Search results for 'mathematical definitions' (try it on Scholar)

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  1. Christopher Belanger (2013). On Two Mathematical Definitions of Observational Equivalence: Manifest Isomorphism and Reconsidered. Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 44 (2):69-76.score: 45.0
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  2. Jamie Tappenden (2008). Mathematical Concepts and Definitions. In Paolo Mancosu (ed.), The Philosophy of Mathematical Practice. Oup Oxford. 256--275.score: 39.0
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  3. S. C. Kleene (1949). Review: K. R. Popper, On the Theory of Deduction, Part I. Derivation and its Generalizations; K. R. Popper, On the Theory of Deduction, Part II. The Definitions of Classical and Intuitionist Negation; K. R. Popper, The Trivialization of Mathematical Logic. [REVIEW] Journal of Symbolic Logic 14 (1):62-63.score: 36.0
  4. Jan Mycielski (2004). On the Tension Between Tarski's Nominalism and His Model Theory (Definitions for a Mathematical Model of Knowledge). Annals of Pure and Applied Logic 126 (1-3):215-224.score: 36.0
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  5. Marwan Rashed (1996). Ex Aequali Ratios in the Greek and Arabic Euclidean Traditions Gregg De Young Euclid Discusses the Ex Aequali Relationship Twice in the Elements. The First is in Book V (Based on Definitions 17 and 18, Propositions 22 and 23), During His Discussion of Arithmetical Relations Between Mathematical Magnitudes In. [REVIEW] Arabic Sciences and Philosophy 6.score: 36.0
  6. Robert McNaughton (1997). Robinson Raphael M.. Restricted Set-Theoretical Definitions in Arithmetic. Proceedings of the American Mathematical Society, Vol. 9 (1958), Pp. 238–242. Robinson Raphael M.. Restricted Set-Theoretical Definitions in Arithmetic. Summaries of Talks Presented at the Summer Institute for Symbolic Logic, Cornell University, 1957, 2nd Edn., Communications Research Division, Institute for Defense Analyses, Princeton, NJ, 1960, Pp. 139–140. [REVIEW] Journal of Symbolic Logic 31 (4):659-660.score: 36.0
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  7. Solomon Feferman, Is the Continuum Hypothesis a Definite Mathematical Problem?score: 24.0
    The purpose of this article is to explain why I believe that the Continuum Hypothesis (CH) is not a definite mathematical problem. My reason for that is that the concept of arbitrary set essential to its formulation is vague or underdetermined and there is no way to sharpen it without violating what it is supposed to be about. In addition, there is considerable circumstantial evidence to support the view that CH is not definite.
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  8. Sanford Shieh (2009). Teaching & Learning Guide For: Frege on Definitions. Philosophy Compass 4 (5):885-888.score: 24.0
    Three clusters of philosophically significant issues arise from Frege's discussions of definitions. First, Frege criticizes the definitions of mathematicians of his day, especially those of Weierstrass and Hilbert. Second, central to Frege's philosophical discussion and technical execution of logicism is the so-called Hume's Principle, considered in The Foundations of Arithmetic . Some varieties of neo-Fregean logicism are based on taking this principle as a contextual definition of the operator 'the number of …', and criticisms of such neo-Fregean programs (...)
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  9. Charlotte Werndl (2009). Justifying Definitions in Mathematics—Going Beyond Lakatos. Philosophia Mathematica 17 (3):313-340.score: 24.0
    This paper addresses the actual practice of justifying definitions in mathematics. First, I introduce the main account of this issue, namely Lakatos's proof-generated definitions. Based on a case study of definitions of randomness in ergodic theory, I identify three other common ways of justifying definitions: natural-world justification, condition justification, and redundancy justification. Also, I clarify the interrelationships between the different kinds of justification. Finally, I point out how Lakatos's ideas are limited: they fail to show how (...)
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  10. Michael Rathjen (1996). Monotone Inductive Definitions in Explicit Mathematics. Journal of Symbolic Logic 61 (1):125-146.score: 24.0
    The context for this paper is Feferman's theory of explicit mathematics, T 0 . We address a problem that was posed in [6]. Let MID be the principle stating that any monotone operation on classifications has a least fixed point. The main objective of this paper is to show that T 0 + MID, when based on classical logic, also proves the existence of non-monotone inductive definitions that arise from arbitrary extensional operations on classifications. From the latter we deduce (...)
