Mathematical Concepts : Fruitfulness and Naturalness 1 Jamie Tappenden

Mathematical Concepts and Definitions

I Definition and Mathematical Practice The basic observation structuring this survey is that mathematicians often set finding the “right” / “proper” / “correct” / “natural” definition as a research objective, and success finding “the proper” definition can be counted as a significant advance in knowledge. Remarks like these from a retrospective on twentieth century algebraic geometry are common:

Frege's Mathematical Setting

Note: This essay was commissioned and written circa 1997 for The Cambridge Companion to Frege, which has not yet appeared. Although quite a bit of good work on Frege and Dedekind’s mathematical antecedents has since appeared (by Jeremy Avigad, Jamie Tappenden and others), I think this essay still provides the student with a useful introduction to many of the central issues. I have since refined...

Jamie Tappenden on Kit Fine ’ S the Limits of Abstraction

بررسی دو شاخص کمی کردن الگوهای چشم‌انداز با استفاده از RS و GIS در منطقه حفاظت شده موته

Landscape ecology as a modern interdisciplinary science offers new concepts, theories, and methods for land evaluation and management. One main part of landscape ecology is describing patterns in the landscape and interpreting the ecological effects of these patterns on flora, fauna, flow of energy and materials. Landscape studies require methods to identify and quantify spatial patterns of lan...

Se p 20 03 Thoughts on the Riemann Hypothesis

The simultaneous appearance in May 2003 of four books on the Riemann hypothesis (RH) provoked these reflections. We briefly discuss whether the RH should be added as a new axiom, or whether a proof of the RH might involve the notion of randomness. New pragmatically-justified mathematical axioms that are not at all self-evident A pragmatically-justified principle is one that is justified by its ...