Results for 'p-adic numbers. [msc2010]03B48'

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  1.  43
    A p-adic probability logic.Angelina Ilić-Stepić, Zoran Ognjanović, Nebojša Ikodinović & Aleksandar Perović - 2012 - Mathematical Logic Quarterly 58 (4):263-280.
    In this article we present a p-adic valued probabilistic logic equation image which is a complete and decidable extension of classical propositional logic. The key feature of equation image lies in ability to formally express boundaries of probability values of classical formulas in the field equation image of p-adic numbers via classical connectives and modal-like operators of the form Kr, ρ. Namely, equation image is designed in such a way that the elementary probability sentences Kr, ρα actually do (...)
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  2.  51
    A p‐adic probability logic.Angelina Ilić-Stepić, Zoran Ognjanović, Nebojša Ikodinović & Aleksandar Perović - 2012 - Mathematical Logic Quarterly 58 (4-5):263-280.
    In this article we present a p-adic valued probabilistic logic equation image which is a complete and decidable extension of classical propositional logic. The key feature of equation image lies in ability to formally express boundaries of probability values of classical formulas in the field equation image of p-adic numbers via classical connectives and modal-like operators of the form Kr, ρ. Namely, equation image is designed in such a way that the elementary probability sentences Kr, ρα actually do (...)
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  3.  10
    Expansions of the padic numbers that interpret the ring of integers.Nathanaël Mariaule - 2020 - Mathematical Logic Quarterly 66 (1):82-90.
    Let be the field of p‐adic numbers in the language of rings. In this paper we consider the theory of expanded by two predicates interpreted by multiplicative subgroups and where are multiplicatively independent. We show that the theory of this structure interprets Peano arithmetic if α and β have positive p‐adic valuation. If either α or β has zero valuation we show that the theory of has the NIP (“negation of the independence property”) and therefore does not interpret (...)
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  4.  12
    One dimensional groups definable in the p-adic numbers.Juan Pablo Acosta López - 2021 - Journal of Symbolic Logic 86 (2):801-816.
    A complete list of one dimensional groups definable in the p-adic numbers is given, up to a finite index subgroup and a quotient by a finite subgroup.
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  5.  14
    The field of p-adic numbers with a predicate for the powers of an integer.Nathanaël Mariaule - 2017 - Journal of Symbolic Logic 82 (1):166-182.
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  6.  71
    Logics for Reasoning About Processes of Thinking with Information Coded by p-adic Numbers.Angelina Ilić Stepić & Zoran Ognjanović - 2015 - Studia Logica 103 (1):145-174.
    In this paper we present two types of logics and \ ) where certain p-adic functions are associated to propositional formulas. Logics of the former type are p-adic valued probability logics. In each of these logics we use probability formulas K r,ρ α and D ρ α,β which enable us to make sentences of the form “the probability of α belongs to the p-adic ball with the center r and the radius ρ”, and “the p-adic distance (...)
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  7.  25
    More on definable sets of p-adic numbers.Philip Scowcroft - 1988 - Journal of Symbolic Logic 53 (3):912-920.
  8.  69
    A version of p-adic minimality.Raf Cluckers & Eva Leenknegt - 2012 - Journal of Symbolic Logic 77 (2):621-630.
    We introduce a very weak language L M on p-adic fields K, which is just rich enough to have exactly the same definable subsets of the line K that one has using the ring language. (In our context, definable always means definable with parameters.) We prove that the only definable functions in the language L M are trivial functions. We also give a definitional expansion $L\begin{array}{*{20}{c}} ' \\ M \\ \end{array} $ of L M in which K has quantifier (...)
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  9.  15
    James Ax and Simon Kochen. Diophantine problems over local fields I. American journal of mathematics, vol. 87 , pp. 605–630. - James Ax and Simon Kochen. Diophantine problems over local fields II. A complete set of axioms for p-adic number theory. American journal of mathematics, vol. 87 , pp. 631–648. - James Ax and Simon Kochen. Diophantine problems over local fields III. Decidable fields. Annals of mathematics, vol. 83 , pp. 437–456. [REVIEW]Abraham Robinson - 1971 - Journal of Symbolic Logic 36 (4):683-684.
