Results for 'Smooth infinitesimal analysis'

999 found
Order:
  1. Elastic Membrane Based Model of Human Perception.Alexander Egoyan - 2011 - Toward a Science of Consciousness.
    Undoubtedly the Penrose-Hameroff Orch OR model may be considered as a good theory for describing information processing mechanisms and holistic phenomena in the human brain, but it doesn’t give us satisfactory explanation of human perception. In this work a new approach explaining our perception is introduced, which is in good agreement with Orch OR model and other mainstream science theories such as string theory, loop quantum gravity and holographic principle. It is shown that human perception cannot be explained in the (...)
    Download  
    Translate
     
     
    Export citation  
     
    Bookmark  
  2. The Role of Physics in Science Integration.Alexander Egoyan - 2005 - Albert Einstein Century International Conference.
    Special and General theories of relativity may be considered as the most significant examples of integrative thinking. From these works we see that Albert Einstein attached great importance to how we understand geometry and dimensions. It is shown that physics powered by the new multidimensional elastic geometry is a reliable basis for science integration. Instead of searching for braneworlds (elastic membranes - EM) in higher dimensions we will start by searching them in our 3+1 dimensional world. The cornerstone of the (...)
    Download  
     
    Export citation  
     
    Bookmark   1 citation  
  3. Infinitesimals as an Issue of Neo-Kantian Philosophy of Science.Thomas Mormann & Mikhail Katz - 2013 - Hopos: The Journal of the International Society for the History of Philosophy of Science (2):236-280.
    We seek to elucidate the philosophical context in which one of the most important conceptual transformations of modern mathematics took place, namely the so-called revolution in rigor in infinitesimal calculus and mathematical analysis. Some of the protagonists of the said revolution were Cauchy, Cantor, Dedekind,and Weierstrass. The dominant current of philosophy in Germany at the time was neo-Kantianism. Among its various currents, the Marburg school (Cohen, Natorp, Cassirer, and others) was the one most interested in matters scientific and (...)
    Download  
     
    Export citation  
     
    Bookmark   12 citations  
  4. À Maneira de Um Colar de Pérolas?André Porto - 2017 - Revista Portuguesa de Filosofia 73 (3-4):1381-1404.
    This paper offers an overview of various alternative formulations for Analysis, the theory of Integral and Differential Calculus, and its diverging conceptions of the topological structure of the continuum. We pay particularly attention to Smooth Analysis, a proposal created by William Lawvere and Anders Kock based on Grothendieck’s work on a categorical algebraic geometry. The role of Heyting’s logic, common to all these alternatives is emphasized.
    Download  
    Translate
     
     
    Export citation  
     
    Bookmark  
  5.  85
    Blinking Fractals and Their Quantitative Analysis Using Infinite and Infinitesimal Numbers.Yaroslav Sergeyev - 2007 - Chaos, Solitons and Fractals 33 (1):50-75.
    The paper considers a new type of objects – blinking fractals – that are not covered by traditional theories studying dynamics of self-similarity processes. It is shown that the new approach allows one to give various quantitative characteristics of the newly introduced and traditional fractals using infinite and infinitesimal numbers proposed recently. In this connection, the problem of the mathematical modelling of continuity is discussed in detail. A strong advantage of the introduced computational paradigm consists of its well-marked numerical (...)
    Download  
    Translate
     
     
    Export citation  
     
    Bookmark   4 citations  
  6. Parting Smoothly?Nicholas Shackel - 2007 - Analysis 67 (4):321–324.
    In ‘How to part ways smoothly’ Hud Hudson (2007) presents ‘two temporally-continuous spatially unextended material objects that ... share all of their temporal parts up until their very last time-slice’ (2007: 156). They share their location throughout all but the last instant of their lives, at which instant they are a metre apart. Hudson claims that they part smoothly. I shall show that they don’t.
    Download  
     
    Export citation  
     
    Bookmark  
  7. Numerical Infinities and Infinitesimals: Methodology, Applications, and Repercussions on Two Hilbert Problems.Yaroslav Sergeyev - 2017 - EMS Surveys in Mathematical Sciences 4 (2):219–320.
    In this survey, a recent computational methodology paying a special attention to the separation of mathematical objects from numeral systems involved in their representation is described. It has been introduced with the intention to allow one to work with infinities and infinitesimals numerically in a unique computational framework in all the situations requiring these notions. The methodology does not contradict Cantor’s and non-standard analysis views and is based on the Euclid’s Common Notion no. 5 “The whole is greater than (...)
    Download  
     
