Leibniz's Theory of Propositional Terms: a Reply to Massimo
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An Axiomatic Approach to Physical Systems
' An Axiomatic Approach $ to Physical Systems & % Januari 2004 ❦ ' Summary $ Mereology is generally considered as a formal theory of the part-whole relation- ship concerning material bodies, such as planets, pickles and protons. We argue that mereology can be considered more generally as axiomatising the concept of a physical system, such as a planet in a gravitation-potential, a pickle in heart- burn and a proton in an electro-magnetic field. We design a theory of sets and physical systems by extending standard set-theory (ZFC) with mereological axioms. The resulting theory deductively extends both `Mereology' of Tarski & L`esniewski as well as the well-known `calculus of individuals' of Leonard & Goodman. We prove a number of theorems and demonstrate that our theory extends ZFC con- servatively and hence equiconsistently. We also erect a model of our theory in ZFC. The lesson to be learned from this paper reads that not only is a marriage between standard set-theory and mereology logically respectable, leading to a rigorous vin- dication of how physicists talk about physical systems, but in addition that sets and physical systems interact at the formal level both quite smoothly and non- trivially. & % Contents 0 Pre-Mereological Investigations 1 0.0 Overview . 1 0.1 Motivation . 1 0.2 Heuristics . 2 0.3 Requirements . 5 0.4 Extant Mereological Theories . 6 1 Mereological Investigations 8 1.0 The Language of Physical Systems . 8 1.1 The Domain of Mereological Discourse . 9 1.2 Mereological Axioms . 13 1.2.0 Plenitude vs. Parsimony . 13 1.2.1 Subsystem Axioms . 15 1.2.2 Composite Physical Systems . -
On the Boundary Between Mereology and Topology
On the Boundary Between Mereology and Topology Achille C. Varzi Istituto per la Ricerca Scientifica e Tecnologica, I-38100 Trento, Italy [email protected] (Final version published in Roberto Casati, Barry Smith, and Graham White (eds.), Philosophy and the Cognitive Sciences. Proceedings of the 16th International Wittgenstein Symposium, Vienna, Hölder-Pichler-Tempsky, 1994, pp. 423–442.) 1. Introduction Much recent work aimed at providing a formal ontology for the common-sense world has emphasized the need for a mereological account to be supplemented with topological concepts and principles. There are at least two reasons under- lying this view. The first is truly metaphysical and relates to the task of charac- terizing individual integrity or organic unity: since the notion of connectedness runs afoul of plain mereology, a theory of parts and wholes really needs to in- corporate a topological machinery of some sort. The second reason has been stressed mainly in connection with applications to certain areas of artificial in- telligence, most notably naive physics and qualitative reasoning about space and time: here mereology proves useful to account for certain basic relation- ships among things or events; but one needs topology to account for the fact that, say, two events can be continuous with each other, or that something can be inside, outside, abutting, or surrounding something else. These motivations (at times combined with others, e.g., semantic transpar- ency or computational efficiency) have led to the development of theories in which both mereological and topological notions play a pivotal role. How ex- actly these notions are related, however, and how the underlying principles should interact with one another, is still a rather unexplored issue. -
A Translation Approach to Portable Ontology Specifications
