Corpus ID: 32155253

Please Read How You Can Help Keep the Encyclopedia Free Nominalism in the Philosophy of Mathematics

  title={Please Read How You Can Help Keep the Encyclopedia Free Nominalism in the Philosophy of Mathematics},
  • Published 2013
objects | mathematics, philosophy of | mathematics, philosophy of: indispensability arguments in the | mathematics, philosophy of: Platonism | nominalism: in metaphysics | ontological commitment | Platonism: in metaphysics | plural quantification | Quine, Willard van Orman 
Philosophy of Mathematics for the Masses : Extending the scope of the philosophy of mathematics
One of the important discussions in the philosophy of mathematics, is that centered on Benacerraf’s Dilemma. Benacerraf’s dilemma challenges theorists to provide an epistemology and semantics for mExpand
The Epistemology of Modality and the Epistemology of Mathematics
In this paper I explore some connections between the epistemology of modality and the epistemology of mathematics, and argue that they have far more in common than it may initially seem to be theExpand
Logic and Metaphysical Presuppositions
Does logic3⁄4in particular, classical logic3⁄4have metaphysical presuppositions? It may be thought that it doesn’t: logical principles and logical inferences are often taken as not requiring theExpand
Deflationary Nominalism’s Commitment to Meinongianism
Deflationary nominalism is a novel view in the philosophy of mathematics on which there are mathematical statements, such as ‘There are prime numbers’ that are literally true despite the nonexistenceExpand
An anti-realist account of the application of mathematics
Mathematical concepts play at least three roles in the application of mathematics: an inferential role, a representational role, and an expressive role. In this paper, I argue that, despite what hasExpand
Putnam’s indispensability argument revisited, reassessed, revived
Crucial to Hilary Putnam’s realism in the philosophy of mathematics is to maintain the objectivity of mathematics without the commitment to the existence of mathematical objects. Putnam’sExpand
Realism and Anti-Realism about Science
Pyrrhonists provide a way of investigating the world in which conflicting views about a given topic are critically compared, assessed, and juxtaposed. Since Pyrrhonists are ultimately unable toExpand
Metaphor and the Philosophical Implications of Embodied Mathematics
It is suggested that closer interaction between the philosophy and cognitive science of mathematics could yield a more precise, empirically informed account of what mathematics is and how the authors come to have knowledge of it. Expand
Structural realism and the nature of structure
Ontic Structural Realism is a version of realism about science according to which by positing the existence of structures, understood as basic components of reality, one can resolve centralExpand
True Nominalism: Referring versus Coding
One major motivation for nominalism, at least according to Hartry Field, is the desirability of intrinsic explanations: explanations that don’t invoke objects that are causally irrelevant to theExpand


Reason's Proper Study: Essays Towards a Neo-Fregean Philosophy of Mathematics
A Nominalist's Dilemma and its Solution
Current versions of nominalism in the philosophy of mathematics have the benefit of avoiding commitment to the existence of mathematical objects. But this comes with a cost: to avoid commitment toExpand
Mathematics and Reality
1. Introduction 2. Naturalism and Ontology 3. The Indispensability of Mathematics 4. Naturalism and Mathematical Practice 5. Naturalism and Scientific Practice 6. Naturalized Ontology 7. MathematicsExpand
Constructibility and mathematical existence
PART I: THE CONSTRUCTIBILITY THEORY: The Problem of Existence in Mathematics The Constructibility Quantifiers Constructibility and Open-Sentences The Deductive System Cardinality and Number TheoryExpand
Philosophy of mathematics : structure and ontology
Do numbers, sets, and so forth, exist? What do mathematical statements mean? Are they literally true or false, or do they lack truth values altogether? Addressing questions that have attracted livelyExpand
There is No Easy Road to Nominalism
Hartry Field has shown us a way to be nominalists: we must purge our scientific theories of quantification over abstracta and we must prove the appropriate conservativeness results. This is not aExpand
Mathematics as a science of patterns
Mathematics as a Science of Patterns is the definitive exposition of a system of ideas about the nature of mathematics which Michael Resnik has been elaborating for a number of years. In callingExpand
On the Plurality of Worlds.
Preface. 1. A Philosopher's Paradise. The Thesis of Pluraliry of Worlds. Modal Realism at Work: Modality. Modal Realism at Work: Closeness. Modal Realism at Work: Content. Modal Realism at Work:Expand
A Subject with No Object: Strategies for Nominalistic Interpretation of Mathematics
Numbers and other mathematical objects are exceptional in having no locations in space or time or relations of cause and effect. This makes it difficult to account for the possibility of theExpand
Metaphysical Myths, Mathematical Practice: The Ontology and Epistemology of the Exact Sciences
Acknowledgements Part I. Mathematical Practice and its Puzzles: 1. Metaphysical inertness 2. Metaphysical inertness and reference 3. The virtues of (second-order) theft 4. Intuitions about referenceExpand