Essays on the Foundations of Mathematics and Logic 2

This book is the second volume of "Essays on the Foundations of Mathematics and Logic", the first publication included in the "Advanced Studies in Mathematics and Logic", a new book series dedicated to the following questions: i) What were, what are and what could be the meanings of the term "mathematics"? ii) What were, what are and what could be the meanings of the term "logic"? iii) What were, what are and what could be the goals of mathematics? iv) What were, what are and what could be the goals of logic? v) What were, what are and what could be the different kinds of logico-mathematical branches? vi) What were, what are and what could be the applications of mathematics to other scientific domains? vii) What were, what are and what could be the applications of logic to other scientific domains? viii) How were, how are and how could be constructed the multiple types of logico-mathematical tools (e.g. models/systems/languages and, more in general, structures) for working scientists? ix) What was, what is and what could be the role of mathematics in the different kinds of cultures, societies and economies? x) What was, what is and what could be the role of logic in the different kinds of cultures, societies and economies? xi) How to teach mathematics and logic in different contexts, at different degrees, for different purposes? This series aims to publish volumes which propose an open and continuous discussion about the possible identities of mathematics and logic, directing the research perspectives towards the future (what could be ...), not forgetting the present (what is ...) and the past roots (what was ...): the frameworks of knowledge are made up through plural histories, localized in different cultural, social and economical backgrounds and developed in relation to different needs, equally important and considerable.