Knowledge Systems Laboratory September 1992 Technical Report KSL 92-71 Revised April 1993 A Translation Approach to Portable Ontology Specifications by Thomas R. Gruber Appeared in Knowledge Acquisition, 5(2):199-220, 1993. KNOWLEDGE SYSTEMS LABORATORY Computer Science Department Stanford University Stanford, California 94305 A Translation Approach to Portable Ontology Specifications Thomas R. Gruber Knowledge System Laboratory Stanford University 701 Welch Road, Building C Palo Alto, CA 94304 [email protected] Abstract To support the sharing and reuse of formally represented knowledge among AI systems, it is useful to define the common vocabulary in which shared knowledge is represented. A specification of a representational vocabulary for a shared domain of discourse — definitions of classes, relations, functions, and other objects — is called an ontology. This paper describes a mechanism for defining ontologies that are portable over representation systems. Definitions written in a standard format for predicate calculus are translated by a system called Ontolingua into specialized representations, including frame-based systems as well as relational languages. This allows researchers to share and reuse ontologies, while retaining the computational benefits of specialized implementations. We discuss how the translation approach to portability addresses several technical problems. One problem is how to accommodate the stylistic and organizational differences among representations while preserving declarative content. Another is how -
François Duchesneau, Leibniz, Le Vivant Et L'organisme, Paris: J. Vrin
François Duchesneau, Leibniz, le vivant et l’organisme, Paris: J. Vrin, 2010. 348 p. Reviewed by Justin E. H. Smith, Concordia University or some time, this reviewer has been championing the translation into English of François Duchesneau’s many books on the natural philosophy of Leibniz. GreaterF availability of his work in the English-speaking world, along with that of Michel Fichant and, more recently, the contributions of Anne-Lise Rey, Raphaële Andrault, and Arnaud Pelletier, would in combination play a powerful role in helping scholars to form a richer picture of Leibniz’s natural-philosophical model of the corporeal world, and of this model’s centrality to his deepest and most mature philosophical project. With the publication of his most recent book, Duchesneau has reconfirmed the urgency of learning about this side of Leibniz. The principal purpose of this review will be simply to summarize the recent book and to impart in a synoptic way the picture of Leibniz it draws for readers who may not have the time or capacity to work through the French text. If I am successful, this synopsis might then serve as an argument for the eventual publication of a translation. Following this, I will conclude by raising a few questions that I see as arising from this rich study, questions that might in turn serve as the germs of future research along the path Duchesneau has carved. Duchesneau’s book has six principal theses. First, he argues that Leibniz is committed to the need for a distinct philosophical account of the living being within the order of nature, as well as of the integrated and functional character of the micromachines that compose it. -
Semantics of First-Order Logic
CSC 244/444 Lecture Notes Sept. 7, 2021 Semantics of First-Order Logic A notation becomes a \representation" only when we can explain, in a formal way, how the notation can make true or false statements about some do- main; this is what model-theoretic semantics does in logic. We now have a set of syntactic expressions for formalizing knowledge, but we have only talked about the meanings of these expressions in an informal way. We now need to provide a model-theoretic semantics for this syntax, specifying precisely what the possible ways are of using a first-order language to talk about some domain of interest. Why is this important? Because, (1) that is the only way that we can verify that the facts we write down in the representation actually can mean what we intuitively intend them to mean; representations without formal semantics have often turned out to be incoherent when examined from this perspective; and (2) that is the only way we can judge whether proposed methods of making inferences are reasonable { i.e., that they give conclusions that are guaranteed to be true whenever the premises are, or at least are probably true, or at least possibly true. Without such guarantees, we will probably end up with an irrational \intelligent agent"! Models Our goal, then, is to specify precisely how all the terms, predicates, and formulas (sen- tences) of a first-order language can be interpreted so that terms refer to individuals, predicates refer to properties and relations, and formulas are either true or false. So we begin by fixing a domain of interest, called the domain of discourse: D. -
