Philosophy of Mathematics

Edited by Øystein Linnebo (University of Oslo)
Assistant editor: Sam Roberts (Birkbeck College, University of Oslo)
33 found
Order:
  1. added 2018-10-13
    A Naturalistic Justification of the Generic Multiverse with a Core.Matteo de Ceglie - 2018 - In Proceedings of the 41st Internation Wittgenstein Symposium. 2880 Kirchberg am Wechsel, Austria: pp. 34-36.
    In this paper, I argue that a naturalist approach in philosophy of mathematics justifies a pluralist conception of set theory. For the pluralist, there is not a Single Universe, but there is rather a Multiverse, composed by a plurality of universes generated by various set theories. In order to justify a pluralistic approach to sets, I apply the two naturalistic principles developed by Penelope Maddy (cfr. Maddy (1997)), UNIFY and MAXIMIZE, and analyze through them the potential of the set theoretic (...)
    Remove from this list   Direct download  
     
    Export citation  
     
    My bibliography  
  2. added 2018-10-10
    Outer and Inner Surfaces of Bodies.Rush Rhees - 2017 - Philosophical Investigations 40 (1):10-31.
    Remove from this list   Direct download  
    Translate
     
     
    Export citation  
     
    My bibliography  
  3. added 2018-10-03
    Margaret Cavendish on the Order and Infinitude of Nature.Michael Bennett McNulty - 2018 - History of Philosophy Quarterly 35 (3):219-239.
    In this paper, I develop a new interpretation of the order of nature, its function, and its implications in Margaret Cavendish’s philosophy. According to the infinite balance account, the order of nature consists in a balance among the infinite varieties of nature. That is, for Cavendish, nature contains an infinity of different types of matter: infinite species, shapes, and motions. The potential tumult implicated by such a variety, however, is tempered by the counterbalancing of the different kinds and motions of (...)
    Remove from this list   Direct download  
     
    Export citation  
     
    My bibliography  
  4. added 2018-10-01
    Deflationary Nominalism and Puzzle Avoidance.David Mark Kovacs - forthcoming - Philosophia Mathematica:nky019.
    In a series of works, Jody Azzouni has defended deflationary nominalism, the view that certain sentences quantifying over mathematical objects are literally true, although such objects do not exist. One alleged attraction of this view is that it avoids various philosophical puzzles about mathematical objects. I argue that this thought is misguided. I first develop an ontologically neutral counterpart of Field’s reliability challenge and argue that deflationary nominalism offers no distinctive answer to it. I then show how this reasoning generalizes (...)
    Remove from this list   Direct download (2 more)  
     
    Export citation  
     
    My bibliography  
  5. added 2018-09-29
    Dummett on Indefinite Extensibility.Øystein Linnebo - forthcoming - Philosophical Issues.
    Dummett’s notion of indefinite extensibility is influential but obscure. The notion figures centrally in an alternative Dummettian argument for intuitionistic logic and anti-realism, distinct from his more famous, meaning-theoretic arguments to the same effect. Drawing on ideas from Dummett, a precise analysis of indefinite extensibility is proposed. This analysis is used to reconstruct the poorly understood alternative argument. The plausibility of the resulting argument is assessed.
    Remove from this list   Direct download (4 more)  
     
    Export citation  
     
    My bibliography  
  6. added 2018-09-27
    Structuralist Neologicism†.Francesca Boccuni & Jack Woods - forthcoming - Philosophia Mathematica:nky017.
    ABSTRACT Neofregeanism and structuralism are among the most promising recent approaches to the philosophy of mathematics. Yet both have serious costs. We develop a view, structuralist neologicism, which retains the central advantages of each while avoiding their more serious costs. The key to our approach is using arbitrary reference to explicate how mathematical terms, introduced by abstraction principles, refer. Focusing on numerical terms, this allows us to treat abstraction principles as implicit definitions determining all properties of the numbers, achieving a (...)
    Remove from this list   Direct download (2 more)  
    Translate
     
     
    Export citation  
     
    My bibliography  
  7. added 2018-09-21
    The Adverbial Theory of Numbers: Some Clarifications.Joongol Kim - forthcoming - Synthese:1-20.
    In a forthcoming paper in this journal, entitled “Bad company objection to Joongol Kim’s adverbial theory of numbers”, Namjoong Kim presents an ingenious Russell-style paradox based on an analogue of Kim’s definition of the number 1, and argues that Kim’s theory needs to provide a criterion of demarcation between acceptable and unacceptable definitions of adverbial entities. This paper addresses this ‘bad company’ objection and some other related issues concerning Kim’s adverbial theory by clarifying the purposes and uses of the formal (...)
    Remove from this list   Direct download (2 more)  
     
