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Directory:Jon Awbrey/Papers/Peirce's 1870 Logic Of Relatives (view source)
Revision as of 19:45, 23 October 2007
, 19:45, 23 October 2007→Commentary Note 10.2: markup
===Commentary Note 10.2===
===Commentary Note 10.2===
To say that a relative term "imparts a relation" is to say that it conveys information about the space of tuples in a cartesian product, that is, it determines a particular subset of that space.
To say that a relative term "imparts a relation"
is to say that it conveys information about the
space of tuples in a cartesian product, that is,
it determines a particular subset of that space.
When we study the combinations of relative terms, from the most
When we study the combinations of relative terms, from the most elementary forms of composition to the most complex patterns of correlation, we are considering the ways that these constraints, determinations, and informations, as imparted by relative terms, can be compounded in the formation of syntax.
elementary forms of composition to the most complex patterns of
correlation, we are considering the ways that these constraints,
determinations, and informations, as imparted by relative terms,
can be compounded in the formation of syntax.
Let us go back and look more carefully at just how it happens that
Let us go back and look more carefully at just how it happens that Peirce's jacent terms and subjacent indices manage to impart their respective measures of information about relations.
Peirce's jacent terms and subjacent indices manage to impart their
respective measures of information about relations.
I will begin with the two examples illustrated in Figures 1 and 2,
I will begin with the two examples illustrated in Figures 1 and 2, where I have drawn in the corresponding lines of identity between the subjacent marks of reference #, $, %.
where I have drawn in the corresponding lines of identity between
the subjacent marks of reference #, $, %.
<pre>
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Figure 1. Lover of a Servant of a Woman
Figure 1. Lover of a Servant of a Woman
</pre>
<pre>
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Figure 2. Giver of a Horse to a Lover of a Woman
Figure 2. Giver of a Horse to a Lover of a Woman
</pre>
One way to approach the problem of "information fusion"
One way to approach the problem of "information fusion" in Peirce's syntax is to soften the distinction between jacent terms and subjacent signs, and to treat the types of constraints that they separately signify more on a par with each other.
in Peirce's syntax is to soften the distinction between
jacent terms and subjacent signs, and to treat the types
of constraints that they separately signify more on a par
with each other.
To that purpose, I will set forth a way of thinking about
To that purpose, I will set forth a way of thinking about relational composition that emphasizes the set-theoretic constraints involved in the construction of a composite.
relational composition that emphasizes the set-theoretic
constraints involved in the construction of a composite.
For example, suppose that we are given the relations L c X x Y, M c Y x Z.
For example, suppose that we are given the relations ''L'' ⊆ ''X'' × ''Y'', ''M'' ⊆ ''Y'' × ''Z''. Table 3 and Figure 4 present a couple of ways of picturing the constraints that are involved in constructing the relational composition ''L'' o ''M'' ⊆ ''X'' × ''Z''.
Table 3 and Figure 4 present a couple of ways of picturing the constraints
that are involved in constructing the relational composition L o M c X x Z.
<pre>
Table 3. Relational Composition
Table 3. Relational Composition
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