THE FIFTH WORLD CONGRESS ON ANALOGY
APRIL 13-17, 2027 CRETE, GREECE
@Marcin Sokalski
Marcin GMYS
Editor-in-chief of Copernicus. De Musica
Editor-in-chief of Res Facta Nova (2014–2021)
Director of Polish Radio Chopin (2017–2024)
Institute of Musicology, Faculty of Art Sciences, Adam Mickiewicz University, Poznań, Poland
From Structural Analogy to Metaphor. A Musical Perspective
(This talk was planned to be presented at the Fourth World Congress on Analogy)
ABSTRACT
The process of creating a structural analogy, which may not seem so obvious at first glance, is one of the most important compositional strategies in the history of music. Already, after all, the counterpoint technique, which is based on carrying out the initial theme (dux) in close or free imitation (comes), is in fact, if one may put it that way, a structural analogy in musical action. The first part of the text will discuss instances of the more interesting structural analogies in musical masterpieces from the 19th to the 21st century. One of the most difficult structural analogies to decipher in the history of music turned out to be Beethoven’s strategy employed by him in the String Quartet in C sharp minor, Op. 131 (1826), which waited 140 years for its decipherment (it was only identified by Joseph Kerman in his 1967 monograph The Beethoven Quartets). Then, echoes of the structural analogy of this quartet in the novel Immortality (1988) by Milan Kundera and in the String Quartet “Arcadiana” (1994) by Thomas Adès will be shown. Here, too, the question of structural analogy in symphonies and chamber music written according to the scheme of per aspera ad astra dramaturgy will be addressed. In the second part of the text, situations will be presented in which structural analogies become components of the metaphorization processes that form the semantic core of musical compositions. Two masterpieces will be chosen as examples – Gustav Mahler’s Symphony No. 7 (1904-1905) and Ferruccio Busoni’s opera Doktor Faust (1918-1924). Each of these scores in a completely different way (the media used by both composers are distinct), but each time through a structural analogy becomes a metaphor for the idea of eternal return outlined by Friedrich Nietzsche in his book Thus Spoke Zarathustra.
@Bartosz Kałużny
Andrzej INDRZEJCZAK
University of Łódź, Poland
Head of the Department of Logic and Methodology of Science
Editor-in-Chief of Bulletin of the Section of Logic
Chairman of the Editorial Board of Studia Logica
The Role of Analogy in Proof Theory
ABSTRACT
Proof theory is concerned, among other things, with the analysis of the notion of proof and the construction of different kinds of formal systems. So far the notion of analogy was not dealt with in this area. In particular, no formal systems devoted to the analysis of reasoning by analogy were provided. However, analogy itself plays an important role in the construction of deductive systems. In the talk we provide some illustrations of the use of analogy in finding well-behaved rules for new kinds of deductive systems. In particular, we focus on the problem of formalization of term-forming operators, an area of proof theory which is recently dynamically developed.
@Anne-Françoise Schmid
Anne-Françoise SCHMID
Chaire de Théorie et Méthodes de la conception innovante (Mines Paris Tech), Paris, France
Archives Poincaré (UMR 7117 du CNRS), Nancy, France
Can We Think Without Analogy?
ABSTRACT
It is known that during the Gallic Wars, Caesar dictated a treatise titled *De analogia*, which has unfortunately been lost. It was a treatise on stylistics defending Atticism against Cicero’s Asianism—a form of simplicity, such as “Flumen est Arar.”
On the other hand, can we connect the “ana” of analogy (an ascent, akin to the arsis in music, as Michaël Levinas does) to the “kata” of the catalog (the descent into multiplicity: there is no catalog for a single item)?
To think without analogy would be to follow a single attribute without encounter (Deleuze); it would be the path of madness with no possibility of reversal (Deleuze had told Laruelle, at the café near the former National Library of France: “Stupidity is infinite, but it is reversible”).
Thinking without analogy would consist in the hallucinatory dream of thinking without multiplicity or return. One ascends, and remains at the top, like the stylite, and the return could only be a fall, and not the thesis of the musician-composer. The fall is thus avoided by style.
Analogy, then, deals with multiplicity and style. It is up to us to invent their connections.
