Peirce's 1870 “Logic Of Relatives ” • Selection 9

Post   : Peirce's 1870 “Logic Of Relatives” • Selection 9
http://inquiryintoinquiry.com/2014/02/23/peirces-1870-logic-of-relatives-%e2%80%a2-selection-9/
Posted : February 23, 2014 at 11:30 pm
Author : Jon Awbrey

We continue with §3. Application of the Algebraic Signs to Logic.

<quote>

The Signs for Multiplication (cont.)

It is obvious that multiplication into a multiplicand
indicated by a comma is commutative,[1] that is,

s,l  =  l,s

This multiplication is effectively the same as that of
Boole in his logical calculus.  Boole's unity is my 1,
that is, it denotes whatever is.

1.  It will often be convenient to speak of the whole operation of affixing a comma and then
multiplying as a commutative multiplication, the sign for which is the comma.  But though this is
allowable, we shall fall into confusion at once if we ever forget that in point of fact it is not a
different multiplication, only it is multiplication by a relative whose meaning — or rather whose
syntax — has been slightly altered;  and that the comma is really the sign of this modification of
the foregoing term.

(Peirce, CP 3.74)

</quote>

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