Vectors and Tensors in a Finite-Dimensional Space

  • Mikhail Itskov
Chapter
Part of the Mathematical Engineering book series (MATHENGIN)

Abstract

Recently, it has been suggested that there is a need for a conceptual clarification of the relation between personal epistemology (PE) and philosophical epistemology. I attempt to do this in this chapter. First, I clarify the task of traditional epistemology as understood by philosophers and point out how it is different from epistemology as understood by PE researchers: epistemology is not postmodernist; it has a normative goal, which is different from empirical research; subfields of epistemology are briefly mentioned and implications for PE research suggested. Second, I point out the existence of several conceptual pitfalls that should be avoided by individuals working in this area: epistemic versus epistemological, 1st person versus 3rd person perspectives, and an important ambiguity in the concept of cognition. Third, the concept of cognitive flexibility in relation to epistemology needs to be carefully discussed, especially in relation to the issue of domain specificity and domain generality. This is discussed in the context of an epistemology of pragmatism. Finally, I mention the recent revolution produced by naturalistic epistemology and the implications of this challenge for understanding the relation between PE and traditional epistemology.

Keywords

Tensor Product Orthonormal Basis Dual Basis Arbitrary Vector Identity Tensor 
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.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Mikhail Itskov
    • 1
  1. 1.Department of Continuum MechanicsRWTH Aachen UniversityAachenGermany

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