MoL-2012-09:
Florio, Antonio
(2012)
*Science in Axiomatic Perspective.*
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## Abstract

The axiomatic method counts two thousand and three hundred years

circa. Suppes has proposed the category of Euclidean-Archimedean

tradition to refer to the axiomatic theories that have been developed

before the inven- tion/discovery of the non-Euclidean

geometries. Among these theories the first axiomatic system that we

know is Euclid’s Elements, a mathemat- ical tractate consisting of

thirteen books in which three centuries of Greek mathematical

knowledge were given an order and were presented as a unified theory.1

Euclid produced another axiomatic theory, the Optics. This represents

a theory of vision in Euclidean perspective rather than a tractate on

physical optics. It is interesting that Archimedes’s Treatise,

probably the first book on mathematical physics, is an axiomatic

theory.

The axiomatic method in the Euclidean-Aristotelian tradition was

trans- mitted during the medieval age and scholarship in history of

science has established the use of the axiomatic method in scientific

tractates through all periods from antiquity up to the

sixteenth–seventeenth-century Scientific Revolution. In the context of

the Scientific Revolution an important ax- iomatic theory is Newton’s

Principia.

The axiomatic method covers a too big period of history and philosophy

of science and we cannot deal with it in this thesis. So we skip the

analysis of the axiomatic method in the Euclean-Archimedean tradition

and begin our analysis in the nineteenth century when the axiomatic

method entered in the modern phase. As Suppes puts it: “The historical

source of the modern viewpoint toward the axiomatic method was the

intense scrutiny of the foundations of geometry in the nineteenth

century. Undoubtedly the most important driving force behind this

effort was the discovery and development of non-Euclidean geometry at

the beginning of the nineteenth century by Bolyai, Lobachevski, and

Gauss.”.

Item Type: | Report |
---|---|

Report Nr: | MoL-2012-09 |

Series Name: | Master of Logic Thesis (MoL) Series |

Year: | 2012 |

Uncontrolled Keywords: | Logic, Philosophy |

Depositing User: | Tanja Kassenaar |

Date Deposited: | 12 Oct 2016 14:38 |

Last Modified: | 12 Oct 2016 14:38 |

URI: | https://eprints.illc.uva.nl/id/eprint/875 |

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