Extremal axioms. Logical, mathematical and cognitive aspects

Loading...
Thumbnail Image

Date

2019

Advisor

Editor

Journal Title

Journal ISSN

Volume Title

Publisher

Wydawnictwo Nauk Społecznych i Humanistycznych UAM

Title alternative

Abstract

The book is devoted to extremal axioms in mathematics and is addressed mainly to cognitive scientists. As far as I am aware it is the first monograph to tackle this issue. The author relativizes extremal axioms to models in the metamathematical sense. Such an approach is the book’s main theoretical virtue, especially with respect to the so-called intended models. It should be stressed that intended models are distinguished on the basis of pragmatic criteria and as such are not reducible to purely semantic or syntactic constructions. In this context the role of extremal axioms is fundamental. Such axioms are formulated not necessarily at the very beginning of a theory but rather only after theoretical constructions have already been present for a long time in the research practice of mathematicians. A question that arises is how extremal axioms distinguish between standard and non-standard models, and whether they do so in a complete way.

Description

Sponsor

Keywords

extremal axiom, intended model, standard model, mathematical intuition

Citation

Pogonowski J., Extremal axioms. Logical, mathematical and cognitive aspects, Poznań 2019.

Seria

ISBN

978-83-64902-78-9

ISSN

DOI

Title Alternative

Rights Creative Commons

Creative Commons License

Uniwersytet im. Adama Mickiewicza w Poznaniu
Biblioteka Uniwersytetu im. Adama Mickiewicza w Poznaniu
Ministerstwo Nauki i Szkolnictwa Wyższego