Calculemus! the Problem of the Application of Logic and Mathematics
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From Physics to Physicalism
FROM PHYSICS TO PHYSICALISM a version of this paper is published in Physicalism and its Discontents ed, Gillett and Loewer Cambridge University Press 2001 Introduction Hilary Putnam explains that: The appeal of materialism lies precisely in this, in its claim to be natural metaphysics within the bounds of science. That a doctrine which promises to gratify our ambition (to know the noumenal) and our caution (not to be unscientific) should have great appeal is hardly something to be wondered at. (Putnam (1983), p.210) Materialism says that all facts, in particular all mental facts, obtain in virtue of the spatio- temporal distribution, and properties, of matter. It was, as Putnam says, “metaphysics within the bounds of science”, but only so long as science was thought to say that the world is made out of matter.1 In this century physicists have learned that there is more in the world than matter and, in any case, matter isn’t quite what it seemed to be. For this reason many philosophers who think that metaphysics should be informed by science advocate physicalism in place of materialism. Physicalism claims that all facts obtain in virtue of the distribution of the fundamental entities and properties –whatever they turn out to be- of completed fundamental physics. Later I will discuss a more precise formulation. But not all contemporary philosophers embrace physicalism. Some- and though a minority not a small or un-influential one- think that physicalism is rather the metaphysics for an unjustified scientism; i.e. it is scientistic metaphysics. Those among them that think that physicalism can be clearly formulated think that it characterizes a cold, colorless, unfeeling and uninteresting world and not, they think, the world we live in. -
An Exploration of the Relationship Between Mathematics and Music
An Exploration of the Relationship between Mathematics and Music Shah, Saloni 2010 MIMS EPrint: 2010.103 Manchester Institute for Mathematical Sciences School of Mathematics The University of Manchester Reports available from: http://eprints.maths.manchester.ac.uk/ And by contacting: The MIMS Secretary School of Mathematics The University of Manchester Manchester, M13 9PL, UK ISSN 1749-9097 An Exploration of ! Relation"ip Between Ma#ematics and Music MATH30000, 3rd Year Project Saloni Shah, ID 7177223 University of Manchester May 2010 Project Supervisor: Professor Roger Plymen ! 1 TABLE OF CONTENTS Preface! 3 1.0 Music and Mathematics: An Introduction to their Relationship! 6 2.0 Historical Connections Between Mathematics and Music! 9 2.1 Music Theorists and Mathematicians: Are they one in the same?! 9 2.2 Why are mathematicians so fascinated by music theory?! 15 3.0 The Mathematics of Music! 19 3.1 Pythagoras and the Theory of Music Intervals! 19 3.2 The Move Away From Pythagorean Scales! 29 3.3 Rameau Adds to the Discovery of Pythagoras! 32 3.4 Music and Fibonacci! 36 3.5 Circle of Fifths! 42 4.0 Messiaen: The Mathematics of his Musical Language! 45 4.1 Modes of Limited Transposition! 51 4.2 Non-retrogradable Rhythms! 58 5.0 Religious Symbolism and Mathematics in Music! 64 5.1 Numbers are God"s Tools! 65 5.2 Religious Symbolism and Numbers in Bach"s Music! 67 5.3 Messiaen"s Use of Mathematical Ideas to Convey Religious Ones! 73 6.0 Musical Mathematics: The Artistic Aspect of Mathematics! 76 6.1 Mathematics as Art! 78 6.2 Mathematical Periods! 81 6.3 Mathematics Periods vs. -
Divine Idealism As Physicalism? Reflections on the Structural Definition of Physicalism
DIVINE IDEALISM AS PHYSICALISM? REFLECTIONS ON THE STRUCTURAL DEFINITION OF PHYSICALISM Jon W. Thompson Hempel’s Dilemma remains at the center of the problem of defining phys- icalism. In brief, the dilemma asks whether physicalism should be defined by appeal to current or future physics. If defined by current physics, phys- icalism is almost certainly false. If defined by an ideal future physics, then physicalism has little determinable content. Montero and Papineau have innovatively suggested that the dilemma may be avoided by defining phys- icalism structurally. While their definition is one among many definitions, it is significant in that—if successful—it would break the impasse for defining physicalism. I argue, however, that the structural definition fails because it counts metaphysical frameworks (crucially, versions of divine idealism) as “physicalist”—an unwelcome result for physicalists. This paper thus furthers the debate on the definition of physicalism and sheds light on the relationship between physicalism and idealism. 