Charles Sanders Peirce - His "remarkable theorem" regarding triadic relations


This remarkable text is drawn from Joseph Brent, 
Charles Sanders Peirce: A Life 
Blomington and Indianapolis 1993
Page 331

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"There are only three fundamental kinds of relations:
monadic, dyadic and triadic; ... 
by combining triads, all relations
greater than the number  three
can be generated; and ...
all those of a greater number than three
can be reduced to triads.
Since, in addition, 
triads cannot be reduced to dyads,
nor dyads to monads,
monads, dyads and triads
constitute the fundamental categories of relations.
At the same time, triads are made up of
dyads and monads,
and dyads of monads.
Hence, in logical order,
monads are first,
dyads second,
and triads third.,
which gives a second group of relations:
first, second, and third.
Hypostatic abstraction provides
a third group of relations:
firstness, secondness, and thirdness,
which contain first second and third,
which in turn contain monads, dyads, and triads.
Altogether, these elements constitute
the abstract,formal mathematical categories
and relations
that constitute the elements of thought."

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