[Inquiry] Re: Futures Of Logical Graphs

[Jon Awbrey]

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FOLG.  Note 22

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Cybernetics List, Peirce List,

In thinking about mappings between categories of structured individuals,
we can take each mapping in two parts.  At the first level of analysis,
there is the part that maps individuals to individuals.  At the second
level of analysis, there is the part that maps the structural parts of
each individual to the structural parts of the individual that forms
its its counterpart under the first part of the mapping in question.

The general scheme of things is suggested by the following Figure,
where the mapping f from cosi U to cosi V is analyzed in terms of
a mapping g that takes individuals to individuals, ignoring their
inner structures, and a set of mappings h_j, where j ranges over
the individuals of cosi U and where h_j stipulates just how the
parts of j map to the parts of g(j), its counterpart under g.

` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` `
` ` ` ` ` ` ` U ` ` ` ` ` ` ` f ` ` ` ` ` ` ` V ` ` ` ` ` ` `
` ` ` ` ` ` ` O ` ` --------------------> ` ` O ` ` ` ` ` ` `
` ` ` ` ` ` `/`\` ` ` ` ` ` ` ` ` ` ` ` ` ` `/`\` ` ` ` ` ` `
` ` ` ` ` ` / ` \ ` ` ` ` ` ` ` ` ` ` ` ` ` / ` \ ` ` ` ` ` `
` ` ` ` ` `/` ` `\` ` ` ` ` ` ` ` ` ` ` ` `/` ` `\` ` ` ` ` `
` ` ` ` ` / ` ` ` \ ` ` ` ` ` ` ` ` ` ` ` / ` ` ` \ ` ` ` ` `
` ` ` ` `/` ` ` ` `\` ` ` ` ` g ` ` ` ` `/` ` ` ` `\` ` ` ` `
` ` ` ` o ` `...` ` o ` ` --------> ` ` o ` `...` ` o ` ` ` `
` ` ` `/`\` ` ` ` `/`\` ` ` ` ` ` ` ` `/`\` ` ` ` `/`\` ` ` `
` ` ` / ` \ ` ` ` / ` \ ` ` ` ` ` ` ` / ` \ ` ` ` / ` \ ` ` `
` ` `/` ` `\` ` `/` ` `\` ` ` ` ` ` `/` ` `\` ` `/` ` `\` ` `
` ` o->-o->-o ` o->-o->-o ` ` ` ` ` o->-o->-o ` o->-o->-o ` `
` ` `\` ` ` ` ` ` ` ` ` ` ` ` ` ` `/` ` ` ` ` ` ` ` ` ` ` ` `
` ` ` \ ` ` ` ` ` ` ` ` ` ` ` ` ` / ` ` ` ` ` ` ` ` ` ` ` ` `
` ` ` `\` ` ` ` ` ` ` ` ` ` ` ` `/` ` ` ` ` ` ` ` ` ` ` ` ` `
` ` ` ` \ ` ` ` ` ` ` ` ` ` ` ` / ` ` ` ` ` ` ` ` ` ` ` ` ` `
` ` ` ` `\` ` ` ` h_j ` ` ` ` `/` ` ` ` ` ` ` ` ` ` ` ` ` ` `
` ` ` ` ` o-------->----------o ` ` ` ` ` ` ` ` ` ` ` ` ` ` `
` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` `

Next time we'll apply this general scheme to the
En and Ex interpretations of logical graphs, and
see how it helps us to sort out the varieties of
iconic mapping that are involved in that setting.

Jon Awbrey

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inquiry e-lab: http://stderr.org/pipermail/inquiry/
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