Dirk Schlimm

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To analyze the task of mental arithmetic with external representations in different number systems we model algorithms for addition and multiplication with Arabic and Roman numerals. This demonstrates that Roman numerals are not only informationally equivalent to Arabic ones but also computationally similar—a claim that is widely disputed. An analysis of(More)
This paper is a contribution to the question of how aspects of science have been perceived through history. In particular, I will discuss how the contribution of axiomatics to the development of science and mathematics was viewed in 20th century philosophy of science and philosophy of mathematics. It will turn out that in connection with scientific(More)
In discussions of mathematical practice the role axiomatics has often been confined to providing the starting points for formal proofs, with little or no effect on the discovery or creation of new mathematics. For example, quite recently Patras wrote that the axiomatic method “never allows for authentic creation” (Patras 2001, 159), and similar views have(More)
1.1 Mathematical concepts and notation In recent years philosophers of mathematics have begun to show greater interest in the activities involved in doing mathematics. This turn to mathematical practice is motivated in part by the belief that an understanding of what mathematicians do will lead to a better understanding of what mathematics is. One obvious(More)
1.1 Overview The aim of this paper is to provide a framework for the discussion of mathematical ontology that is rooted in actual mathematical practice, i.e., the way in which mathematicians have introduced and dealt with mathematical objects. Using this framework, some general trends in the development of mathematics, in particular the transition to modern(More)
In this paper I investigate two notions of concepts that have played a dominant role in 20th century philosophy of mathematics. According to the first, concepts are definite and fixed; in contrast, according to the second notion concepts are open and subject to modifications. The motivations behind these two incompatible notions and how they can be used to(More)