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  11. Uri Nodelman & Edward N. Zalta (2014). Foundations for Mathematical Structuralism. Mind 123 (489):39-78.score: 23.0
    We investigate the form of mathematical structuralism that acknowledges the existence of structures and their distinctive structural elements. This form of structuralism has been subject to criticisms recently, and our view is that the problems raised are resolved by proper, mathematics-free theoretical foundations. Starting with an axiomatic theory of abstract objects, we identify a mathematical structure as an abstract object encoding the truths of a mathematical theory. From such foundations, we derive consequences that address the main questions (...)
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  12. Demetra Christopoulou (2014). Weyl on Fregean Implicit Definitions: Between Phenomenology and Symbolic Construction. Journal for General Philosophy of Science 45 (1):35-47.score: 23.0
    This paper aims to investigate certain aspects of Weyl’s account of implicit definitions. The paper takes under consideration Weyl’s approach to a certain kind of implicit definitions i.e. abstraction principles introduced by Frege.ion principles are bi-conditionals that transform certain equivalence relations into identity statements, defining thereby mathematical terms in an implicit way. The paper compares the analytic reading of implicit definitions offered by the Neo-Fregean program with Weyl’s account which has phenomenological leanings. The paper suggests that (...)
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  13. Thomas Mormann (2005). Mathematical Metaphors in Natorp’s Neo-Kantian Epistemology and Philosophy of Science. In Falk Seeger, Johannes Lenard & Michael H. G. Hoffmann (eds.), Activity and Sign. Grounding Mathematical Education. Springer.score: 21.0
    A basic thesis of Neokantian epistemology and philosophy of science contends that the knowing subject and the object to be known are only abstractions. What really exists, is the relation between both. For the elucidation of this “knowledge relation ("Erkenntnisrelation") the Neokantians of the Marburg school used a variety of mathematical metaphors. In this con-tribution I reconsider some of these metaphors proposed by Paul Natorp, who was one of the leading members of the Marburg school. It is shown that (...)
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  14. Paul Cortois (1996). The Structure of Mathematical Experience According to Jean Cavaillèst. Philosophia Mathematica 4 (1):18-41.score: 21.0
    In this expository article one of the contributions of Jean Cavailles to the philosophy of mathematics is presented: the analysis of ‘mathematical experience’. The place of Cavailles on the logico-philosophical scene of the 30s and 40s is sketched. I propose a partial interpretation of Cavailles's epistemological program of so-called ‘conceptual dialectics’: mathematical holism, duality principles, the notion of formal contents, and the specific temporal structure of conceptual dynamics. The structure of mathematical abstraction is analysed in terms of (...)
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  15. Volker Peckhaus (1999). 19th Century Logic Between Philosophy and Mathematics. Bulletin of Symbolic Logic 5 (4):433-450.score: 21.0
    The history of modern logic is usually written as the history of mathematical or, more general, symbolic logic. As such it was created by mathematicians. Not regarding its anticipations in Scholastic logic and in the rationalistic era, its continuous development began with George Boole's The Mathematical Analysis of Logic of 1847, and it became a mathematical subdiscipline in the early 20th century. This style of presentation cuts off one eminent line of development, the philosophical development of logic, (...)
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  16. S. Friederich (2011). Motivating Wittgenstein's Perspective on Mathematical Sentences as Norms. Philosophia Mathematica 19 (1):1-19.score: 21.0
    The later Wittgenstein’s perspective on mathematical sentences as norms is motivated for sentences belonging to Hilbertian axiomatic systems where the axioms are treated as implicit definitions. It is shown that in this approach the axioms are employed as norms in that they function as standards of what counts as using the concepts involved. This normative dimension of their mode of use, it is argued, is inherited by the theorems derived from them. Having been motivated along these lines, Wittgenstein’s (...)
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  17. R. Eugene Collins (2005). The Mathematical Basis for Physical Laws. Foundations of Physics 35 (5):743-785.score: 21.0
    Laws of mechanics, quantum mechanics, electromagnetism, gravitation and relativity are derived as “related mathematical identities” based solely on the existence of a joint probability distribution for the position and velocity of a particle moving on a Riemannian manifold. This probability formalism is necessary because continuous variables are not precisely observable. These demonstrations explain why these laws must have the forms previously discovered through experiment and empirical deduction. Indeed, the very existence of electric, magnetic and gravitational fields is predicted by (...)
