ONT Re: Differential Logic
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DLOG. Note D55
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Difference Map of Conjunction (cont.)
The difference map DJ can also be given a "dispositional" interpretation.
First, recall that !e!J exhibits the dispositions to change from anywhere
in J to anywhere at all, and EJ enumerates the dispositions to change from
anywhere at all to anywhere in J. Next, observe that each of these classes
of dispositions may be divided in accordance with the case of J versus (J)
that applies to their points of departure and destination, as shown below.
Then, since the dispositions corresponding to !e!J and EJ have in common
the dispositions to preserve J, their symmetric difference (!e!J, EJ) is
made up of all the remaining dispositions, which are in fact disposed to
cross the boundary of J in one direction or the other. In other words,
we may conclude that DJ expresses the collective disposition to make
a definite change with respect to J, no matter what value it holds
in the current state of affairs.
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| !e!J = {Dispositions from J to J } + {Dispositions from J to (J)} |
| |
| EJ = {Dispositions from J to J } + {Dispositions from (J) to J } |
| |
| DJ = (!e!J, EJ) |
| |
| DJ = {Dispositions from J to (J)} + {Dispositions from (J) to J } |
| |
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Jon Awbrey
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