Ontology of Mathematics

Edited by Rafal Urbaniak (Uniwersytetu Gdanskiego, Uniwersytetu Gdanskiego)
Assistant editors: Sam Roberts, Pawel Pawlowski
About this topic
Summary Ontology of mathematics is concerned with the existence and nature of objects that mathematics is about. An important phenomenon in the field is the need of balancing between epistemological and ontological challenges. For instance, prima facie, the ontologically simplest option is to postulate the existence of abstract mathematical objects (like numbers or sets) to which mathematical terms refer. Yet, explaining how we, mundane beings, can have knowledge of such aspatial and atemporal objects, turns out to be quite difficult. The ontologically parsimonious alternative is to deny the existence of such objects. But then, one has to explain what it is that makes mathematical theories true (or at least, correct) and how we can come to know mathematical facts. Various positions arise from various ways of addressing questions of these two sorts. 
Key works Many crucial papers are included in the following anthologies: Benacerraf & Putnam 1964, Hart 1996 and Shapiro 2005.
Introductions A good introductory survey is Horsten 2008. A readable introduction to philosophy of mathematics is Shapiro 2000. A nice, albeit somewhat biased survey of ontological options can be found in the first few chapters of Chihara 1990. A very nice introduction to the development of foundations of mathematics and the interaction between foundations, epistemology and ontology of mathematics is Giaquinto 2002.
Related categories

2635 found
Order:
1 — 50 / 2635
Material to categorize
  1. TGFT condensate cosmology as an example of spacetime emergence in quantum gravity.Daniele Oriti - 2022 - In Antonio Vassallo (ed.), The Foundations of Spacetime Physics: Philosophical Perspectives. Routledge.
  2. Knowledge and the Philosophy of Number. [REVIEW]Richard Lawrence - 2022 - History and Philosophy of Logic 43 (4):404-406.
    Hossack’s project in this book is to provide a new foundation for the philosophy of number inspired by the traditional idea that numbers are magnitudes.
    Remove from this list   Direct download (6 more)  
     
    Export citation  
     
    Bookmark  
  3. Penelope Rush.* Ontology and the Foundations of Mathematics: Talking Past Each Other.Geoffrey Hellman - 2022 - Philosophia Mathematica 30 (3):387-392.
    This compact volume, belonging to the Cambridge Elements series, is a useful introduction to some of the most fundamental questions of philosophy and foundations of mathematics. What really distinguishes realist and platonist views of mathematics from anti-platonist views, including fictionalist and nominalist and modal-structuralist views?1 They seem to confront similar problems of justification, presenting tradeoffs between which it is difficult to adjudicate. For example, how do we gain access to the abstract posits of platonist accounts of arithmetic, analysis, geometry, etc., (...)
    Remove from this list   Direct download (3 more)  
     
    Export citation  
     
    Bookmark  
  4. Multi-Channel Mathematics.Ilexa Yardley - 2022 - Https://Medium.Com/the-Circular-Theory.
  5. Reconciling Anti-Nominalism and Anti-Platonism in Philosophy of Mathematics.John P. Burgess - 2022 - Disputatio 11 (20).
    The author reviews and summarizes, in as jargon-free way as he is capable of, the form of anti-platonist anti-nominalism he has previously developed in works since the 1980s, and considers what additions and amendments are called for in the light of such recently much-discussed views on the existence and nature of mathematical objects as those known as hyperintensional metaphysics, natural language ontology, and mathematical structuralism.
    Remove from this list  
     
    Export citation  
     
    Bookmark  
  6. In defense of Countabilism.David Builes & Jessica M. Wilson - 2022 - Philosophical Studies 179 (7):2199-2236.
    Inspired by Cantor's Theorem (CT), orthodoxy takes infinities to come in different sizes. The orthodox view has had enormous influence in mathematics, philosophy, and science. We will defend the contrary view---Countablism---according to which, necessarily, every infinite collection (set or plurality) is countable. We first argue that the potentialist or modal strategy for treating Russell's Paradox, first proposed by Parsons (2000) and developed by Linnebo (2010, 2013) and Linnebo and Shapiro (2019), should also be applied to CT, in a way that (...)
    Remove from this list   Direct download (4 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  7. Calculus of Qualia: Introduction to Qualations 7 2 2022.Paul Merriam - manuscript
    The basic idea is to put qualia into equations (broadly understood) to get what might as well be called qualations. Qualations arguably have different truth behaviors than the analogous equations. Thus ‘black’ has a different behavior than ‘ █ ’. This is a step in the direction of a ‘calculus of qualia’. It might help clarify some issues.
    Remove from this list   Direct download  
     
