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

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  1. Wojciech Buszkowski (1997). Mathematical Linguistics and Proof Theory. In Benthem & Meulen (eds.), Handbook of Logic and Language. Mit Press. 683--736.score: 45.0
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  2. Joseph S. Ullian (1974). Review: Robert Wall, Introduction to Mathematical Linguistics. [REVIEW] Journal of Symbolic Logic 39 (3):615-616.score: 45.0
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  3. M. V. Aldridge (1992). The Elements of Mathematical Semantics. Mouton De Gruyter.score: 39.0
    Chapter Some topics in semantics Aims of this study The central preoccupation of this study is semantic. It is intended as a modest contribution to the ...
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  4. O. Mcnamara (1995). Saussurian Linguistics Revisited: Can It Inform Our Interpretation of Mathematical Activity? Science and Education 4 (3):253-266.score: 36.0
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  5. Lawrence S. Moss (1992). Partee Barbara H., ter Meulen Alice, and Wall Robert E.. Mathematical Methods in Linguistics. Studies in Linguistics and Philosophy, Vol. 30. Kluwer Academic Publishers, Dordrecht, Boston, and London, 1990, Xx+ 663 Pp. [REVIEW] Journal of Symbolic Logic 57 (1):271-272.score: 36.0
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  6. Lawrence S. Moss (1992). Review: Barbara H. Partee, Alice ter Meulen, Robert E. Wall, Mathematical Methods in Linguistics. [REVIEW] Journal of Symbolic Logic 57 (1):271-272.score: 36.0
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  7. Benedikt Löwe, Wolfgang Malzkorn & Thoralf Räsch (2003). Foundations of the Formal Sciences II. Applications of Mathematical Logic in Philosophy and Linguistics. Kluwer.score: 36.0
     
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  8. Lev Dmitrievich Beklemishev (1999). Provability, Complexity, Grammars. American Mathematical Society.score: 30.0
    (2) Vol., Classification of Propositional Provability Logics LD Beklemishev Introduction Overview. The idea of an axiomatic approach to the study of ...
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  9. Gerhard Jäger (2004). Residuation, Structural Rules and Context Freeness. Journal of Logic, Language and Information 13 (1):47-59.score: 30.0
    The article presents proofs of the context freeness of a family of typelogical grammars, namely all grammars that are based on a uni- ormultimodal logic of pure residuation, possibly enriched with thestructural rules of Permutation and Expansion for binary modes.
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  10. Petr Sgall (ed.) (1984). Contributions to Functional Syntax, Semantics, and Language Comprehension. J. Benjamins Pub. Co..score: 30.0
    On the Notion "Type of Language" Petr Sgall It is well known that the high frequency of terminological vagueness and confusion has been a serious obstacle ...
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  11. P. Braffort & F. van Scheepen (eds.) (1968). Automation in Language Translation and Theorem Proving. Brussels, Commission of the European Communities, Directorate-General for Dissemination of Information.score: 30.0
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  12. Wolfram Hinzen & Juan Uriagereka (2006). On the Metaphysics of Linguistics. Erkenntnis 65 (1):71-96.score: 27.0
    Mind–body dualism has rarely been an issue in the generative study of mind; Chomsky himself has long claimed it to be incoherent and unformulable. We first present and defend this negative argument but then suggest that the generative enterprise may license a rather novel and internalist view of the mind and its place in nature, different from all of, (i) the commonly assumed functionalist metaphysics of generative linguistics, (ii) physicalism, and (iii) Chomsky’s negative stance. Our argument departs from the (...)
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  13. Wolfgang Rautenberg (2006). A Concise Introduction to Mathematical Logic. Springer.score: 27.0
    Traditional logic as a part of philosophy is one of the oldest scientific disciplines. Mathematical logic, however, is a relatively young discipline and arose from the endeavors of Peano, Frege, Russell and others to create a logistic foundation for mathematics. It steadily developed during the 20th century into a broad discipline with several sub-areas and numerous applications in mathematics, informatics, linguistics and philosophy. While there are already several well-known textbooks on mathematical logic, this book is unique in (...)
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  14. Ian Chiswell (2007). Mathematical Logic. Oxford University Press.score: 27.0
    Assuming no previous study in logic, this informal yet rigorous text covers the material of a standard undergraduate first course in mathematical logic, using natural deduction and leading up to the completeness theorem for first-order logic. At each stage of the text, the reader is given an intuition based on standard mathematical practice, which is subsequently developed with clean formal mathematics. Alongside the practical examples, readers learn what can and can't be calculated; for example the correctness of a (...)
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  15. Gabriel V. Orman (ed.) (1991). Proceedings of the Third Colloquium on Logic, Language, Mathematics Linguistics, Brasov, 23-25 Mai 1991. Society of Mathematics Sciences.score: 27.0
  16. John Hale (2006). Uncertainty About the Rest of the Sentence. Cognitive Science 30 (4):643-672.score: 24.0
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  17. Stephen K. Land (1974). From Signs to Propositions: The Concept of Form in Eighteenth-Century Semantic Theory. Longman.score: 24.0
     
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  18. Waldemar Skrzypczak (2006). Analog-Based Modelling of Meaning Representations in English. Nicolaus Copernicus University Press.score: 24.0
     
