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Summary
This summary is machine-generated.

This study explores if "thin" mathematical objects simplify the epistemology of mathematics. It finds that while not all thin objects are transparent, this lack of transparency is a key feature of abstract mathematics.

Keywords:
Rice's theoremabstractionthin objectsØystein Linnebo

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Area of Science:

  • Philosophy of Mathematics
  • Epistemology

Background:

  • The concept of "thin" objects, as defined by Linnebo, is central to certain philosophical discussions in mathematics.
  • Epistemology of mathematics investigates the nature and justification of mathematical knowledge.

Purpose of the Study:

  • To analyze whether the assumption of "thin" mathematical objects simplifies the epistemology of mathematics.
  • To introduce and examine the concept of transparency in relation to thin objects.

Main Methods:

  • Conceptual analysis of "thin" objects and their properties.
  • Introduction of the notion of "transparency" for mathematical objects.
  • Argumentation based on the relationship between thinness, transparency, and abstract mathematics.

Main Results:

  • The study demonstrates that not all "thin" mathematical objects possess transparency.
  • It is shown that the lack of transparency in some thin objects is not a deficiency.

Conclusions:

  • The lack of transparency in certain "thin" mathematical objects is a "fruitful characteristic mark" of abstract mathematics.
  • This finding contributes to understanding the nature of mathematical objects and knowledge acquisition in abstract mathematics.