Search results for 'Mathematical literature' (try it on Scholar)

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  1. Emilia Anvarovna Taissina (2008). Philosophical Truth in Mathematical Terms and Literature Analogies. Proceedings of the Xxii World Congress of Philosophy 53:273-278.score: 120.0
    The article is based upon the following starting position. In this post-modern time, it seems that no scholar in Europe supports what is called “Enlightenment Project” with its naïve objectivism and Correspondence Theory of Truth1, - though not being really hostile, just strongly skeptical about it. No old-fasioned “classical” academical texts; only His Majesty Discourse as chain of interpretations and reinterpretations. What was called objectivity “proved to be” intersubjectivity; what was called Object (in Latin and German and Russian tradition) now (...)
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  2. National Reference Center for Bioethics Literature (2001). After BIOETHICSLINE: Online Searching of the Bioethics Literature. Kennedy Institute of Ethics Journal 11 (4):387-389.score: 120.0
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  3. National Reference Center for Bioethics Literature (2007). News From the National Reference Center for Bioethics Literature (NRCBL) and the National Information Resource on Ethics and Human Genetics (NIREHG). Kennedy Institute of Ethics Journal 17 (4).score: 120.0
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  4. David Reed (1995). Figures of Thought: Mathematics and Mathematical Texts. Routledge.score: 96.0
    Figures of Thought looks at how mathematical works can be read as texts and examines their textual strategies. David Reed offers the first sustained and critical attempt to find a consistent argument or narrative thread in mathematical texts. Reed selects mathematicians from a range of historical periods and compares their approaches to organizing and arguing texts, using an extended commentary on Euclid's Elements as a central structuring framework. He develops fascinating interpretations of mathematicians' work throughout history, from Descartes (...)
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  5. Adrian Heathcote (2014). On the Exhaustion of Mathematical Entities by Structures. Axiomathes 24 (2):167-180.score: 66.0
    There has been considerable discussion in the literature of one kind of identity problem that mathematical structuralism faces: the automorphism problem, in which the structure is unable to individuate the mathematical entities in its domain. Shapiro (Philos Math 16(3):285–309, 2008) has partly responded to these concerns. But I argue here that the theory faces an even more serious kind of identity problem, which the theory can’t overcome staying within its remit. I give two examples to make the (...)
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  6. Robert Schwartz (1995). Is Mathematical Competence Innate? Philosophy of Science 62 (2):227-40.score: 58.0
    Despite a vast philosophical literature on the epistemology of mathematics and much speculation about how, in principle, knowledge of this domain is possible, little attention has been paid to the psychological findings and theories concerning the acquisition, comprehension and use of mathematical knowledge. This contrasts sharply with recent philosophical work on language where comparable issues and problems arise. One topic that is the center of debate in the study of mathematical cognition is the question of innateness. This (...)
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  7. A. Baker (2003). Does the Existence of Mathematical Objects Make a Difference? Australasian Journal of Philosophy 81 (2):246 – 264.score: 54.0
    In this paper I examine a strategy which aims to bypass the technicalities of the indispensability debate and to offer a direct route to nominalism. The starting-point for this alternative nominalist strategy is the claim that--according to the platonist picture--the existence of mathematical objects makes no difference to the concrete, physical world. My principal goal is to show that the 'Makes No Difference' (MND) Argument does not succeed in undermining platonism. The basic reason why not is that the makes-no-difference (...)
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  8. Aidan Lyon (2012). Mathematical Explanations Of Empirical Facts, And Mathematical Realism. Australasian Journal of Philosophy 90 (3):559 - 578.score: 54.0
    A main thread of the debate over mathematical realism has come down to whether mathematics does explanatory work of its own in some of our best scientific explanations of empirical facts. Realists argue that it does; anti-realists argue that it doesn't. Part of this debate depends on how mathematics might be able to do explanatory work in an explanation. Everyone agrees that it's not enough that there merely be some mathematics in the explanation. Anti-realists claim there is nothing mathematics (...)
