Results for 'empirical philosophy of mathematics'

954 found
Order:
  1. (1 other version)Assessing the “Empirical Philosophy of Mathematics”.Markus Pantsar - 2015 - Discipline Filosofiche:111-130.
    Abstract In the new millennium there have been important empirical developments in the philosophy of mathematics. One of these is the so-called “Empirical Philosophy of Mathematics”(EPM) of Buldt, Löwe, Müller and Müller-Hill, which aims to complement the methodology of the philosophy of mathematics with empirical work. Among other things, this includes surveys of mathematicians, which EPM believes to give philosophically important results. In this paper I take a critical look at the (...)
    Direct download  
     
    Export citation  
     
    Bookmark   1 citation  
  2. Methodological Triangulation in Empirical Philosophy.Benedikt Löwe & Bart Van Kerkhove - 2019 - In Andrew Aberdein & Matthew Inglis (eds.), Advances in Experimental Philosophy of Logic and Mathematics. London: Bloomsbury Academic. pp. 15-37.
  3.  66
    Mathematical Structure and Empirical Content.Michael E. Miller - unknown - British Journal for the Philosophy of Science 74 (2):511-532.
    Approaches to the interpretation of physical theories provide accounts of how physical meaning accrues to the mathematical structure of a theory. According to many standard approaches to interpretation, meaning relations are captured by maps from the mathematical structure of the theory to statements expressing its empirical content. In this article I argue that while such accounts adequately address meaning relations when exact models are available or perturbation theory converges, they do not fare as well for models that give rise (...)
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   7 citations  
  4.  73
    Explanation in mathematical conversations: An empirical investigation.Alison Pease, Andrew Aberdein & Ursula Martin - 2019 - Philosophical Transactions of the Royal Society A 377.
    Analysis of online mathematics forums can help reveal how explanation is used by mathematicians; we contend that this use of explanation may help to provide an informal conceptualization of simplicity. We extracted six conjectures from recent philosophical work on the occurrence and characteristics of explanation in mathematics. We then tested these conjectures against a corpus derived from online mathematical discussions. To this end, we employed two techniques, one based on indicator terms, the other on a random sample of (...)
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   7 citations  
  5.  30
    Empirical, Mathematical, and Logical Knowledge in Hegel.Stany Mazurkievic - 2015 - Balkan Journal of Philosophy 7 (1):77-84.
    This paper considers the rediscovery of Hegel currently taking place in the analytic philosophy. Going back to the Hegelian texts themselves, I will try to show how they can help to decisively solve some problems of contemporary philosophy. I will concentrate on the theme of knowledge, and especially mathematical knowledge, in relation to Hegelian dialectical logic.
    No categories
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   2 citations  
  6. Mathematical Modeling in Biology: Philosophy and Pragmatics.Rasmus Grønfeldt Winther - 2012 - Frontiers in Plant Evolution and Development 2012:1-3.
    Philosophy can shed light on mathematical modeling and the juxtaposition of modeling and empirical data. This paper explores three philosophical traditions of the structure of scientific theory—Syntactic, Semantic, and Pragmatic—to show that each illuminates mathematical modeling. The Pragmatic View identifies four critical functions of mathematical modeling: (1) unification of both models and data, (2) model fitting to data, (3) mechanism identification accounting for observation, and (4) prediction of future observations. Such facets are explored using a recent exchange between (...)
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   6 citations  
  7. Mathematics as a quasi-empirical science.Gianluigi Oliveri - 2004 - Foundations of Science 11 (1-2):41-79.
    The present paper aims at showing that there are times when set theoretical knowledge increases in a non-cumulative way. In other words, what we call ‘set theory’ is not one theory which grows by simple addition of a theorem after the other, but a finite sequence of theories T1, ..., Tn in which Ti+1, for 1 ≤ i < n, supersedes Ti. This thesis has a great philosophical significance because it implies that there is a sense in which mathematical theories, (...)
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark   3 citations  
  8. A New Role for Mathematics in Empirical Sciences.Atoosa Kasirzadeh - 2021 - Philosophy of Science 88 (4):686-706.
    Mathematics is often taken to play one of two roles in the empirical sciences: either it represents empirical phenomena or it explains these phenomena by imposing constraints on them. This article identifies a third and distinct role that has not been fully appreciated in the literature on applicability of mathematics and may be pervasive in scientific practice. I call this the “bridging” role of mathematics, according to which mathematics acts as a connecting scheme in (...)
    Direct download (5 more)  
     
