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Added by: Berta Grimau, Contributed by: Matt Clemens
Abstract: This talk surveys a range of positions on the fundamental metaphysical and epistemological questions about elementary logic, for example, as a starting point: what is the subject matter of logic - what makes its truths true? how do we come to know the truths of logic? A taxonomy is approached by beginning from well-known schools of thought in the philosophy of mathematics - Logicism, Intuitionism, Formalism, Realism - and sketching roughly corresponding views in the philosophy of logic. Kant, Mill, Frege, Wittgenstein, Carnap, Ayer, Quine, and Putnam are among the philosophers considered along the way.Ismael, Jenann. Quantum Mechanics2014, The Standford Encyclopedia of Philosophy-
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Added by: Laura Jimenez
Introduction: Quantum mechanics is, at least at first glance and at least in part, a mathematical machine for predicting the behaviors of microscopic particles - or, at least, of the measuring instruments we use to explore those behaviors - and in that capacity, it is spectacularly successful: in terms of power and precision, head and shoulders above any theory we have ever had. Mathematically, the theory is well understood; we know what its parts are, how they are put together, and why, in the mechanical sense (i.e., in a sense that can be answered by describing the internal grinding of gear against gear), the whole thing performs the way it does, how the information that gets fed in at one end is converted into what comes out the other. The question of what kind of a world it describes, however, is controversial; there is very little agreement, among physicists and among philosophers, about what the world is like according to quantum mechanics. Minimally interpreted, the theory describes a set of facts about the way the microscopic world impinges on the macroscopic one, how it affects our measuring instruments, described in everyday language or the language of classical mechanics. Disagreement centers on the question of what a microscopic world, which affects our apparatuses in the prescribed manner, is, or even could be, like intrinsically; or how those apparatuses could themselves be built out of microscopic parts of the sort the theory describes.Comment: The paper does not deal with the problem of the interpretation of quantum mechanics, but with the mathematical heart of the theory; the theory in its capacity as a mathematical machine. It is recommendable to read this paper before starting to read anything about the interpretations of the theory. The explanation is very clear and introductory and could serve as an introductory reading for both undergraduate and postgraduate courses in philosophy of science focused on the topic of quantum mechanics. Though clearly written, there is enough mathematics here to potentially put off symbol-phobes.
Cauman, Leigh S.. First Order Logic: An Introduction1998, Walter de Gruyter & Co.-
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Added by: Berta Grimau, Contributed by: Matt Clemens
Publisher's Note: This teaching book is designed to help its readers to reason systematically, reliably, and to some extent self-consciously, in the course of their ordinary pursuits-primarily in inquiry and in decision making. The principles and techniques recommended are explained and justified - not just stated; the aim is to teach orderly thinking, not the manipulation of symbols. The structure of material follows that of Quine's Methods of Logic, and may be used as an introduction to that work, with sections on truth-functional logic, predicate logic, relational logic, and identity and description. Exercises are based on problems designed by authors including Quine, John Cooley, Richard Jeffrey, and Lewis Carroll.Comment: This book is adequate for a first course on formal logic. Moreover, its table of contents follows that of Quine's "Methods of Logic", thus it can serve as an introduction or as a reference text for the study of the latter.
Fisher, Jennifer. On the Philosophy of Logic2007, Cengage Learning.-
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Added by: Berta Grimau, Contributed by: Matt Clemens
Publisher's Note: Jennifer Fisher's On the Philosophy of Logic explores questions about logic often overlooked by philosophers. Which of the many different logics available to us is right? How would we know? What makes a logic right in the first place? Is logic really a good guide to human reasoning? An ideal companion text for any course in symbolic logic, this lively and accessible book explains important logical concepts, introduces classical logic and its problems and alternatives, and reveals the rich and interesting philosophical issues that arise in exploring the fundamentals of logic.Comment: This book provides an introduction to some traditional questions within philosophy of logic. Moreover, it presents some non-classical logics. It includes an introduction to formal classical logic, so no previous technical knowledge is required. Adequate for a first course on philosophy of logic, either as main or further reading.