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  18. A. T. Balaban (2005). Reflections About Mathematical Chemistry. Foundations of Chemistry 7 (3):289-306.score: 21.0
    A personal account is presented for the present status of mathematical chemistry, with emphasis on non-numerical applications. These use mainly graph-theoretical concepts. Most computational chemical applications involve quantum chemistry and are therefore largely reducible to physics, while discrete mathematical applications often do not. A survey is provided for opinions and definitions of mathematical chemistry, and then for journals, books and book series, as well as symposia of mathematical chemistry.
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  19. John Mandel (1964/1984). The Statistical Analysis of Experimental Data. Dover.score: 21.0
    First half of book presents fundamental mathematical definitions, concepts and facts while remaining half deals with statistics primarily as an interpretive tool. Well-written text, numerous worked examples with step-by-step presentation. 116 tables.
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  20. Reinhard Kahle (2002). Mathematical Proof Theory in the Light of Ordinal Analysis. Synthese 133 (1/2):237 - 255.score: 21.0
    We give an overview of recent results in ordinal analysis. Therefore, we discuss the different frameworks used in mathematical proof-theory, namely "subsystem of analysis" including "reverse mathematics", "Kripke-Platek set theory", "explicit mathematics", "theories of inductive definitions", "constructive set theory", and "Martin-Löf's type theory".
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  21. Tyler Marghetis & Rafael Núñez (2013). The Motion Behind the Symbols: A Vital Role for Dynamism in the Conceptualization of Limits and Continuity in Expert Mathematics. Topics in Cognitive Science 5 (2):299-316.score: 21.0
    The canonical history of mathematics suggests that the late 19th-century “arithmetization” of calculus marked a shift away from spatial-dynamic intuitions, grounding concepts in static, rigorous definitions. Instead, we argue that mathematicians, both historically and currently, rely on dynamic conceptualizations of mathematical concepts like continuity, limits, and functions. In this article, we present two studies of the role of dynamic conceptual systems in expert proof. The first is an analysis of co-speech gesture produced by mathematics graduate students while proving (...)
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  22. Kajsa Bråting (2012). Ambiguities of Fundamental Concepts in Mathematical Analysis During the Mid-Nineteenth Century. Foundations of Science 17 (4):301-320.score: 21.0
    In this paper we consider the major development of mathematical analysis during the mid-nineteenth century. On the basis of Jahnke’s (Hist Math 20(3):265–284, 1993 ) distinction between considering mathematics as an empirical science based on time and space and considering mathematics as a purely conceptual science we discuss the Swedish nineteenth century mathematician E.G. Björling’s general view of real- and complexvalued functions. We argue that Björling had a tendency to sometimes consider mathematical objects in a naturalistic way. One (...)
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  23. Matthew Donald (1995). A Mathematical Characterization of the Physical Structure of Observers. Foundations of Physics 25 (4):529-571.score: 21.0
    It is proposed that the physical structure of an observer in quantum mechanics is constituted by a pattern of elementary localized switching events. A key preliminary step in giving mathematical expression to this proposal is the introduction of an equivalence relation on sequences of spacetime sets which relates a sequence to any other sequence to which it can be deformed without change of causal arrangement. This allows an individual observer to be associated with a finite structure. The identification of (...)
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  24. Andrew Aberdein (2013). Mathematical Wit and Mathematical Cognition. Topics in Cognitive Science 5 (2):231-250.score: 21.0
    The published works of scientists often conceal the cognitive processes that led to their results. Scholars of mathematical practice must therefore seek out less obvious sources. This article analyzes a widely circulated mathematical joke, comprising a list of spurious proof types. An account is proposed in terms of argumentation schemes: stereotypical patterns of reasoning, which may be accompanied by critical questions itemizing possible lines of defeat. It is argued that humor is associated with risky forms of inference, which (...)
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  25. Thomas Forster (2007). Implementing Mathematical Objects in Set Theory. Logique Et Analyse 50 (197):79-86.score: 21.0
    In general little thought is given to the general question of how to implement mathematical objects in set theory. It is clear that—at various times in the past—people have gone to considerable lengths to devise implementations with nice properties. There is a litera- ture on the evolution of the Wiener-Kuratowski ordered pair, and a discussion by Quine of the merits of an ordered-pair implemen- tation that makes every set an ordered pair. The implementation of ordinals as Von Neumann ordinals (...)