    Export citation  
     
    Bookmark   2 citations  
  9.  33
    A missing link: The influence of László Kalmár's empirical view on Lakatos' philosophy of mathematics.Dezső Gurka - 2006 - Perspectives on Science 14 (3):263-281.
    . The circumstance, that the text of Imre Lakatos' doctoral thesis from the University of Debrecen did not survive, makes the evaluation of his career in Hungary and the research of aspects of continuity of his lifework difficult. My paper tries to reconstruct these newer aspects of continuity, introducing the influence of László Kalmár the mathematician and his fellow student, and Sándor Karácsony the philosopher and his mentor on Lakatos' work. The connection between the understanding of the empirical basis (...)
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark   6 citations  
  10.  47
    A missing link: The infuence of lászló kalmár's empirical view on Lakatos' philosophy of mathematics.Deszo Gurka - 2006 - Perspectives on Science 14 (3):263-281.
    The circumstance that the text of Imre Lakatos' doctoral thesis from the University of Debrecen did not survive makes the evaluation of his career in Hungary and the research of aspects of continuity of his lifework difficult. My paper tries to reconstruct these newer aspects of continuity, introducing the influence of László Kalmár the mathematician and his fellow student, and Sándor Karácsony the philosopher and his mentor on Lakatos' work. The connection between the understanding of the empirical basis of (...)
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   4 citations  
  11. Empirical regularities in Wittgenstein's philosophy of mathematics.Mark Steiner - 2009 - Philosophia Mathematica 17 (1):1-34.
    During the course of about ten years, Wittgenstein revised some of his most basic views in philosophy of mathematics, for example that a mathematical theorem can have only one proof. This essay argues that these changes are rooted in his growing belief that mathematical theorems are ‘internally’ connected to their canonical applications, i.e. , that mathematical theorems are ‘hardened’ empirical regularities, upon which the former are supervenient. The central role Wittgenstein increasingly assigns to empirical regularities had (...)
    Direct download (9 more)  
     