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  9. Waldyr A. Rodrigues Jr, Quintino A. G. De Souza & Yuri Bozhkov (1995). The Mathematical Structure of Newtonian Spacetime: Classical Dynamics and Gravitation. [REVIEW] Foundations of Physics 25 (6):871-924.score: 54.0
    We give a precise and modern mathematical characterization of the Newtonian spacetime structure (ℕ). Our formulation clarifies the concepts of absolute space, Newton's relative spaces, and absolute time. The concept of reference frames (which are “timelike” vector fields on ℕ) plays a fundamental role in our approach, and the classification of all possible reference frames on ℕ is investigated in detail. We succeed in identifying a Lorentzian structure on ℕ and we study the classical electrodynamics of Maxwell and Lorentz (...)
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  10. A. Baker (2012). Science-Driven Mathematical Explanation. Mind 121 (482):243-267.score: 54.0
    Philosophers of mathematics have become increasingly interested in the explanatory role of mathematics in empirical science, in the context of new versions of the Quinean ‘Indispensability Argument’ which employ inference to the best explanation for the existence of abstract mathematical objects. However, little attention has been paid to analysing the nature of the explanatory relation involved in these mathematical explanations in science (MES). In this paper, I attack the only articulated account of MES in the literature (an (...)
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  11. Nabil I. Al-Najjar & Jonathan Weinstein (2009). The Ambiguity Aversion Literature: A Critical Assessment. Economics and Philosophy 25 (3):249-284.score: 54.0
    We provide a critical assessment of the ambiguity aversion literature, which we characterize in terms of the view that Ellsberg choices are rational responses to ambiguity, to be explained by relaxing Savage's Sure-Thing principle and adding an ambiguity-aversion postulate. First, admitting Ellsberg choices as rational leads to behaviour, such as sensitivity to irrelevant sunk cost, or aversion to information, which most economists would consider absurd or irrational. Second, we argue that the mathematical objects referred to as in the (...)
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  12. Kevin Davey (2003). Is Mathematical Rigor Necessary in Physics? British Journal for the Philosophy of Science 54 (3):439-463.score: 54.0
    Many arguments found in the physics literature involve concepts that are not well-defined by the usual standards of mathematics. I argue that physicists are entitled to employ such concepts without rigorously defining them so long as they restrict the sorts of mathematical arguments in which these concepts are involved. Restrictions of this sort allow the physicist to ignore calculations involving these concepts that might lead to contradictory results. I argue that such restrictions need not be ad hoc, but (...)
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  13. Johan van Benthem & David Pearce (1984). A Mathematical Characterization of Interpretation Between Theories. Studia Logica 43 (3):295-303.score: 54.0
    Of the various notions of reduction in the logical literature, relative interpretability in the sense of Tarskiet al. [6] appears to be the central one. In the present note, this syntactic notion is characterized semantically, through the existence of a suitable reduction functor on models. The latter mathematical condition itself suggests a natural generalization, whose syntactic equivalent turns out to be a notion of interpretability quite close to that of Ershov [1], Szczerba [5] and Gaifman [2].
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  14. Martti Kuokkanen (1993). Structuralist Constraints and Mathematical Social Theorizing. Erkenntnis 38 (3):351 - 370.score: 54.0
    Several case studies and theoretical reports indicate that the structuralist concept of a constraint has a central role in the reconstruction of physical theories. It is surprising that there is, in the literature, only little theoretical discussion on the relevance of constraints for the reconstruction of social scientific theories. Almost all structuralist reconstructions of social theorizing are vacuously constrained. Consequently, constraints are methodologically irrelevant.In this paper I try to show that there really exist constraint-type assumptions in mathematical modelling (...)
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  15. Thomas L. Saaty (1959). Mathematical Methods of Operations Research. New York, Mcgraw-Hill.score: 54.0
    This text is an ideal introduction for students to the basic mathematics of operations research as well as a valuable source of references to early literature ...
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  16. Johan Van Benthem & David Pearce (1984). A Mathematical Characterization of Interpretation Between Theories. Studia Logica 43 (3):295 - 303.score: 54.0
    Of the various notions of reduction in the logical literature, relative interpretability in the sense of Tarski et al. [6] appears to be the central one. In the present note, this syntactic notion is characterized semantically, through the existence of a suitable reduction functor on models. The latter mathematical condition itself suggests a natural generalization, whose syntactic equivalent turns out to be a notion of interpretability quite close to that of Ershov [1], Szczerba [5] and Gaifman [2].
