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Revision as of 21:03, 1 July 2008

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<p>Where number is irrelevant, regimented mathematical technique has hitherto tended to be lacking.  Thus it is that the progress of natural science has depended so largely upon the discernment of measurable quantity of one sort or another.</p>
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Where number is irrelevant, regimented mathematical technique has hitherto tended to be lacking.  Thus it is that the progress of natural science has depended so largely upon the discernment of measurable quantity of one sort or another.
 
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<p>Measurement consists in correlating our subject matter with the series of real numbers;  and such correlations are desirable because, once they are set up, all the well-worked theory of numerical mathematics lies ready at hand as a tool for our further reasoning.</p>
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Measurement consists in correlating our subject matter with the series of real numbers;  and such correlations are desirable because, once they are set up, all the well-worked theory of numerical mathematics lies ready at hand as a tool for our further reasoning.
 
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<p>You will hardly know who I am or what I mean,<br>
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You will hardly know who I am or what I mean,<br>
 
But I shall be good health to you nevertheless,<br>
 
But I shall be good health to you nevertheless,<br>
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And filter and fibre your blood.</p>
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And filter and fibre your blood.
 
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<p>But no science can rest entirely on measurement, and many scientific investigations are quite out of reach of that device.  To the scientist longing for non-quantitative techniques, then, mathematical logic brings hope.</p>
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But no science can rest entirely on measurement, and many scientific investigations are quite out of reach of that device.  To the scientist longing for non-quantitative techniques, then, mathematical logic brings hope.
 
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<p>To the scientist longing for non-quantitative techniques, then, mathematical logic brings hope.  It provides explicit techniques for manipulating the most basic ingredients of discourse.</p>
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To the scientist longing for non-quantitative techniques, then, mathematical logic brings hope.  It provides explicit techniques for manipulating the most basic ingredients of discourse.
 
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==A Differential Extension of Propositional Calculus==
 
==A Differential Extension of Propositional Calculus==
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<p>Fire over water:<br>
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Fire over water:<br>
 
The image of the condition before transition.<br>
 
The image of the condition before transition.<br>
 
Thus the superior man is careful<br>
 
Thus the superior man is careful<br>
 
In the differentiation of things,<br>
 
In the differentiation of things,<br>
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So that each finds its place.</p>
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So that each finds its place.
 
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| align="right" | &mdash; ''I Ching'', Hexagram 64, [Wil, 249]
 
| align="right" | &mdash; ''I Ching'', Hexagram 64, [Wil, 249]
 
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===Differential Propositions : The Qualitative Analogues of Differential Equations===
 
===Differential Propositions : The Qualitative Analogues of Differential Equations===
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<p>There would have been no beginnings:  instead, speech would proceed from me, while I stood in its path &ndash; a slender gap &ndash; the point of its possible disappearance.</p>
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There would have been no beginnings:  instead, speech would proceed from me, while I stood in its path &ndash; a slender gap &ndash; the point of its possible disappearance.
 
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<p>At the moment of speaking, I would like to have perceived a nameless voice, long preceding me, leaving me merely to enmesh myself in it, taking up its cadence, and to lodge myself, when no one was looking, in its interstices as if it had paused an instant, in suspense, to beckon to me.</p>
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At the moment of speaking, I would like to have perceived a nameless voice, long preceding me, leaving me merely to enmesh myself in it, taking up its cadence, and to lodge myself, when no one was looking, in its interstices as if it had paused an instant, in suspense, to beckon to me.
 
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===Intentional Propositions===
 
===Intentional Propositions===
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<p>Do you guess I have some intricate purpose?<br>
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Do you guess I have some intricate purpose?<br>
 
Well I have . . . . for the April rain has, and the mica on<br>
 
Well I have . . . . for the April rain has, and the mica on<br>
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&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;the side of a rock has.</p>
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&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;the side of a rock has.
 
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| align="right" | &mdash; Walt Whitman, ''Leaves of Grass'', [Whi, 45]
 
| align="right" | &mdash; Walt Whitman, ''Leaves of Grass'', [Whi, 45]
 
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===Life on Easy Street===
 
===Life on Easy Street===
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<p>Failing to fetch me at first keep encouraged,<br>
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Failing to fetch me at first keep encouraged,<br>
 
Missing me one place search another,<br>
 
Missing me one place search another,<br>
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I stop some where waiting for you</p>
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I stop some where waiting for you
 
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| align="right" | &mdash; Walt Whitman, ''Leaves of Grass'', [Whi, 88]
 
| align="right" | &mdash; Walt Whitman, ''Leaves of Grass'', [Whi, 88]
 
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==Back to the Beginning : Some Exemplary Universes==
 
==Back to the Beginning : Some Exemplary Universes==
Jon Awbrey
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