This paper proposes a definition of the reference relation which casts new light on the theory of reference in semiotics, on the theory of relations in logic, and on the theory of rhythm in music.
KeywordsConstructional Method Reference Relation Joint Limit Open Sentence Constructional Format
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- 1.Summarized under the heading ‘Basic Musicianship’ in the National Association of Schools of Music Handbook for examiners.Google Scholar
- 2.Research during the past decade in comprehensive music theory, yielding several papers in aesthetics, a monograph in progress relating music theory to logic and semiotics, and an introductory textbook going to press in 1981 (“Comprehending Music”; New York, Schirmer Books).Google Scholar
- 3.Envisioned in the seventeenth century by Leibniz as Characteristica Universalis adumbrated in the nineteenth century by Ernst Mach in “The Analysis of Sensations” (Jena, 1886), explicitly named and developed in the twentieth century by Bertrand Russell in “Principia Mathematica” (Cambridge, 1910–13) and “Our Knowledge of the External World” (Chicago, 191+), continued and refined by Rudolf Carnap in “The Logical Construction of the World” (Berlin, 1928), which served as the point of departure for Nelson Goodman’s “The Structure of Appearance” (Indianapolis, 1951), but never before to my knowledge used to construc theorists today t a music theory, although some music are using symbolic logic.Google Scholar
- 4.Discovered by Peirce in papers of about 1880 and 1902 but not published until 1933; meanwhile independently discovered by Sheffer in 1913; ever since then a standard logical notion.Google Scholar
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- 6.cf. Prior, Philosophy A.N.: “Negation” in The Encyclopedia of Philosophy; New York, 1967; volume 5, pages 458–463.Google Scholar
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- 8.These sy mbols are used by W.V. Quine in “Set Theory and Its Logic” (Cambridge, Mass., 1969; revised editio n, formula 9.6, page 62) for a two-termed relati on; we adapt them to singular relational terms but d o not thereby assume that a singular relational term might be defined as a form of self-reference, <x, x> , since this might confuse °x’A,A with x’A, A.Google Scholar