    Export citation  
     
    Bookmark   2 citations  
  8.  46
    Numerical Point of View on Calculus for Functions Assuming Finite, Infinite, and Infinitesimal Values Over Finite, Infinite, and Infinitesimal Domains.Yaroslav Sergeyev - 2009 - Nonlinear Analysis Series A 71 (12):e1688-e1707.
    The goal of this paper consists of developing a new (more physical and numerical in comparison with standard and non-standard analysis approaches) point of view on Calculus with functions assuming infinite and infinitesimal values. It uses recently introduced infinite and infinitesimal numbers being in accordance with the principle ‘The part is less than the whole’ observed in the physical world around us. These numbers have a strong practical advantage with respect to traditional approaches: they are representable at (...)
    Download  
     
    Export citation  
     
    Bookmark   5 citations  
  9. Independence of the Grossone-Based Infinity Methodology From Non-Standard Analysis and Comments Upon Logical Fallacies in Some Texts Asserting the Opposite.Yaroslav D. Sergeyev - 2019 - Foundations of Science 24 (1):153-170.
    This paper considers non-standard analysis and a recently introduced computational methodology based on the notion of ①. The latter approach was developed with the intention to allow one to work with infinities and infinitesimals numerically in a unique computational framework and in all the situations requiring these notions. Non-standard analysis is a classical purely symbolic technique that works with ultrafilters, external and internal sets, standard and non-standard numbers, etc. In its turn, the ①-based methodology does not use any (...)
    Download  
     
    Export citation  
     
    Bookmark  
  10. Fermat’s Last Theorem Proved in Hilbert Arithmetic. III. The Quantum-Information Unification of Fermat’s Last Theorem and Gleason’s Theorem.Vasil Penchev - forthcoming - Logic and Philosophy of Mathematics eJournal (Elsevier: SSRN):1-30.
    The previous two parts of the paper demonstrate that the interpretation of Fermat’s last theorem (FLT) in Hilbert arithmetic meant both in a narrow sense and in a wide sense can suggest a proof by induction in Part I and by means of the Kochen - Specker theorem in Part II. The same interpretation can serve also for a proof FLT based on Gleason’s theorem and partly similar to that in Part II. The concept of (probabilistic) measure of a subspace (...)
    Download  
     
    Export citation  
     
    Bookmark  
  11. Fair Infinite Lotteries.Sylvia Wenmackers & Leon Horsten - 2013 - Synthese 190 (1):37-61.
    This article discusses how the concept of a fair finite lottery can best be extended to denumerably infinite lotteries. Techniques and ideas from non-standard analysis are brought to bear on the problem.
    Download  
     
    Export citation  
     
    Bookmark   38 citations  
  12. The Logic and Topology of Kant's Temporal Continuum.Riccardo Pinosio & Michiel van Lambalgen - manuscript
    In this article we provide a mathematical model of Kant?s temporal continuum that satisfies the (not obviously consistent) synthetic a priori principles for time that Kant lists in the Critique of pure Reason (CPR), the Metaphysical Foundations of Natural Science (MFNS), the Opus Postumum and the notes and frag- ments published after his death. The continuum so obtained has some affinities with the Brouwerian continuum, but it also has ‘infinitesimal intervals’ consisting of nilpotent infinitesimals, which capture Kant’s theory of (...)
    Download  
     
    Export citation  
     
    Bookmark  
  13. Numerical Infinities Applied for Studying Riemann Series Theorem and Ramanujan Summation.Yaroslav Sergeyev - 2018 - In AIP Conference Proceedings 1978. AIP. pp. 020004.
    A computational methodology called Grossone Infinity Computing introduced with the intention to allow one to work with infinities and infinitesimals numerically has been applied recently to a number of problems in numerical mathematics (optimization, numerical differentiation, numerical algorithms for solving ODEs, etc.). The possibility to use a specially developed computational device called the Infinity Computer (patented in USA and EU) for working with infinite and infinitesimal numbers numerically gives an additional advantage to this approach in comparison with traditional methodologies (...)
    Download  
     