SEEING ALL THINGS in SPACE Kant and the Reality of Space in the Context of Early Modern Philosophy
Reports from the Department of Philosophy Vol. 43 SEEING ALL THINGS IN SPACE Kant and the Reality of Space in the Context of Early Modern Philosophy Jan Johansson University of Turku Finland Copyright © 2020 Jan Johansson SERIES EDITORS: Olli Koistinen Juha Räikkä Department of Philosophy University of Turku FI-20014 Finland ISSN 1457-9332 ISBN 978-951-29-7813-7 (print) ISBN 978-951-29-7814-4 (pdf) Painosalama Oy, Turku 2020 Written by Jan Johansson Doctoral Programme of Social and Behavioural Sciences, University of Turku, Faculty of Social Sciences, Department of Philosophy, Contemporary History and Political Science Supervised by Professor Olli Koistinen Dr Hemmo Laiho University of Turku, Faculty of Social Sciences, Department of Philosophy, Contemporary History and Political Science Reviewed by Professor Corey W. Dyck University of Western Ontario Dr Anssi Korhonen University of Helsinki Opponent Professor Corey W. Dyck University of Western Ontario Chairperson (custos) Professor Olli Koistinen University of Turku, Faculty of Social Sciences, Department of Philosophy, Contemporary History and Political Science Turun yliopiston laatujärjestelemän mukaisesti tämän julkaisun alkuperäisyys on tarkastettu Turnitin OriginalityCheck-järjestelmällä. The originality of this dissertation has been checked in accordance with the University of Turk quality assurance system using the Turnitin OriginalityCheck service. ACKNOWLEDGEMENTS In May 2006, at a seminar on Leibniz in Uppsala, with Lilli Alanen and John Carriero, I had the great pleasure and honour of making acquaintance with Olli Koistinen. I made a remark on Kant’s metaphysics, which Olli did not think was particularly accurate. But to my surprise, Olli later chatted me up, and it turned out that he had taken keen interest in Kant’s lectures on metaphysics. -
Anubav Vasudevan
Anubav Vasudevan University of Chicago Tel: (773) 702-4234 Department of Philosophy Email: [email protected] 1115 E. 58th St. Office: Rosenwald Hall 218C Chicago, IL 60637 Education 2012 Ph.D., Philosophy, Columbia University 2004 M.A., Philosophy, Virginia Polytechnic Institute and State University 2002 B.S., Physics, Virginia Polytechnic Institute and State University, summa cum laude Employment 2011- Assistant Professor, Philosophy Department, University of Chicago 2009-2011 Core Curriculum Preceptor, Columbia University Publications Malink, M. and Vasudevan, A. (2018). Leibniz on the Logic of Conceptual Containment and Coincidence. In de Risi, V., editor, Leibniz on the Structure of Sciences: Modern Essays in Logic, Mathematics, Dynamics. Forthcoming from Springer International Publishing Vasudevan, A. (2018). Chance, Determinism and the Classical Theory of Probability. Studies in History and Philosophy of Science Part A, 67:32{43 Vasudevan, A. (2017). Entropy and Insufficient Reason: A Note on the Judy Benjamin problem. Forthcoming in British Journal for the Philosophy of Science. Vasudevan, A. (2017). Biased Information and the Exchange Paradox. Forthcoming in Synthese. Malink, M. and Vasudevan, A. (2017). Leibniz's Theory of Propositional Terms: A reply to Massimo Mugnai. The Leibniz Review, 27:139{55 Kim, B. and Vasudevan, A. (2017). How to Expect a Surprising Exam. Synthese, 194:3101{33 Malink, M. and Vasudevan, A. (2016). The Logic of Leibniz's Generales inquisitiones de analysi notionum et veritatum. Review of Symbolic Logic, 9:686{751 Vasudevan, A. (2013). On the A Priori and A Posteriori Assessment of Probabilities. Journal of Applied Logic, 11(4):440{451 Gaifman, H. and Vasudevan, A. (2012). -
Leibniz on Logic, Language and Signs: a Bibliography (L- Z)
