Changes

</font><br>

</font><br>

Figures&nbsp;40-a through 40-d present several views of the enlarged proposition EJ.

Figures&nbsp;40-a through 40-d present several views of the enlarged proposition E''J''.

<pre>

<br>

o---------------------------------------o

<p>[[Image:Diff Log Dyn Sys -- Figure 40-a -- Enlargement of J.gif|center]]</p>

|                                       |

<p><center><font size="+1">'''Figure 40-a.  Enlargement of ''J''&nbsp;&nbsp;(Areal)'''</font></center></p>

|                  /%\                  |

|  o---+---o      o      o---+---o  |

Figure 40-a.  Enlargement of J (Areal)

</pre>

<pre>

<br>

                                                  o-----------------------------o

<p>[[Image:Diff Log Dyn Sys -- Figure 40-b -- Enlargement of J.gif|center]]</p>

                                                  |                             |

<p><center><font size="+1">'''Figure 40-b.  Enlargement of ''J''&nbsp;&nbsp;(Bundle)'''</font></center></p>

                                                  |    /       \ /      \    |

Figure 40-b.  Enlargement of J (Bundle)

</pre>

<pre>

<br>

o---------------------------------------------------------------------o

<p>[[Image:Diff Log Dyn Sys -- Figure 40-c -- Enlargement of J.gif|center]]</p>

|                                                                     |

<p><center><font size="+1">'''Figure 40-c.  Enlargement of ''J''&nbsp;&nbsp;(Compact)'''</font></center></p>

|          /                     \ /                    \          |

|    |                      |  -->--  |                      |    |

|    |    u    o---------------->@<----------------o    v    |    |

Figure 40-c.  Enlargement of J (Compact)

</pre>

<pre>

<br>

o-----------------------------------------------------------o

<p>[[Image:Diff Log Dyn Sys -- Figure 40-d -- Enlargement of J.gif|center]]</p>

<p><center><font size="+1">'''Figure 40-d.  Enlargement of ''J''&nbsp;&nbsp;(Digraph)'''</font></center></p>

|                        (du).(dv)                        |

|                          --->---                          |

Figure 40-d.  Enlargement of J (Digraph)

</pre>

An intuitive reading of the proposition E''J'' becomes available at this point, and may be useful.  Recall that propositions in the extended universe E''U''^&nbsp;&bull; express the ''dispositions'' of system and the constraints that are placed on them.  In other words, a differential proposition in E''U''^&nbsp;&bull; can be read as referring to various changes that a system might undergo in and from its various states.  In particular, we can understand E''J'' as a statement that tells us what changes need to be made with regard to each state in the universe of discourse in order to reach the ''truth'' of ''J'', that is, the region of the universe where ''J'' is true.  This interpretation is visibly clear in the Figures above, and appeals to the imagination in a satisfying way, but it has the added benefit of giving fresh meaning to the original name of the shift operator E.  Namely, E''J'' can be read as a proposition that ''enlarges'' on the meaning of ''J'', in the sense of explaining its practical bearings and clarifying what it means in terms of the available options for differential action and the consequential effects that result from each choice.

An intuitive reading of the proposition E''J'' becomes available at this point, and may be useful.  Recall that propositions in the extended universe E''U''^&nbsp;&bull; express the ''dispositions'' of system and the constraints that are placed on them.  In other words, a differential proposition in E''U''^&nbsp;&bull; can be read as referring to various changes that a system might undergo in and from its various states.  In particular, we can understand E''J'' as a statement that tells us what changes need to be made with regard to each state in the universe of discourse in order to reach the ''truth'' of ''J'', that is, the region of the universe where ''J'' is true.  This interpretation is visibly clear in the Figures above, and appeals to the imagination in a satisfying way, but it has the added benefit of giving fresh meaning to the original name of the shift operator E.  Namely, E''J'' can be read as a proposition that ''enlarges'' on the meaning of ''J'', in the sense of explaining its practical bearings and clarifying what it means in terms of the available options for differential action and the consequential effects that result from each choice.