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  10.  9
    Review: James Ax, Simon Kochen, Diophantine Problems Over Local Fields I; James Ax, Simon Kochen, Diophantine Problems Over Local Fields II. A Complete set of Axioms for $p$-adic number theory; James Ax, Simon Kochen, Diophantine Problems over Local Field III. Decidable Fields. [REVIEW]Abraham Robinson - 1971 - Journal of Symbolic Logic 36 (4):683-684.
  11.  21
    p-Adic valued logical calculi in simulations of the slime mould behaviour.Andrew Schumann - 2015 - Journal of Applied Non-Classical Logics 25 (2):125-139.
    In this paper we consider possibilities for applying p-adic valued logic BL to the task of designing an unconventional computer based on the medium of slime mould, the giant amoebozoa that looks for attractants and reaches them by means of propagating complex networks. If it is assumed that at any time step t of propagation the slime mould can discover and reach not more than attractants, then this behaviour can be coded in terms of p-adic numbers. As a (...)
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  12.  91
    Cell decomposition for semibounded p-adic sets.Eva Leenknegt - 2013 - Archive for Mathematical Logic 52 (5-6):667-688.
    We study a reduct ${\mathcal{L}_*}$ of the ring language where multiplication is restricted to a neighbourhood of zero. The language is chosen such that for p-adically closed fields K, the ${\mathcal{L}_*}$ -definable subsets of K coincide with the semi-algebraic subsets of K. Hence structures (K, ${\mathcal{L}_*}$ ) can be seen as the p-adic counterpart of the o-minimal structure of semibounded sets. We show that in this language, p-adically closed fields admit cell decomposition, using cells similar to p-adic semi-algebraic (...)
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  13.  6
    Model completion of scaled lattices and co‐Heyting algebras of padic semi‐algebraic sets.Luck Darnière - 2019 - Mathematical Logic Quarterly 65 (3):305-331.
    Let p be prime number, K be a p‐adically closed field, a semi‐algebraic set defined over K and the lattice of semi‐algebraic subsets of X which are closed in X. We prove that the complete theory of eliminates quantifiers in a certain language, the ‐structure on being an extension by definition of the lattice structure. Moreover it is decidable, contrary to what happens over a real closed field for. We classify these ‐structures up to elementary equivalence, and get in particular (...)
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  14.  29
    A note on groups definable in the p -adic field.Anand Pillay & Ningyuan Yao - 2019 - Archive for Mathematical Logic 58 (7-8):1029-1034.
    It is known Hrushovski and Pillay that a group G definable in the field \ of p-adic numbers is definably locally isomorphic to the group \\) of p-adic points of a algebraic group H over \. We observe here that if H is commutative then G is commutative-by-finite. This shows in particular that any one-dimensional group G definable in \ is commutative-by-finite. This result extends to groups definable in p-adically closed fields. We prove our results in the more (...)
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  15.  93
    Science, Pseudoscience, and Science Falsely So-CaIIed.Daniel P. Thurs & Ronald L. Numbers - 2013 - In Massimo Pigliucci & Maarten Boudry (eds.), Philosophy of Pseudoscience: Reconsidering the Demarcation Problem. University of Chicago Press. pp. 121.
    This chapter presents a historical analysis of pseudoscience, tracking down the coinage and currency of the term and explaining its shifting meaning in tandem with the emerging historical identity of science. The discussions cover the invention of pseudoscience; science and pseudoscience in the late nineteenth century; pseudoscience in the new century; and pseudoscience and its critics in the late twentieth century.
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  16.  22
    Knowledge, attitude and practice of medical ethics among medical intern students in a Medical College in Kathmandu.Ramesh P. Aacharya & Yagya L. Shakya - 2016 - Bangladesh Journal of Bioethics 6 (3):1-9.