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  17. Elijah Chudnoff (forthcoming). Intuition in Mathematics. In Barbara Held & Lisa Osbeck (eds.), Rational Intuition. Cambridge University Press.score: 46.0
    The literature on mathematics suggests that intuition plays a role in it as a ground of belief. This article explores the nature of intuition as it occurs in mathematical thinking. Section 1 suggests that intuitions should be understood by analogy with perceptions. Section 2 explains what fleshing out such an analogy requires. Section 3 discusses Kantian ways of fleshing it out. Section 4 discusses Platonist ways of fleshing it out. Section 5 sketches a proposal for resolving the main (...)
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  18. Juha Saatsi (forthcoming). On the 'Indispensable Explanatory Role' of Mathematics. Mind.score: 46.0
    The literature on the indispensability argument for mathematical realism often refers to the ‘indispensable explanatory role’ of mathematics. I argue that we should examine the notion of explanatory indispensability from the point of view of specific conceptions of scientific explanation. The reason is that explanatory indispensability in and of itself turns out to be insufficient for justifying the ontological conclusions at stake. To show this I introduce a distinction between different kinds of explanatory roles – some 'thick' and (...)
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  19. Lucia M. Flevares & Jamie R. Schiff (2014). Learning Mathematics in Two Dimensions: A Review and Look Ahead at Teaching and Learning Early Childhood Mathematics with Children’s Literature. Frontiers in Psychology 5.score: 40.0
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  20. Elvira Laskowski-Caujolle (2001). Jacques Roubaud: Literature, Mathematics, and the Quest for Truth. Substance 30 (3):71-87.score: 40.0
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  21. Paolo Mancosu (1999). Literature Survey: Recent Publications in the History and Philosophy of Mathematics From the Renaissance to Berkeley. [REVIEW] Metascience 8 (1):102-124.score: 40.0
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  22. Reinhard Siegmund-Schultze (2003). The Late Arrival of Academic Applied Mathematics in the United States: A Paradox, Theses, and Literature. Ntm International Journal of History and Ethics of Natural Sciences, Technology & Medicine 11 (2):116-127.score: 40.0
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  23. John P. Burgess & Gideon A. Rosen (1997). A Subject with No Object: Strategies for Nominalistic Interpretation of Mathematics. Oxford University Press.score: 38.0
    Numbers and other mathematical objects are exceptional in having no locations in space or time or relations of cause and effect. This makes it difficult to account for the possibility of the knowledge of such objects, leading many philosophers to embrace nominalism, the doctrine that there are no such objects, and to embark on ambitious projects for interpreting mathematics so as to preserve the subject while eliminating its objects. This book cuts through a host of technicalities that have obscured (...)
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  24. Carlo Ierna (2012). Brentano and Mathematics. In Ion Tănăsescu (ed.), Franz Brentano's Metaphysics and Psychology. Zeta.score: 38.0
    Franz Brentano is not usually associated with mathematics. Generally, only Brentano’s discussion of the continuum and his critique of the mathematical accounts of it is treated in the literature. It is this detailed critique which suggests that Brentano had more than a superficial familiarity with mathematics. Indeed, considering the authors and works quoted in his lectures, Brentano appears well-informed and quite interested in the mathematical research of his time. I specifically address his lectures here as there is (...)
     
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  25. Carlo Ierna (2011). Brentano and Mathematics. Revue Roumaine de Philosophie 55 (1):149-167.score: 38.0
    Franz Brentano is not usually associated with mathematics. Generally, only Brentano’s discussion of the continuum and his critique of the mathematical accounts of it is treated in the literature. It is this detailed critique which suggests that Brentano had more than a superficial familiarity with mathematics. Indeed, considering the authors and works quoted in his lectures, Brentano appears well-informed and quite interested in the mathematical research of his time. I specifically address his lectures here as there is (...)
