Mathematical and Empirical Concepts

Chapter
Part of the Studies in History and Philosophy of Science book series (AUST, volume 28)

Abstract

Buzaglo (as well as Manders (J Philos LXXXVI(10):553–562, 1989)) shows the way in which it is rational even for a realist to consider ‘development of concepts’, and documents the theory by numerous examples from the area of mathematics. A natural question arises: in which way can the phenomenon of expanding mathematical concepts influence empirical concepts? But at the same time a more general question can be formulated: in which way do the mathematical concepts influence empirical concepts? What I want to show in the present paper can be described as follows.

The problem articulated by Buzaglo deserves some semantic refinements. Following explications are needed:
  • What is meaning? (In particular: What are concepts?)

  • What are questions? (Or, equivalently: Semantics of interrogative sentences.)

Further, a useful notion will be the notion of problem. Taking over the notion of conceptual system from Materna (Conceptual Systems. Logos, Berlin, 2004) and using Tichý’s Transparent intensional logic (TIL) I can try to solve the problem of the relation between mathematical and empirical concepts (not only for the case of expanding some mathematical concepts).

Keywords

Actual World Mathematical Concept Free Variable Conceptual System Simple Concept 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowledgment

The present paper has been supported by the Grant Agency of Czech Republic, project No 401/07/0451.

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Copyright information

© Springer Science+Business Media B.V. 2012

Authors and Affiliations

  1. 1.Department of PhilosophyMasaryk UniversityBrnoCzech republic

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