1. Hempel’s Dilemma Physicalism is often defined as the view that all that exists is what physics studies; but many voices have raised concerns over such a definition. In- deed, the problem of defining physicalism has been with us for some time now.1 “Hempel’s Dilemma” puts the problem in exacting focus: when the physicalist claims that all that exists is physical, is she claiming that [A] All that exists is what is studied by current physics or that [B] All that exists is what is studied by some ideal, perhaps future, physics?2 If the physi- calist intends [A], then physicalism is clearly false. -
An Immaterial Thing: the Case for Dualism Today We Turn to Our Second Big Question: What Are You?
What am I? An immaterial thing: the case for dualism Today we turn to our second big question: What are you? We can focus this question a little bit by introducing the idea of a physical or material thing. To a first approximation, a material thing is a thing entirely composed of the sorts of things described in physics: electrons, quarks, etc. Materialism, or physicalism, in general is the claim that every thing — every thing that exists — is a material thing. There are two views opposed to materialism. One is dualism. According to dualism (as the name suggests) there are two sorts of things: material things, and immaterial things. The second opposed view is idealism. According to idealism, there are no material things, and everything that exists is immaterial. According to materialism about human beings, you are material thing. You are something which, like tables, clouds, trees, and amoebae, is entirely composed of the basic particles studied in physics. According to materialism about human beings, you are material thing. You are something which, like tables, clouds, trees, and amoebae, is entirely composed of the basic particles studied in physics. Many of the ways we ordinarily think and talk about ourselves seem to suggest that we endorse materialism about ourselves. Consider, for example, the question of whether you are currently sitting in a chair. Could an immaterial thing occupy space, and sit in a chair? But other ways that we think and talk about ourselves suggest that we think of ourselves as immaterial things. For example, many people think that it is possible for human beings to enjoy life after death, and hence to exist even after one’s body has ceased to exist; and to many it has seemed easiest to understand how this could be possible if think of ourselves, not as immaterial bodies, but as immaterial souls or minds. -
Physicalism and the Possibility of Life After Death
Resurrection of the Body?: Physicalism and the Possibility of Life After Death The 2012 Winifred E. Weter Faculty Award Lecture Seattle Pacific University April 17, 2012 Rebekah L.H. Rice, Ph.D. Associate Professor of Philosophy College of Arts and Sciences Resurrection of the Body?: Physicalism and the Possibility of Life After Death 2012 Winifred E. Weter Lecture April 17, 2012 Seattle Pacific University Rebekah L. H. Rice, Ph.D. Department of Philosophy 1 To Jeremy, Lydia, and Silas Rice (For unparalleled love, support, and bear hugs) To Ken Harrower (Who taught me that when faced with a perplexing question, one might do well to crack open a book.) To Steve Layman, Patrick McDonald, and Leland Saunders (Colleagues than which none better can be conceived!) 2 I. Introduction Christians maintain that, as a result of divine grace, human persons can survive their deaths. This occurs as a result of a remarkable divine act—something we call “resurrection.” And it constitutes an important piece of the “good news” that Christians profess. Conceptually, this is a baffling claim. How can it be that I (God willing) will exist after my bodily death? One answer is to suggest—as Rene Descartes famously did—that I am not my body, and that I am instead an immaterial mind, or “soul.” This yields the following account of post-mortem survival: Upon my bodily death, my soul persists. Since I am my soul, and not my body, I persist. Where (or in what conditions) I will persist is a matter left to divine judgment, but the fact of my persistence is owing to the fact that though my bodily processes cease and my body decays – or worse, that it is obliterated and cast into a billion pieces – my soul persists to become the occupant of a new (glorified) body, or in any case to enjoy continued existence. -
