## Peirce’s 1870 “Logic Of Relatives” • Selection 9

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

### The Signs for Multiplication (cont.)

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

$\mathit{s},\!\mathit{l} ~=~ \mathit{l},\!\mathit{s}$

This multiplication is effectively the same as that of Boole in his logical calculus.  Boole’s unity is my $\mathbf{1},$ 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)

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