     
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  26. Martin Davis (ed.) (1965/2004). The Undecidable: Basic Papers on Undecidable Propositions, Unsolvable Problems, and Computable Functions. Dover Publication.score: 36.0
    "A valuable collection both for original source material as well as historical formulations of current problems."-- The Review of Metaphysics "Much more than a mere collection of papers . . . a valuable addition to the literature."-- Mathematics of Computation An anthology of fundamental papers on undecidability and unsolvability by major figures in the field, this classic reference opens with Godel's landmark 1931 paper demonstrating that systems of logic cannot admit proofs of all true assertions of arithmetic. Subsequent papers (...)
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  27. Eric W. Stein & Norita Ahmad (2009). Using the Analytical Hierarchy Process (Ahp) to Construct a Measure of the Magnitude of Consequences Component of Moral Intensity. Journal of Business Ethics 89 (3):391 - 407.score: 36.0
    The purpose of this work is to elaborate an empirically grounded mathematical model of the magnitude of consequences component of “moral intensity” (Jones, Academy of Management Review 16 (2),366, 1991) that can be used to evaluate different ethical situations. The model is built using the analytical hierarchy process (AHP) (Saaty, The Analytic Hierarchy Process , 1980) and empirical data from the legal profession. One contribution of our work is that it illustrates how AHP can be applied in the field (...)
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  28. Gerard R. Renardel De Lavalette (1984). Descriptions in Mathematical Logic. Studia Logica 43 (3):281 - 294.score: 36.0
    After a discussion of the different treatments in the literature of vacuous descriptions, the notion of descriptor is slightly generalized to function descriptor Ⅎ $\overset \rightarrow \to{y}(x)$ , so as to form partial functions φ = Ⅎ $y(\overset \rightarrow \to{x}).A(\overset \rightarrow \to{x},y)$ which satisfy $\forall \overset \rightarrow \to{x}z(z=\phi \overset \rightarrow \to{x}\leftrightarrow \forall y(A(\overset \rightarrow \to{x},y)\leftrightarrow y=z))$ . We use (intuitionistic, classical or intermediate) logic with existence predicate, as introduced by D. S. Scott, to handle partial functions, and prove that (...)
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  29. Lorenzo Carlucci & John Case (2013). On the Necessity of U-Shaped Learning. Topics in Cognitive Science 5 (1):56-88.score: 36.0
    A U-shaped curve in a cognitive-developmental trajectory refers to a three-step process: good performance followed by bad performance followed by good performance once again. U-shaped curves have been observed in a wide variety of cognitive-developmental and learning contexts. U-shaped learning seems to contradict the idea that learning is a monotonic, cumulative process and thus constitutes a challenge for competing theories of cognitive development and learning. U-shaped behavior in language learning (in particular in learning English past tense) has become a central (...)
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  30. Gerard R. Renardel & de Lavalette (1984). Descriptions in Mathematical Logic. Studia Logica 43 (3):281-294.score: 36.0
    After a discussion of the different treatments in the literature of vacuous descriptions, the notion of descriptor is slightly generalized to function descriptor , so as to form partial functions which satisfy . We use (intuitionistic, classical or intermediate) logic with existence predicate, as introduced by D. S. Scott, to handle partial functions, and prove that adding function descriptors to a theory based on such a logic is conservative. For theories with quantification over functions, the situation is different: there (...)
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  31. Jamie Tappenden, Proof Style and Understanding in Mathematics I: Visualization, Unification and Axiom Choice.score: 34.0
    Mathematical investigation, when done well, can confer understanding. This bare observation shouldn’t be controversial; where obstacles appear is rather in the effort to engage this observation with epistemology. The complexity of the issue of course precludes addressing it tout court in one paper, and I’ll just be laying some early foundations here. To this end I’ll narrow the field in two ways. First, I’ll address a specific account of explanation and understanding that applies naturally to mathematical reasoning: the (...)