    Export citation  
     
    Bookmark   1 citation  
  14. Tools, Objects, and Chimeras: Connes on the Role of Hyperreals in Mathematics.Vladimir Kanovei, Mikhail G. Katz & Thomas Mormann - 2013 - Foundations of Science 18 (2):259-296.
    We examine some of Connes’ criticisms of Robinson’s infinitesimals starting in 1995. Connes sought to exploit the Solovay model S as ammunition against non-standard analysis, but the model tends to boomerang, undercutting Connes’ own earlier work in functional analysis. Connes described the hyperreals as both a “virtual theory” and a “chimera”, yet acknowledged that his argument relies on the transfer principle. We analyze Connes’ “dart-throwing” thought experiment, but reach an opposite conclusion. In S , all definable sets of (...)
    Download  
     
    Export citation  
     
    Bookmark   15 citations  
  15. Clause-Type, Force, and Normative Judgment in the Semantics of Imperatives.Nate Charlow - 2018 - In Daniel Fogal Daniel Harris & Matt Moss (eds.), New Work on Speech Acts. Oxford: Oxford University Press. pp. 67–98.
    I argue that imperatives express contents that are both cognitively and semantically related to, but nevertheless distinct from, modal propositions. Imperatives, on this analysis, semantically encode features of planning that are modally specified. Uttering an imperative amounts to tokening this feature in discourse, and thereby proffering it for adoption by the audience. This analysis deals smoothly with the problems afflicting Portner's Dynamic Pragmatic account and Kaufmann's Modal account. It also suggests an appealing reorientation of clause-type theorizing, in which (...)
    Download  
    Translate
     
     
    Export citation  
     
    Bookmark   4 citations  
  16. Philosophy of Probability: Foundations, Epistemology, and Computation.Sylvia Wenmackers - 2011 - Dissertation, University of Groningen
    This dissertation is a contribution to formal and computational philosophy. -/- In the first part, we show that by exploiting the parallels between large, yet finite lotteries on the one hand and countably infinite lotteries on the other, we gain insights in the foundations of probability theory as well as in epistemology. Case 1: Infinite lotteries. We discuss how the concept of a fair finite lottery can best be extended to denumerably infinite lotteries. The solution boils down to the introduction (...)
    Download  
     
    Export citation  
     
    Bookmark   5 citations  
  17. Hermann Cohen’s History and Philosophy of Science.Lydia Patton - 2004 - Dissertation, McGill University
    In my dissertation, I present Hermann Cohen's foundation for the history and philosophy of science. My investigation begins with Cohen's formulation of a neo-Kantian epistemology. I analyze Cohen's early work, especially his contributions to 19th century debates about the theory of knowledge. I conclude by examining Cohen's mature theory of science in two works, The Principle of the Infinitesimal Method and its History of 1883, and Cohen's extensive 1914 Introduction to Friedrich Lange's History of Materialism. In the former, Cohen (...)
    Download  
     
    Export citation  
     
    Bookmark   9 citations  
  18. Discrete and Continuous: A Fundamental Dichotomy in Mathematics.James Franklin - 2017 - Journal of Humanistic Mathematics 7 (2):355-378.
    The distinction between the discrete and the continuous lies at the heart of mathematics. Discrete mathematics (arithmetic, algebra, combinatorics, graph theory, cryptography, logic) has a set of concepts, techniques, and application areas largely distinct from continuous mathematics (traditional geometry, calculus, most of functional analysis, differential equations, topology). The interaction between the two – for example in computer models of continuous systems such as fluid flow – is a central issue in the applicable mathematics of the last hundred years. This (...)
    Download  
     
    Export citation  
     
    Bookmark   2 citations  
  19.  78
    Review of M. Giaquinto's Visual Thinking in Mathematics. [REVIEW]Andrew Arana - 2009 - Analysis 69 (2):401-403.
    Our visual experience seems to suggest that no continuous curve can cover every point of the unit square, yet in the late nineteenth century Giuseppe Peano proved that such a curve exists. Examples like this, particularly in analysis (in the sense of the infinitesimal calculus) received much attention in the nineteenth century. They helped instigate what Hans Hahn called a “crisis of intuition”, wherein visual reasoning in mathematics came to be thought to be epistemically problematic. Hahn described this (...)
    Download  
     