    This baseline study was conducted to find out the knowledge, attitudes and practices of medical ethics among the undergraduate medical interns who did not have structured ethics curriculum in their course. A descriptive, cross-sectional study was carried out using a self-administered structured questionnaire among the medical undergraduate interns of Maharajgunj Medical Campus, the pioneer medical college of Nepal which enrols 60 students in a year. A total of 46 interns participated in the study. The most common source of knowledge on (...)
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  17. The Mathematical Basis of Creation in Hinduism.Mukundan P. R. - 2022 - In The Modi-God Dialogues: Spirituality for a New World Order. New Delhi: Akansha Publishing House. pp. 6-14.
    The Upanishads reveal that in the beginning, nothing existed: “This was but non-existence in the beginning. That became existence. That became ready to be manifest”. (Chandogya Upanishad 3.15.1) The creation began from this state of non-existence or nonduality, a state comparable to (0). One can add any number of zeros to (0), but there will be nothing except a big (0) because (0) is a neutral number. If we take (0) as Nirguna Brahman (God without any form and attributes), then (...)
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  18. Computability and Logic.George Boolos, John Burgess, Richard P. & C. Jeffrey - 1980 - New York: Cambridge University Press. Edited by John P. Burgess & Richard C. Jeffrey.
    Computability and Logic has become a classic because of its accessibility to students without a mathematical background and because it covers not simply the staple topics of an intermediate logic course, such as Godel's incompleteness theorems, but also a large number of optional topics, from Turing's theory of computability to Ramsey's theorem. This 2007 fifth edition has been thoroughly revised by John Burgess. Including a selection of exercises, adjusted for this edition, at the end of each chapter, it offers a (...)
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  19. The adicity of 'believes' and the hidden indexical theory.P. Ludlow - 1996 - Analysis 56 (2):97-101.
  20. The numbers in italics refer to the pages on which the complete references are listed.R. P. Abeles, J. Adelson, A. Ahlgren, M. D. S. Ainsworth, G. W. Allport, R. Alpert, D. Anderson, M. Arnold, J. Aronfreed & Averill Jr - 1975 - In David J. DePalma & Jeanne M. Foley (eds.), Moral Development: Current Theory and Research. Halsted Press.
     
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  21.  23
    Representation, reasoning, and relational structures: a hybrid logic manifesto.P. Blackburn - 2000 - Logic Journal of the IGPL 8 (3):339-365.
    This paper is about the good side of modal logic, the bad side of modal logic, and how hybrid logic takes the good and fixes the bad.In essence, modal logic is a simple formalism for working with relational structures . But modal logic has no mechanism for referring to or reasoning about the individual nodes in such structures, and this lessens its effectiveness as a representation formalism. In their simplest form, hybrid logics are upgraded modal logics in which reference to (...)
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  22. List of Contents: Volume 17, Number 1, February 2004.P. Caban, M. Forys, J. Rembielinski, Lorentz-Covariant Canonical, Gennaro Auletta, Gino Tarozzi & Wavelike Correlations Versus Path - 2004 - Foundations of Physics 34 (4).
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  23.  31
    Bounded arithmetic for NC, ALogTIME, L and NL.P. Clote & G. Takeuti - 1992 - Annals of Pure and Applied Logic 56 (1-3):73-117.
    We define theories of bounded arithmetic, whose definable functions and relations are exactly those in certain complexity classes. Based on a recursion-theoretic characterization of NC in Clote , the first-order theory TNC, whose principal axiom scheme is a form of short induction on notation for nondeterministic polynomial-time computable relations, has the property that those functions having nondeterministic polynomial-time graph Θ such that TNC x y Θ are exactly the functions in NC, computable on a parallel random-access machine in polylogarithmic parallel (...)
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  24.  62
    Decidability and undecidability of theories with a predicate for the primes.P. T. Bateman, C. G. Jockusch & A. R. Woods - 1993 - Journal of Symbolic Logic 58 (2):672-687.
    It is shown, assuming the linear case of Schinzel's Hypothesis, that the first-order theory of the structure $\langle \omega; +, P\rangle$ , where P is the set of primes, is undecidable and, in fact, that multiplication of natural numbers is first-order definable in this structure. In the other direction, it is shown, from the same hypothesis, that the monadic second-order theory of $\langle\omega; S, P\rangle$ is decidable, where S is the successor function. The latter result is proved using a general (...)