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  32. Alberto Artosi (2010). Please Don't Use Science or Mathematics in Arguing for Human Rights or Natural Law. Ratio Juris 23 (3):311-332.score: 34.0
    In the vast literature on human rights and natural law one finds arguments that draw on science or mathematics to support claims to universality and objectivity. Here are two such arguments: 1) Human rights are as universal (i.e., valid independently of their specific historical and cultural Western origin) as the laws and theories of science; and 2) principles of natural law have the same objective (metahistorical) validity as mathematical principles. In what follows I will examine these arguments in (...)
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  33. Knut Radbruch (1995). Literatur als Medium einer Kulturgeschichte der Mathematik. NTM International Journal of History and Ethics of Natural Sciences, Technology and Medicine 3 (1):201-226.score: 34.0
    Throughout the ages writers have been concerned with contemporary problems. Their reflection became part of their literary works. By tracing and interpretating mathematical references in literature information can be obtained: on the attitude towards mathematics, on its prestige in society, its cultural recognition and its significance for education. This article analyses the implication of mathematics in some exemplary novels, essays and theoretical writings on literature of authors from the 17th to the 20th century.
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  34. Pieter A. M. Seuren, Venanizo Capretta & Herman Geuvers (2001). The Logic and Mathematics of Occasion Sentences. Linguistics and Philosophy 24 (5):531-595.score: 34.0
    The prime purpose of this paper is, first, to restore to discourse-bound occasion sentences their rightful central place in semantics and secondly, taking these as the basic propositional elements in the logical analysis of language, to contribute to the development of an adequate logic of occasion sentences and a mathematical (Boolean) foundation for such a logic, thus preparing the ground for more adequate semantic, logical and mathematical foundations of the study of natural language. Some of the insights elaborated (...)
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  35. Pieter A. M. Seuren, Venanzio Capretta & Herman Geuvers (2001). The Logic and Mathematics of Occasion Sentences. Linguistics and Philosophy 24 (5):531 - 595.score: 34.0
    The prime purpose of this paper is, first, to restore to discourse-bound occasion sentences their rightful central place in semantics and secondly, taking these as the basic propositional elements in the logical analysis of language, to contribute to the development of an adequate logic of occasion sentences and a mathematical (Boolean) foundation for such a logic, thus preparing the ground for more adequate semantic, logical and mathematical foundations of the study of natural language. Some of the insights elaborated (...)
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  36. Tony Lévy (2003). Arabic Algebra in Hebrew Texts (1). An Unpublished Work by Isaac Ben Salomon Al-a[Hudot]Dab (14th Century). Arabic Sciences and Philosophy 13 (2):269-301.score: 30.0
    It has long been considered that Arabic algebra scarcely left any traces in mathematical literature of Hebrew expression. Thanks to the unpublished sources we have discovered, and to an attentive examination of already-known texts, one can no longer subscribe to such a judgement. The evidence we examine in this first article sheds light on the circulation, in erudite Jewish circles, of Arabic algebraic knowledge in Spain, Italy, Provence, and Sicily, between the 12th and the 14th centuries. The Epistle (...)
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  37. David W. Wood (2012). "Mathesis of the Mind": A Study of Fichte's Wissenschaftslehre and Geometry. Rodopi.score: 28.0
    This is the first major study in any language on J.G. Fichte’s philosophy of mathematics and theory of geometry. It investigates both the external formal and internal cognitive parallels between the axioms, intuitions and constructions of geometry and the scientific methodology of the Fichtean system of philosophy. In contrast to “ordinary” Euclidean geometry, in his Erlanger Logik of 1805 Fichte posits a model of an “ursprüngliche” or original geometry – that is to say, a synthetic and constructivistic conception grounded in (...)
     
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  38. 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: 27.0
    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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  39. Shelley M. Park (2005). Real (M)Othering: The Metaphysics of Maternity in Children's Literature. In Real (M)othering: The Metaphysics of Maternity in Children's Literature. In Sally Haslanger and Charlotte Witt, eds. Adoption Matters: Philosophical and Feminist Essays. Ithaca, NY: Cornell University Press. 171-194.score: 27.0
    This paper examines the complexity and fluidity of maternal identity through an examination of narratives about "real motherhood" found in children's literature. Focusing on the multiplicity of mothers in adoption, I question standard views of maternity in which gestational, genetic and social mothering all coincide in a single person. The shortcomings of traditional notions of motherhood are overcome by developing a fluid and inclusive conception of maternal reality as authored by a child's own perceptions.