    Export citation  
     
    Bookmark   19 citations  
  12.  56
    Philosophy from an Empirical Standpoint: Essays on Carl Stumpf.Andrea Staiti - 2018 - Philosophical Quarterly 68 (270):212-214.
    © The Author 2017. Published by Oxford University Press on behalf of The Scots Philosophical Association and the University of St Andrews. All rights reserved. For permissions, please e-mail: journals.permissions@oup.com...Denis Fisette and Riccardo Martinelli have put together the most comprehensive, ambitious, and engaging collection of essays on the philosophy of Carl Stumpf to date. The volume is impressive in both scope and depth. It covers every single aspect of Stumpf's contribution to philosophy, including issues in the philosophy (...)
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark  
  13. On the Empirical Application of Mathematics and Some of Its Philosophical Aspects in The Kaleidoscope of Science. The Israel Colloquium: Studies in History, Philosophy, and Sociology of Science. Volume I. [REVIEW]S. Korner - 1986 - Boston Studies in the Philosophy of Science 94:1-16.
  14.  88
    Mathematical rigor and proof.Yacin Hamami - 2022 - Review of Symbolic Logic 15 (2):409-449.
    Mathematical proof is the primary form of justification for mathematical knowledge, but in order to count as a proper justification for a piece of mathematical knowl- edge, a mathematical proof must be rigorous. What does it mean then for a mathematical proof to be rigorous? According to what I shall call the standard view, a mathematical proof is rigorous if and only if it can be routinely translated into a formal proof. The standard view is almost an orthodoxy among contemporary (...)
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   23 citations  
  15.  69
    Three Roles of Empirical Information in Philosophy: Intuitions on Mathematics do Not Come for Free.Deniz Sarikaya, José Antonio Pérez-Escobar & Deborah Kant - 2021 - Kriterion – Journal of Philosophy 35 (3):247-278.
    This work gives a new argument for ‘Empirical Philosophy of Mathematical Practice’. It analyses different modalities on how empirical information can influence philosophical endeavours. We evoke the classical dichotomy between “armchair” philosophy and empirical/experimental philosophy, and claim that the latter should in turn be subdivided in three distinct styles: Apostate speculator, Informed analyst, and Freeway explorer. This is a shift of focus from the source of the information towards its use by philosophers. We present (...)
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   7 citations  
  16. Mathematics and its Applications: A Transcendental-Idealist Perspective.Jairo José da Silva - 2017 - Cham: Springer Verlag.
    This monograph offers a fresh perspective on the applicability of mathematics in science. It explores what mathematics must be so that its applications to the empirical world do not constitute a mystery. In the process, readers are presented with a new version of mathematical structuralism. The author details a philosophy of mathematics in which the problem of its applicability, particularly in physics, in all its forms can be explained and justified. Chapters cover: mathematics as (...)
  17.  59
    Mathematical understanding and the physical sciences.Harry Collins - 2007 - Studies in History and Philosophy of Science Part A 38 (4):667-685.
    The author claims to have developed interactional expertise in gravitational wave physics without engaging with the mathematical or quantitative aspects of the subject. Is this possible? In other words, is it possible to understand the physical world at a high enough level to argue and make judgments about it without the corresponding mathematics? This question is empirically approached in three ways: anecdotes about non-mathematical physicists are presented; the author undertakes a reflective reading of a passage of physics, first without (...)
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  18.  13
    Mathematics Education Research on Mathematical Practice.Keith Weber & Matthew Inglis - 2024 - In Bharath Sriraman (ed.), Handbook of the History and Philosophy of Mathematical Practice. Cham: Springer. pp. 2637-2663.
    In the mathematics education research literature, there is a growing body of scholarship on how mathematicians practice their craft. The purpose of this chapter is to survey some of this literature and explain how it can contribute to the philosophy of mathematical practice. We first describe how mathematics educators use empirical methodologies to investigate the behaviors of mathematicians and argue that findings from these studies can inform the philosophy of mathematical practice. We then illustrate this (...)
    No categories
    Direct download  
     
    Export citation  
     
    Bookmark  
  19.  99
    Mathematics and Metalogic.Daniel Bonevac - 1984 - The Monist 67 (1):56-71.
    In this paper I shall attempt to outline a nominalistic theory of mathematical truth. I call my theory nominalistic because it avoids a real (see [4]) ontological commitment to abstract entities. Traditionally, nominalists have found it difficult to justify any reference to infinite collections in mathematics. Even those who have tried to do so have typically restricted themselves to predicative and, thus, denumerable realms. I Indeed, many have linked impredicative definitions to platonism; nominalists have tended to agree with Weyl (...)
    Direct download (6 more)  
     
    Export citation  
     
    Bookmark  
  20. Mathematics and indispensability.Elliott Sober - 1993 - Philosophical Review 102 (1):35-57.
    Realists persuaded by indispensability arguments af- firm the existence of numbers, genes, and quarks. Van Fraassen's empiricism remains agnostic with respect to all three. The point of agreement is that the posits of mathematics and the posits of biology and physics stand orfall together. The mathematical Platonist can take heart from this consensus; even if the existence of num- bers is still problematic, it seems no more problematic than the existence of genes or quarks. If the two positions just (...)
    Direct download (7 more)  
     
    Export citation  
     
    Bookmark   93 citations  
  21. Mathematics and Program Explanations.Juha Saatsi - 2012 - Australasian Journal of Philosophy 90 (3):579-584.
    Aidan Lyon has recently argued that some mathematical explanations of empirical facts can be understood as program explanations. I present three objections to his argument.
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   20 citations  
  22. Naturalising Mathematics? A Wittgensteinian Perspective.Jan Stam, Martin Stokhof & Michiel Van Lambalgen - 2022 - Philosophies 7 (4):85.
    There is a noticeable gap between results of cognitive neuroscientific research into basic mathematical abilities and philosophical and empirical investigations of mathematics as a distinct intellectual activity. The paper explores the relevance of a Wittgensteinian framework for dealing with this discrepancy.
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  23. Magicicada, Mathematical Explanation and Mathematical Realism.Davide Rizza - 2011 - Erkenntnis 74 (1):101-114.
    Baker claims to provide an example of mathematical explanation of an empirical phenomenon which leads to ontological commitment to mathematical objects. This is meant to show that the positing of mathematical entities is necessary for satisfactory scientific explanations and thus that the application of mathematics to science can be used, at least in some cases, to support mathematical realism. In this paper I show that the example of explanation Baker considers can actually be given without postulating mathematical objects (...)
    Direct download (5 more)  
     