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  25. Operational analysis.P. W. Bridgman - 1938 - Philosophy of Science 5 (2):114-131.
    In the October 1937 number of Philosophy of Science Lindsay has made certain criticisms of the adequacy of the “operational method” of analyzing and giving meaning to the concepts of physics, documenting his criticisms chiefly from my own writings. In these criticisms he has made statements as to the method which I would by no means accept. This is not characteristic of his paper only, for I have seldom indeed seen a printed discussion of the method which I would accept (...)
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  26.  18
    Varieties of BL-Algebras II.P. Aglianò & F. Montagna - 2018 - Studia Logica 106 (4):721-737.
    In this paper we introduce a poset of subvarieties of BL-algebras, whose completion is the entire lattice of subvarietes; we exhibit also a description of this poset in terms of finite sequences of functions on the natural numbers.
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  27. Second thoughts on simulation.Stephen P. Stich & Shaun Nichols - 1995 - In Martin Davies & Tony Stone (eds.), Mental Simulation. Blackwell.
    The essays in this volume make it abundantly clear that there is no shortage of disagreement about the plausibility of the simulation theory. As we see it, there are at least three factors contributing to this disagreement. In some instances the issues in dispute are broadly empirical. Different people have different views on which theory is favored by experiments reported in the literature, and different hunches about how future experiments are likely to turn out. In 3.1 and 3.3 we will (...)
     
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  28.  43
    Complexity and post-modernism: understanding complex systems.P. Cilliers & David Spurrett - 1999 - South African Journal of Philosophy 18 (2):258-274.
    This is a review article of Paul Cillier's 1999 book _Complexity and Postmodernism_. The review article is generally encouraging and constructive, although isolates a number of areas in need of clarification or development in Cillier's work. The volume of the _South African Journal of Philosophy_ in which the review article appeared also printed a response by Cilliers.
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  29.  18
    Hybrid completeness.P. Blackburn & M. Tzakova - 1998 - Logic Journal of the IGPL 6 (4):625-650.
    In this paper we discuss two hybrid languages, ℒ and ℒ, and provide them with complete axiomatizations. Both languages combine features of modal and classical logic. Like modal languages, they contain modal operators and have a Kripke semantics. Unlike modal languages, in these systems it is possible to 'label' states by using A and ↓ to bind special state variables.This paper explores the consequences of hybridization for completeness. As we shall show, the challenge is to blend the modal idea of (...)
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  30.  33
    Islamic Millenarianism in West Africa: A ‘Revolutionary’ Ideology?: P. B. CLARKE.P. B. Clarke - 1980 - Religious Studies 16 (3):317-339.
    Social and political scientists, historians and others, have put forward a number of widely differing views concerning the ‘character’ of Islamic millenarian and/or Mahdist movements in Africa. The same is true of course with regard to the opinions ofscholars concerning the transformative capacity of Islam as an ideology. In this paper I want to look at one aspect only of Islamic millenarianism in the West African context, viz. its allegedly revolutionary character.
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  31.  82
    The Cambridge Handbook of Situated Cognition.Murat Aydede & P. Robbins (eds.) - 2008 - Cambridge: Cambridge University Press.
    Since its inception some fifty years ago, cognitive science has seen a number of sea changes. Perhaps the best known is the development of connectionist models of cognition as an alternative to classical, symbol-based approaches. A more recent - and increasingly influential - trend is that of dynamical-systems-based, ecologically oriented models of the mind. Researchers suggest that a full understanding of the mind will require systematic study of the dynamics of interaction between mind, body, and world. Some argue that this (...)
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  32. Spreading of risk and stabilization of animal numbers.P. J. Boer - 1968 - Acta Biotheoretica 18 (1-4).