Friend, Michele. Introducing Philosophy of Mathematics2007, Acumen; reprinted by Routledge (2014).-
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Added by: Berta Grimau, Contributed by: Matt Clemens
Publisher's Note: What is mathematics about? Does the subject-matter of mathematics exist independently of the mind or are they mental constructions? How do we know mathematics? Is mathematical knowledge logical knowledge? And how is mathematics applied to the material world? In this introduction to the philosophy of mathematics, Michele Friend examines these and other ontological and epistemological problems raised by the content and practice of mathematics. Aimed at a readership with limited proficiency in mathematics but with some experience of formal logic it seeks to strike a balance between conceptual accessibility and correct representation of the issues. Friend examines the standard theories of mathematics - Platonism, realism, logicism, formalism, constructivism and structuralism - as well as some less standard theories such as psychologism, fictionalism and Meinongian philosophy of mathematics. In each case Friend explains what characterises the position and where the divisions between them lie, including some of the arguments in favour and against each. This book also explores particular questions that occupy present-day philosophers and mathematicians such as the problem of infinity, mathematical intuition and the relationship, if any, between the philosophy of mathematics and the practice of mathematics. Taking in the canonical ideas of Aristotle, Kant, Frege and Whitehead and Russell as well as the challenging and innovative work of recent philosophers like Benacerraf, Hellman, Maddy and Shapiro, Friend provides a balanced and accessible introduction suitable for upper-level undergraduate courses and the non-specialist.Comment: This book provides an introduction to the philosophy of mathematics. No previous mathematical skills/knowledge required. Suitable for undergraduate courses on philosophy of mathematics.
Uckelman, Sara L.. A Quantified Temporal Logic for Ampliation and Restriction2013, Vivarium 51(1-4): 485-510.-
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Added by: Berta Grimau, Contributed by: Sara L. Uckelman
Abstract: Temporal logic as a modern discipline is separate from classical logic; it is seen as an addition or expansion of the more basic propositional and predicate logics. This approach is in contrast with logic in the Middle Ages, which was primarily intended as a tool for the analysis of natural language. Because all natural language sentences have tensed verbs, medieval logic is inherently a temporal logic. This fact is most clearly exemplified in medieval theories of supposition. As a case study, we look at the supposition theory of Lambert of Lagny (Auxerre), extracting from it a temporal logic and providing a formalization of that logic.Comment: This article employs modal-temporal logic with Kripke semantics to formalize a particular supposition theory (Lambert of Lagny’s). Thus, it includes an original proposal. Moreover, it provides both an introduction to medieval supposition theory and an introduction to Kripke semantics. So, it could be used as a means to work on either of those topics. It does not involve many technicalities, but a bit of familiarity with modal logic is recommended.
Sagi, Gil. Models and Logical Consequence2014, Journal of Philosophical Logic 43(5): 943-964.-
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Added by: Berta Grimau
Abstract: This paper deals with the adequacy of the model-theoretic definition of logical consequence. Logical consequence is commonly described as a necessary relation that can be determined by the form of the sentences involved. In this paper, necessity is assumed to be a metaphysical notion, and formality is viewed as a means to avoid dealing with complex metaphysical questions in logical investigations. Logical terms are an essential part of the form of sentences and thus have a crucial role in determining logical consequence. Gila Sher and Stewart Shapiro each propose a formal criterion for logical terms within a model-theoretic framework, based on the idea of invariance under isomorphism. The two criteria are formally equivalent, and thus we have a common ground for evaluating and comparing Sher and Shapiro philosophical justification of their criteria. It is argued that Shapiro's blended approach, by which models represent possible worlds under interpretations of the language, is preferable to Sher’s formal-structural view, according to which models represent formal structures. The advantages and disadvantages of both views’ reliance on isomorphism are discussed.Comment: This paper provides an original view on the debate on the adequacy of the model-theoretic notion of logical consequence as well as a good overview of the relevant part of the debate. It can be used as standing on its own, but it can also serve as a complement to Sher (1996), also written by a female logician, and Shapiro (1998). Adequate for a general course on philosophy of logic or in a more specialized course on logical consequence. The paper is not technical, although students should've have taken at least an introductory logic course.
