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 Added by: Berta Grimau, Contributed by:
Publisher’s Note: Professor Merrie Bergmann presents an accessible introduction to the subject of manyvalued and fuzzy logic designed for use on undergraduate and graduate courses in nonclassical logic. Bergmann discusses the philosophical issues that give rise to fuzzy logic – problems arising from vague language – and returns to those issues as logical systems are presented. For historical and pedagogical reasons, threevalued logical systems are presented as useful intermediate systems for studying the principles and theory behind fuzzy logic. The major fuzzy logical systems – Lukasiewicz, Gödel, and product logics – are then presented as generalisations of threevalued systems that successfully address the problems of vagueness. A clear presentation of technical concepts, this book includes exercises throughout the text that pose straightforward problems, that ask students to continue proofs begun in the text, and that engage students in the comparison of logical systems.
Comment: In the words of the author: 'This textbook can be used as a complete basis for an introductory course on formal manyvalued and fuzzy logics, at either the upperlevel undergraduate or the graduate level, and it can also be used as a supplementary text in a variety of courses. There is considerable flexibility in either case. The truthvalued semantic chapters are independent of the algebraic and axiomatic ones, so that either of the latter may be skipped. Except for Section 13.3 of Chapter 13, the axiomatic chapters are also independent of the algebraic ones, and an instructor who chooses to skip the algebraic material can simply ignore the latter part of 13.3. Finally, Lukasiewicz fuzzy logic is presented independently of Gödel and product fuzzy logics, thus allowing an instructor to focus solely on the former. There are exercises throughout the text. Some pose straightforward problems for the student to solve, but many exercises also ask students to continue proofs begun in the text, to prove results analogous to those in the text, and to compare the various logical systems that are presented.' The book does include a review of classical propositional and firstorder logic, but the students should've taken at least one basic logic course before getting into this material.[This is a stub entry. Please add your comments to help us expand it]

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 Added by: Berta Grimau, Contributed by:
Abstract: This paper argues that the prominent accounts of logical knowledge have the consequence that they conflict with ordinary reasoning. On these accounts knowing a logical principle, for instance, is having a disposition to infer according to it. These accounts in particular conflict with socalled ‘reasoned change in view’, where someone does not infer according to a logical principle but revise their views instead. The paper also outlines a propositional account of logical knowledge which does not conflict with ordinary reasoning.
Comment: This paper proposes a certain characterisation of what it is to have knowledge of logical principles which makes it compatible with the way in which we reason ordinarily. It can be seen as an alternative to Harman's view in 'Change in View' according to which ordinary people do not at all 'employ' a deductive logic in reasoning. Thus this paper could be used in a course on the role of logic in reasoning, following the reading of Harman's work. More generally, this reading is suitable for any advanced undergraduate course or postgraduate course on the topic of rationality.[This is a stub entry. Please add your comments to help us expand it]

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 Added by: Sara Peppe, Contributed by:
Abstract: I propose a framework that explicates and distinguishes the epistemic roles of data and models within empirical inquiry through consideration of their use in scientific practice. After arguing that Suppes’ characterization of data models falls short in this respect, I discuss a case of data processing within exploratory research in plant phenotyping and use it to highlight the difference between practices aimed to make data usable as evidence and practices aimed to use data to represent a specific phenomenon. I then argue that whether a set of objects functions as data or models does not depend on intrinsic differences in their physical properties, level of abstraction or the degree of human intervention involved in generating them, but rather on their distinctive roles towards identifying and characterizing the targets of investigation. The paper thus proposes a characterization of data models that builds on Suppes’ attention to data practices, without however needing to posit a fixed hierarchy of data and models or a highly exclusionary definition of data models as statistical constructs.
Comment: This article deepens the role of model an data in the scientific investigation taking into account the scientific practice. Obviously, a general framework of the themes the author takes into account is needed.[This is a stub entry. Please add your comments to help us expand it]

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 Added by: Sara Peppe, Contributed by:
Publisher’s Note: Hannah Arendt’s last philosophical work was an intended threepart project entitled The Life of the Mind. Unfortunately, Arendt lived to complete only the first two parts, Thinking and Willing. Of the third, Judging, only the title page, with epigraphs from Cato and Goethe, was found after her death. As the titles suggest, Arendt conceived of her work as roughly parallel to the three Critiques of Immanuel Kant. In fact, while she began work on The Life of the Mind, Arendt lectured on “Kant’s Political Philosophy,” using the Critique of Judgment as her main text. The present volume brings Arendt’s notes for these lectures together with other of her texts on the topic of judging and provides important clues to the likely direction of Arendt’s thinking in this area.
Comment: This book provides a good overview of Arendt's perspective on Kant's political philosophy. Previous knowledge on Kant is needed.[This is a stub entry. Please add your comments to help us expand it]

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 Added by: Sara Peppe, Contributed by:
Introduction: From a logical point of view the measurement problem of quantum mechanics, can be described as a characteristic question of ‘semantical closure’ of a theory: to what extent can a consistent theory (in this case 2R) be closed with respect to the objects and the concepfs which are described and expressed in its metatheory?
Comment: This paper considers the measurement problem in Quantum Mechanics from a logical perspective. Previous and deep knowledge of logics and Quantum Mechanics' theories is vital.[This is a stub entry. Please add your comments to help us expand it]

