[Inquiry] Re: Logic Of Relatives

[Jon Awbrey]

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LOR.  Note 7

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| The Signs for Multiplication (cont.)
|
| The associative principle does not hold in this counting
| of factors.  Because it does not hold, these subjacent
| numbers are frequently inconvenient in practice, and
| I therefore use also another mode of showing where
| the correlate of a term is to be found.  This is
| by means of the marks of reference, † ‡ || § ¶,
| which are placed subjacent to the relative
| term and before and above the correlate.
| Thus, giver of a horse to a lover of
| a woman may be written:
|
| `g`_†‡ †'l'_|| ||w ‡h.
|
| The asterisk I use exclusively to refer to the last
| correlate of the last relative of the algebraic term.
|
| Now, considering the order of multiplication to be: --
| a term, a correlate of it, a correlate of that correlate,
| etc. -- there is no violation of the associative principle.
| The only violations of it in this mode of notation are that
| in thus passing from relative to correlate, we skip about
| among the factors in an irregular manner, and that we
| cannot substitute in such an expression as `g`'o'h
| a single letter for 'o'h.
|
| I would suggest that such a notation may be found useful in treating other
| cases of non-associative multiplication.  By comparing this with what was
| said above [in CP 3.55] concerning functional multiplication, it appears
| that multiplication by a conjugative term is functional, and that the
| letter denoting such a term is a symbol of operation.  I am therefore
| using two alphabets, the Greek and Kennerly, where only one was
| necessary.  But it is convenient to use both.
|
| C.S. Peirce, CP 3.71-72
|
| Charles Sanders 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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