    Export citation  
     
    Bookmark  
  8. Thinking About Thought.Ilexa Yardley - 2022 - Https://Medium.Com/the-Circular-Theory/.
    A thought is not possible without the conservation of a circle. Thus, the representation of a thought is, also, not possible without (the conservation of) a circle.
    Remove from this list   Direct download  
     
    Export citation  
     
    Bookmark  
  9. David Armstrong on the Metaphysics of Mathematics.Thomas Donaldson - 2020 - Dialectica 74 (4):113-136.
    This paper has two components. The first, longer component (sec. 1-6) is a critical exposition of Armstrong’s views about the metaphysics of mathematics, as they are presented in Truth and Truthmakers and Sketch for a Systematic Metaphysics. In particular, I discuss Armstrong’s views about the nature of the cardinal numbers, and his account of how modal truths are made true. In the second component of the paper (sec. 7), which is shorter and more tentative, I sketch an alternative account of (...)
    Remove from this list   Direct download (3 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  10. “In Nature as in Geometry”: Du Châtelet and the Post-Newtonian Debate on the Physical Significance of Mathematical Objects.Aaron Wells - forthcoming - In Between Leibniz, Newton, and Kant, Second Edition. Springer.
    Du Châtelet holds that mathematical representations play an explanatory role in natural science. Moreover, things proceed in nature as they do in geometry. How should we square these assertions with Du Châtelet’s idealism about mathematical objects, on which they are ‘fictions’ dependent on acts of abstraction? The question is especially pressing because some of her important interlocutors (Wolff, Maupertuis, and Voltaire) denied that mathematics informs us about the properties of real things. After situating Du Châtelet in this debate, this chapter (...)
    Remove from this list   Direct download  
     
    Export citation  
     
    Bookmark   1 citation  
  11. Man-Made Systems vs. Mind-Made Systems.Ilexa Yardley - 2022 - Https://Medium.Com/the-Circular-Theory.
    Mind does not operate using sequence (also known, to ‘man,’ as ‘time’). Think: philosophical, and physical, fusion.
    Remove from this list   Direct download  
     
    Export citation  
     
    Bookmark  
  12. Hofweber’s Nominalist Naturalism.Eric Snyder, Richard Samuels & Stewart Shapiro - 2022 - In Gianluigi Oliveri, Claudio Ternullo & Stefano Boscolo (eds.), Objects, Structures, and Logics. Cham, Switzerland: pp. 31-62.
    In this paper, we outline and critically evaluate Thomas Hofweber’s solution to a semantic puzzle he calls Frege’s Other Puzzle. After sketching the Puzzle and two traditional responses to it—the Substantival Strategy and the Adjectival Strategy—we outline Hofweber’s proposed version of Adjectivalism. We argue that two key components—the syntactic and semantic components—of Hofweber’s analysis both suffer from serious empirical difficulties. Ultimately, this suggests that an altogether different solution to Frege’s Other Puzzle is required.
    Remove from this list   Direct download  
     
    Export citation  
     
    Bookmark   1 citation  
  13. Time as Relevance: Gendlin's Phenomenology of Radical Temporality.Joshua Soffer - manuscript
    In this paper, I discuss Eugene Gendlin’s contribution to radically temporal discourse , situating it in relation to Husserl and Heidegger’s analyses of time, and contrasting it with a range of interlinked approaches in philosophy and psychology that draw inspiration from, but fall short in their interpretation of the phenomenological work of Husserl and Heidegger. Gendlin reveals the shortcomings of these approaches with regard to the understanding of the relation between affect, motivation and intention, intersubjectivity, attention , reflective and pre-reflective (...)
    Remove from this list   Direct download (2 more)  
     
