Changes

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

Before I can discuss Peirce's "number of" function in greater detail I will need to deal with an expositional difficulty that I have been very carefully dancing around all this time, but that 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 2-adic relations, so the "number of" function itself is already to be numbered among the types of 2-adic relatives that we've been explictly mentioning and implicitly using all this time.  But Peirce's way of talking about a 2-adic relative term is to list the "relate" first and the "correlate" second, a convention that goes over into functional terms as making the functional value first and the functional antecedent second, whereas almost anyone brought up in our present time frame has difficulty thinking of a function any other way than as a set of ordered pairs where the order in each pair lists the functional argument, or domain element, first and the functional value, or codomain element, second.

Functions have long been understood, from well before Peirce's time to ours, as special cases of 2-adic relations, so the "number of" function itself is already to be numbered among the types of 2-adic relatives that we've been explictly mentioning and implicitly using all this time.  But Peirce's way of talking about a 2-adic relative term is to list the "relate" first and the "correlate" second, a convention that goes over into functional terms as making the functional value first and the functional argument second, whereas almost anyone brought up in our present time frame has difficulty thinking of a function any other way than as a set of ordered pairs where the order in each pair lists the functional argument first and the functional value second.

It is possible to work all this out in a very nice way within a very general context of flexible conventions, but not without introducing an order of anachronisms into Peirce's presentation that I am presently trying to avoid as much as possible.  Thus, I will need to experiment with various sorts of compromise formations.

It is possible to work all this out in a very nice way within a very general context of flexible conventions, but not without introducing an order of anachronisms into Peirce's presentation that I am presently trying to avoid as much as possible.  Thus, I will need to experiment with various types of compromise formations.

===Commentary Note 11.3===

===Commentary Note 11.3===