Leibniz on Logic, Language and Signs: a Bibliography (L- Z) https://www.historyoflogic.com/biblio/leibniz-logic-biblio-two.htm History of Logic from Aristotle to Gödel by Raul Corazzon | e-mail: [email protected] Leibniz on Logic, Language and Semiotics. Annotated bibliography (Second Part: L - Z) BIBLIOGRAPHY 1. Lenders, Winfried. 1971. Die Analytische Begriffs- Und Urteilstheorie Von G.W. Leibniz Und Chr. Wolff. Hildesheim: Georg Olms. 2. Lenzen, Wolfgang. 1983. "Leibniz Und Die Entwicklung Der Modernen Logik." In Leibniz, Werk Und Wirkung. Iv. Internationaler Leibniz-Kongress (Hannover, 14 - 19 November 1983), 418-425. Hannover: Gottfried Wilhelm Leibniz Gesellschaft. Reprinted in revised form in: W. Lenzen - Calculus Universalis (2004) pp. 15-22 3. ———. 1983. "Zur 'Extensionalen' Und 'Intensionalen' Interpretation Der Leibnizschen Logik." Studia Leibnitiana no. 15:129-148. Reprinted in revised form in: W. Lenzen - Calculus Universalis (2004) pp. 23-46. "Against the prevailing opinion expressed, e.g., by L. Couturat it is argued that the so-called "intensional" point of view which Leibniz mostly preferred to the nowadays usual extensional interpretation is neither "confuse et vague" nor may it be made responsible for the alleged "échec final de son système" (Couturat, La logique de Leibniz, 387). We present a precise definition of an "intensional" semantics which reflects the Leibnizian ideas and which may be proven to be equivalent to standard extensional semantics." 4. ———. 1984. "'Unbestimmte Begriffe' Bei Leibniz." Studia Leibnitiana -
Leibniz and the Foundations of Physics: the Later Years
Leibniz and the Foundations of Physics: The Later Years The Harvard community has made this article openly available. Please share how this access benefits you. Your story matters Citation McDonough, Jeffrey K. 2016. Leibniz and the Foundations of Physics: The Later Years. Philosophical Review 125, no. 1: 1–34. doi:10.1215/00318108-3321711. Published Version doi:10.1215/00318108-3321711 Citable link http://nrs.harvard.edu/urn-3:HUL.InstRepos:30780190 Terms of Use This article was downloaded from Harvard University’s DASH repository, and is made available under the terms and conditions applicable to Open Access Policy Articles, as set forth at http:// nrs.harvard.edu/urn-3:HUL.InstRepos:dash.current.terms-of- use#OAP Leibniz and the Foundations of Physics: The Later Years Jeffrey K. McDonough 0. Introduction In the opening paragraphs of his now classic paper “Leibniz and the Foundations of Physics: The Middle Years,” Daniel Garber suggests that Leibniz must seem something of a paradox to contemporary readers (1985, 27). On the one hand, Leibniz is commonly held to have advanced a broadly idealist metaphysics according to which the world is ultimately grounded in mind-like monads whose properties are exhausted by their perceptions and appetites. On such a picture, physical bodies would seem to be nothing more than the perceptions or thoughts (or contents thereof) enjoyed by immaterial substances.1 On the other hand, it is generally recognized (if perhaps less clearly) that Leibniz was also a prominent physicist in his own day and that he saw his work in physics as supporting, and being supported by, his metaphysics.2 But how, in light of his idealism, could that be? How could Leibniz think that his pioneering work in physics might lend support to his idealist metaphysics, and conversely that his Earlier versions of this essay were presented to audiences at the Westfälische Wilhelms-Universität Münster, Yale University, Brown University, and Dartmouth College. -
Solutions to Inclass Problems Week 2, Wed
Massachusetts Institute of Technology 6.042J/18.062J, Fall ’05: Mathematics for Computer Science September 14 Prof. Albert R. Meyer and Prof. Ronitt Rubinfeld revised September 13, 2005, 1279 minutes Solutions to InClass Problems Week 2, Wed. Problem 1. For each of the logical formulas, indicate whether or not it is true when the domain of discourse is N (the natural numbers 0, 1, 2, . ), Z (the integers), Q (the rationals), R (the real numbers), and C (the complex numbers). ∃x (x2 =2) ∀x ∃y (x2 =y) ∀y ∃x (x2 =y) ∀x�= 0∃y (xy =1) ∃x ∃y (x+ 2y=2)∧ (2x+ 4y=5) Solution. Statement N Z Q R √ C ∃x(x2= 2) f f f t(x= 2) t ∀x∃y(x2=y) t t t t(y=x2) t ∀y∃x(x2=y) f f f f(take y <0)t ∀x�=∃ 0y(xy= 1) f f t t(y=/x 1 ) t ∃x∃y(x+ 2y= 2)∧ (2x+ 