     
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  33.  11
    Treatise on the origin of humanity (Taishō volume 45, number 1886).John P. Keenan, Sengzhao, Rafal Felbur, Jan Yün-hua, Vasubandhu & Zongmi - 2017 - In John P. Keenan, Sengzhao, Rafal Felbur, Jan Yün-hua, Vasubandhu & Zongmi (eds.), Three short treatises by Vasubandhu, Sengzhao, and Zongmi. Moraga, California: BDK America.
  34. A Mahayana demonstration on the theme of action (Taishō volume 31, number 1609).John P. Keenan, Sengzhao, Rafal Felbur, Jan Yün-hua, Vasubandhu & Zongmi - 2017 - In John P. Keenan, Sengzhao, Rafal Felbur, Jan Yün-hua, Vasubandhu & Zongmi (eds.), Three short treatises by Vasubandhu, Sengzhao, and Zongmi. Moraga, California: BDK America.
  35.  6
    Essays of Sengzhao (Taishō volume 45, number 1858).John P. Keenan, Sengzhao, Rafal Felbur, Jan Yün-hua, Vasubandhu & Zongmi - 2017 - In John P. Keenan, Sengzhao, Rafal Felbur, Jan Yün-hua, Vasubandhu & Zongmi (eds.), Three short treatises by Vasubandhu, Sengzhao, and Zongmi. Moraga, California: BDK America.
  36.  26
    The apparent magnitude of number scaled by random production.William P. Banks & David K. Hill - 1974 - Journal of Experimental Psychology 102 (2):353.
  37.  93
    Should Zelen pre-randomised consent designs be used in some neonatal trials?P. Allmark - 1999 - Journal of Medical Ethics 25 (4):325-329.
    My aim is to suggest that there is a case for using a randomised consent design in some neonatal trials. As an example I use the trials of extracorporeal membrane oxygenation (ECMO) in neonates suffering pulmonary hypertension. In some trials the process of obtaining consent has the potential to harm the subject, for example, by disappointing those who end in the control group and by creating additional anxiety at times of acute illness. An example of such were the trials of (...)
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  38.  36
    Decisions vs. Willingness-to-Pay in Social Choice.P. Anand - 2000 - Environmental Values 9 (4):419-430.
    The paper compares use of willingness to pay values with multi-attribute utility as ways of modelling social choice problems in the environment. A number of reasons for moving away from willingness to pay are reviewed. The view proposed is that social choice is about the integration of competing claim types (utilities, rights, social contracts and beliefs about due process). However, willingness to pay is only indirectly related to the first of these and assumes an Arrovian approach, namely one in which (...)
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  39.  24
    Hobbes without Grotius.P. Zagorin - 2000 - History of Political Thought 21 (1):16-40.
    This essay presents a critique of current views of Hugo Grotius which erroneously see him as a major theorist of natural rights and a formative influence upon the rights theory of Thomas Hobbes. Especially singled out for criticism are the misconceptions due to Richard Tuck in a number of writings that discuss the political ideas of Grotius and Hobbes and the relationship between them. In an examination of Hobbes's conception of natural rights, the essay reaffirms its originality and notes its (...)
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  40.  41
    Philosophical Investigations.P. M. S. Hacker & Joachim Schulte (eds.) - 2009 - Wiley-Blackwell.
    Incorporating significant editorial changes from earlier editions, the fourth edition of Ludwig Wittgenstein's _Philosophical Investigations_ is the definitive _en face_ German-English version of the most important work of 20th-century philosophy The extensively revised English translation incorporates many hundreds of changes to Anscombe’s original translation Footnoted remarks in the earlier editions have now been relocated in the text What was previously referred to as ‘Part 2’ is now republished as _Philosophy of Psychology – A Fragment_, and all the remarks in it (...)
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  41.  31
    Constructive definition of certain analytic sets of numbers.P. Lorenzen & J. Myhill - 1959 - Journal of Symbolic Logic 24 (1):37-49.
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  42.  39
    Corrigendum.P. A. Brunt - 1973 - The Classical Review 23 (02):295-.
    Line 24 on page 218 in the July number of this volume of Philosophy should read as follows: naturally out of matter itself lifeless or that consciousness and intelli-.
