[Inquiry] Re: Relatives Of Second Intention

[Jon Awbrey]

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ROSI.  Note 13

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| Let 'A', 'B', 'C', etc., denote objects of any kind.  These letters may be
| conceived to be finite or innumerable.  The sum of them, each affected by a
| numerical coefficient (which may be equal to 0), is called an 'absolute term'.
| Let 'x' be such a term;  then we write
|
|    'x'  =  ('x')_a 'A' + ('x')_b 'B' + ('x')_c 'C' + etc.  =  Sum_i ('x')_i 'I'.
|
| Here ('x'), etc., are numbers, which may be permitted to be imaginary
| or restricted to being real or positive, or to being roots of any given
| equation, algebraic or transcendental.  ...
|
| Two peculiar absolute terms are suggested by the logic
| of the subject.  I call them terms of second intention.
| The first is zero, 0, and is defined by the equation
|
|    (0)_i  =  0
|
|        or
|
|     0  =  0.'A' + 0.'B' + 0.'C' + etc.
|
| The other is 'ens' (or non-relative unity), ~0,
| and is defined by the equation
|
|    (~0)_i  =  1
|
|        or
|
|     ~0  =  'A' + 'B' + 'C' + etc.
|
| C.S. Peirce, 'Collected Papers', CP 3.306-307
|
|"Brief Description of the Algebra of Relatives", privately printed, pp. 1-6,
| January 7, 1882, with a postscript dated January 16, 1882, Baltimore, MD.
|'Collected Papers' (CP 3.306-322), 'Chronological Edition' (CE 4, 328-333).

NB.  In this transcription I use "Sum" for Greek Sigma
     and "~0" where Peirce uses "0" with a bar over it.

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