Peirce’s 1870 “Logic of Relatives” • Comment 11.3

Peirce’s 1870 “Logic of Relatives”Comment 11.3

Before I can discuss Peirce’s “number of” function in greater detail I will need to deal with an expositional difficulty I have been carefully dancing around all this time, but one which will no longer abide its assigned place under the rug.

Functions have long been understood, from well before Peirce’s time to ours, as special cases of dyadic relations, so the “number of” function is already to be numbered among the class of dyadic relatives we’ve been dealing with all this time.  But Peirce’s manner of representing a dyadic relative term mentions the “rèlate” first and the “correlate” second, a convention going over into functional terms as making the functional value first and the functional argument second.  The problem is, almost anyone brought up in our present time frame is accustomed to thinking of a function as a set of ordered pairs where the order in each pair lists the functional argument first and the functional value second.

Syntactic wrinkles of this sort can be ironed out smoothly enough in a framework of flexible interpretive conventions, but not without introducing an order of anachronism into Peirce’s text I want to avoid as much as possible.  This will require me to experiment with various styles of compromise.  Among other things, the interpretation of Peirce’s 1870 “Logic of Relatives” can be facilitated by introducing a few items of background material on relations in general, as regarded from a combinatorial point of view.

Resources

cc: CyberneticsOntolog ForumStructural ModelingSystems Science
cc: FB | Peirce MattersLaws of Form • Peirce List (1) (2) (3) (4) (5) (6) (7)

This entry was posted in C.S. Peirce, Logic, Logic of Relatives, Logical Graphs, Mathematics, Relation Theory, Visualization and tagged , , , , , , . Bookmark the permalink.

5 Responses to Peirce’s 1870 “Logic of Relatives” • Comment 11.3

  1. Pingback: Survey of Relation Theory • 3 | Inquiry Into Inquiry

  2. Pingback: Peirce’s 1870 “Logic Of Relatives” • Overview | Inquiry Into Inquiry

  3. Pingback: Peirce’s 1870 “Logic Of Relatives” • Comment 1 | Inquiry Into Inquiry

  4. Pingback: Survey of Relation Theory • 4 | Inquiry Into Inquiry

  5. Pingback: Survey of Relation Theory • 5 | Inquiry Into Inquiry

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s

This site uses Akismet to reduce spam. Learn how your comment data is processed.