Tolerance Puzzles

This chapter provides a general schema for regimenting a broad family of puzzles of modal variation. These puzzles begin with a ‘Tolerance’ premise according to which an objects (or a certain kind of object) can differ in any small way along a certain parameter. This is supplemented with a ‘Non-contingency’ premise according to which the Tolerance premise is necessarily true if true at all, an ‘Iteration’ premise according to which anything possibly possible is possible, and a ‘Persistent Closeness’ premise according to which what counts as a ‘small difference’ is modally constant. These premises jointly imply the conclusion, ‘Hypertolerance’, that the object or objects in question can differ arbitrarily along the relevant parameter. We show how this schema is general enough to subsume puzzles involving time or objective chance, and discuss some difficulties that arise in trying to formulate compelling instantiations of the schema involving variation in originating matter.

“And a Droplet Reflects the World.” Imaginary Discord in Modal Theory, and Modal Development in Small Forms and Fragments

В данной статье рассматриваются принципы ладового развития в небольших произведениях и построениях. В избранных для анализа миниатюрной песне Листа «Радость и горе», четырехтактном фрагменте из «Хованщины» и ряде других образцов из музыки Шопена, Римского-Корсакова, Дебюсси, Слонимского, Лигети выявлены такие принципы модального и тонального становления, как сохранение или пополнение звукоряда, взаимодополняемость модусов, тональное и модальное модулирование, сбережение тона, модальная вариантность, отражение в формообразовании логики истории. В статье уточнены некоторые аспекты теории лада через призму концепций в области гармонии двух представителей санкт-петербургской и московской научных школ. Ощущение противоборства и непримиримости их трактовок создалось отчасти после острых формулировок Т. Бершадской: «Недоразумение, становящееся традицией»; «Изначальная ошибка популярной концепции». Автору данной статьи, внесшему некоторые корректировки и разъяснения, расхождения сторон представляются, однако, несущественными и даже мнимыми. Понимание лада как бинарной системы позволило в ладовом развитии выделить две его ветви - модальную и тональную, которые, как правило, находятся в тесном взаимосплетении при обычно определяющей роли одной из них. Предпринятые анализы произведений каждой из этих ветвей имеют различия, хоть они и направлены к осмыслению общих методологических принципов, которое для музыковедческой науки остается насущным. This article deals with the principles of modal development in short pieces and structures. The selected for the analysis Liszt's miniature song “Joy and Woe,” a four-beat fragment from “Khovanshchina” and a number of other examples from the music of Chopin, Rimsky-Korsakov, Debussy, Slonimsky, and Ligeti reveal such principles of modal and tonal formation as: preservation or enrichment of the scale, complementarity of the modes, tonal and modal modulation, preservation of tone, modal variation, reflection of the logic of history in creating the musical form. The article clarifies some aspects of the modal theory through the prism of the concepts in the field of harmony as presented by two exponents of St. Petersburg and Moscow schools of music theory. The sentiment of confrontation and irreconcilability of their interpretations was created, in part, by T. Bershadskaya's sharp statements: “Misunderstanding that becomes a tradition,” “The initial mistake of the popular concept.” However, the author of this article, having made some adjustments and clarifications, considers the differences between the parties rather insignificant and even imaginary. The understanding of mode as a binary system made it possible to distinguish two branches in modal development-modal and tonal, which, as a rule, are closely intertwined, with one of them usually playing a determining role. The undertaken analyses of the works by each of these branches have certain differences, although they are aimed at understanding the general methodological principles, which remain essential for musicology.

Variation and Modal Characteristic of Tangential Threshing Cylinder Undergoing Threshing Dynamics

During the rice-threshing process, straws always attached to a threshing cylinder and induced vibration and modal variation. In this paper, the constraint and threshing modals of the threshing cylinder were tested under idling and load conditions, and the causes of vibration and modal variation were explained. Based on the constraint and modal of the threshing cylinder, the vibration amplitudes and frequencies undergoing rice threshing were tested and analyzed. Results showed that mass of straws decreased gradually with the separation of rice grains and straws. And there was a nonuniform change in the circumferential resistance of the threshing cylinder. The fluctuating torque, speed, and frequencies during threshing process would cause vibration of the threshing cylinder. During rice-threshing process, the other natural frequencies were greater than the excitation frequency. With the accumulation of a large amount of straws, the threshing modal frequencies of the tangential threshing cylinder increased. The threshing bars caused vibration of the tangential threshing cylinder in the left and right direction mainly at two frequencies. At idling state of no-load, the vibration frequency 42.97 Hz of the tangential threshing cylinder in X direction was close to the constraint modal frequency 41.58 Hz. The eccentric load caused the excitation frequency to increase during the rice-threshing process. The vibration frequency was also closely related to the threshing modal. The tangential threshing cylinder with low vibration characteristics could be designed by using the eccentric vibration characteristics during the threshing process.

On Emily Paul on Brian Leftow

Emily Paul has recently argued that Brian Leftow’s account of why the import of God’s becoming Incarnate is not temporal but modal fails. She argues that Leftow’s required modal variation is not satisfied. That is, we do not have the required variation across logical space concerning the Incarnation. Paul examines her argument on two possible worlds theories: theistic ersatzism and (what I call) Lewisian theism. She thinks that both possible worlds theories face difficulties. I argue that Paul fails to provide a compelling argument against Leftow because, firstly, her defence of one her premises fails, and, secondly, she misjudges what is required for some of Leftow’s claims to be true. I also argue that some of the problematic consequences that Paul raises for theistic ersatzism and Lewisian theism either are not problematic or can be avoided.

Incarnation, Divine Timelessness, and Modality

A central part of the Christian doctrine of the incarnation is that the Son of God ‘becomes’ incarnate. Furthermore, according to classical theism, God is timeless: He exists ‘outside’ of time, and His life has no temporal stages. A consequence of this ‘atemporalist’ view is that a timeless being cannot undergo intrinsic change—for this requires the being to be one way at one time, and a different way at a later time. How, then, can we understand the central Christian claim that the Son of God ‘becomes’ human? This paper examines one such explanation, drawn from a brief remark by Brian Leftow: the Word takes on flesh by exhibiting modal variation with regards to the incarnation. On this account, a timeless God ‘becomes’ incarnate simply due to variation across logical space: at some possible worlds He is incarnate and at others He is not. Modal variation need not, therefore, require temporality: it only requires variation across (static) possible worlds. I draw out the problems with Leftow’s modal claim under the heads of Ersatzism and Genuine Modal Realism about possible worlds, respectively. I argue that in both instances, Leftow’s desired cross–worldly variation of the Son’s incarnation cannot be achieved.

Modal Variation Regularity of Inner-Decaying Villages in the Process of Urbanization in China

The rapid development of urbanization in China brought serious challenges for the rural development and led to the phenomenon of inner-decaying village. Through a on-the-spot investigation, detailed informations of typical villages over the past 30 years are obtained. By the quantitative analysis of the home interview and field measurement data, and interpretation of satellite images, this paper summarizes the shape change regularity of villages in urbanization process, systematically analyzes the causes of inner-decaying village and then proposes solutions of it.