The Relationship Between Consciousness and Intentionality
University of Central Florida STARS HIM 1990-2015 2013 The relationship between consciousness and intentionality Jordan Bell University of Central Florida Part of the Philosophy Commons Find similar works at: https://stars.library.ucf.edu/honorstheses1990-2015 University of Central Florida Libraries http://library.ucf.edu This Open Access is brought to you for free and open access by STARS. It has been accepted for inclusion in HIM 1990-2015 by an authorized administrator of STARS. For more information, please contact [email protected]. Recommended Citation Bell, Jordan, "The relationship between consciousness and intentionality" (2013). HIM 1990-2015. 1384. https://stars.library.ucf.edu/honorstheses1990-2015/1384 THE RELATIONSHIP BETWEEN CONSCIOUSNESS AND INTENTIONALITY by JORDAN BELL A thesis submitted in partial fulfillment of the requirements for the Honors in the Major Program in Philosophy in the College of Arts & Humanities and in The Burnett Honors College at the University of Central Florida Orlando, Florida Spring Term 2013 Thesis Chair: Dr. Mason Cash ABSTRACT Within the Philosophy of Mind two features of our mental life have been acknowledged as the most perplexing—consciousness, the phenomenal “what it is likeness” of our mental states, and intentionality, the aboutness or directedness of our mental states. As such, it has become commonplace to develop theories about these phenomena which seek to explain them naturalistically, that is, without resort to magic or miracles. Traditionally this has been done by analyzing consciousness and intentionality apart from one another. However, in more recent years the tide has turned. In contemporary theories these phenomena are typically analyzed in terms of the other. -
1 a REFUTATION of QUALIA-PHYSICALISM Michael
1 To appear in M. O’Rourke and C. Washington (eds.), Situating Semantics: Essays on the Philosophy of John Perry (MIT Press) A REFUTATION OF QUALIA-PHYSICALISM Michael McKinsey Wayne State University Recent defenders of reductive physicalism such as Brian Loar (1990, 1997) and John Perry (2001) have adopted an intriguing new strategy:i (1) accept as so much common sense (nearly) everything that property-dualists want to say about sensory qualia, including the central claims that sensory qualia determine ‘what it’s like’ to have a given sense experience, and that persons are directly aware of these qualia in the having of such experiences; (2) contend that while these common sense facts about qualia may show that our ways of thinking and speaking about qualia are conceptually different from our ways of thinking and speaking about physical properties of the brain, these facts do not show that sensory qualia themselves (as opposed to our ways of thinking and speaking about them) are distinct from physical properties of the brain; (3) use this contention to turn aside the few existing arguments against reductive physicalism by such property dualists as Kripke (1972), Nagel (1974), Jackson (1982), and Chalmers (1996); and finally (4) insist that sensory qualia are in fact just identical with physical properties of the brain, so that consequently, the facts about the sensory qualities of conscious experience are nothing over and above physical facts about the brain. I will call the view that incorporates this strategy ‘qualia-physicalism’, or ‘Q-physicalism’ for short. In this paper I will argue that Q-physicalism is false. -
1 a NEW MUSIC COMPOSITION TECHNIQUE USING NATURAL SCIENCE DATA D.M.A Document Presented in Partial Fulfillment of the Requiremen
