Two points:

1. It is certainly true that you can map A gives B to C into a form that uses only dyadic relation.

2. But Peirce was trying to explain that you have simply converted one triad into a triad of a different form.

I'll just use predicate calculus notation, since it's easy to type.  But the point is obvious when you use a graph notation.

With a triadic relation:

     gives(A,B,C)

With three dyadic relations and a monadic relation give(x):

     (Ex) give(x) & agent(x,A) & theme(x,B) & recipient(x,C)

In the first version, you have a triadic connection of A, B, and C to the relation named gives.

In the second version, you have a triadic connection of A to agent to give, B to theme to give, and C to recipient to give.

You still have a triad, but the central node is called give instead of gives.

John

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