Keefe, Rosanna. Theories of Vagueness2000, Cambridge University Press.-
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Added by: Berta Grimau
Publisher's Note: Most expressions in natural language are vague. But what is the best semantic treatment of terms like 'heap', 'red' and 'child'? And what is the logic of arguments involving this kind of vague expression? These questions are receiving increasing philosophical attention, and in this timely book Rosanna Keefe explores the questions of what we should want from an account of vagueness and how we should assess rival theories. Her discussion ranges widely and comprehensively over the main theories of vagueness and their supporting arguments, and she offers a powerful and original defence of a form of supervaluationism, a theory that requires almost no deviation from standard logic yet can accommodate the lack of sharp boundaries to vague predicates and deal with the paradoxes of vagueness in a methodologically satisfying way. Her study will be of particular interest to readers in philosophy of language and of mind, philosophical logic, epistemology and metaphysics.Comment: This book could be used in a philosophy of logic or a philosophy of language course which had a section on vagueness (either at undergraduate or postgraduate level). The first chapter provides a good main reading for such purpose. The book can also be used in a course focused on vagueness exclusively. The technical discussion is minimized throughout and presupposes only some familiarity with elementary logic.
Massimi, Michela, Duncan Pritchard. What is this thing called science?2014, in M. Massimi (ed.), Philosophy and the Sciences for Everyone. Routledge-
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Added by: Laura Jimenez
Summary: This chapter offers a general introduction to philosophy of science. The first part of the chapter takes the reader through the famous relativist debate about Galileo and Cardinal Bellarmine. Several important questions on the topic are explored, such as what makes scientific knowledge special compared with other kinds of knowledge or the importance of demarcating science from non-science. Finally, the chapters gives an overview on how philosophers such as Popper, Duhem, Quine and Kuhn came to answer these questions.Comment: This chapter could be used as in introductory reading to review the nature of scientific knowledge and the most important debates about the scientific method. It is recommendable for undergraduate courses in philosophy of science. No previous knowledge of the field is needed in order to understand the content. The chapter is an introduction to the rest of the book Philosophy and the Sciences for Everyone. Some discussions explored here, such as the problem of underdetermination or Tomas Kuhn's view of scientific knowledge are central to the following chapters in philosophy of cosmology.
Massimi, Michela, John Peacock. What are dark matter and dark energy?2014, in M. Massimi (ed.), Philosophy and the Sciences for Everyone. Routledge-
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Added by: Laura Jimenez
Summary: According to the currently accepted model in cosmology, our universe is made up of 5% of ordinary matter, 25% cold dark matter, and 70% dark energy. But what kind of entities are dark matter and dark energy? This chapter asks what the evidence for these entities is and which rival theories are currently available. This provides with an opportunity to explore a well-known philosophical problem known as under-determination of theory by evidence.Comment: This Chapter could serve as an introduction to contemporary cosmology and particle physics or as an example to illustrate the problem of under-determination of theory by evidence. The chapter looks at alternative theories that explain the same experimental evidence without recourse to the hypothesis of dark matter and dark energy and discusses the rationale for choosing between rival research programs. Like the rest of the chapters in this book, it is a reading recommendable for undergraduate students. It is recommended to read it after Chapter 2 of the same book.
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Maddy, Penelope. The Philosophy of Logic
2012, Bulletin of Symbolic Logic 18(4): 481-504.
Comment: This is a survey article which considers positions within philosophy of logic analogous to the views held by the various schools of the philosophy of mathematics. The article touches briefly on many positions and authors and is thus an excellent introduction to the philosophy of logic, specially for students already familiar with the philosophy of mathematics. The text is informal and it does not involve any proofs.