A NEW MUSIC COMPOSITION TECHNIQUE USING NATURAL SCIENCE DATA D.M.A Document Presented in Partial Fulfillment of the Requirements for the Degree Doctor of Musical Arts in the Graduate School of The Ohio State University By Joungmin Lee, B.A., M.M. Graduate Program in Music The Ohio State University 2019 D.M.A. Document Committee Dr. Thomas Wells, Advisor Dr. Jan Radzynski Dr. Arved Ashby 1 Copyrighted by Joungmin Lee 2019 2 ABSTRACT The relationship of music and mathematics are well documented since the time of ancient Greece, and this relationship is evidenced in the mathematical or quasi- mathematical nature of compositional approaches by composers such as Xenakis, Schoenberg, Charles Dodge, and composers who employ computer-assisted-composition techniques in their work. This study is an attempt to create a composition with data collected over the course 32 years from melting glaciers in seven areas in Greenland, and at the same time produce a work that is expressive and expands my compositional palette. To begin with, numeric values from data were rounded to four-digits and converted into frequencies in Hz. Moreover, the other data are rounded to two-digit values that determine note durations. Using these transformations, a prototype composition was developed, with data from each of the seven Greenland-glacier areas used to compose individual instrument parts in a septet. The composition Contrast and Conflict is a pilot study based on 20 data sets. Serves as a practical example of the methods the author used to develop and transform data. One of the author’s significant findings is that data analysis, albeit sometimes painful and time-consuming, reduced his overall composing time. -
The Euclidean Algorithm Generates Traditional Musical Rhythms
The Euclidean Algorithm Generates Traditional Musical Rhythms Godfried Toussaint∗ School of Computer Science, McGill University Montreal,´ Quebec,´ Canada [email protected] Abstract The Euclidean algorithm (which comes down to us from Euclid’s Elements) computes the greatest com- mon divisor of two given integers. It is shown here that the structure of the Euclidean algorithm may be used to generate, very efficiently, a large family of rhythms used as timelines (ostinatos), in sub-Saharan African music in particular, and world music in general. These rhythms, here dubbed Euclidean rhythms, have the property that their onset patterns are distributed as evenly as possible. Euclidean rhythms also find application in nuclear physics accelerators and in computer science, and are closely related to several families of words and sequences of interest in the study of the combinatorics of words, such as Euclidean strings, to which the Euclidean rhythms are compared. 1. Introduction What do African rhythms, spallation neutron source (SNS) accelerators in nuclear physics, string theory (stringology) in computer science, and an ancient algorithm described by Euclid have in common? The short answer is: patterns distributed as evenly as possible. For the long answer please read on. Mathematics and music have been intimately intertwined since the days of Pythagoras. However, most of this interaction has been in the domain of pitch and scales. For some historical snapshots of this interaction the reader is referred to H. S. M. Coxeter’s delightful account [9]. Rhythm, on the other hand has been his- torically mostly ignored. Here we make some mathematical connections between musical rhythm and other areas of knowledge such as nuclear physics and computer science, as well as the work of another famous ancient Greek mathematician, Euclid of Alexandria. -
Eidos Fecha De Recepción: Marzo 3 De 2011 ISSN 1692-8857 Fecha De Aceptación: Julio 28 De 2011 Issne 2011-7477
eidos Fecha de recepción: marzo 3 de 2011 ISSN 1692-8857 Fecha de aceptación: julio 28 de 2011 ISSNe 2011-7477 IS THE PANPSYCHIST BETTER OFF AS AN IDEALIST? SOME LEIBNIZIAN REMARKS ON CONSCIOUSNESS AND COMPOSITION Michael Blamauer University of Vienna, Department of Philosophy [email protected] RESUMEN Algunos filósofos de la mente han defendido la idea de considerar la mente como otra característica fundamental de la realidad, además de las propiedades físicas. De ahí que la mayoría de ellos sean propiamente dualistas. Sin embargo, algunos de ellos son pansiquistas. En este artículo sostendré que ser propiamente un dualista implica, en esencia, ser pansiqui- sta. Incluso, si el pansiquismo aborda ciertas dificultades relacionadas con el problema de la conciencia de manera muy elegante, éstas permanecen inmodificables. Siendo partidario del carácter fundamental de la mente, de- fenderé la idea de que sólo mediante una revisión radical de la metafísica el pansiquista podrá evitar tales problemas y, en