    Export citation  
     
    Bookmark   31 citations  
  24. Phenomenology and mathematical practice.Mary Leng - 2002 - Philosophia Mathematica 10 (1):3-14.
    A phenomenological approach to mathematical practice is sketched out, and some problems with this sort of approach are considered. The approach outlined takes mathematical practices as its data, and seeks to provide an empirically adequate philosophy of mathematics based on observation of these practices. Some observations are presented, based on two case studies of some research into the classification of C*-algebras. It is suggested that an anti-realist account of mathematics could be developed on the basis of these (...)
    Direct download (9 more)  
     
    Export citation  
     
    Bookmark   39 citations  
  25. On representing the relationship between the mathematical and the empirical.Otávio Bueno, Steven French & James Ladyman - 2002 - Philosophy of Science 69 (3):497-518.
    We examine, from the partial structures perspective, two forms of applicability of mathematics: at the “bottom” level, the applicability of theoretical structures to the “appearances”, and at the “top” level, the applicability of mathematical to physical theories. We argue that, to accommodate these two forms of applicability, the partial structures approach needs to be extended to include a notion of “partial homomorphism”. As a case study, we present London's analysis of the superfluid behavior of liquid helium in terms of (...)
    Direct download (12 more)  
     
    Export citation  
     
    Bookmark   82 citations  
  26. Mathematical reasoning: induction, deduction and beyond.David Sherry - 2006 - Studies in History and Philosophy of Science Part A 37 (3):489-504.
    Mathematics used to be portrayed as a deductive science. Stemming from Polya, however, is a philosophical movement which broadens the concept of mathematical reasoning to include inductive or quasi-empirical methods. Interest in inductive methods is a welcome turn from foundationalism toward a philosophy grounded in mathematical practice. Regrettably, though, the conception of mathematical reasoning embraced by quasi-empiricists is still too narrow to include the sort of thought-experiment which Mueller describes as traditional mathematical proof and which Lakatos examines (...)
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark   4 citations  
  27. Volume Introduction – Method, Science and Mathematics: Neo-Kantianism and Analytic Philosophy.Scott Edgar - 2018 - Journal for the History of Analytical Philosophy 6 (3):1-10.
    Introduction to the Special Volume, “Method, Science and Mathematics: Neo-Kantianism and Analytic Philosophy,” edited by Scott Edgar and Lydia Patton. At its core, analytic philosophy concerns urgent questions about philosophy’s relation to the formal and empirical sciences, questions about philosophy’s relation to psychology and the social sciences, and ultimately questions about philosophy’s place in a broader cultural landscape. This picture of analytic philosophy shapes this collection’s focus on the history of the (...) of mathematics, physics, and psychology. The following essays uncover, reflect on, and exemplify modes of philosophy that are engaged with these allied disciplines. They make the case that, to the extent that analytic philosophers are still concerned with philosophy’s ties to these disciplines, we would do well to pay attention to neo-Kantian views on those ties. (shrink)
    Direct download (6 more)  
     
    Export citation  
     
    Bookmark   3 citations  
  28. Experimental Mathematics.Alan Baker - 2008 - Erkenntnis 68 (3):331-344.
    The rise of the field of “ experimental mathematics” poses an apparent challenge to traditional philosophical accounts of mathematics as an a priori, non-empirical endeavor. This paper surveys different attempts to characterize experimental mathematics. One suggestion is that experimental mathematics makes essential use of electronic computers. A second suggestion is that experimental mathematics involves support being gathered for an hypothesis which is inductive rather than deductive. Each of these options turns out to be inadequate, (...)
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   17 citations  
  29. Can Mathematics Explain Physical Phenomena?Otávio Bueno & Steven French - 2012 - British Journal for the Philosophy of Science 63 (1):85-113.
    Batterman raises a number of concerns for the inferential conception of the applicability of mathematics advocated by Bueno and Colyvan. Here, we distinguish the various concerns, and indicate how they can be assuaged by paying attention to the nature of the mappings involved and emphasizing the significance of interpretation in this context. We also indicate how this conception can accommodate the examples that Batterman draws upon in his critique. Our conclusion is that ‘asymptotic reasoning’ can be straightforwardly accommodated within (...)
    Direct download (9 more)  
     
