their "impressionistic", "nominal", "subjective", "superficial", or "topical" sense, implying the sorts of qualities that one can judge "by inspection" of the expression and its immediate situation, and without the need of a prolonged investigation.  Thus, none of their intentions is damaged for this purpose by prefacing their proposal with an attitude of "seeming".  For all one cares in these concerns, "seems X" = "X", for X = C, L, M.  This makes the judgment of these qualities a matter of "seeming syntax" and "seeming semantics", involving only the sorts of decision that are commonly and easily made without carrying out complex computations or without delving into the abstruse equivalence classes of expressions.

In this connection, when I mention one of these properties it is only meant as a representative of its class.  Also, as they are used in this context, these terms are intended only in what is diversely called their ''impressionistic'', ''nominal'', ''subjective'', ''superficial'', or ''topical'' sense, implying the sorts of qualities that one can judge &ldquo;by inspection&rdquo; of the expression and its immediate situation, and without the need of a prolonged investigation.  Thus, none of their intentions is damaged for this purpose by prefacing their proposal with an attitude of ''seeming''.  For all one cares in these concerns, "seems X" = "X", for X = C, L, M.  This makes the judgment of these qualities a matter of "seeming syntax" and "seeming semantics", involving only the sorts of decision that are commonly and easily made without carrying out complex computations or without delving into the abstruse equivalence classes of expressions.

People frequently use the adverbs "immediately" or "intuitively" to get this sense across, and even though these terms have technical meanings that prevent me from using them in this way in anything but a casual setting, they can do for the moment.  Still, when I use "immediately" in this sense it is meant in contrast only to "ultimately", and more or less synonymous to "mediately", suggesting that which holds in the meantime.  In a pinch, a determination of seeming certainty or seeming clarity is enough to put an inquiry on hold for a time being, but the distinction between "seeming so to me, for now" and "seeming so to all, forever" still holds, with only the latter deserving the title of "being so".

People frequently use the adverbs ''immediately'' or ''intuitively'' to get this sense across, and even though these terms have technical meanings that prevent me from using them in this way in anything but a casual setting, they can do for the moment.  Still, when I use ''immediately'' in this sense it is meant in contrast only to ''ultimately'', and more or less synonymous to ''mediately'', suggesting that which holds in the meantime.  In a pinch, a determination of seeming certainty or seeming clarity is enough to put an inquiry on hold for a time being, but the distinction between ''seeming so to me, for now'' and ''seeming so to all, forever'' still holds, with only the latter deserving the title of ''being so''.

These observations on im/mediate, intuitive, or meantime determinations of certainty, clarity, and distinctness have a bearing on the styles of mathematical formulation and the modes of computational implementation that are candidates for mediating a natural style of inquiry, in other words, the sort of inquiry that a human being can relate to.  Because a decision that a sign or expression has one of the virtues C, L, M, even to a mediate, a moderate, or a modest degree, is often enough to end an inquiry on a temporary basis, it becomes necessary to recognize a form of recursive foundation that also rests on a temporal basis.  And yet, because these modes of judgment are all the while fallible and subject to change, it is possible that deeper foundations remain to be found.

These observations on im/mediate, intuitive, or meantime determinations of certainty, clarity, and distinctness have a bearing on the styles of mathematical formulation and the modes of computational implementation that are candidates for mediating a natural style of inquiry, in other words, the sort of inquiry that a human being can relate to.  Because a decision that a sign or expression has one of the virtues <math>C, L, M,</math> even to a mediate, a moderate, or a modest degree, is often enough to end an inquiry on a temporary basis, it becomes necessary to recognize a form of recursive foundation that also rests on a temporal basis.  And yet, because these modes of judgment are all the while fallible and subject to change, it is possible that deeper foundations remain to be found.

What does this mean for the topic of reflection?  Well, reflection is precisely that mode of thinking that is capable of beginning with the axioms and working backward, that is, of searching out the more basic forms that conceivably underlie one's received formulations.

What does this mean for the topic of reflection?  Well, reflection is precisely that mode of thinking that is capable of beginning with the axioms and working backward, that is, of searching out the more basic forms that conceivably underlie one's received formulations.

I thereby concluded that I was a substance, of which the whole essence or nature consists in thinking, and which, in order to exist, needs no place and depends on no material thing;  so that this "I", that is to say, the mind, by which I am what I am, is entirely distinct from the body, and even that it is easier to know than the body, and moreover, that even if the body were not, it would not cease to be all that it is.

Rene Descartes, Discourse on Method, [Des1, 54]

<p>I thereby concluded that I was a substance, of which the whole essence or nature consists in thinking, and which, in order to exist, needs no place and depends on no material thing;  so that this &ldquo;I&rdquo;, that is to say, the mind, by which I am what I am, is entirely distinct from the body, and even that it is easier to know than the body, and moreover, that even if the body were not, it would not cease to be all that it is.</p>

| align="right" | Rene Descartes, ''Discourse on Method'', [Des1, 54]

And voila, I have, finally, spontaneously returned to there where I wanted to be.  For because it now be known to me that bodies themselves are properly perceived not by the senses or by the faculty of imagining, but rather by the intellect alone, and that bodies are perceived not from thence that they would be touched or seen, but rather from thence only that they were to be understood, I cognize overtly that nothing can be perceived by me more easily or more evidently than my mind.

Rene Descartes, Meditations on First Philosophy, [Des2, 117]

<p>And voila, I have, finally, spontaneously returned to there where I wanted to be.  For because it now be known to me that bodies themselves are properly perceived not by the senses or by the faculty of imagining, but rather by the intellect alone, and that bodies are perceived not from thence that they would be touched or seen, but rather from thence only that they were to be understood, I cognize overtly that nothing can be perceived by me more easily or more evidently than my mind.</p>

| align="right" | Rene Descartes, ''Meditations on First Philosophy'', [Des2, 117]

On reflection, the observation that appeared just before these last questions arose can be seen to make a very broad claim about a certain class of properties affecting expressions, namely, all those properties that can be analogous to the ordered measures of expressive quality.  For future reference, let me call this the "monotone assumption" (MA).  This generatrix of so many future and specious assumptions takes for granted a sweeping claim about the ways that an order of analysis of expressions translates into an order of comparison of their measures under one of these properties.  But this entire and previously unstated assumption is itself just another manner of working hypothesis for the mental procedure or the process of inquiry that makes use of it, and its proper understanding is perhaps better served if it is rephrased as a question:  Can the X of a claim or a concept be greater than the X of the subordinate claims and concepts that it calls on, where "X" stands for "certainty", "clarity", or any one of the corresponding class of measures, orders, properties, qualities, or virtues?

On reflection, the observation that appeared just before these last questions arose can be seen to make a very broad claim about a certain class of properties affecting expressions, namely, all those properties that can be analogous to the ordered measures of expressive quality.  For future reference, let me call this the "monotone assumption" (MA).  This generatrix of so many future and specious assumptions takes for granted a sweeping claim about the ways that an order of analysis of expressions translates into an order of comparison of their measures under one of these properties.  But this entire and previously unstated assumption is itself just another manner of working hypothesis for the mental procedure or the process of inquiry that makes use of it, and its proper understanding is perhaps better served if it is rephrased as a question:  Can the X of a claim or a concept be greater than the X of the subordinate claims and concepts that it calls on, where "X" stands for "certainty", "clarity", or any one of the corresponding class of measures, orders, properties, qualities, or virtues?