    Export citation  
     
    Bookmark  
  20. Changing Subjects of Education in the Bologna Process.Lavinia Marin - 2015 - In Council for European Studies’ Twenty - Second International Conference of Europeanists on “Contradictions: Envisioning European Futures ”. Paris:
    One of the purposes of the Bologna Process was to facilitate the construction of a Europe of Knowledge through educational governance, yet it fails to reach its purpose because of several unexplained assumptions that undermine the conceptual standing of the whole project; it is the purpose of this paper to bring these assumptions to light. -/- A knowledge economy cannot exist without the knowledge workers which were previously formed in educational institutions, therefore the project for a Europe of Knowledge is (...)
    Download  
     
    Export citation  
     
    Bookmark  
  21. Managing Transitions: Coping Strategies for New Principals in Colleges of Education, Ghana.Caroline Aggrey-Fynn - 2020 - International Journal of Scientific Research and Management (IJSRM) 8 (1).
    Principals’ transition in Colleges of Education in Ghana is critical to quality teacher education and training, but it comes with complexities and challenges to newly appointed principals. However, there is a seeming absence of research on strategies for smooth transitions in Colleges of Education in Ghana. This study was therefore conducted to establish strategies that promoted the College of Education principals’ transition management in Ghana. Phenomenological research design was used for the study. Ten (10) newly appointed principals of public (...)
    Download  
    Translate
     
     
    Export citation  
     
    Bookmark  
  22.  68
    The Harsanyi-Rawls Debate: Political Philosophy as Decision Theory Under Uncertainty.Ramiro Ávila Peres - forthcoming - Manuscrito: Revista Internacional de Filosofía.
    Social decisions are often made under great uncertainty – in situations where political principles, and even standard subjective expected utility, do not apply smoothly. In the first section, we argue that the core of this problem lies in decision theory itself – it is about how to act when we do not have an adequate representation of the context of the action and of its possible consequences. Thus, we distinguish two criteria to complement decision theory under ignorance – Laplace’s principle (...)
    Download  
     
    Export citation  
     
    Bookmark  
  23.  47
    An Unattractive Hypothesis – RCTs' Descent to Non-Science.Clifford Miller - 2011 - International Journal of Person Centered Medicine 1 (4):841-842.
    Eyal Shahar’s essay review [1] of James Penston’s remarkable book [2] seems more inspired playful academic provocation than review or essay, expressing dramatic views of impossible validity. The account given of modern biostatistical causation reveals the slide from science into the intellectual confusion and non-science RCTs have created: “…. the purpose of medical research is to estimate the magnitude of the effect of a causal contrast, for example the probability ratio of a binary outcome …” But Shahar’s world is simultaneously (...)
    Download  
     
    Export citation  
     
    Bookmark  
  24. Headteachers’ Perception of the Implementation of the Capitation Grant Scheme In The Sunyani West District of the Brong Ahafo Region.Georgina Cate Foli - 2019 - International Journal of Scientific Research and Management (IJSRM) 7 (9).
    This study was conducted to find out head teachers' perception of the implementation of the capitation grant scheme in Sunyani West East District of the Brong Ahafo Region. The study specifically focused on explaining how head teachers conceptualised the concept of capitation grant scheme, the implementation process, and the challenges associated with the implementation of the scheme. A descriptive research design was adopted for the study, and a questionnaire and an interview guide were designed and administered to a sample of (...)
    Download  
    Translate
     
     
    Export citation  
     
    Bookmark  
  25.  71
    Colombeau Solutions to Einstein Field Equations.Gravitational Singularities.Jaykov Foukzon - manuscript
    In contemporary mathematics, a Colombeau algebra of Colombeau generalized functions is an algebra of a certain kind containing the space of Schwartz distributions. While in classical distribution theory a general multiplication of distributions is not possible, Colombeau algebras provide a rigorous framework for this. Remark 1.1.1.Such a multiplication of distributions has been a long time mistakenly believed to be impossible because of Schwartz’ impossibility result, which basically states that there cannot be a differential algebra containing the space of distributions and (...)
    Download  
     
