[Inquiry] Re: Relatives Of Second Intention

[Jon Awbrey]

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ROSI.  Note 8

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| Classification of Simple Relatives (cont.)
|
| e.  The fifth division is into relatives some power (i.e. repeated product)
|     of which contains* elements of the form (A:A), and those of which this
|     is not true.  The former I term 'cyclic', the latter 'non-cyclic'*
|     relatives.  As an example of the former, take
|
|        (A:B) +, (B:A) +, (C:D) +, (D:E) +, (E:C).
|
|     The product of this into itself is
|
|        (A:A) +, (B:B) +, (C:E) +, (D:C) +, (E:D).
|
|     The third power is
|
|        (A:B) +, (B:A) +, (C:C) +, (D:D) +, (E:E).
|
|     The fourth power is
|
|        (A:A) +, (B:B) +, (C:D) +, (D:E) +, (E:C).
|
|     The fifth power is
|
|        (A:B) +, (B:A) +, (C:E) +, (D:C) +, (E:D).
|
|     The sixth power is
|
|        (A:A) +, (B:B) +, (C:C) +, (D:D) +, (E:E),
|
|     where all the terms are of the form (A:A).
|     Such relatives, as 'cousin of __' are cyclic.
|     All equiparants are cyclic.
|
|* [Marginal Note] "Insert 'only' between contains and
|  'elements';  for 'non-cyclic' substitute 'acyclic'"
|
| C.S. Peirce, CP 3.136
|
| C.S. Peirce,
|"Description of a Notation for the Logic of Relatives,
| Resulting from an Amplification of the Conceptions of Boole's Calculus of Logic",
|'Memoirs of the American Academy', Volume 9, pages 317-378, 26 January 1870,
|'Collected Papers' (CP 3.45-149), 'Chronological Edition' (CE 2, 359-429).

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