    Export citation  
     
    My bibliography  
  8. added 2018-09-21
    Easy Ontology Without Deflationary Metaontology.Daniel Z. Korman - forthcoming - Philosophy and Phenomenological Research.
    This is a contribution to a symposium on Amie Thomasson’s Ontology Made Easy (2015). Thomasson defends two deflationary theses: that philosophical questions about the existence of numbers, tables, properties, and other disputed entities can all easily be answered, and that there is something wrong with prolonged debates about whether such objects exist. I argue that the first thesis (properly understood) does not by itself entail the second. Rather, the case for deflationary metaontology rests largely on a controversial doctrine about the (...)
    Remove from this list   Direct download  
     
    Export citation  
     
    My bibliography   1 citation  
  9. added 2018-09-20
    Exploring Predicativity.Laura Crosilla - 2018 - In Proof and Computation. pp. 83-108.
    Prominent constructive theories of sets as Martin-Löf type theory and Aczel and Myhill constructive set theory, feature a distinctive form of constructivity: predicativity. This may be phrased as a constructibility requirement for sets, which ought to be finitely specifiable in terms of some uncontroversial initial “objects” and simple operations over them. Predicativity emerged at the beginning of the 20th century as a fundamental component of an influential analysis of the paradoxes by Poincaré and Russell. According to this analysis the paradoxes (...)
    Remove from this list  
     
    Export citation  
     
    My bibliography  
  10. added 2018-09-20
    Predicativity and Feferman.Laura Crosilla - 2018 - In Feferman on Foundations. pp. 423-447.
    Predicativity is a notable example of fruitful interaction between philosophy and mathematical logic. It originated at the beginning of the 20th century from methodological and philosophical reflections on a changing concept of set. A clarification of this notion has prompted the development of fundamental new technical instruments, from Russell's type theory to an important chapter in proof theory, which saw the decisive involvement of Kreisel, Feferman and Schütte. The technical outcomes of predica-tivity have since taken a life of their own, (...)
    Remove from this list  
     
    Export citation  
     
    My bibliography  
  11. added 2018-09-20
    Tutorial for Minlog.Laura Crosilla, Monika Seisenberger & Helmut Schwichtenberg - 2011 - Minlog Proof Assistant - Freely Distributed.
    This is a tutorial for the Minlog Proof Assistant, version 5.0.
    Remove from this list  
     
    Export citation  
     
    My bibliography  
  12. added 2018-09-19
    The Principle of Equivalence as a Criterion of Identity.Ryan Samaroo - forthcoming - Synthese:1-25.
    In 1907 Einstein had the insight that bodies in free fall do not “feel” their own weight. This has been formalized in what is called “the principle of equivalence.” The principle motivated a critical analysis of the Newtonian and special-relativistic concepts of inertia, and it was indispensable to Einstein’s development of his theory of gravitation. A great deal has been written about the principle. Nearly all of this work has focused on the content of the principle and whether it has (...)
    Remove from this list   Direct download (5 more)  
     
    Export citation  
     
    My bibliography  
  13. added 2018-09-14
    From Models to Simulations.Franck Varenne - 2018 - London, UK: Routledge.
    This book analyses the impact computerization has had on contemporary science and explains the origins, technical nature and epistemological consequences of the current decisive interplay between technology and science: an intertwining of formalism, computation, data acquisition, data and visualization and how these factors have led to the spread of simulation models since the 1950s. -/- Using historical, comparative and interpretative case studies from a range of disciplines, with a particular emphasis on the case of plant studies, the author shows how (...)
    Remove from this list   Direct download (4 more)  
     
    Export citation  
     
    My bibliography  
  14. added 2018-09-07
    O nouă filosofie a matematicii?Gabriel Târziu - 2012 - Symposion – A Journal of Humanities 10 (2):361-377.
    O tendinţă relativ nouă în filosofia contemporană a matematicii este reprezentată de nemulţumirea manifestată de un număr din ce în ce mai mare de filosofi faţă de viziunea tradiţională asupra matematicii ca având un statut special ce poate fi surprins doar cu ajutorul unei epistemologii speciale. Această nemulţumire i-a determinat pe mulţi să propună o nouă perspectivă asupra matematicii – una care ia în serios aspecte până acum neglijate de filosofia matematicii, precum latura sociologică, istorică şi empirică a cercetării matematice (...)
    Remove from this list   Direct download  
    Translate
     