consecuencia, que debe adoptar el idealismo leibniciano. PALABRAS CLAVE Panpsiquismo, Leibniz, filosofía de la mente, dualismo, composición. ABSTRACT Some philosophers of mind have argued for considering consciousness as a further fundamental feature of reality in addition to its physical prop- erties. Hence most of them are property dualists. But some of them are panpsychists. In the present paper it will be argued that being a real prop- erty dualist essentially entails being a panpsychist. Even if panpsychism deals rather elegantly with certain problems of the puzzle of consciousness, there’s no way around the composition problem. Adhering to the funda- mentality claim of the mind, it will be shown that only a radical revision of metaphysics will allow the panpsychist to avoid these troubles, and hence that a panpsychist must adopt Leibnizian idealism. -
The Distance Geometry of Music
The Distance Geometry of Music Erik D. Demaine∗ Francisco Gomez-Martin† Henk Meijer‡ David Rappaport§ Perouz Taslakian¶ Godfried T. Toussaint§k Terry Winograd∗∗ David R. Wood†† Abstract We demonstrate relationships between the classical Euclidean algorithm and many other fields of study, particularly in the context of music and distance geometry. Specifically, we show how the structure of the Euclidean algorithm defines a family of rhythms that encompass over forty timelines (ostinatos) from traditional world music. We prove that these Euclidean rhythms have the mathematical property that their onset patterns are distributed as evenly as possible: they maximize the sum of the Euclidean distances between all pairs of onsets, viewing onsets as points on a circle. Indeed, Euclidean rhythms are the unique rhythms that maximize this notion of evenness. We also show that essentially all Euclidean rhythms are deep: each distinct distance between onsets occurs with a unique multiplicity, and these multiplicities form an interval 1, 2, . , k − 1. Finally, we characterize all deep rhythms, showing that they form a subclass of generated rhythms, which in turn proves a useful property called shelling. All of our results for musical rhythms apply equally well to musical scales. In addition, many of the problems we explore are interesting in their own right as distance geometry problems on the circle; some of the same problems were explored by Erd˝osin the plane. ∗Computer Science and Artificial Intelligence Laboratory, Massachusetts Institute of Technology, -
Euclidean Rhythm Music Sequencer Using Actors in Python
Euclidean Rhythm Music Sequencer using Actors in Python Daniel Prince Department of Electrical and Computer Engineering University of Dayton 300 College Park Dayton, Ohio 45469 USA [email protected] ABSTRACT entry by the user, and can feel tedious at worst. In this A real-time sequencer that implements the Euclidean Rhythm work, the Euclidean rhythm algorithm is explored for its Algorithm is created for creative generation of drum se- immediacy and ability to quickly define complex sequences. quences by musicians or producers. The Actor model of Audio production software necessitates a unique set of concurrency is used to simplify the communication required technical demands in order to facilitate an experience con- for interactivity and musical timing. Generator comprehen- sistent with modern standards. Software used for music pro- sions and higher-order functions are used for simplification. duction must not only provide precise timing for the gener- The resulting application sends Musical Instrument Digital ation and playback of musical passages that often involves Interface data interactively to another application for sound demanding digital signal processing algorithms, but it must generation. also provide an interface to a user that allows for real-time configuration of the model behind the music. This combi- nation of synchronous and asynchronous work is a demand- 1. INTRODUCTION ing task for synchronization models. Fundamental models A vast range of music production software has become of synchronization such as semaphores would be difficult to available recently due to the increasing power of personal scale to applications involving several concurrent tasks. Due computers and increasing popularity of audio production to the complex synchronization issues related to creating an among hobbyists and professionals alike.