4y=5)f f f f f � Problem 2. The goal of this problem is to translate some assertions about binary strings into logic notation. The domain of discourse is the set of all finitelength binary strings: λ, 0, 1, 00, 01, 10, 11, 000, 001, . (Here λdenotes the empty string.) In your translations, you may use all the ordinary logic symbols (including =), variables, and the binary symbols 0, 1 denoting 0, 1. A string like 01x0yof binary symbols and variables denotes the concatenation of the symbols and the binary strings represented by the variables. For example, if the value of xis 011 and the value of yis 1111, then the value of 01x0yis the binary string 0101101111. -
Leibniz on Human Finitude, Progress, and Eternal Recurrence: the Argument of the ‘Apokatastasis’ Essay Drafts and Related Texts
Leibniz on Human Finitude, Progress, and Eternal Recurrence: The Argument of the ‘Apokatastasis’ Essay Drafts and Related Texts Forthcoming in Oxford Studies in Early Modern Philosophy DAVID FORMAN In a draft essay from around 1701, Leibniz argues that because humanity can express only a finite number of unique statements, it will eventually run out of new things to say. From this, Leibniz draws the further conclusion that if humanity lasts long enough, ‘there must also be a time when the same deeds would return and when nothing would be done that had not been done before, for deeds provide matter for speech’ (F 58). This is a remarkable conclusion, its conditional formulation notwithstanding: it recalls the cyclical cosmology, defended by ancient Stoics and Platonists, in which future world ages will be indistinguishable from the present one. And far from distancing this conclusion from such ancient antecedents, Leibniz invites us to consider it as their rehabilitation: ‘Indeed, there would necessarily be certain periods like the Platonic year, such that in the course of one age exactly the same things would be done, as far as the senses are concerned, as were done before in another age’ (F 56–58). One reason that this apparent rehabilitation of an ancient cyclical cosmology is remarkable is that it stands in such obvious conflict with the sacred history and prophecy contained in Christian Scripture, which contains several unique events: for example, the fall of mankind into corruption, the incarnation of God in the person of Jesus, and the redemption of the elected in the world to come after the destruction of the present world. -
The Conflict of Philosophy
THE CONFLICT OF PHILOSOPHY A HISTORY OF REASON DISORDER RAWAA MAHMOUD HUSSAIN Publishing Partner: IJSRP In Publication Partner: International Journal of Scientific and Research Publications (ISSN: 2250-3153) THE CONFLICT OF PHILOSOPHY A HISTORY OF REASON DISORDER RAWAA MAHMOUD HUSSAIN Publishing Partner: IJSRP Inc. www.ijsrp.org Publication Partner: International Journal of Scientific and Research Publications (ISSN: 2250-3153) Preface I have been inquiring about the ongoing nature of human relations and wondering: Whether the conflict represents a fundamental value that determines the international relationships or is there a way to the possibility of human coexistence and world peace? Today, in my work, “The Conflict of Philosophy,” I am trying to discover this idea in a new and different field, Philosophy. This book has been written and designed to collect the philosophy and its history as a methodology of research to study the conflict of philosophy. It is started with an introduction to understanding Samuel Huntington’s project of the Clash of Civilizations. It also maintains to search for the shadows and historical, social, cultural, scientific and religious extensions of this idea: Galileo Galilei (1564–1642): The message of science, the creation of the universe, Religion and life, the death of philosophy, and the turbulence of reason. I have also started, in chapter 1, with the most prominent eras in philosophy, which is the era of Greek philosophy, represented by Socrates (470/469 – 399 BC), Plato (c. 427 – 347 BCE), and Aristotle (c. 384 – 322 BCE). In chapter 2, I moved directly to the modern philosophy stated by Francis Bacon (1561–1626) and René Descartes (1596–1650).