# Applying Inconsistent Mathematics

@inproceedings{Colyvan2009ApplyingIM, title={Applying Inconsistent Mathematics}, author={M. Colyvan}, year={2009} }

Inconsistent mathematics has a special place in the history of philosophy. The realisation, at the end of the nineteenth century, that a mathematical theory—naive set theory—was inconsistent prompted radical changes to mathematics, pushing research in new directions and even resulted in changes to mathematical methodology. The resulting work in developing a consistent set theory was exciting and saw a departure from the existing practice of looking for self-evident axioms. Instead, following… Expand

#### 12 Citations

The Philosophy of Mathematics: A Study of Indispensability and Inconsistency

- Mathematics
- 2016

This thesis examines possible philosophies to account for the practice of mathematics, exploring the metaphysical, ontological, and epistemological outcomes of each possible theory. Through a study… Expand

Is science inconsistent?

- Philosophy, Computer Science
- Synthese
- 2014

Over the past few decades philosophers have taken a particular and increasing interest in inconsistency in science, and in 2002 the first collection of articles specifically dedicated to the topic was published: Inconsistency in Science, edited by Joke Meheus and published by Kluwer. Expand

Inconsistency in mathematics and the mathematics of inconsistency

- Computer Science
- Synthese
- 2014

This paper wants to explore issues, using classic examples such as infinitesimals, complex numbers, and infinity, that mathematics is basically inconsistent and does not need a mathematics of inconsistency. Expand

Theological Underpinnings of the Modern Philosophy of Mathematics.

- Philosophy
- 2016

Abstract The study is focused on the relation between theology and mathematics in the situation of increasing secularization. My main concern is nineteenth-century mathematics. Theology was present… Expand

Representing the World with Inconsistent Mathematics

- Mathematics
- The British Journal for the Philosophy of Science
- 2020

According to standard accounts of mathematical representations of physical phenomena, positing structure-preserving mappings between a physical target system and the structure(s) picked out by a… Expand

Realismo científico y entidades inconsistentes. Críticas a la metafísica de Colyvan

- Philosophy
- 2015

According to Mark Colyvan, certain mature scientific developments (specifically, Newtonian cosmology, descriptive oceanography, early calculus and Dirac's quantum theory) contain contradictory… Expand

Mathematics and Philosophy

- 2020

The article considers mathematics as a way of teaching reasoning in symbolic non-verbal communication. Particular attention is paid to mathematical ways of thinking when studying the nature and its… Expand

In Pursuit of the Non-Trivial

- Philosophy
- Episteme
- 2019

Abstract This paper is about the underlying logical principles of scientific theories. In particular, it concerns ex contradictione quodlibet (ECQ) the principle that anything follows from a… Expand

How to avoid inconsistent idealizations

- Mathematics, Computer Science
- Synthese
- 2014

It is argued that the claim that an idealization requires inconsistent beliefs is often incorrect and that it turns out that a more mathematical perspective allows us to understand how the idealization can be interpreted consistently. Expand

The Undeniable Effectiveness of Mathematics in the Special Sciences

- Mathematics, Computer Science
- New Directions in the Philosophy of Science
- 2014

It is argued that idealising away from complicating causal details often gives a clearer view of whatreally matters, and often what really matters is not the push and shove of base-level causal processes, but higher-level predictions and (non-causal) explanations. Expand

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