Re: Relations & Their Relatives

It may help to clarify the relationship between logical relatives
and mathematical relations.  The word =93relative=94 as used in logic
is short for =93relative term=94 =97 as such it refers to an article of
language that is used to denote a formal object.  So what kind of
object is that?  The way things work in mathematics, we are free
to make up a formal object that corresponds directly to the term,
so long as we can form a consistent theory of it, but it's easier
and more practical in the long run to relate the relative term to
the kinds of relations that are ordinarily treated in mathematics
and universally applied in relational databases.

In these contexts a relation is just a set of ordered tuples
and, if you are a fan of strong typing like I am, such a set
is always set in a specific setting, namely, it's a subset
of a specified Cartesian product.

Peirce wrote k-tuples (x_1, x_2, ..., x_(k-1), x_k) in the form
x_1 : x_2 : ... : x_(k-1) : x_k and referred to them as elementary
k-adic relatives.  He expressed a set of k-tuples as a =93logical sum=94
or =93logical aggregate=94, what we would call a logical disjunction of
these elementary relatives, and he frequently regarded them as being
arranged in the form of k-dimensional arrays.

Time for some concrete examples, which I will give in the next post ...

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