     
    Export citation  
     
    My bibliography  
  15. added 2018-09-04
    Mathematical Shortcomings in a Simulated Universe.Samuel Alexander - 2018 - The Reasoner 12 (9):71-72.
    I present an argument that for any computer-simulated civilization we design, the mathematical knowledge recorded by that civilization has one of two limitations. It is untrustworthy, or it is weaker than our own mathematical knowledge. This is paradoxical because it seems that nothing prevents us from building in all sorts of advantages for the inhabitants of said simulation.
    Remove from this list   Direct download  
     
    Export citation  
     
    My bibliography  
  16. added 2018-08-31
    Importance and Explanatory Relevance: The Case of Mathematical Explanations.Gabriel Târziu - 2018 - Journal for General Philosophy of Science / Zeitschrift für Allgemeine Wissenschaftstheorie 49 (3):393-412.
    A way to argue that something plays an explanatory role in science is by linking explanatory relevance with importance in the context of an explanation. The idea is deceptively simple: a part of an explanation is an explanatorily relevant part of that explanation if removing it affects the explanation either by destroying it or by diminishing its explanatory power, i.e. an important part is an explanatorily relevant part. This can be very useful in many ontological debates. My aim in this (...)
    Remove from this list   Direct download (3 more)  
     
    Export citation  
     
    My bibliography  
  17. added 2018-08-29
    Mathematical Explanations and the Piecemeal Approach to Thinking About Explanation.Gabriel Târziu - forthcoming - Logique Et Analyse.
    A new trend in the philosophical literature on scientific explanation is that of starting from a case that has been somehow identified as an explanation and then proceed to bringing to light its characteristic features and to constructing an account for the type of explanation it exemplifies. A type of this approach to thinking about explanation – the piecemeal approach, as I will call it – is used, among others, by Lange (2013) and Pincock (2015) in the context of their (...)
    Remove from this list   Direct download (2 more)  
     
    Export citation  
     
    My bibliography  
  18. added 2018-08-25
    Programming Planck Units From a Virtual Electron; a Simulation Hypothesis.Malcolm J. Macleod - 2018 - European Physical Journal Plus 133:278.
    The simulation hypothesis proposes that all of reality is an artificial simulation. In this article I describe a simulation model that derives Planck level units as geometrical forms from a virtual (dimensionless) electron formula $f_e$ that is constructed from 2 unit-less mathematical constants; the fine structure constant $\alpha$ and $\Omega$ = 2.00713494... ($f_e = 4\pi^2r^3, r = 2^6 3 \pi^2 \alpha \Omega^5$). The mass, space, time, charge units are embedded in $f_e$ according to these ratio; ${M^9T^{11}/L^{15}} = (AL)^3/T$ (units = (...)
    Remove from this list   Direct download  
     
    Export citation  
     
    My bibliography  
  19. added 2018-08-25
    Univalent Foundations as a Foundation for Mathematical Practice.Harry Crane - manuscript
    I prove that invoking the univalence axiom is equivalent to arguing 'without loss of generality' (WLOG) within Propositional Univalent Foundations (PropUF), the fragment of Univalent Foundations (UF) in which all homotopy types are mere propositions. As a consequence, I argue that practicing mathematicians, in accepting WLOG as a valid form of argument, implicitly accept the univalence axiom and that UF rightly serves as a Foundation for Mathematical Practice. By contrast, ZFC is inconsistent with WLOG as it is applied, and therefore (...)
    Remove from this list   Direct download (3 more)  
     
    Export citation  
     
    My bibliography  
  20. added 2018-08-24
    On the Coherence of Strict Finitism.Auke Alesander Montesano Montessori - 2018 - Kriterion - Journal of Philosophy:1-14.
    Strict finitism is the position that only those natural numbers exist that we can represent in practice. Michael Dummett, in a paper called Wang’s Paradox, famously tried to show that strict finitism is an incoherent position. By using the Sorites paradox, he claimed that certain predicates the strict finitist is committed to are incoherent. More recently, Ofra Magidor objected to Dummett’s claims, arguing that Dummett fails to show the incoherence of strict finitism. In this paper, I shall investigate whether Magidor (...)
    Remove from this list   Direct download  
     
