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Revision as of 17:58, 9 April 2009
, 17:58, 9 April 2009→Commentary Note 10.1
===Commentary Note 10.1===
===Commentary Note 10.1===
What Peirce is attempting to do in CP 3.75 is absolutely amazing, and I personally did not see anything on par with it again until I began to study the application of mathematical category theory to computation and logic, back in the mid 1980's. To completely evaluate the success of this attempt, we would have to return to Peirce's earlier paper "Upon the Logic of Mathematics" (1867) to pick up some of the ideas about arithmetic that he set out there.
What Peirce is attempting to do in CP 3.75 is absolutely amazing, and I personally did not see anything on par with it again until I began to study the application of mathematical category theory to computation and logic, back in the mid 1980's. To completely evaluate the success of this attempt we would have to return to Peirce's earlier paper "Upon the Logic of Mathematics" (1867) to pick up some of the ideas about arithmetic that he set out there.
Another branch of the investigation would require that we examine more careully the entire syntactic mechanics of "subjacent signs" that Peirce uses to establish linkages among relational domains. It is important to note that these types of indices constitute a diacritical, interpretive, syntactic category under which Peirce also places the comma functor.
Another branch of the investigation would require that we examine more carefully the entire syntactic mechanics of ''subjacent signs'' that Peirce uses to establish linkages among relational domains. It is important to note that these types of indices constitute a diacritical, interpretive, syntactic category under which Peirce also places the comma functor.
The way that I would currently approach both of these branches of the investigation would be to open up a wider context for the study of relational compositions, attempting to get at the essence of what is going on we when relate relations, possibly complex, to other relations, possibly simple.
The way that I would currently approach both of these branches of the investigation would be to open up a wider context for the study of relational compositions, attempting to get at the essence of what is going on we when relate relations, possibly complex, to other relations, possibly simple.
===Commentary Note 10.2===
===Commentary Note 10.2===
