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Directory talk:Jon Awbrey/Papers/Differential Logic and Dynamic Systems 2.0 (view source)

Revision as of 02:52, 9 July 2008

725 bytes removed ,  02:52, 9 July 2008
→‎Reality at the Threshold of Logic
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===Reality at the Threshold of Logic===
 
===Reality at the Threshold of Logic===
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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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| align="right" colspan="3" | — W.V. Quine, ''Mathematical Logic'', [Qui, 7]
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Table 5 accumulates an array of notation that I hope will not be too distracting.  Some of it is rarely needed, but has been filled in for the sake of completeness.  Its purpose is simple, to give literal expression to the visual intuitions that come with venn diagrams, and to help build a bridge between our qualitative and quantitative outlooks on dynamic systems.
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{| align="center" border="1" cellpadding="8" cellspacing="0" style="text-align:left; width:96%"
   
|+ '''Table 5.  A Bridge Over Troubled Waters'''
 
|+ '''Table 5.  A Bridge Over Troubled Waters'''
 
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! Linear Space
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! <math>\mbox{Linear Space}\!</math>
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! Liminal Space
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! <math>\mbox{Liminal Space}\!</math>
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! Logical Space
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! <math>\mbox{Logical Space}\!</math>
 
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<font face="lucida calligraphy">X</font><br>
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<math>\begin{matrix}
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{''x''<sub>1</sub>, &hellip;, ''x''<sub>''n''</sub>}<br>
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\mathcal{X}          \\
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cardinality ''n''
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\{x_1, \ldots, x_n\}  \\
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\mbox{cardinality}\ n \\
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\end{matrix}</math>
 
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<font face="lucida calligraphy"><u>X</u></font><br>
 
<font face="lucida calligraphy"><u>X</u></font><br>
Jon Awbrey
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