Click here for a French version of the abstract.
@Yuko Abe
Marcin J. SCHROEDER
Professor Emeritus, Akita International University (AIU), Japan
Editor-in-Chief of the journal Philosophies (MDPI)
Vice-President for Research (former President 2019-2021) of the International Society for the Study of Information (IS4SI)
Academic President of the International Society for Interdisciplinary Studies of Symmetry (SIS)
From Analogy to Abstraction
ABSTRACT
It may be surprising that one of the most fundamental ideas, that of similarity (here understood as a synonym of analogy), still generates confusion not only among lay people but among philosophers and scientists. This confusion cannot be blamed on the negligence of mathematics, where similarity relations, called tolerance relations, have extensive literature [1], although their mathematical formalization is rather a newcomer, going not much further than half a century [2]. We can only speculate that the choice of the term “tolerance relation” by Christopher Zeeman, who was one of the earliest mathematicians formalizing similarity at the beginning of the 1960s, contributed to the very limited popularity of and interest in the mathematical theory of similarity. There is a surprising contrast between the status of equivalence relations (a special case of transitive tolerance relations) taught already in early mathematical education and present in virtually all mathematical theories, and general tolerance relations unknown to many mathematicians working outside of general algebra, who believe that such a general concept cannot have interesting properties. On the other hand, Ludwig Wittgenstein’s idea of Familienähnlichkeit, which he expressed in English as “family likeness” [3,4], gave new meaning to the concept of "family resemblance" already present in literature, now commonly associated with Wittgenstein, and promoted similarity to a slightly mysterious concept, but with central status in philosophy [5]. Wittgenstein referred to family likeness as a tool to dethrone equivalence relations as the main language tool for concept construction, categorization, and abstraction. Thus, while the mathematical formalization of similarity, which started at the beginning of the 1960s, has been marginalized as a legitimate mathematical research topic but only of secondary importance, in philosophy, similarity rose at the end of the 1950s to the central philosophical concept generating many discussions and inquiries carried out within the study of language on its role in cognition. This direction of inquiry, consistent with the spirit of Wittgenstein’s thought, avoided formalization but lost control over the conceptual framework. The present work is intended as a bridge between the mathematical formalism of similarity and philosophical inquiry into cognition, going beyond the limits of language with the tools of information study. The key departure from the tradition of Wittgenstein’s inquiry is abandoning his claim 5.6 from the Tractatus Logico-Philosophicus that “The limits of my language mean the limits of my world” and making language (any language) only an important but limited instance of an information system. Similarity relations (not only transitive ones, i.e., equivalence relations) assume the fundamental role in cognition, which includes transitivization leading to abstraction of information as a natural mechanism to reduce information complexity independently of language [7].
References
[1] Schroeder, M.J., Wright, M.H. Tolerance and weak tolerance relations, J. Combin. Math. and Combin. Comput., 11(1992), 123-160.
[2] Zeeman, E.C. The topology of the brain and visual perception. In M.K. Fort, Jr. (ed.) Topology of 3-manifolds and related topics, Proceedings of the University of Georgia Institute 1961, pp. 240-256. Prentice-Hall, Englewood Cliffs, N.J. 1962.
[3] Wittgenstein, L. Philosophical Investigations (Philosophische Untersuchungen). Transl. G.E. Anscombe. Blackwell, London, 1953.
[4] Wittgenstein, L., The Blue and Brown Books, Blackwell, Oxford, 1958.
[5] Lackey, D.P. What are the modern classics? The Baruch poll of great philosophy in the twentieth century. Philosophical Forum, 1999, 30(4), 329–346.
[6] Wittgenstein, L. Tractatus Logico-Philosophicus. Transl. F.P. Ramsey and C.K. Ogden, Kegan Paul, London, 1922.
[7] Schroeder, M.J. Reduction of Information Complexity by Abstraction: Venn Gates and a Set Theoretic Logarithmic Operation. To appear in Fazekas, S.Z., Sin'ya, R. Algebras, Logic and Related Areas in Computer Science, RIMS Kôkyûroku: Kyoto, Japan; Research Institute for Mathematical Sciences, Kyoto University: Kyoto, Japan; pp.31.