    Export citation  
     
    Bookmark  
  14. What the Tortoise Said to Achilles: Lewis Carroll’s paradox in terms of Hilbert arithmetic.Vasil Penchev - 2021 - Logic and Philosophy of Mathematics eJournal (Elsevier: SSRN) 13 (22):1-32.
    Lewis Carroll, both logician and writer, suggested a logical paradox containing furthermore two connotations (connotations or metaphors are inherent in literature rather than in mathematics or logics). The paradox itself refers to implication demonstrating that an intermediate implication can be always inserted in an implication therefore postponing its ultimate conclusion for the next step and those insertions can be iteratively and indefinitely added ad lib, as if ad infinitum. Both connotations clear up links due to the shared formal structure with (...)
    Remove from this list   Direct download (3 more)  
     
    Export citation  
     
    Bookmark  
  15. Mathematics, isomorphism, and the identity of objects.Graham White - 2021 - Journal of Knowledge Structures and Systems 2 (2):56-58.
    We compare the medieval projects of commentaries and disputations with the modern projects of formal ontology and of mathematics.
    Remove from this list   Direct download  
     
    Export citation  
     
    Bookmark  
  16. Zero—a Tangible Representation of Nonexistence: Implications for Modern Science and the Fundamental.Sudip Bhattacharyya - 2021 - Sophia 60 (3):655-676.
    A defining characteristic of modern science is its ability to make immensely successful predictions of natural phenomena without invoking a putative god or a supernatural being. Here, we argue that this intellectual discipline would not acquire such an ability without the mathematical zero. We insist that zero and its basic operations were likely conceived in India based on a philosophy of nothing, and classify nothing into four categories—balance, absence, emptiness and nonexistence. We argue that zero is a tangible representation of (...)
    Remove from this list   Direct download (4 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  17. Dominique Pradelle. Intuition et idéalités. Phénoménologie des objets mathématiques [Intuition and idealities: Phenomenology of mathematical objects.] Collection Épiméthée. [REVIEW]Bruno Leclercq - forthcoming - Philosophia Mathematica:nkab014.
    _Dominique Pradelle. ** Intuition et idéalités. Phénoménologie des objets mathématiques _ [Intuition and idealities: Phenomenology of mathematical objects.] Collection Épiméthée. Paris: PUF [Presses universitaires de France], 2020. Pp. 550. ISBN: 978-2-13-082237-0.
    Remove from this list   Direct download (3 more)  
     
    Export citation  
     
    Bookmark  
  18. Objectivity in Mathematics, Without Mathematical Objects†.Markus Pantsar - 2021 - Philosophia Mathematica 29 (3):318-352.
    I identify two reasons for believing in the objectivity of mathematical knowledge: apparent objectivity and applications in science. Focusing on arithmetic, I analyze platonism and cognitive nativism in terms of explaining these two reasons. After establishing that both theories run into difficulties, I present an alternative epistemological account that combines the theoretical frameworks of enculturation and cumulative cultural evolution. I show that this account can explain why arithmetical knowledge appears to be objective and has scientific applications. Finally, I will argue (...)
    Remove from this list   Direct download (3 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  19. Review of John Heil, The Universe As We Find It. [REVIEW]Alyssa Ney - 2014 - British Journal for the Philosophy of Science 65:881-886.
    Remove from this list   Direct download  
     
    Export citation  
     
    Bookmark   1 citation  
  20. Neues System der philosophischen Wissenschaften im Grundriss. Band II: Mathematik und Naturwissenschaft.Dirk Hartmann - 2021 - Paderborn: Mentis.
    Volume II deals with philosophy of mathematics and general philosophy of science. In discussing theoretical entities, the notion of antirealism formulated in Volume I is further elaborated: Contrary to what is usually attributed to antirealism or idealism, the author does not claim that theoretical entities do not really exist, but rather that their existence is not independent of the possibility to know about them.
    Remove from this list   Direct download (2 more)  
     
