Questions Concerning Certain Faculties Claimed For Signs

Re: Peirce List (1) (2) (3) • Helmut Raulien

Looking back over many previous discussions, I think one of the main things keeping people from being on the same page, or even being able to understand what others write on their individual pages, is the question of what makes a relation.

There’s a big difference between a single ordered tuple, say, and a whole set of ordered tuples that it takes to make up a -place relation.  The language we use to get a handle on the structure of relations goes like this:

Say the variable ranges over the set
and the variable ranges over the set

and the variable ranges over the set

Then the set of all possible -tuples ranges over a set notated as and called the “cartesian product” of the “domains” to

There are two different ways in common use of defining a -place relation.

1. Some define a relation on the domains to as a subset of the cartesian product in symbols,
2. Others like to make the domains of the relation an explicit part of the definition, saying that a relation is a list of domains plus a subset of their cartesian product.

Sounds like a mess but it’s usually pretty easy to translate between the two conventions, so long as one watches out for the difference.

By way of a geometric image, the cartesian product may be viewed as a space in which many different relations reside, each one cutting a different figure in that space.

To be continued …

Resources

• Peirce’s 1870 Logic Of Relatives : The Wiki Article
• Peirce’s 1870 Logic Of Relatives : The Series Pilot

cc: Peirce List (1) (2) (3)