### Abstract

It is easy to show that in many natural axiomatic formulations of physical and even mathematical theories, there are many superfluous concepts usually assumed as primitive. This happens mainly when these theories are formulated in the language of standard set theories, such as Zermelo–Fraenkel’s. In 1925, John von Neumann created a set theory where sets are definable by means of functions. We provide a reformulation of von Neumann’s set theory and show that it can be used to formulate physical and mathematical theories with a lower number of primitive concepts very naturally. Our basic proposal is to offer a new kind of set-theoretic language that offers advantages with respect to the standard approaches, since it doesn’t introduce dispensable primitive concepts. We show how the proposal works by considering significant physical theories, such as non-relativistic classical particle mechanics and classical field theories, as well as a well-known mathematical theory, namely, group theory. This is a first step of a research program we intend to pursue.

Original language | English (US) |
---|---|

Pages (from-to) | 257-281 |

Number of pages | 25 |

Journal | Erkenntnis |

Volume | 79 |

Issue number | 2 |

DOIs | |

State | Published - Apr 1 2014 |

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### ASJC Scopus subject areas

- Philosophy
- Logic

### Cite this

*Erkenntnis*,

*79*(2), 257-281. https://doi.org/10.1007/s10670-013-9491-y

**Sets and Functions in Theoretical Physics.** / Sant’Anna, Adonai S.; Bueno, Otavio.

Research output: Contribution to journal › Article

*Erkenntnis*, vol. 79, no. 2, pp. 257-281. https://doi.org/10.1007/s10670-013-9491-y

}

TY - JOUR

T1 - Sets and Functions in Theoretical Physics

AU - Sant’Anna, Adonai S.

AU - Bueno, Otavio

PY - 2014/4/1

Y1 - 2014/4/1

N2 - It is easy to show that in many natural axiomatic formulations of physical and even mathematical theories, there are many superfluous concepts usually assumed as primitive. This happens mainly when these theories are formulated in the language of standard set theories, such as Zermelo–Fraenkel’s. In 1925, John von Neumann created a set theory where sets are definable by means of functions. We provide a reformulation of von Neumann’s set theory and show that it can be used to formulate physical and mathematical theories with a lower number of primitive concepts very naturally. Our basic proposal is to offer a new kind of set-theoretic language that offers advantages with respect to the standard approaches, since it doesn’t introduce dispensable primitive concepts. We show how the proposal works by considering significant physical theories, such as non-relativistic classical particle mechanics and classical field theories, as well as a well-known mathematical theory, namely, group theory. This is a first step of a research program we intend to pursue.

AB - It is easy to show that in many natural axiomatic formulations of physical and even mathematical theories, there are many superfluous concepts usually assumed as primitive. This happens mainly when these theories are formulated in the language of standard set theories, such as Zermelo–Fraenkel’s. In 1925, John von Neumann created a set theory where sets are definable by means of functions. We provide a reformulation of von Neumann’s set theory and show that it can be used to formulate physical and mathematical theories with a lower number of primitive concepts very naturally. Our basic proposal is to offer a new kind of set-theoretic language that offers advantages with respect to the standard approaches, since it doesn’t introduce dispensable primitive concepts. We show how the proposal works by considering significant physical theories, such as non-relativistic classical particle mechanics and classical field theories, as well as a well-known mathematical theory, namely, group theory. This is a first step of a research program we intend to pursue.

UR - http://www.scopus.com/inward/record.url?scp=84956801132&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84956801132&partnerID=8YFLogxK

U2 - 10.1007/s10670-013-9491-y

DO - 10.1007/s10670-013-9491-y

M3 - Article

AN - SCOPUS:84956801132

VL - 79

SP - 257

EP - 281

JO - Erkenntnis

JF - Erkenntnis

SN - 0165-0106

IS - 2

ER -