    Export citation  
     
    Bookmark  
  26. Infinitesimal Probabilities.Sylvia Wenmackers - 2016 - In Richard Pettigrew & Jonathan Weisberg (eds.), The Open Handbook of Formal Epistemology. PhilPapers Foundation. pp. 199-265.
    Non-Archimedean probability functions allow us to combine regularity with perfect additivity. We discuss the philosophical motivation for a particular choice of axioms for a non-Archimedean probability theory and answer some philosophical objections that have been raised against infinitesimal probabilities in general.
    Download  
     
    Export citation  
     
    Bookmark   4 citations  
  27. Infinitesimal Differences: Controversies Between Leibniz and His Contemporaries. [REVIEW]Françoise Monnoyeur-Broitman - 2010 - Journal of the History of Philosophy 48 (4):527-528.
    Leibniz is well known for his formulation of the infinitesimal calculus. Nevertheless, the nature and logic of his discovery are seldom questioned: does it belong more to mathematics or metaphysics, and how is it connected to his physics? This book, composed of fourteen essays, investigates the nature and foundation of the calculus, its relationship to the physics of force and principle of continuity, and its overall method and metaphysics. The Leibnizian calculus is presented in its origin and context together (...)
    Download  
     
    Export citation  
     
    Bookmark   1 citation  
  28. Smooth Coping: An Embodied, Heideggerian Approach to Dual-Process Theory.Zachariah A. Neemeh - 2021 - Adaptive Behavior 1:1-16.
    Dual-process theories divide cognition into two kinds of processes: Type 1 processes that are autonomous and do not use working memory, and Type 2 processes that are decoupled from the immediate situation and use working memory. Often, Type 1 processes are also fast, high capacity, parallel, nonconscious, biased, contextualized, and associative, while Type 2 processes are typically slow, low capacity, serial, conscious, normative, abstract, and rule-based. This article argues for an embodied dual-process theory based on the phenomenology of Martin Heidegger. (...)
    Download  
     
    Export citation  
     
    Bookmark  
  29. What Makes a Theory of Infinitesimals Useful? A View by Klein and Fraenkel.Vladimir Kanovei, K. Katz, M. Katz & Thomas Mormann - 2018 - Journal of Humanistic Mathematics 8 (1):108 - 119.
    Felix Klein and Abraham Fraenkel each formulated a criterion for a theory of infinitesimals to be successful, in terms of the feasibility of implementation of the Mean Value Theorem. We explore the evolution of the idea over the past century, and the role of Abraham Robinson's framework therein.
    Download  
     
    Export citation  
     
    Bookmark   2 citations  
  30. Robustness Analysis as Explanatory Reasoning.Jonah N. Schupbach - 2016 - British Journal for the Philosophy of Science:axw008.
    When scientists seek further confirmation of their results, they often attempt to duplicate the results using diverse means. To the extent that they are successful in doing so, their results are said to be robust. This paper investigates the logic of such "robustness analysis" [RA]. The most important and challenging question an account of RA can answer is what sense of evidential diversity is involved in RAs. I argue that prevailing formal explications of such diversity are unsatisfactory. I propose (...)
    Download  
     
    Export citation  
     
    Bookmark   36 citations  
  31. Hermann Cohen’s Principle of the Infinitesimal Method: A Defense.Scott Edgar - 2020 - Hopos: The Journal of the International Society for the History of Philosophy of Science 10 (2):440-470.
    In Bertrand Russell's 1903 Principles of Mathematics, he offers an apparently devastating criticism of the neo-Kantian Hermann Cohen's Principle of the Infinitesimal Method and its History (PIM). Russell's criticism is motivated by his concern that Cohen's account of the foundations of calculus saddles mathematics with the paradoxes of the infinitesimal and continuum, and thus threatens the very idea of mathematical truth. This paper defends Cohen against that objection of Russell's, and argues that properly understood, Cohen's views of limits (...)
    Download  
     