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  43.  34
    The foundations of quantum mechanics.P. J. Bussey - 1988 - Foundations of Physics 18 (5):491-528.
    Starting from a set of assumptions mainly of an “operational” or experimentally based nature, a derivation of quantum mechanics is presented, with the aim of clarifying the essential features of the theory and their interpretation. Various properties of quantum mechanics such as the addition of amplitudes, the calculation of probabilities, de Broglie's equations, and energy-momentum conservation are derived from first principles. It is investigated whether quantum amplitudes may be constructed from quantities of higher order than complex numbers. Measurable physical quantitics, (...)
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  44.  17
    Tableaux variants of some modal and relevant systems.P. I. Bystrov - 1988 - Bulletin of the Section of Logic 17 (3/4):92-98.
    The tableaux-constructions have a number of properties which advantageously distinguish them from equivalent axiomatic systems . The proofs in the form of tableaux-constructions have a full accordance with semantic interpretation and subformula property in the sense of Gentzen’s Hauptsatz. Method of tatleaux-construction gives a good substitute of Gentzen’s methods and thus opens a good perspective for the investigations of theoretical as well as applied aspects of logical calculi. It should be noted that application of tableau method in modal, tense, relevant (...)
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  45.  5
    Constructive Definition of Certain Analytic Sets of Numbers.P. Lorenzen & J. Myhill - 1968 - Journal of Symbolic Logic 33 (2):295-295.
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  46. Squeezing arguments.P. Smith - 2011 - Analysis 71 (1):22-30.
    Many of our concepts are introduced to us via, and seem only to be constrained by, roughand-ready explanations and some sample paradigm positive and negative applications. This happens even in informal logic and mathematics. Yet in some cases, the concepts in question – although only informally and vaguely characterized – in fact have, or appear to have, entirely determinate extensions. Here’s one familiar example. When we start learning computability theory, we are introduced to the idea of an algorithmically computable function (...)
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  47. For pluralism and against realism about species.P. Kyle Stanford - 1995 - Philosophy of Science 62 (1):70-91.
    I argue for accepting a pluralist approach to species, while rejecting the realism about species espoused by P. Kitcher and a number of other philosophers of biology. I develop an alternative view of species concepts as divisions of organisms into groups for study which are relative to the systematic explanatory interests of biologists at a particular time. I also show how this conception resolves a number of difficult puzzles which plague the application of particular species concepts.
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  48.  12
    Empirical research in bioethical journals. A quantitative analysis.P. Borry - 2006 - Journal of Medical Ethics 32 (4):240-245.
    Objectives: The objective of this research is to analyse the evolution and nature of published empirical research in the fields of medical ethics and bioethics.Design: Retrospective quantitative study of nine peer reviewed journals in the field of bioethics and medical ethics .Results: In total, 4029 articles published between 1990 and 2003 were retrieved from the journals studied. Over this period, 435 studies used an empirical design. The highest percentage of empirical research articles appeared in Nursing Ethics , followed by the (...)
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  49.  41
    Impertinent reflections on history of science.P. W. Bridgman - 1950 - Philosophy of Science 17 (1):63-73.
    History of Science is a many-sided subject, permitting approach from the point of view of various human interests, and presenting a wide variety of problems, many of them paradoxical and perhaps not capable of satisfactory solution. In the following it will probably seem to the reader a number of times that I am talking at cross purposes. Anything that I can say is of necessity limited by my background as a physicist.
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  50.  58
    Peer-review practices of psychological journals: The fate of published articles, submitted again.Douglas P. Peters & Stephen J. Ceci - 1982 - Behavioral and Brain Sciences 5 (2):187-255.
    A growing interest in and concern about the adequacy and fairness of modern peer-review practices in publication and funding are apparent across a wide range of scientific disciplines. Although questions about reliability, accountability, reviewer bias, and competence have been raised, there has been very little direct research on these variables.The present investigation was an attempt to study the peer-review process directly, in the natural setting of actual journal referee evaluations of submitted manuscripts. As test materials we selected 12 already published (...)
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