What is Non-Classical Mathematics

The 20th century has witnessed several attempts to build (parts of) mathematics on grounds other than those provided by classical logic. The original intuitionist and constructivist renderings of set theory, arithmetic, analysis, etc. were later accompanied by those based on relevant, paraconsistent, contraction-free, modal, and other non-classical logical frameworks. The subject studying such theories can be called non-classical mathematics and formally understood as a study of (any part of) mathematics that is, or can in principle be, formalized in some logic other than classical logic.

The scope of non-classical mathematics includes any mathematical discipline that can be formalized in a non-classical logic or in an alternative foundational theory over classical logic, and topics closely related to such non-classical or alternative theories. Particular topics of interest include (but are not limited to) the following:

This webpage gathers the activities in non-classical mathematics following the first conference on non-classical mathematics held in Hejnice (Czech Republic), June 2009.