    Export citation  
     
    My bibliography  
  21. added 2018-08-15
    Testimony and Children’s Acquisition of Number Concepts.Helen De Cruz - 2018 - In Sorin Bangu (ed.), Naturalizing Logico-Mathematical Knowledge. Approaches from Philosophy, Psychology and Cognitive Science. London, UK: pp. 172-186.
    An enduring puzzle in philosophy and developmental psychology is how young children acquire number concepts, in particular the concept of natural number. Most solutions to this problem conceptualize young learners as lone mathematicians who individually reconstruct the successor function and other sophisticated mathematical ideas. In this chapter, I argue for a crucial role of testimony in children’s acquisition of number concepts, both in the transfer of propositional knowledge (e.g., the cardinality concept), and in knowledge-how (e.g., the counting routine).
    Remove from this list   Direct download  
     
    Export citation  
     
    My bibliography  
  22. added 2018-08-14
    Autour des Principia Mathematica de Russell et Whitehead.Alexandre Guay - 2012 - 21000 Dijon, France: Éditions Universitaires de Dijon.
    Il y a cent ans paraissaient un ouvrage de logique qui a marqué considérablement les études dans ce domaine tout au long du XXe siècle, soit que l’on en poursuivit le projet, soit, au contraire, que l’on en critiqua la démarche. Les Principia Mathematica de Russell et Whitehead sont donc une œuvre majeure sur laquelle il n’était par inutile de revenir en ce début du XXIe siècle. Certes la question à laquelle ils étaient censés répondre, c'est-à-dire celle d’un fondement rigoureux (...)
    Remove from this list  
    Translate
     
     
    Export citation  
     
    My bibliography  
  23. added 2018-08-14
    Zeno of Elea' Paradoxes (The Dialectic of Stability and Motion from a Contemporary Mathematical View) مفارقات زينون: جدل الثبات والحركة من منظور رياضي معاصر.Salah Osman - 2004 - Menoufia University, Faculty of Arts Journal, Egypt 58:99 - 139.
    لا شك أن مفارقات زينون في الحركة قد تم تناولها – تحليلاً ونقدًا – في كثيرٍ من أدبيات العلم والفلسفة قديمًا وحديثًا، حتى لقد ساد الظن بأن ملف المفارقات قد أغُلق تمامًا، لاسيما بعد أن نجح الحساب التحليلي في التعامل منطقيًا مع صعوبات الأعداد اللامتناهية، لكن الفرض الأساسي لهذا البحث يزعم عكس ذلك؛ أعني أن الملف مازال مفتوحًا وبقوة – خصوصًا على المستوى الرياضي الفيزيائي – وأن إغلاقه النهائي قد لا يتم في المستقبل القريب. من جهة أخرى، إذا كانت فكرة (...)
    Remove from this list   Direct download (2 more)  
    Translate
     
     
    Export citation  
     
    My bibliography  
  24. added 2018-08-07
    Critical Studies/Book Reviews.Simon Hewitt - forthcoming - Philosophia Mathematica:nky016.
    CraigWilliam Lane.* * God andObjects – The Coherence of Theism : Aseity.Springer, 2017. ISBN: 978-3-319-55383-2 ; 978-3-319-55384-9. Pp. xv + 540.
    Remove from this list   Direct download (2 more)  
     
    Export citation  
     
    My bibliography  
  25. added 2018-08-06
    Mathematical Knowledge, the Analytic Method, and Naturalism.Fabio Sterpetti - 2018 - In Sorin Bangu (ed.), Naturalizing Logico-Mathematical Knowledge. Approaches from Philosophy, Psychology and Cognitive Science. New York, Stati Uniti: pp. 268-293.
    This chapter tries to answer the following question: How should we conceive of the method of mathematics, if we take a naturalist stance? The problem arises since mathematical knowledge is regarded as the paradigm of certain knowledge, because mathematics is based on the axiomatic method. Moreover, natural science is deeply mathematized, and science is crucial for any naturalist perspective. But mathematics seems to provide a counterexample both to methodological and ontological naturalism. To face this problem, some authors tried to naturalize (...)
    Remove from this list   Direct download  
     