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  26. Steven Kieffer, Jeremy Avigad & Harvey Friedman, A Language for Mathematical Knowledge Management.score: 21.0
    We argue that the language of Zermelo Fraenkel set theory with definitions and partial functions provides the most promising bedrock semantics for communicating and sharing mathematical knowledge. We then describe a syntactic sugaring of that language that provides a way of writing remarkably readable assertions without straying far from the set-theoretic semantics. We illustrate with some examples of formalized textbook definitions from elementary set theory and point-set topology. We also present statistics concerning the complexity of these (...), under various complexity measures. (shrink)
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  27. Helen De Cruz & Johan De Smedt (2013). Mathematical Symbols as Epistemic Actions. Synthese 190 (1):3-19.score: 18.0
    Recent experimental evidence from developmental psychology and cognitive neuroscience indicates that humans are equipped with unlearned elementary mathematical skills. However, formal mathematics has properties that cannot be reduced to these elementary cognitive capacities. The question then arises how human beings cognitively deal with more advanced mathematical ideas. This paper draws on the extended mind thesis to suggest that mathematical symbols enable us to delegate some mathematical operations to the external environment. In this view, mathematical symbols (...)
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  28. P. B. Andrews (2002). An Introduction to Mathematical Logic and Type Theory: To Truth Through Proof. Kluwer Academic Publishers.score: 18.0
    This introduction to mathematical logic starts with propositional calculus and first-order logic. Topics covered include syntax, semantics, soundness, completeness, independence, normal forms, vertical paths through negation normal formulas, compactness, Smullyan's Unifying Principle, natural deduction, cut-elimination, semantic tableaux, Skolemization, Herbrand's Theorem, unification, duality, interpolation, and definability. The last three chapters of the book provide an introduction to type theory (higher-order logic). It is shown how various mathematical concepts can be formalized in this very expressive formal language. This expressive notation (...)
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  29. Valeria Giardino (2010). Intuition and Visualization in Mathematical Problem Solving. Topoi 29 (1):29-39.score: 18.0
    In this article, I will discuss the relationship between mathematical intuition and mathematical visualization. I will argue that in order to investigate this relationship, it is necessary to consider mathematical activity as a complex phenomenon, which involves many different cognitive resources. I will focus on two kinds of danger in recurring to visualization and I will show that they are not a good reason to conclude that visualization is not reliable, if we consider its use in (...) practice. Then, I will give an example of mathematical reasoning with a figure, and show that both visualization and intuition are involved. I claim that mathematical intuition depends on background knowledge and expertise, and that it allows to see the generality of the conclusions obtained by means of visualization. (shrink)
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  30. Giuseppe Longo & Arnaud Viarouge (2010). Mathematical Intuition and the Cognitive Roots of Mathematical Concepts. Topoi 29 (1):15-27.score: 18.0
    The foundation of Mathematics is both a logico-formal issue and an epistemological one. By the first, we mean the explicitation and analysis of formal proof principles, which, largely a posteriori, ground proof on general deduction rules and schemata. By the second, we mean the investigation of the constitutive genesis of concepts and structures, the aim of this paper. This “genealogy of concepts”, so dear to Riemann, Poincaré and Enriques among others, is necessary both in order to enrich the foundational analysis (...)
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  31. Helen De Cruz & Johan De Smedt (2010). The Innateness Hypothesis and Mathematical Concepts. Topoi 29 (1):3-13.score: 18.0
    In historical claims for nativism, mathematics is a paradigmatic example of innate knowledge. Claims by contemporary developmental psychologists of elementary mathematical skills in human infants are a legacy of this. However, the connection between these skills and more formal mathematical concepts and methods remains unclear. This paper assesses the current debates surrounding nativism and mathematical knowledge by teasing them apart into two distinct claims. First, in what way does the experimental evidence from infants, nonhuman animals and neuropsychology (...)
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  32. José Ferreirós (2009). Hilbert, Logicism, and Mathematical Existence. Synthese 170 (1):33 - 70.score: 18.0
    David Hilbert’s early foundational views, especially those corresponding to the 1890s, are analysed here. I consider strong evidence for the fact that Hilbert was a logicist at that time, following upon Dedekind’s footsteps in his understanding of pure mathematics. This insight makes it possible to throw new light on the evolution of Hilbert’s foundational ideas, including his early contributions to the foundations of geometry and the real number system. The context of Dedekind-style logicism makes it possible to offer a new (...)
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  33. Simon Fokt (2012). Pornographic Art - A Case From Definitions. British Journal of Aesthetics 52 (3):287-300.score: 18.0
    On the whole, neither those who hold that pornography can never be art nor their opponents specify what they actually mean by ‘art’, even though it seems natural that their conclusions should vary depending on how the concept is understood. This paper offers a ‘definitional crossword’ and confronts some definitions of pornography with the currently most well-established definitions of art. My discussion shows that following any of the modern definitions entails that at least some pornography not only (...)
