Logic of Relatives

[Jon Awbrey]

Logic of Relatives
• https://inquiryintoinquiry.com/2024/08/05/logic-of-relatives-a/

Relations Via Relative Terms —

The logic of relatives is the study of relations
as represented in symbolic forms known as rhemes,
rhemata, or relative terms.

Introduction —

The logic of relatives, more precisely, the logic of relative terms,
is the study of relations as represented in symbolic forms called
rhemes, rhemata, or relative terms. The treatment of relations
by way of their corresponding relative terms affords a distinctive
perspective on the subject, even though all angles of approach must
ultimately converge on the same formal subject matter.

The consideration of relative terms has its roots in antiquity
but it entered a radically new phase of development with the
work of Charles Sanders Peirce, beginning with his paper
“Description of a Notation for the Logic of Relatives,
Resulting from an Amplification of the Conceptions
of Boole's Calculus of Logic” (1870).

References —

• Peirce, C.S., “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, 1870. Reprinted, Collected Papers CP 3.45–149. Reprinted,
Chronological Edition CE 2, 359–429.
• https://www.jstor.org/stable/25058006
• https://archive.org/details/jstor-25058006
• https://books.google.com/books?id=fFnWmf5oLaoC

Readings —

• Aristotle, “The Categories”, Harold P. Cooke (trans.),
pp. 1–109 in Aristotle, Vol. 1, Loeb Classical Library,
William Heinemann, London, UK, 1938.

• Aristotle, “On Interpretation”, Harold P. Cooke (trans.),
pp. 111–179 in Aristotle, Vol. 1, Loeb Classical Library,
William Heinemann, London, UK, 1938.

• Aristotle, “Prior Analytics”, Hugh Tredennick (trans.),
pp. 181–531 in Aristotle, Vol. 1, Loeb Classical Library,
William Heinemann, London, UK, 1938.

• Boole, George, An Investigation of the Laws of Thought
on Which are Founded the Mathematical Theories of Logic
and Probabilities, Macmillan, 1854. Reprinted with
corrections, Dover Publications, New York, NY, 1958.

• 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,
Volume 2, 1867–1871, Peirce Edition Project (eds.), Indiana University
Press, Bloomington, IN, 1984. Cited as CE 2.

Resources —

Charles Sanders Peirce
• https://mywikibiz.com/Charles_Sanders_Peirce

Relation Theory
• https://oeis.org/wiki/Relation_theory

Survey of Relation Theory
• https://inquiryintoinquiry.com/2024/03/23/survey-of-relation-theory-8/

Peirce's 1870 Logic of Relatives
• https://oeis.org/wiki/Peirce%27s_1870_Logic_Of_Relatives_%E2%80%A2_Overview

Regards,

Jon

cc: https://www.academia.edu/community/5AEQjj