    Export citation  
     
    Bookmark   2 citations  
  32. The Exact (Up to Infinitesimals) Infinite Perimeter of the Koch Snowflake and its Finite Area.Yaroslav Sergeyev - 2016 - Communications in Nonlinear Science and Numerical Simulation 31 (1-3):21–29.
    The Koch snowflake is one of the first fractals that were mathematically described. It is interesting because it has an infinite perimeter in the limit but its limit area is finite. In this paper, a recently proposed computational methodology allowing one to execute numerical computations with infinities and infinitesimals is applied to study the Koch snowflake at infinity. Numerical computations with actual infinite and infinitesimal numbers can be executed on the Infinity Computer being a new supercomputer patented in USA (...)
    Download  
     
    Export citation  
     
    Bookmark   3 citations  
  33. Corpus Analysis in Philosophy.Roland Bluhm - 2016 - In Martin Hinton (ed.), Evidence, Experiment and Argument in Linguistics and the Philosophy of Language. Peter Lang. pp. 91-109.
    The experimental philosophy movement advocates the use of empirical methods in philosophy. The methods most often discussed and in fact employed in experimental philosophy are appropriated from the experimental paradigm in psychology. But there is a variety of other (at least partly) empirical methods from various disciplines that are and others that could be used in philosophy. The paper explores the application of corpus analysis to philosophical issues. Although the method is well established in linguistics, there are only a (...)
    Download  
     
    Export citation  
     
    Bookmark   15 citations  
  34. The Constitution of Weyl’s Pure Infinitesimal World Geometry.C. D. McCoy - 2022 - Hopos: The Journal of the International Society for the History of Philosophy of Science 12 (1):189–208.
    Hermann Weyl was one of the most important figures involved in the early elaboration of the general theory of relativity and its fundamentally geometrical spacetime picture of the world. Weyl’s development of “pure infinitesimal geometry” out of relativity theory was the basis of his remarkable attempt at unifying gravitation and electromagnetism. Many interpreters have focused primarily on Weyl’s philosophical influences, especially the influence of Husserl’s transcendental phenomenology, as the motivation for these efforts. In this article, I argue both that (...)
    Download  
     
    Export citation  
     
    Bookmark  
  35. An Analysis of the Interaction Between Intelligent Software Agents and Human Users.Christopher Burr, Nello Cristianini & James Ladyman - 2018 - Minds and Machines 28 (4):735-774.
    Interactions between an intelligent software agent and a human user are ubiquitous in everyday situations such as access to information, entertainment, and purchases. In such interactions, the ISA mediates the user’s access to the content, or controls some other aspect of the user experience, and is not designed to be neutral about outcomes of user choices. Like human users, ISAs are driven by goals, make autonomous decisions, and can learn from experience. Using ideas from bounded rationality, we frame these interactions (...)
    Download  
     
    Export citation  
     
    Bookmark   27 citations  
  36. Semantical Analysis of Weak Kleene Logics.Roberto Ciuni & Massimiliano Carrara - 2019 - Journal of Applied Non-Classical Logics 29 (1):1-36.
    This paper presents a semantical analysis of the Weak Kleene Logics Kw3 and PWK from the tradition of Bochvar and Halldén. These are three-valued logics in which a formula takes the third value if at least one of its components does. The paper establishes two main results: a characterisation result for the relation of logical con- sequence in PWK – that is, we individuate necessary and sufficient conditions for a set.
    Download  
     
    Export citation  
     
    Bookmark   12 citations  
  37. Conceptual Analysis and Epistemic Progress.Magdalena Balcerak Jackson - 2013 - Synthese 190 (15):3053-3074.
    This essay concerns the question of how we make genuine epistemic progress through conceptual analysis. Our way into this issue will be through consideration of the paradox of analysis. The paradox challenges us to explain how a given statement can make a substantive contribution to our knowledge, even while it purports merely to make explicit what one’s grasp of the concept under scrutiny consists in. The paradox is often treated primarily as a semantic puzzle. However, in “Sect. 1” (...)
    Download  
     
    Export citation  
     
    Bookmark   8 citations  
  38. Sentiment Analysis on Online Social Network.Vijaya Abhinandan - forthcoming - International Journal of Computer Science, Information Technology, and Security.
    A large amount of data is maintained in every Social networking sites.The total data constantly gathered on these sites make it difficult for methods like use of field agents, clipping services and ad-hoc research to maintain social media data. This paper discusses the previous research on sentiment analysis.
    Download  
    Translate
     
