Peirce’s 1870 “Logic of Relatives” • Selection 9

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

Peirce’s 1870 “Logic of Relatives”Selection 9

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)


  • Peirce, C.S. (1870), “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 of Arts and Sciences 9, 317–378, 26 January 1870.  Reprinted, Collected Papers 3.45–149, Chronological Edition 2, 359–429.  Online (1) (2) (3).
  • Peirce, C.S., Collected Papers of Charles Sanders Peirce, vols. 1–6, Charles Hartshorne and Paul Weiss (eds.), vols. 7–8, Arthur W. Burks (ed.), Harvard University Press, Cambridge, MA, 1931–1935, 1958.
  • Peirce, C.S., Writings of Charles S. Peirce : A Chronological Edition, Peirce Edition Project (eds.), Indiana University Press, Bloomington and Indianapolis, IN, 1981–.


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7 Responses to Peirce’s 1870 “Logic of Relatives” • Selection 9

  1. Pingback: Survey of Relation Theory • 3 | Inquiry Into Inquiry

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