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 Added by: Berta Grimau, Contributed by:
Summary: This article provides the basics of a typical logic, sometimes called ‘classical elementary logic’ or ‘classical firstorder logic’, in a rigorous yet accessible manner. Section 2 develops a formal language, with a syntax and grammar. Section 3 sets up a deductive system for the language, in the spirit of natural deduction. Section 4 provides a modeltheoretic semantics. Section 5 turns to the relationships between the deductive system and the semantics, and in particular, the relationship between derivability and validity. The authors show that an argument is derivable only if it is valid (soundness). Then they establish a converse: that an argument is valid only if it is derivable (completeness). They also briefly indicate other features of the logic, some of which are corollaries to soundness and completeness. The final section, Section 6, is devoted to a brief examination of the philosophical position that classical logic is ‘the one right logic’.
Comment: This article introduces all the necessary tools in order to understand both the prooftheoretic and the modeltheoretic aspects of firstorder classical logical consequence. As such it can be used as a main reading in an introductory logic course covering classical firstorder logic (assuming the students will have already looked at classical propositional logic). Moreover, the article covers some metatheoretic results (soundness, completeness, compactness, upward and downward LöwenheimSkolem), which makes it suitable as a reading for a slightly more advanced course in logic. Finally, the article includes a brief incursion into the topic of logical pluralism. This makes it suitable to be used in a course on nonclassical logics with an introduction module on classical logic.[This is a stub entry. Please add your comments to help us expand it]

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Publisher’s Note: Although sequent calculi constitute an important category of proof systems, they are not as well known as axiomatic and natural deduction systems. Addressing this deficiency, Proof Theory: Sequent Calculi and Related Formalisms presents a comprehensive treatment of sequent calculi, including a wide range of variations. It focuses on sequent calculi for various nonclassical logics, from intuitionistic logic to relevance logic, linear logic, and modal logic. In the first chapters, the author emphasizes classical logic and a variety of different sequent calculi for classical and intuitionistic logics. She then presents other nonclassical logics and metalogical results, including decidability results obtained specifically using sequent calculus formalizations of logics.
Comment: This book can be used in a variety of advanced undergraduate and postgraduate courses. Chapters 1, 2, 3 and 8 may be useful in an advanced undergraduate or beginning graduate course, where an emphasis is placed on classical logic and on a range of different proof calculi (mainly for classical logic). Chapters 4, 5 and 6 deal almost exclusively with nonclassical logics. Chapters 7 and 9 are rich in metalogical results, including results that have been obtained specifically using sequent calculus formalizations of various logics. These last five chapters might be used in a graduate course that embraces classical and nonclassical logics together with their metatheory. To facilitate the use of the book as a text in a course, the text is peppered with exercises. In general, the starring indicates an increase in difficulty, however, sometimes an exercise is starred simply because it goes beyond the scope of the book or it is very lengthy. Solutions to selected exercises may be found on the web at the URL www.ualberta.ca/˜bimbo/ProofTheoryBook.[This is a stub entry. Please add your comments to help us expand it]

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 Added by: Sara Peppe, Contributed by:
Abstract: The aim of this paper is to summarize a particular approach of doing metaphysics through physics – the primitive ontology approach. The idea is that any fundamental physical theory has a welldefined architecture, to the foundation of which there is the primitive ontology, which represents matter. According to the framework provided by this approach when applied to quantum mechanics, the wave function is not suitable to represent matter. Rather, the wave function has a nomological character, given that its role in the theory is to implement the law of evolution for the primitive ontology.
Comment: This article works well as a secondary reading since it refers to specific theories of physics. Previous knowledge on the cornerstones of philosophy of physics is needed.[This is a stub entry. Please add your comments to help us expand it]

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 Added by: Sara Peppe, Contributed by:
Publisher’s Note: Not limited to merely mathematics, probability has a rich and controversial philosophical aspect. ‘A Philosophical Introduction to Probability’ showcases lesserknown philosophical notions of probability and explores the debate over their interpretations. Galavotti traces the history of probability and its mathematical properties and then discusses various philosophical positions on probability, from the Pierre Simon de Laplace’s ‘classical’ interpretation of probability to the logical interpretation proposed by John Maynard Keynes. This book is a valuable resource for students in philosophy and mathematics and all readers interested in notions of probability
Comment: Very good article for philosophy of science and philosophy of probability courses. It works perfectly to build basic knowledge on the theme of probability.[This is a stub entry. Please add your comments to help us expand it]

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 Added by: Sara Peppe, Contributed by:
Abstract: This paper argues that it is scientific realists who should be most concerned about the issue of Platonism and antiPlatonism in mathematics. If one is merely interested in accounting for the practice of pure mathematics, it is unlikely that a story about the ontology of mathematical theories will be essential to such an account. The question of mathematical ontology comes to the fore, however, once one considers our scientific theories. Given that those theories include amongst their laws assertions that imply the existence of mathematical objects, scientific realism, when construed as a claim about the truth or approximate truth of our scientific theories, implies mathematical Platonism. However, a standard argument for scientific realism, the ‘no miracles’ argument, falls short of establishing mathematical Platonism. As a result, this argument cannot establish scientific realism as it is usually defined, but only some weaker position. Scientific ‘realists’ should therefore either redefine their position as a claim about the existence of unobservable physical objects, or alternatively look for an argument for their position that does establish mathematical Platonism.
Comment: Previous knowledge both on Platonism in philosophy of mathematics and scientific realism is needed. Essential paper for advanced courses of philosophy of science.[This is a stub entry. Please add your comments to help us expand it]