• Publications
  • Influence
Modeling ancient and modern arithmetic practices: Addition and multiplication with Arabic and Roman numerals
TLDR
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. Expand
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  • 2
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On the creative role of axiomatics. The discovery of lattices by Schröder, Dedekind, Birkhoff, and others
  • D. Schlimm
  • Mathematics, Computer Science
  • Synthese
  • 1 November 2011
TLDR
Three different ways in which systems of axioms can contribute to the discovery of new notions are presented and they are illustrated by the various lattices have been introduced in mathematics. Expand
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Dedekind’s Analysis of Number: Systems and Axioms
TLDR
In 1888 Hilbert made his Rundreise from Königsberg to other German university towns. Expand
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The Cognitive Advantages of Counting Specifically: A Representational Analysis of Verbal Numeration Systems in Oceanic Languages
TLDR
The domain of numbers provides a paradigmatic case for investigating interactions of culture, language, and cognition: Numerical competencies are considered a core domain of knowledge, and yet the development of specifically human abilities presupposes cultural and linguistic input by way of counting sequences, the cross-linguistic variability of which has implications for number representation and processing. Expand
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Learning from the existence of models: On psychic machines, tortoises, and computer simulations
TLDR
Using four examples of models and computer simulations from the history of psychology, I discuss some of the methodological aspects involved in their construction and use, and illustrate how the existence of a model can demonstrate the viability of a hypothesis that had previously been deemed impossible on a priori grounds. Expand
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Methodological Reflections on Typologies for Numerical Notations
TLDR
This paper provides a general framework for assessing the efficacy of these typologies relative to certain desiderata, and it uses this framework to discuss the two influential typologies of Zhang & Norman and Chrisomalis. Expand
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Axioms in Mathematical Practice
  • 25
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On Frege's Begriffsschrift Notation for Propositional Logic: Design Principles and Trade-Offs
TLDR
This paper focuses mainly on the propositional fragment of the Begriffsschrift, because it embodies the characteristic features that distinguish it from other expressively equivalent notations. Expand
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Pasch's Philosophy of Mathematics
  • D. Schlimm
  • Computer Science
  • Rev. Symb. Log.
  • 1 March 2010
TLDR
Moritz Pasch (1843–1930) gave the first rigorous axiomatization of projective geometry in Vorlesungen uber neuere Geometrie (1882), in which he also clearly formulated the view that deductions must be independent from the meanings of the nonlogical terms involved. Expand
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Dedekind's Abstract Concepts: Models and Mappings
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