    Export citation  
     
    My bibliography  
  26. added 2018-08-06
    Rejection in Łukasiewicz's and Słupecki's Sense.Urszula Wybraniec-Skardowska - 2018 - In Urszula Wybraniec-Skardowska & Ángel Garrido (eds.), The Lvov-Warsaw School. Past and Present. Basel, Switzerland: pp. 575-597.
    The idea of rejection originated by Aristotle. The notion of rejection was introduced into formal logic by Łukasiewicz [20]. He applied it to complete syntactic characterization of deductive systems using an axiomatic method of rejection of propositions [22, 23]. The paper gives not only genesis, but also development and generalization of the notion of rejection. It also emphasizes the methodological approach to biaspectual axiomatic method of characterization of deductive systems as acceptance (asserted) systems and rejection (refutation) systems, introduced by Łukasiewicz (...)
    Remove from this list   Direct download (2 more)  
     
    Export citation  
     
    My bibliography  
  27. added 2018-08-06
    Clarificando o Suporte do Argumento Melhorado da Indispensabilidade Matemática.Eduardo Castro - 2017 - Argumentos 17 (9):57-71.
    The enhanced mathematical indispensability argument, proposed by Alan Baker (2005), argues that we must commit to mathematical entities, because mathematical entities play an indispensable explanatory role in our best scientific theories. This article clarifies the doctrines that support this argument, namely, the doctrines of naturalism and confirmational holism.
    Remove from this list   Direct download  
    Translate
     
     
    Export citation  
     
    My bibliography  
  28. added 2018-07-31
    Introduction to Special Issue: Abstraction Principles.Salvatore Florio - 2017 - Philosophia Mathematica 25 (1):1-2.
    Remove from this list   Direct download  
     
    Export citation  
     
    My bibliography  
  29. added 2018-07-25
    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 - forthcoming - Foundations of Science:1-18.
    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 of these (...)
    Remove from this list   Direct download (3 more)  
     
    Export citation  
     
    My bibliography  
  30. added 2018-07-24
    Towards a Theory of Singular Thought About Abstract Mathematical Objects.James E. Davies - forthcoming - Synthese.
    This essay uses a mental files theory of singular thought—a theory saying that singular thought about and reference to a particular object requires possession of a mental store of information taken to be about that object—to explain how we could have such thoughts about abstract mathematical objects. After showing why we should want an explanation of this I argue that none of three main contemporary mental files theories of singular thought—acquaintance theory, semantic instrumentalism, and semantic cognitivism—can give it. I argue (...)
    Remove from this list   Direct download (2 more)  
     
    Export citation  
     
    My bibliography  
  31. added 2018-07-23
    Generic Structures.Leon Horsten - forthcoming - Philosophia Mathematica:nky015.
    In this article ideas from Kit Fine’s theory of arbitrary objects are applied to questions regarding mathematical structuralism. I discuss how sui generis mathematical structures can be viewed as generic systems of mathematical objects, where mathematical objects are conceived of as arbitrary objects in Fine’s sense.
    Remove from this list   Direct download (2 more)  
     
    Export citation  
     
    My bibliography  
  32. added 2018-07-19
    Against the Iterative Conception of Set.Edward Ferrier - forthcoming - Philosophical Studies:1-23.
    According to the iterative conception of set, each set is a collection of sets formed prior to it. The notion of priority here plays an essential role in explanations of why contradiction-inducing sets, such as the Russell set, do not exist. Consequently, these explanations are successful only to the extent that a satisfactory priority relation is made out. I argue that attempts to do this have fallen short: understanding priority in a straightforwardly constructivist sense threatens the coherence of the empty (...)
    Remove from this list   Direct download (3 more)  
     
    Export citation  
     
    My bibliography  
  33. added 2018-07-19
    Quantification and Paradox.Edward Ferrier - 2018 - Dissertation, University of Massachusetts Amherst
    I argue that absolutism, the view that absolutely unrestricted quantification is possible, is to blame for both the paradoxes that arise in naive set theory and variants of these paradoxes that arise in plural logic and in semantics. The solution is restrictivism, the view that absolutely unrestricted quantification is not possible. -/- It is generally thought that absolutism is true and that restrictivism is not only false, but inexpressible. As a result, the paradoxes are blamed, not on illicit quantification, but (...)
    Remove from this list   Direct download  
     
    Export citation  
     
    My bibliography