    Export citation  
     
    Bookmark   32 citations  
  30.  1
    Wittgenstein on Mathematics.Severin Schroeder - 2024 - Grazer Philosophische Studien 101 (1):71-84.
    In response to Felix Mühlhölzer’s critical discussion of my book Wittgenstein on Mathematics (2021), I argue against his main objections, in particular his view that one shouldn’t even look for coherence in Wittgenstein’s philosophy of mathematics, and his claim that Wittgenstein’s insistence on the empirical applicability of mathematical concepts need not be taken seriously because in one passage it is prefaced by the words ‘I want to say’. I also correct a number of irksome misunderstandings in (...)
    No categories
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark  
  31. Naturalizing Badiou: mathematical ontology and structural realism.Fabio Gironi - 2014 - New York: Palgrave-Macmillan.
    This thesis offers a naturalist revision of Alain Badiou’s philosophy. This goal is pursued through an encounter of Badiou’s mathematical ontology and theory of truth with contemporary trends in philosophy of mathematics and philosophy of science. I take issue with Badiou’s inability to elucidate the link between the empirical and the ontological, and his residual reliance on a Heideggerian project of fundamental ontology, which undermines his own immanentist principles. I will argue for both a bottom-up (...)
  32.  53
    (1 other version)Empirical Adequacy and Scientific Discovery.Samuel Simon - 2008 - Principia 12 (1):35-48.
    http://dx.doi.org/10.5007/1808-1711.2008v12n1p35 This paper aims to show that Bas van Fraassen’s constructive empiricism, such as it is expounded in The Scientific Image , ends up in considerable difficulties in the philosophy of science. The main problem would be the exclusion of mathematics from the conception of science, given its clear absence of empirical adequacy, which is the most important requirement of his formulation. In this sense, it is suggested a more inclusive formulation of scientific theory, aroused from the (...)
    Direct download (6 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  33. Morality and Mathematics.Justin Clarke-Doane - 2020 - Oxford, England: Oxford University Press.
    To what extent are the subjects of our thoughts and talk real? This is the question of realism. In this book, Justin Clarke-Doane explores arguments for and against moral realism and mathematical realism, how they interact, and what they can tell us about areas of philosophical interest more generally. He argues that, contrary to widespread belief, our mathematical beliefs have no better claim to being self-evident or provable than our moral beliefs. Nor do our mathematical beliefs have better claim to (...)
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   40 citations  
  34. Philosophy and mathematics.Andrew Powell - 1997 - Teorema: International Journal of Philosophy 16 (2):97-108.
  35.  28
    Using Crowdsourced Mathematics to Understand Mathematical Practice.Alison Pease, Ursula Martin, Fenner Stanley Tanswell & Andrew Aberdein - 2020 - ZDM 52 (6):1087-1098.
    Records of online collaborative mathematical activity provide us with a novel, rich, searchable, accessible and sizeable source of data for empirical investigations into mathematical practice. In this paper we discuss how the resources of crowdsourced mathematics can be used to help formulate and answer questions about mathematical practice, and what their limitations might be. We describe quantitative approaches to studying crowdsourced mathematics, reviewing work from cognitive history (comparing individual and collaborative proofs); social psychology (on the prospects for (...)
    Direct download  
     
    Export citation  
     
    Bookmark  
  36.  99
    Mathematical Explanation and the Biological Optimality Fallacy.Samantha Wakil & James Justus - 2017 - Philosophy of Science 84 (5):916-930.
    Pure mathematics can play an indispensable role explaining empirical phenomena if recent accounts of insect evolution are correct. In particular, the prime life cycles of cicadas and the geometric structure of honeycombs are taken to undergird an inference to the best explanation about mathematical entities. Neither example supports this inference or the mathematical realism it is intended to establish. Both incorrectly assume that facts about mathematical optimality drove selection for the respective traits and explain why they exist. We (...)
    Direct download (5 more)  
     