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  34. Marianna Antonutti Marfori (2010). Informal Proofs and Mathematical Rigour. Studia Logica 96 (2):261-272.score: 18.0
    The aim of this paper is to provide epistemic reasons for investigating the notions of informal rigour and informal provability. I argue that the standard view of mathematical proof and rigour yields an implausible account of mathematical knowledge, and falls short of explaining the success of mathematical practice. I conclude that careful consideration of mathematical practice urges us to pursue a theory of informal provability.
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  35. Michał Walicki (2012). Introduction to Mathematical Logic. World Scientific.score: 18.0
    A history of logic -- Patterns of reasoning -- A language and its meaning -- A symbolic language -- 1850-1950 mathematical logic -- Modern symbolic logic -- Elements of set theory -- Sets, functions, relations -- Induction -- Turning machines -- Computability and decidability -- Propositional logic -- Syntax and proof systems -- Semantics of PL -- Soundness and completeness -- First order logic -- Syntax and proof systems of FOL -- Semantics of FOL -- More semantics -- Soundness (...)
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  36. W. V. Quine (1951). Mathematical Logic. Cambridge, Harvard University Press.score: 18.0
    INTRODUCTION MATHEMATICAL logic differs from the traditional formal logic so markedly in method, and so far surpasses it in power and subtlety, ...
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  37. Margaret Catherine Morrison (2006). Scientific Understanding and Mathematical Abstraction. Philosophia 34 (3):337-353.score: 18.0
    This paper argues for two related theses. The first is that mathematical abstraction can play an important role in shaping the way we think about and hence understand certain phenomena, an enterprise that extends well beyond simply representing those phenomena for the purpose of calculating/predicting their behaviour. The second is that much of our contemporary understanding and interpretation of natural selection has resulted from the way it has been described in the context of statistics and mathematics. I argue for (...)
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  38. Gualtiero Piccinini (2003). Alan Turing and the Mathematical Objection. Minds and Machines 13 (1):23-48.score: 18.0
    This paper concerns Alan Turing’s ideas about machines, mathematical methods of proof, and intelligence. By the late 1930s, Kurt Gödel and other logicians, including Turing himself, had shown that no finite set of rules could be used to generate all true mathematical statements. Yet according to Turing, there was no upper bound to the number of mathematical truths provable by intelligent human beings, for they could invent new rules and methods of proof. So, the output of a (...)
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  39. Hao Wang (1981/1993). Popular Lectures on Mathematical Logic. Dover Publications.score: 18.0
    Noted logician and philosopher addresses various forms of mathematical logic, discussing both theoretical underpinnings and practical applications. After historical survey, lucid treatment of set theory, model theory, recursion theory and constructivism and proof theory. Place of problems in development of theories of logic, logic’s relationship to computer science, more. Suitable for readers at many levels of mathematical sophistication. 3 appendixes. Bibliography. 1981 edition.
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  40. Axel Gelfert (2011). Mathematical Formalisms in Scientific Practice: From Denotation to Model-Based Representation. Studies in History and Philosophy of Science 42 (2):272-286.score: 18.0
    The present paper argues that ‘mature mathematical formalisms’ play a central role in achieving representation via scientific models. A close discussion of two contemporary accounts of how mathematical models apply—the DDI account (according to which representation depends on the successful interplay of denotation, demonstration and interpretation) and the ‘matching model’ account—reveals shortcomings of each, which, it is argued, suggests that scientific representation may be ineliminably heterogeneous in character. In order to achieve a degree of unification that is compatible (...)
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  41. Imre Lakatos (1976). Proofs and Refutations: The Logic of Mathematical Discovery. Cambridge University Press.score: 18.0
    Proofs and Refutations is essential reading for all those interested in the methodology, the philosophy and the history of mathematics. Much of the book takes the form of a discussion between a teacher and his students. They propose various solutions to some mathematical problems and investigate the strengths and weaknesses of these solutions. Their discussion (which mirrors certain real developments in the history of mathematics) raises some philosophical problems and some problems about the nature of mathematical discovery or (...)
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  42. Richard Tieszen (2010). Mathematical Problem-Solving and Ontology: An Exercise. [REVIEW] Axiomathes 20 (2-3):295-312.score: 18.0
    In this paper the reader is asked to engage in some simple problem-solving in classical pure number theory and to then describe, on the basis of a series of questions, what it is like to solve the problems. In the recent philosophy of mind this “what is it like” question is one way of signaling a turn to phenomenological description. The description of what it is like to solve the problems in this paper, it is argued, leads to several morals (...)