     
    Export citation  
     
    Bookmark  
  39.  48
    Evaluating the Exact Infinitesimal Values of Area of Sierpinski's Carpet and Volume of Menger's Sponge.Yaroslav Sergeyev - 2009 - Chaos, Solitons and Fractals 42: 3042–3046.
    Very often traditional approaches studying dynamics of self-similarity processes are not able to give their quantitative characteristics at infinity and, as a consequence, use limits to overcome this difficulty. For example, it is well know that the limit area of Sierpinski’s carpet and volume of Menger’s sponge are equal to zero. It is shown in this paper that recently introduced infinite and infinitesimal numbers allow us to use exact expressions instead of limits and to calculate exact infinitesimal values (...)
    Download  
    Translate
     
     
    Export citation  
     
    Bookmark   2 citations  
  40. Analysis of Faith.Bradley Rettler - 2018 - Philosophy Compass 13 (9):e12517.
    In recent years, many philosophers of religion have turned their attention to the topic of faith. Given the ubiquity of the word “faith” both in and out of religious contexts, many of them have chosen to begin their forays by offering an analysis of faith. But it seems that there are many kinds of faith: religious faith, non‐religious faith, interpersonal faith, and propositional faith, to name a few. In this article, I discuss analyses of faith that have been offered (...)
    Download  
     
    Export citation  
     
    Bookmark   8 citations  
  41. Is Meta-Analysis the Platinum Standard of Evidence?Jacob Stegenga - 2011 - Studies in History and Philosophy of Science Part C: Studies in History and Philosophy of Biological and Biomedical Sciences 42 (4):497-507.
    An astonishing volume and diversity of evidence is available for many hypotheses in the biomedical and social sciences. Some of this evidence—usually from randomized controlled trials (RCTs)—is amalgamated by meta-analysis. Despite the ongoing debate regarding whether or not RCTs are the ‘gold-standard’ of evidence, it is usually meta-analysis which is considered the best source of evidence: meta-analysis is thought by many to be the platinum standard of evidence. However, I argue that meta-analysis falls far short of (...)
    Download  
     
    Export citation  
     
    Bookmark   60 citations  
  42. An Analysis of the Demarcation Problem in Philosophy of Science and Its Application to Homeopathy.Alper Bilgehan Yardımcı - 2018 - Flsf 1 (25):91-107.
    This paper presents a preliminary analysis of homeopathy from the perspective of the demarcation problem in the philosophy of science. In this context, Popper, Kuhn and Feyerabend’s solution to the problem will be given respectively and their criteria will be applied to homeopathy, aiming to shed some light on the controversy over its scientific status. It then examines homeopathy under the lens of demarcation criteria to conclude that homeopathy is regarded as science by Feyerabend and is considered as pseudoscience (...)
    Download  
     
    Export citation  
     
    Bookmark   7 citations  
  43. Solving Ordinary Differential Equations by Working with Infinitesimals Numerically on the Infinity Computer.Yaroslav Sergeyev - 2013 - Applied Mathematics and Computation 219 (22):10668–10681.
    There exists a huge number of numerical methods that iteratively construct approximations to the solution y(x) of an ordinary differential equation (ODE) y′(x) = f(x,y) starting from an initial value y_0=y(x_0) and using a finite approximation step h that influences the accuracy of the obtained approximation. In this paper, a new framework for solving ODEs is presented for a new kind of a computer – the Infinity Computer (it has been patented and its working prototype exists). The new computer is (...)
    Download  
     
    Export citation  
     
    Bookmark   4 citations  
  44. Rational Analysis, Intractability, and the Prospects of ‘as If’-Explanations.Iris van Rooij, Cory D. Wright, Johan Kwisthout & Todd Wareham - 2018 - Synthese 195 (2):491-510.
    Despite their success in describing and predicting cognitive behavior, the plausibility of so-called ‘rational explanations’ is often contested on the grounds of computational intractability. Several cognitive scientists have argued that such intractability is an orthogonal pseudoproblem, however, since rational explanations account for the ‘why’ of cognition but are agnostic about the ‘how’. Their central premise is that humans do not actually perform the rational calculations posited by their models, but only act as if they do. Whether or not the problem (...)
    Download  
     
