Axiomatic (and non-axiomatic) mathematics

Abduction in Non-Axiomatic Logic

This paper introduces various inference rules (deduction, abduction, and induction) in NonAxiomatic Logic. These rules are represented in a term-oriented language, and justified according to a common semantic foundation. The implementation and application of these rules are briefly described. Finally, this approach is compared with the other approaches, specially with respect to abduction.

Intuition and the Axiomatic Method Intuition and the Axiomatic Method

On Dedekind’s axiomatic approach to the foundations of mathematics

This paper brings together some points made previously in (Sieg and Schlimm 2005) and (Sieg and Schlimm 2014) focusing on some aspects of Dedekind’s axiomatic approach to the foundations of mathematics. In particular the terminology for his axiomatic definitions of concepts and the development of the notion of mapping are discussed.

Axiomatic Redistricting*

In a framework with two parties, deterministic voter preferences and geographical constraints, we propose a set of simple axioms and show that they jointly characterize the districting rule that maximizes the number of districts a party can win, given an electoral outcome (the " optimal gerrymandering rule "). As a corollary, we obtain that no districting rule can satisfy our axioms and treat p...

Axiomatic Neuroeconomics

Those of us who pursue neuroeconomic research do so in the belief that neurobiological and decision theoretic research will prove highly complementary. The hoped for complementarities rest in part on the fact that model-building and quantification are as highly valued within neuroscience as they are in economics. Yet methodological tensions remain. In particular, the ‘axiomatic’ modeling method...