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

@inproceedings{2013PleaseRH, title={Please Read How You Can Help Keep the Encyclopedia Free Nominalism in the Philosophy of Mathematics}, author={}, year={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

#### 18 Citations

Philosophy of Mathematics for the Masses : Extending the scope of the philosophy of mathematics

- Philosophy
- 2016

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 m… Expand

The Epistemology of Modality and the Epistemology of Mathematics

- Psychology
- 2017

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 the… Expand

Logic and Metaphysical Presuppositions

- 2017

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 the… Expand

Deflationary Nominalism’s Commitment to Meinongianism

- Philosophy
- 2016

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 nonexistence… Expand

An anti-realist account of the application of mathematics

- Philosophy
- 2016

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 has… Expand

Putnam’s indispensability argument revisited, reassessed, revived

- Philosophy
- 2018

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’s… Expand

Realism and Anti-Realism about Science

- 2014

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 to… Expand

Metaphor and the Philosophical Implications of Embodied Mathematics

- Psychology, Medicine
- Frontiers in Psychology
- 2020

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

- Philosophy
- 2015

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 central… Expand

True Nominalism: Referring versus Coding

- Mathematics
- The British Journal for the Philosophy of Science
- 2016

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 the… Expand

#### References

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Reason's Proper Study: Essays Towards a Neo-Fregean Philosophy of Mathematics

- Philosophy
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I. ONTOLOGY AND ABSTRACTION PRINCIPLES II. RESPONSES TO CRITICS III. HUME'S PRINCIPLE IV. ON THE DIFFERENTIATION OF ABSTRACTA V. BEYOND NUMBER-THEORY

A Nominalist's Dilemma and its Solution

- Philosophy
- 2005

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 to… Expand

Mathematics and Reality

- Mathematics
- 2010

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. Mathematics… Expand

Constructibility and mathematical existence

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- 1990

PART I: THE CONSTRUCTIBILITY THEORY: The Problem of Existence in Mathematics The Constructibility Quantifiers Constructibility and Open-Sentences The Deductive System Cardinality and Number Theory… Expand

Philosophy of mathematics : structure and ontology

- Mathematics
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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 lively… Expand

There is No Easy Road to Nominalism

- Philosophy
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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 a… Expand

Mathematics as a science of patterns

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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 calling… Expand

On the Plurality of Worlds.

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- 1986

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

- Philosophy
- 2001

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 the… Expand

Metaphysical Myths, Mathematical Practice: The Ontology and Epistemology of the Exact Sciences

- Philosophy
- 1994

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 reference… Expand