    Export citation  
     
    Bookmark  
  21. Our Knowledge of Mathematical Objects.Kit Fine - 2005 - In Tamar Szabo Gendler & John Hawthorne (eds.), Oxford Studies in Epistemology Volume 1. Oxford University Press.
    Remove from this list  
     
    Export citation  
     
    Bookmark   21 citations  
  22. Strict Finitism and the Logic of Mathematical Applications, Synthese Library, vol. 355.Feng Ye - 2011 - Springer.
    This book intends to show that, in philosophy of mathematics, radical naturalism (or physicalism), nominalism and strict finitism (which does not assume the reality of infinity in any format, not even potential infinity) can account for the applications of classical mathematics in current scientific theories about the finite physical world above the Planck scale. For that purpose, the book develops some significant applied mathematics in strict finitism, which is essentially quantifier-free elementary recursive arithmetic (with real numbers encoded as elementary recursive (...)
    Remove from this list  
     
    Export citation  
     
    Bookmark  
  23. How Nature ‘Tokenizes’ Reality.Ilexa Yardley - 2021 - Https://Medium.Com/the-Circular-Theory/.
    Pi in mathematics is mind in Nature, explaining the tokenization of 'reality.'.
    Remove from this list   Direct download  
     
    Export citation  
     
    Bookmark  
  24. For Better and for Worse. Abstractionism, Good Company, and Pluralism.Andrea Sereni, Maria Paola Sforza Fogliani & Luca Zanetti - 2021 - Review of Symbolic Logic:1-30.
    A thriving literature has developed over logical and mathematical pluralism – i.e. the views that several rival logical and mathematical theories can be equally correct. These have unfortunately grown separate; instead, they both could gain a great deal by a closer interaction. Our aim is thus to present some novel forms of abstractionist mathematical pluralism which can be modeled on parallel ways of substantiating logical pluralism (also in connection with logical anti-exceptionalism). To do this, we start by discussing the Good (...)
    Remove from this list   Direct download (2 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  25. Foucault, Deleuze, and Nietzsche.Ilexa Yardley - 2021 - Https://Medium.Com/the-Circular-Theory/.
  26. Ms.Natasha Bailie - forthcoming - British Journal for the History of Mathematics.
    The reception of Newton's Principia in 1687 led to the attempt of many European scholars to ‘mathematicise' their field of expertise. An important example of this ‘mathematicisation' lies in the work of Irish-Scottish philosopher Francis Hutcheson, a key figure in the Scottish Enlightenment. This essay aims to discuss the mathematical aspects of Hutcheson's work and its impact on British thought in the following centuries, providing a case in point for the importance of the interactions between mathematics and philosophy throughout time.
    Remove from this list  
     
    Export citation  
     
    Bookmark  
  27. How (and Why) the Conservation of a Circle is the Core (and only) Dynamic in Nature.Ilexa Yardley - 2021 - Https://Medium.Com/the-Circular-Theory/.
    Solving Navier-Stokes and integrating it with Bose-Einstein. Moving beyond ‘mathematics’ and ‘physics.’ And, philosophy. Integrating 'point' 'line' 'circle.' (Euclid with 'reality.').
    Remove from this list   Direct download  
     
    Export citation  
     
    Bookmark  
  28. Eliminating the Speed of Light as a ‘Constant’.Ilexa Yardley - 2021 - Https://Medium.Com/the-Circular-Theory.
  29. Hiromi's Voice (Multi-Channel Mathematics).Ilexa Yardley - 2021 - Https://Medium.Com/Musical-Notes/.
    Using Hiromi’s ‘Voice’ to understand ‘physics.’ (The underlying relationship between mind and music.) (The relationship between mind and mathematics.) The relationship between the arithmetic numbers 'two' and 'three.' The relationship between light (an infinite line) and sound (an infinite circle) (where it is impossible to have one without the other).
    Remove from this list   Direct download  
     
