## Relations & Their Relatives • 2

What is the relationship between “logical relatives” and “mathematical relations”?  The word relative used as a noun in logic is short for relative term — as such it refers to an item of language used to denote a formal object.

What kind of object is that?  The way things work in mathematics we are free to make up a formal object corresponding directly to the term, so long as we can form a consistent theory of it, but it’s probably easier and more practical in the long run to relate the relative term to the kinds of relations ordinarily treated in mathematics and universally applied in relational databases.

In those 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 $(x_1, x_2, \ldots, x_{k-1}, x_k)$ in the form $x_1 : x_2 : \ldots : x_{k-1} : x_k$ and referred to them as elementary $k$-adic relatives.  He treated a collection of $k$-tuples as a logical aggregate or logical sum and often regarded them as being arranged in $k$-dimensional arrays.

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

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