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  43. Andrea Cantini (1996). Logical Frameworks for Truth and Abstraction: An Axiomatic Study. Elsevier Science B.V..score: 18.0
    This English translation of the author's original work has been thoroughly revised, expanded and updated. The book covers logical systems known as type-free or self-referential . These traditionally arise from any discussion on logical and semantical paradoxes. This particular volume, however, is not concerned with paradoxes but with the investigation of type-free sytems to show that: (i) there are rich theories of self-application, involving both operations and truth which can serve as foundations for property theory and formal semantics; (ii) these (...)
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  44. Stephen Cole Kleene (1967/2002). Mathematical Logic. Dover Publications.score: 18.0
    Undergraduate students with no prior classroom instruction in mathematical logic will benefit from this evenhanded multipart text by one of the centuries greatest authorities on the subject. Part I offers an elementary but thorough overview of mathematical logic of first order. The treatment does not stop with a single method of formulating logic; students receive instruction in a variety of techniques, first learning model theory (truth tables), then Hilbert-type proof theory, and proof theory handled through derived rules. Part (...)
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  45. David Sherry (2009). The Role of Diagrams in Mathematical Arguments. Foundations of Science 14 (1-2):59-74.score: 18.0
    Recent accounts of the role of diagrams in mathematical reasoning take a Platonic line, according to which the proof depends on the similarity between the perceived shape of the diagram and the shape of the abstract object. This approach is unable to explain proofs which share the same diagram in spite of drawing conclusions about different figures. Saccheri’s use of the bi-rectangular isosceles quadrilateral in Euclides Vindicatus provides three such proofs. By forsaking abstract objects it is possible to give (...)
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  46. Christopher Clarke (forthcoming). Multi-Level Selection and the Explanatory Value of Mathematical Decompositions. British Journal for the Philosophy of Science.score: 18.0
    Do multi-level selection explanations of the evolution of social traits deepen the understanding provided by single-level explanations? Central to the former is a mathematical theorem, the multi-level Price decomposition. I build a framework through which to understand the explanatory role of such non-empirical decompositions in scientific practice. Applying this general framework to the present case places two tasks on the agenda. The first task is to distinguish the various ways of suppressing within-collective variation in fitness, and moreover to evaluate (...)
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  47. A. Prestel (2011). Mathematical Logic and Model Theory: A Brief Introduction. Springer.score: 18.0
    Therefore, the text is divided into three parts: an introduction into mathematical logic (Chapter 1), model theory (Chapters 2 and 3), and the model theoretic ...
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  48. Christian Hennig (2010). Mathematical Models and Reality: A Constructivist Perspective. [REVIEW] Foundations of Science 15 (1):29-48.score: 18.0
    To explore the relation between mathematical models and reality, four different domains of reality are distinguished: observer-independent reality (to which there is no direct access), personal reality, social reality and mathematical/formal reality. The concepts of personal and social reality are strongly inspired by constructivist ideas. Mathematical reality is social as well, but constructed as an autonomous system in order to make absolute agreement possible. The essential problem of mathematical modelling is that within mathematics there is agreement (...)
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  49. Jennifer Wilson Mulnix (2008). Reliabilism, Intuition, and Mathematical Knowledge. Filozofia 62 (8):715-723.score: 18.0
    It is alleged that the causal inertness of abstract objects and the causal conditions of certain naturalized epistemologies precludes the possibility of mathematical know- ledge. This paper rejects this alleged incompatibility, while also maintaining that the objects of mathematical beliefs are abstract objects, by incorporating a naturalistically acceptable account of ‘rational intuition.’ On this view, rational intuition consists in a non-inferential belief-forming process where the entertaining of propositions or certain contemplations results in true beliefs. This view is free (...)
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  50. Mauro Dorato (2012). Mathematical Biology and the Existence of Biological Laws. In DieksD (ed.), Probabilities, Laws and Structure. Springer.score: 18.0
    An influential position in the philosophy of biology claims that there are no biological laws, since any apparently biological generalization is either too accidental, fact-like or contingent to be named a law, or is simply reducible to physical laws that regulate electrical and chemical interactions taking place between merely physical systems. In the following I will stress a neglected aspect of the debate that emerges directly from the growing importance of mathematical models of biological phenomena. My main aim is (...)
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