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  40. Derek Attridge (2004). The Singularity of Literature. Routledge.score: 24.0
    There is no shortage of testimony to literature's puzzling, unsettling, intoxicating, affecting, delighting powers. Nor has there been a shortage of attempts to define literature as a concept, a body of texts or a cultural practice. However, no definition has been able to pin down the peculiarity of literature or to chart our experience of the literary. In this volume, Derek Attridge ask us to confront with him the resistance to definition in order to explore afresh the (...)
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  41. Jean-Paul Sartre (1988). "What is Literature?" and Other Essays. Harvard University Press.score: 24.0
    This new edition of "What is Literature?" also collects three other crucial essays of Sartre's for the first time in a volume of his.
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  42. Jeffrey Koperski (2005). Should We Care About Fine-Tuning? British Journal for the Philosophy of Science 56 (2):303-319.score: 24.0
    There is an ongoing debate over cosmological fine-tuning between those holding that design is the best explanation and those who favor a multiverse. A small group of critics has recently challenged both sides, charging that their probabilistic intuitions are unfounded. If the critics are correct, then a growing literature in both philosophy and physics lacks a mathematical foundation. In this paper, I show that just such a foundation exists. Cosmologists are now providing the kinds of measure-theoretic arguments needed (...)
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  43. Rasmus Grønfeldt Winther, Michael J. Wade & Christopher C. Dimond (2013). Pluralism in Evolutionary Controversies: Styles and Averaging Strategies in Hierarchical Selection Theories. Biology and Philosophy 28 (6):957-979.score: 24.0
    Two controversies exist regarding the appropriate characterization of hierarchical and adaptive evolution in natural populations. In biology, there is the Wright–Fisher controversy over the relative roles of random genetic drift, natural selection, population structure, and interdemic selection in adaptive evolution begun by Sewall Wright and Ronald Aylmer Fisher. There is also the Units of Selection debate, spanning both the biological and the philosophical literature and including the impassioned group-selection debate. Why do these two discourses exist separately, and interact relatively (...)
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  44. Helen De Cruz & Johan De Smedt (2013). Mathematical Symbols as Epistemic Actions. Synthese 190 (1):3-19.score: 24.0
    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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  45. Michael Weisberg, Models for Modeling.score: 24.0
    Contemporary literature in philosophy of science has begun to emphasize the practice of modeling, which differs in important respects from other forms of representation and analysis central to standard philosophical accounts. This literature has stressed the constructed nature of models, their autonomy, and the utility of their high degrees of idealization. What this new literature about modeling lacks, however, is a comprehensive account of the models that figure in to the practice of modeling. This paper offers a (...)
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  46. Boudewijn de Bruin (2005). Game Theory in Philosophy. Topoi 24 (2):197-208.score: 24.0
    Game theory is the mathematical study of strategy and conflict. It has wide applications in economics, political science, sociology, and, to some extent, in philosophy. Where rational choice theory or decision theory is concerned with individual agents facing games against nature, game theory deals with games in which all players have preference orderings over the possible outcomes of the game. This paper gives an informal introduction to the theory and a survey of applications in diverse branches of philosophy. No (...)
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  47. Peter Lamarque (2007). Aesthetics and Literature: A Problematic Relation? Philosophical Studies 135 (1):27 - 40.score: 24.0
    The paper argues that there is a proper place for literature within aesthetics but that care must be taken in identifying just what the relation is. In characterising aesthetic pleasure associated with literature it is all too easy to fall into reductive accounts, for example, of literature as merely “fine writing”. Belleslettrist or formalistic accounts of literature are rejected, as are two other kinds of reduction, to pure meaning properties and to a kind of narrative realism. (...)
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  48. P. B. Andrews (2002). An Introduction to Mathematical Logic and Type Theory: To Truth Through Proof. Kluwer Academic Publishers.score: 24.0
    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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  49. Valeria Giardino (2010). Intuition and Visualization in Mathematical Problem Solving. Topoi 29 (1):29-39.score: 24.0
    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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