Peirce often stressed his Logic of Relatives as the key to unlocking many puzzles.  As I read him, it was Peirce’s drive to understand the Logic of Science that required the grounding of logic in the mathematical forms of triadic sign relations and this in turn demanded a leap forward in the understanding of relations in general.

My long ago encounter with Peirce’s 1870 paper, “Description of a Notation for the Logic of Relatives, Resulting from an Amplification of the Conceptions of Boole’s Calculus of Logic”, was one of the events precipitating my return from the hazier heights of philosophy to the solid plains of mathematics below.  Over the years I copied out various drafts of my study notes to the web, consisting of selections from Peirce’s paper along with my running commentary.  A few years back I serialized what progress I had made so far to this blog and this Overview consists of links to those installments.

Peirce’s 1870 “Logic of Relatives”

• Preliminaries
• Selection 1 • Use of the Letters
• Selection 2 • Numbers Corresponding to Letters
• Selection 3 • The Signs of Inclusion, Equality, Etc.
• Selection 4 • The Signs for Addition
• Selection 5 • The Signs for Multiplication
• Selection 6 • The Signs for Multiplication (cont.)
  • Comment 6.1 • Sets as Sums
• Selection 7 • The Signs for Multiplication (cont.)
  • Comment 7.1 • Proto-Graphical Syntax
• Selection 8 • The Signs for Multiplication (cont.)
  • Comment 8.1
  • Comment 8.2
  • Comment 8.3
  • Comment 8.4
  • Comment 8.5
  • Comment 8.6
• Selection 9 • The Signs for Multiplication (cont.)
  • Comment 9.1
  • Comment 9.2
  • Comment 9.3
  • Comment 9.4
  • Comment 9.5
  • Comment 9.6
  • Comment 9.7
• Selection 10 • The Signs for Multiplication (cont.)
  • Comment 10.1
  • Comment 10.2
  • Comment 10.3
  • Comment 10.4
  • Comment 10.5
  • Comment 10.6
  • Comment 10.7
  • Comment 10.8
  • Comment 10.9
  • Comment 10.10
  • Comment 10.11
  • Comment 10.12
• Selection 11 • The Signs for Multiplication (concl.)
  • Comment 11.1
  • Comment 11.2
  • Comment 11.3
  • Comment 11.4
  • Comment 11.5
  • Comment 11.6
  • Comment 11.7
  • Comment 11.8
  • Comment 11.9
  • Comment 11.10
  • Comment 11.11
  • Comment 11.12
  • Comment 11.13
  • Comment 11.14
  • Comment 11.15
  • Comment 11.16
  • Comment 11.17
  • Comment 11.18
  • Comment 11.19
  • Comment 11.20
  • Comment 11.21
  • Comment 11.22
  • Comment 11.23
  • Comment 11.24
• Selection 12 • The Sign of Involution
• Comment 12.1
• Comment 12.2
• Comment 12.3
• Comment 12.4
• Comment 12.5
• Intermezzo

References

• 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 (CP 3.45–149), Chronological Edition (CE 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.  Cited as (CP volume.paragraph).
• Peirce, C.S., Writings of Charles S. Peirce : A Chronological Edition, Peirce Edition Project (eds.), Indiana University Press, Bloomington and Indianapolis, IN, 1981–.  Cited as (CE volume, page).

Resources

• Peirce’s 1870 Logic of Relatives

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