    Export citation  
     
    Bookmark   7 citations  
  37.  21
    Mathematics—Application and Applicability.Mark Steiner - 2005 - In Stewart Shapiro (ed.), Oxford Handbook of Philosophy of Mathematics and Logic. Oxford and New York: Oxford University Press.
    This chapter discusses various senses in which mathematics is applied to the material world. It distinguishes between canonical and noncanonical applications of mathematics, the former being those for which the mathematics was developed to deal with in the first place. It also distinguishes between empirical and nonempirical applications, thus yielding four different kinds of applications. Examples of each are provided, and philosophical problems connected with each are treated.
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark   16 citations  
  38.  90
    How Do You Apply Mathematics?Graham Priest - 2022 - Axiomathes 32 (3):1169-1184.
    As far as disputes in the philosophy of pure mathematics goes, these are usually between classical mathematics, intuitionist mathematics, paraconsistent mathematics, and so on. My own view is that of a mathematical pluralist: all these different kinds of mathematics are equally legitimate. Applied mathematics is a different matter. In this, a piece of pure mathematics is applied in an empirical area, such as physics, biology, or economics. There can then certainly be (...)
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark  
  39.  48
    Absolute, true and mathematical time in Newton’s Principia.Katherine Brading - unknown
    I discuss the three distinctions “absolute and relative”, “true and apparent”, and “mathematical and common”, for the specific case of time in Newton’s Principia. I argue that all three distinctions are needed for the project of the Principia and can be understood within the context of that project without appeal to Newton’s wider metaphysical and theological commitments. I argue that, within the context of the Principia, the three claims that time is absolute rather than relative, true rather than apparent, and (...)
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark  
  40.  40
    Confirming Mathematical Conjectures by Analogy.Francesco Nappo, Nicolò Cangiotti & Caterina Sisti - 2024 - Erkenntnis 89 (6):2493-2519.
    Analogy has received attention as a form of inductive reasoning in the empirical sciences. Its role in mathematics has, instead, received less consideration. This paper provides a novel account of how an analogy with a more familiar mathematical domain can contribute to the confirmation of a mathematical conjecture. By reference to case-studies, we propose a distinction between an _incremental_ and a _non-incremental_ form of confirmation by mathematical analogy. We offer an account of the former within the popular framework (...)
    No categories
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark  
  41. On the parallel between mathematics and morals.James Franklin - 2004 - Philosophy 79 (1):97-119.
    The imperviousness of mathematical truth to anti-objectivist attacks has always heartened those who defend objectivism in other areas, such as ethics. It is argued that the parallel between mathematics and ethics is close and does support objectivist theories of ethics. The parallel depends on the foundational role of equality in both disciplines. Despite obvious differences in their subject matter, mathematics and ethics share a status as pure forms of knowledge, distinct from empirical sciences. A pure understanding of (...)
    Direct download (8 more)  
     
    Export citation  
     
    Bookmark   8 citations  
  42. The indispensability argument and multiple foundations for mathematics.Alan Baker - 2003 - Philosophical Quarterly 53 (210):49–67.
    One recent trend in the philosophy of mathematics has been to approach the central epistemological and metaphysical issues concerning mathematics from the perspective of the applications of mathematics to describing the world, especially within the context of empirical science. A second area of activity is where philosophy of mathematics intersects with foundational issues in mathematics, including debates over the choice of set-theoretic axioms, and over whether category theory, for example, may provide an (...)
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   16 citations  
  43. The ethics–mathematics analogy.Justin Clarke-Doane - 2019 - Philosophy Compass 15 (1):e12641.
    Ethics and mathematics have long invited comparisons. On the one hand, both ethical and mathematical propositions can appear to be knowable a priori, if knowable at all. On the other hand, mathematical propositions seem to admit of proof, and to enter into empirical scientific theories, in a way that ethical propositions do not. In this article, I discuss apparent similarities and differences between ethical (i.e., moral) and mathematical knowledge, realistically construed -- i.e., construed as independent of human mind (...)
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   2 citations  
  44.  36
    Mathematics in the biological sciences.Not By Me - 1992 - International Studies in the Philosophy of Science 6 (3):241 – 248.
    Although mathematical descriptions of the dynamics of system are widely employed in the physical sciences, they are employed infrequently in the biological sciences. The explanation for this usually appeals to the complexity of biological systems. I contend that quite the opposite is true and that such descriptions, in fact, enable complexity to be tamed. Moreover, in those areas in which mathematical descriptions have been used in the biological sciences, they provide a powerful vehicle for expanding our understanding of the systems (...)
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark  
  45. Topics in Mathematical Consciousness Science.Johannes Kleiner - 2024 - Dissertation, Munich Center for Mathematical Philosophy & Graduate School of Systemic Neurosciences, Ludwig Maximilian University of Munich
    The scientific study of consciousness, also referred to as consciousness science, is a young scientific field devoted to understanding how conscious experiences and the brain relate. It comprises a host of theories, experiments, and analyses that aim to investigate the problem of consciousness empirically, theoretically, and conceptually. This thesis addresses some of the questions that arise in these investigations from a formal and mathematical perspective. These questions concern theories of consciousness, experimental paradigms, methodology, and artificial consciousness. -/- Regarding theories of (...)
    No categories
    Direct download  
     
