ONT Re: Differential Logic A -- Discussion
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DLOG A. Discussion Note 18
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One of the times -- or is it most of the times? -- that the gap between
a reality and a representation becomes rather glaringly obvious is when
we have several representations of what is regarded as the same reality,
for instance, as illustrated in the following picture for the reality x
and the alternative representations u and v.
u x v
o<-------------o------------->o
/|\ /|\
/ | \ / | \
/ | \ / | \
/ | \ / | \
o o o o o o
u_1 u_2 u_3 v_1 v_2 v_3
There are times when the variant representations are easily brought
into felicitous correspondence with one another, and then there are
times when the different views are so incommensurable that we begin
to doubt that they are really looking on the same worldscape at all.
In the examples of regular representations of groups that I discussed
a while back, we have already seen cases of variant representations of
the same object that are easily related to each other at various levels
of abstraction. Just for a stock example of alternative representations
that are not quite so trivially related to each other, one might think of
the complementary interpretations of the same quantum phenomenon in terms
of particles and in terms of waves.
Jon Awbrey
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http://www.cs.bsu.edu/homepages/mighty/history.html
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