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  19. 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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  20. Geoffrey K. Pullum (2011). On the Mathematical Foundations of Syntactic Structures. Journal of Logic, Language and Information 20 (3):277-296.score: 21.0
    Chomsky’s highly influential Syntactic Structures ( SS ) has been much praised its originality, explicitness, and relevance for subsequent cognitive science. Such claims are greatly overstated. SS contains no proof that English is beyond the power of finite state description (it is not clear that Chomsky ever gave a sound mathematical argument for that claim). The approach advocated by SS springs directly out of the work of the mathematical logician Emil Post on formalizing proof, but few linguists are (...)
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  21. Dunja Jutronić (2007). Platonism in Linguistics. Croatian Journal of Philosophy 7 (2):163-176.score: 21.0
    Jim Brown (1991, viii) says that platonism, in mathematics involves the following: 1. mathematical objects exist independently of us; 2. mathematical objects are abstract; 3. we learn about mathematical objects by the faculty of intuition. The same is being claimed by Jerrold Katz (1981, 1998) in his platonistic approach to linguistics. We can take the object of linguistic analysis to be concrete physical sounds as held by nominalists, or we can assume that the object of linguistic (...)
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  22. Nadia Stoyanova Kennedy (2013). Math Habitus, the Structuring of Mathematical Classroom Practices, and Possibilities for Transformation. Childhood and Philosophy 8 (16):421-441.score: 21.0
    In this paper, I discuss the social philosopher Pierre Bourdieu’s concept of habitus, and use it to locate and examine dispositions in a larger constellation of related concepts, exploring their dynamic relationship within the social context, and their construction, manifestation, and function in relation to classroom mathematics practices. I describe the main characteristics of habitus that account for its invisible effects: its embodiment, its deep and pre-reflective internalization as schemata, orientation, and taste that are learned and yet unthought, and are (...)
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  23. G. Neumann (2008). A Computational Linguistics Perspective on the Anticipatory Drive. Constructivist Foundations 4 (1):26-28.score: 21.0
    Open peer commentary on the target article “How and Why the Brain Lays the Foundations for a Conscious Self” by Martin V. Butz. Excerpt: In this commentary to Martin V. Butz’s target article I am especially concerned with his remarks about language (§33, §§71–79, §91) and modularity (§32, §41, §48, §81, §§94–98). In that context, I would like to bring into discussion my own work on computational models of self-monitoring (cf. Neumann 1998, 2004). In this work I explore the idea (...)
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  24. Luke Jerzykiewicz (2012). Mathematical Realism and Conceptual Semantics. In Oleg Prosorov & Vladimir Orevkov (eds.), Philosophy, Mathematics, Linguistics: Aspects of Interaction. Euler International Mathematical Institute.score: 19.0
    The dominant approach to analyzing the meaning of natural language sentences that express mathematical knowl- edge relies on a referential, formal semantics. Below, I discuss an argument against this approach and in favour of an internalist, conceptual, intensional alternative. The proposed shift in analytic method offers several benefits, including a novel perspective on what is required to track mathematical content, and hence on the Benacerraf dilemma. The new perspective also promises to facilitate discussion between philosophers of mathematics and (...)
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  25. Michael Devitt (2006). Intuitions in Linguistics. British Journal for the Philosophy of Science 57 (3):481-513.score: 18.0
    Linguists take the intuitive judgments of speakers to be good evidence for a grammar. Why? The Chomskian answer is that they are derived by a rational process from a representation of linguistic rules in the language faculty. The paper takes a different view. It argues for a naturalistic and non-Cartesian view of intuitions in general. They are empirical central-processor responses to phenomena differing from other such responses only in being immediate and fairly unreflective. Applying this to linguistic intuitions yields an (...)
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  26. Guy Longworth (2009). Ignorance of Linguistics: A Note on Devitt's Ignorance of Language. Croatian Journal of Philosophy 25 (1):21-34.score: 18.0
    Michael Devitt has argued that Chomsky, along with many other Linguists and philosophers, is ignorant of the true nature of Generative Linguistics. In particular, Devitt argues that Chomsky and others wrongly believe the proper object of linguistic inquiry to be speakers' competences, rather than the languages that speakers are competent with. In return, some commentators on Devitt's work have returned the accusation, arguing that it is Devitt who is ignorant about Linguistics. In this note, I consider whether there (...)
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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. 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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  34. Barbara C. Scholz, Francis Jeffry Pelletier & Geoffrey K. Pullum (2000). Philosophy and Linguistics. Dialogue 39 (3):605-607.score: 18.0
    Philosophy of linguistics is the philosophy of science as applied to linguistics. This differentiates it sharply from the philosophy of language, traditionally concerned with matters of meaning and reference.
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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. Fritz J. McDonald (2009). Linguistics, Psychology, and the Ontology of Language. Croatian Journal of Philosophy 9 (3):291-301.score: 18.0
    Noam Chomsky’s well-known claim that linguistics is a “branch of cognitive psychology” has generated a great deal of dissent—not from linguists or psychologists, but from philosophers. Jerrold Katz, Scott Soames, Michael Devitt, and Kim Sterelny have presented a number of arguments, intended to show that this Chomskian hypothesis is incorrect. On both sides of this debate, two distinct issues are often conflated: (1) the ontological status of language and (2) the relation between psychology and linguistics. The ontological issue (...)
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  40. 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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  41. 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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  42. 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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  43. 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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  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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