    Export citation  
     
    Bookmark  
  46.  40
    Mathematics and its applications in the sciences.James K. Feibleman - 1956 - Philosophy of Science 23 (3):204-215.
    We have undertaken to discuss the nature of mathematical systems, the way in which they are discovered, and the uses to which they are put in the empirical sciences. The empirical sciences employ mathematical systems in framing final formulations, but adopt mathematical techniques long before reaching that stage. It is a prerequisite that the mathematics they employ has been developed separately and within its own domain. We shall return to the relation between mathematics and the (...) sciences before we are done, but in the meanwhile we shall be constrained to begin by discussing the situation in mathematics in isolation from any empirical considerations. (shrink)
    Direct download (8 more)  
     
    Export citation  
     
    Bookmark  
  47. Visualizations in mathematics.Kajsa Bråting & Johanna Pejlare - 2008 - Erkenntnis 68 (3):345 - 358.
    In this paper we discuss visualizations in mathematics from a historical and didactical perspective. We consider historical debates from the 17th and 19th centuries regarding the role of intuition and visualizations in mathematics. We also consider the problem of what a visualization in mathematical learning can achieve. In an empirical study we investigate what mathematical conclusions university students made on the basis of a visualization. We emphasize that a visualization in mathematics should always be considered in (...)
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   10 citations  
  48.  21
    Mathematics in the biological sciences.Paul Thompson - 1992 - International Studies in the Philosophy of Science 6 (3):241-248.
    Although mathematical descriptions of the dynamics of system are widely employed in the physical sciences, they are employed infrequently in the biological sciences. The explanation for this usually appeals to the complexity of biological systems. I contend that quite the opposite is true and that such descriptions, in fact, enable complexity to be tamed. Moreover, in those areas in which mathematical descriptions have been used in the biological sciences, they provide a powerful vehicle for expanding our understanding of the systems (...)
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   2 citations  
  49.  18
    (1 other version)Is Economics Empirical Knowledge?Steven Rappaport - 1994 - Economics and Philosophy 10 (2):137-158.
    Alexander Rosenberg has played a large role in creating the philosophy of economics as a distinct area of philosophy. But since the publication of Microeconomic Laws in 1976, Professor Rosenberg's thinking about economics has been casting the subject in an increasingly uncomplimentary light. This development is reflected in Rosenberg's new book Economics–Mathematical Politics or Science of Diminishing Returns? In this stimulating work Rosenberg endorses the view that economics does not constitute scientific empirical knowledge. He says.
    Direct download  
     
    Export citation  
     
    Bookmark  
  50. Saving Economics From Philosophy.Alan Jean Nelson - 1984 - Dissertation, University of Illinois at Chicago
    Chapter 1 is introductory. It identifies a cluster of philosophical problems that arise in the foundations of neoclassical economic theory. Issues growing out of the unusually tenuous connection between the theory and the world are singled out as especially troublesome. Is it, after all, possible for economics to look more like an empirical science like physics than like of branch of mathematics? ;Chapter 2 argues that economic methodology has been constrained by the application of faulty philosophy of (...)
     
    Export citation  
     
    Bookmark  
1 — 50 / 954