    Export citation  
     
    Bookmark   5 citations  
  45. Conceptual Analysis in Metaethics.N. G. Laskowski & Stephen Finlay - 2017 - In Tristram McPherson & David Plunkett (eds.), The Routledge Handbook of Metaethics. Routledge. pp. 536-551.
    A critical survey of various positions on the nature, use, possession, and analysis of normative concepts. We frame our treatment around G.E. Moore’s Open Question Argument, and the ways metaethicists have responded by departing from a Classical Theory of concepts. In addition to the Classical Theory, we discuss synthetic naturalism, noncognitivism (expressivist and inferentialist), prototype theory, network theory, and empirical linguistic approaches. Although written for a general philosophical audience, we attempt to provide a new perspective and highlight some underappreciated (...)
    Download  
     
    Export citation  
     
    Bookmark   5 citations  
  46. A New Applied Approach for Executing Computations with Infinite and Infinitesimal Quantities.Yaroslav D. Sergeyev - 2008 - Informatica 19 (4):567-596.
    A new computational methodology for executing calculations with infinite and infinitesimal quantities is described in this paper. It is based on the principle ‘The part is less than the whole’ introduced by Ancient Greeks and applied to all numbers (finite, infinite, and infinitesimal) and to all sets and processes (finite and infinite). It is shown that it becomes possible to write down finite, infinite, and infinitesimal numbers by a finite number of symbols as particular cases of a (...)
    Download  
    Translate
     
     
    Export citation  
     
    Bookmark   5 citations  
  47. The Analysis of Knowledge.Brian C. Barnett - 2021 - In Introduction to Philosophy: Epistemology. Rebus Community. pp. Chapter 1.
    According to the traditional analysis of propositional knowledge (which derives from Plato's account in the Meno and Theaetetus), knowledge is justified true belief. This chapter develops the traditional analysis, introduces the famous Gettier and lottery problems, and provides an overview of prospective solutions. In closing, I briefly comment on the value of conceptual analysis, note how it has shaped the field, and assess the state of post-Gettier epistemology.
    Download  
     
    Export citation  
     
    Bookmark  
  48. Experience and Prediction: An Analysis of the Foundations and the Structure of Knowledge.Hans Reichenbach - 1938 - Chicago, IL, USA: University of Chicago Press.
    First published in 1949 expressly to introduce logical positivism to English speakers. Reichenbach, with Rudolph Carnap, founded logical positivism, a form of epistemofogy that privileged scientific over metaphysical truths.
    Download  
     
    Export citation  
     
    Bookmark   394 citations  
  49. Empirical Analysis of Current Approaches to Incidental Findings.Frances Lawrenz & Suzanne Sobotka - 2008 - Journal of Law, Medicine and Ethics 36 (2):249-255.
    This paper presents results found through searching publicly available U.S. data sources for information about how to handle incidental fndings (IF) in human subjects research, especially in genetics and genomics research, neuroimaging research, and CT colonography research. We searched the Web sites of 14 federal agencies, 22 professional societies, and 100 universities, as well as used the search engine Google for actual consent forms that had been posted on the Internet. Our analysis of these documents showed that there is (...)
    Download  
     
    Export citation  
     
    Bookmark   13 citations  
  50. Truth Analysis of the Gettier Argument.Yussif Yakubu - 2016 - Metaphilosophy 47 (3):449-466.
    Gettier presented the now famous Gettier problem as a challenge to epistemology. The methods Gettier used to construct his challenge, however, utilized certain principles of formal logic that are actually inappropriate for the natural language discourse of the Gettier cases. In that challenge to epistemology, Gettier also makes truth claims that would be considered controversial in analytic philosophy of language. The Gettier challenge has escaped scrutiny in these other relevant academic disciplines, however, because of its façade as an epistemological (...). This article examines Gettier's methods with the analytical tools of logic and analytic philosophy of language. (shrink)
    Download  
     
    Export citation  
     
    Bookmark   4 citations  
1 — 50 / 999