    Export citation  
     
    Bookmark  
  30. Natural Cybernetics and Mathematical History: The Principle of Least Choice in History.Vasil Penchev - 2020 - Cultural Anthropology (Elsevier: SSRN) 5 (23):1-44.
    The paper follows the track of a previous paper “Natural cybernetics of time” in relation to history in a research of the ways to be mathematized regardless of being a descriptive humanitarian science withal investigating unique events and thus rejecting any repeatability. The pathway of classical experimental science to be mathematized gradually and smoothly by more and more relevant mathematical models seems to be inapplicable. Anyway quantum mechanics suggests another pathway for mathematization; considering the historical reality as dual or “complimentary” (...)
    Remove from this list   Direct download (3 more)  
     
    Export citation  
     
    Bookmark  
  31. Rez. „Adam Drozdek: In the Beginning Was the Apeiron: Infinity in Greek Philosophy, Stuttgart: Steiner, 2008“. [REVIEW]Sergiusz Kazmierski - 2010 - Bryn Mawr Classical Review 2010.
    Es ist das Verdienst der Arbeit von Adam Drozdek, in einem noch grösseren historischen Umfang sowie mit einer noch stärkeren thematischen Gewichtung und Stringenz als dies bereits Sinnige getan hat, nicht nur die entscheidendste Phase der griechischen Philosophie, sondern auch der Mathematik, ausgehend vom physikalischen und mathematischen Infinitätsgedanken dargestellt zu haben.
    Remove from this list   Direct download  
     
    Export citation  
     
    Bookmark  
  32. Mathematics and its Logics: Philosophical Essays.Geoffrey Hellman - 2020 - New York, NY: Cambridge University Press.
    In these essays Geoffrey Hellman presents a strong case for a healthy pluralism in mathematics and its logics, supporting peaceful coexistence despite what appear to be contradictions between different systems, and positing different frameworks serving different legitimate purposes. The essays refine and extend Hellman's modal-structuralist account of mathematics, developing a height-potentialist view of higher set theory which recognizes indefinite extendability of models and stages at which sets occur. In the first of three new essays written for this volume, Hellman shows (...)
    Remove from this list   Direct download  
     
    Export citation  
     
    Bookmark  
  33. Mathematics - an imagined tool for rational cognition.Boris Culina - manuscript
    Analysing several characteristic mathematical models: natural and real numbers, Euclidean geometry, group theory, and set theory, I argue that a mathematical model in its final form is a junction of a set of axioms and an internal partial interpretation of the corresponding language. It follows from the analysis that (i) mathematical objects do not exist in the external world: they are our internally imagined objects, some of which, at least approximately, we can realize or represent; (ii) mathematical truths are not (...)
    Remove from this list   Direct download  
     
    Export citation  
     
    Bookmark   1 citation  
  34. Numbers, Empiricism and the A Priori.Olga Ramírez Calle - 2020 - Logos and Episteme 11 (2):149-177.
    The present paper deals with the ontological status of numbers and considers Frege ́s proposal in Grundlagen upon the background of the Post-Kantian semantic turn in analytical philosophy. Through a more systematic study of his philosophical premises, it comes to unearth a first level paradox that would unset earlier still than it was exposed by Russell. It then studies an alternative path, that departin1g from Frege’s initial premises, drives to a conception of numbers as synthetic a priori in a more (...)
    Remove from this list   Direct download (3 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  35. Does set theory really ground arithmetic truth?Alfredo Roque Freire - manuscript
    We consider the foundational relation between arithmetic and set theory. Our goal is to criticize the construction of standard arithmetic models as providing grounds for arithmetic truth (even in a relative sense). Our method is to emphasize the incomplete picture of both theories and treat models as their syntactical counterparts. Insisting on the incomplete picture will allow us to argue in favor of the revisability of the standard model interpretation. We then show that it is hopeless to expect that the (...)
    Remove from this list  
     
