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Thin Objects Are Not Transparent
Matteo Plebani1, Luca San Mauro2, Giorgio Venturi3
1Dipartimento di Filosofia e Scienze dell'Educazione Università degli Studi di Torino.
Theoria
|March 22, 2024
Summary
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.
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.
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