[Inquiry] Re: Logic Of Relatives

[Jon Awbrey]

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LOR.  Note 36

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As Peirce observes, it is not possible to work with
relations in general without eventually abandoning
all of one's algebraic principles, in due time the
associative and maybe even the distributive, just
as we have already left behind the commutative.
It cannot be helped, as we cannot reflect on
a law if not from a perspective outside it,
that is to say, at any rate, virtually so.

One way to do this would be from the standpoint of the combinator calculus,
and there are places where Peirce verges on systems that are very similar,
but I am making a deliberate effort to remain here as close as possible
within the syntactoplastic chronism of his 1870 Logic of Relatives.
So let us make use of the smoother transitions that are afforded
by the paradigmatic Figures and Tables that I drew up earlier.

For the next few episodes, then, I will examine the examples
that Peirce gives at the next level of complication in the
multiplication of relative terms, for instance, the three
that I have redrawn below.

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|                                                 |
|                                                 |
|         `g`__$__%    $'l'__*   *w   %h          |
|              o  o    o     o   o    o           |
|               \  \  /       \ /    /            |
|                \  \/         @    /             |
|                 \ /\______ ______/              |
|                  @        @                     |
|                                                 |
|                                                 |
o-------------------------------------------------o
Figure 6.  Giver of a Horse to a Lover of a Woman

o-------------------------------------------------o
|                                                 |
|                                                 |
|         `g`__$__%    $'o'__*   *%h              |
|              o  o    o     o   oo               |
|               \  \  /       \ //                |
|                \  \/         @/                 |
|                 \ /\____ ____/                  |
|                  @      @                       |
|                                                 |
|                                                 |
o-------------------------------------------------o
Figure 7.  Giver of a Horse to an Owner of It

o-------------------------------------------------o
|                                                 |
|                                                 |
|        'l',__$__%    $'s'__*   *%w              |
|              o  o    o     o   oo               |
|               \  \  /       \ //                |
|                \  \/         @/                 |
|                 \ /\____ ____/                  |
|                  @      @                       |
|                                                 |
|                                                 |
o-------------------------------------------------o
Figure 8.  Lover that is a Servant of a Woman

Jon Awbrey

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