    Export citation  
     
    Bookmark  
  36. Maddy On The Multiverse.Claudio Ternullo - 2019 - In Deniz Sarikaya, Deborah Kant & Stefania Centrone (eds.), Reflections on the Foundations of Mathematics. Berlin: Springer Verlag. pp. 43-78.
    Penelope Maddy has recently addressed the set-theoretic multiverse, and expressed reservations on its status and merits ([Maddy, 2017]). The purpose of the paper is to examine her concerns, by using the interpretative framework of set-theoretic naturalism. I first distinguish three main forms of 'multiversism', and then I proceed to analyse Maddy's concerns. Among other things, I take into account salient aspects of multiverse-related mathematics , in particular, research programmes in set theory for which the use of the multiverse seems to (...)
    Remove from this list   Direct download  
     
    Export citation  
     
    Bookmark   2 citations  
  37. Forms of Structuralism: Bourbaki and the Philosophers.Jean-Pierre Marquis - 2020 - Structures Meres, Semantics, Mathematics, and Cognitive Science.
    In this paper, we argue that, contrary to the view held by most philosophers of mathematics, Bourbaki’s technical conception of mathematical structuralism is relevant to philosophy of mathematics. In fact, we believe that Bourbaki has captured the core of any mathematical structuralism.
    Remove from this list   Direct download  
     
    Export citation  
     
    Bookmark  
  38. The Ontological Import of Adding Proper Classes.Alfredo Roque Freire & Rodrigo de Alvarenga Freire - 2019 - Manuscrito 42 (2):85-112.
    In this article, we analyse the ontological import of adding classes to set theories. We assume that this increment is well represented by going from ZF system to NBG. We thus consider the standard techniques of reducing one system to the other. Novak proved that from a model of ZF we can build a model of NBG (and vice versa), while Shoenfield have shown that from a proof in NBG of a set-sentence we can generate a proof in ZF of (...)
    Remove from this list   Direct download (5 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  39. On Physics' Faustian Bargain with Mathematics.G. Vision - 2017 - Journal of Consciousness Studies 24 (9-10):59-71.
    Standard physicalism is repudiated by Susan Schneider on the grounds that the science of physics at physicalism's foundation is individuated by mathematics, revealing that science is abstract rather than concrete. She seeks to remedy the situation for physics, though not for physicalism, with a panprotopsychist variant of panpyschism. Her approach is clever and well-developed, but I believe it suffers from at least two flaws. First, with few exceptions individuation is the wrong tool for the discovery of a thing's nature; second, (...)
    Remove from this list   Direct download  
     
    Export citation  
     
    Bookmark  
  40. Mathematical Models of Abstract Systems: Knowing abstract geometric forms.Jean-Pierre Marquis - 2013 - Annales de la Faculté des Sciences de Toulouse 22 (5):969-1016.
    Scientists use models to know the world. It i susually assumed that mathematicians doing pure mathematics do not. Mathematicians doing pure mathematics prove theorems about mathematical entities like sets, numbers, geometric figures, spaces, etc., they compute various functions and solve equations. In this paper, I want to exhibit models build by mathematicians to study the fundamental components of spaces and, more generally, of mathematical forms. I focus on one area of mathematics where models occupy a central role, namely homotopy theory. (...)
    Remove from this list   Direct download (2 more)  
     
    Export citation  
     
    Bookmark  
  41. Constructibility and Mathematical Existence.Michael D. Resnik - 1992 - Journal of Philosophy 89 (12):648.
    Remove from this list   Direct download (3 more)  
     
    Export citation  
     
    Bookmark  
  42. Language and Other Abstract Objects. J. J. Katz. [REVIEW]Mike Dillinger - 1984 - Philosophy of Science 51 (1):175-176.
    Remove from this list   Direct download (5 more)  
     
    Export citation  
     
    Bookmark  
  43. Applying mathematics to empirical sciences: flashback to a puzzling disciplinary interaction.Raphaël Sandoz - 2018 - Synthese 195 (2):875-898.
    This paper aims to reassess the philosophical puzzle of the “applicability of mathematics to physical sciences” as a misunderstood disciplinary interplay. If the border isolating mathematics from the empirical world is based on appropriate criteria, how does one explain the fruitfulness of its systematic crossings in recent centuries? An analysis of the evolution of the criteria used to separate mathematics from experimental sciences will shed some light on this question. In this respect, we will highlight the historical influence of three (...)
    Remove from this list   Direct download (2 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  44. Access Problems and explanatory overkill.Silvia Jonas - 2017 - Philosophical Studies 174 (11):2731-2742.
    I argue that recent attempts to deflect Access Problems for realism about a priori domains such as mathematics, logic, morality, and modality using arguments from evolution result in two kinds of explanatory overkill: the Access Problem is eliminated for contentious domains, and realist belief becomes viciously immune to arguments from dispensability, and to non-rebutting counter-arguments more generally.
    Remove from this list   Direct download (4 more)  
     
