Philosophy of Mathematical Morphology

Introduction to Mathematical Philosophy

logical possibility, be two things which had exactly the same predicates, in the narrow sense in which we have been using the word “predicate.” How does our axiom look when we pass beyond predicates in this narrow sense? In the actual world there seems no way of doubting its empirical truth as regards particulars, owing to spatio-temporal differentiation: no two particulars have exactly the sam...

Mathematical Methods in Philosophy

Mathematics and philosophy have historically enjoyed a mutually beneficial and productive relationship, as a brief review of the work of mathematician-philosophers such as Descartes, Leibniz, Bolzano, Dedekind, Frege, Brouwer, Hilbert, Gödel, and Weyl easily confirms. In the last century, it was especially mathematical logic and research in the foundations of mathematics which, to a significant...

Mathematical Morphology

Aspects of Mathematical Morphology

In this paper we review the basic concepts of integral-geometry-based morphological image analysis. This approach yields an objective, numerical characterization of twoand threedimensional patterns in terms of geometrical and topological descriptors called Minkowski functionals. We review its mathematical foundation and show that it is easy to put the theory into practice by presenting simple c...

Mathematical history, philosophy and education

History of mathematics occupies itself describing processes of growth and development, whereas philosophy of mathematics is concerned with questions of justification. Both play an essential role within the educational context. But there is a problem because genuine historical studies necessitate ever greater particularity whereas mathematics and philosophy require generality and abstraction. Th...