    Export citation  
     
    Bookmark   9 citations  
  45. Mathematical Spandrels.Alan Baker - 2017 - Australasian Journal of Philosophy 95 (4):779-793.
    The aim of this paper is to open a new front in the debate between platonism and nominalism by arguing that the degree of explanatory entanglement of mathematics in science is much more extensive than has been hitherto acknowledged. Even standard examples, such as the prime life cycles of periodical cicadas, involve a penumbra of mathematical features whose presence can only be explained using relatively sophisticated mathematics. I introduce the term ‘mathematical spandrel’ to describe these penumbral properties, and focus on (...)
    Remove from this list   Direct download (6 more)  
     
    Export citation  
     
    Bookmark   10 citations  
  46. Deflating Cold War rationality.Michael Pettit - 2016 - Studies in History and Philosophy of Science Part A 58:46-49.
    Remove from this list   Direct download (3 more)  
     
    Export citation  
     
    Bookmark  
  47. ¿ES LA MATEMÁTICA LA NOMOGONÍA DE LA CONCIENCIA? REFLEXIONES ACERCA DEL ORIGEN DE LA CONCIENCIA Y EL PLATONISMO MATEMÁTICO DE ROGER PENROSE / Is Mathematics the “nomogony” of Consciousness? Reflections on the origin of consciousness and mathematical Platonism of Roger Penrose.Miguel Acosta - 2016 - Naturaleza y Libertad. Revista de Estudios Interdisciplinares 7:15-39.
    Al final de su libro “La conciencia inexplicada”, Juan Arana señala que la nomología, explicación según las leyes de la naturaleza, requiere de una nomogonía, una consideración del origen de las leyes. Es decir, que el orden que observamos en el mundo natural requiere una instancia previa que ponga ese orden específico. Sabemos que desde la revolución científica la mejor manera de explicar dicha nomología ha sido mediante las matemáticas. Sin embargo, en las últimas décadas se han presentado algunas propuestas (...)
    Remove from this list   Direct download  
     
    Export citation  
     
    Bookmark  
  48. What is the Nature of Mathematical–Logical Objects?Stathis Livadas - 2017 - Axiomathes 27 (1):79-112.
    This article deals with a question of a most general, comprehensive and profound content as it is the nature of mathematical–logical objects insofar as these are considered objects of knowledge and more specifically objects of formal mathematical theories. As objects of formal theories they are dealt with in the sense they have acquired primarily from the beginnings of the systematic study of mathematical foundations in connection with logic dating from the works of G. Cantor and G. Frege in the last (...)
    Remove from this list   Direct download (2 more)  
     
    Export citation  
     
    Bookmark   4 citations  
  49. Beyond Quantities and Qualities: Frege and Jevons on Measurement.Raphaël Sandoz - 2016 - Hopos: The Journal of the International Society for the History of Philosophy of Science 6 (2):212-238.
    On which philosophical foundations is the attribution of numerical magnitudes to qualitative phenomena based? That is, what is the philosophical basis for attributing, through measurement operations, numbers to empirical qualities that our senses perceive in the outside world? This question, nowadays rarely addressed in such a way, actually refers to an old debate about the quantification of qualities. A historical analysis reveals that it was a major issue in the “context of discovery” of the first attempts to mathematize new fields (...)
    Remove from this list   Direct download (4 more)  
     
    Export citation  
     
    Bookmark  
  50. Science without Numbers: A Defense of Nominalism. Hartry H. Field.Michael Friedman - 1981 - Philosophy of Science 48 (3):505-506.
1 — 50 / 2635