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Absence perception and the philosophy of zero
1Kurt Gödel Research Center for Mathematical Logic (KGRC), Währinger Straße, 25, 1090 Vienna, Austria.
Synthese
|August 28, 2020
Summary
This study explores the philosophical challenges of zero, integrating collection properties, absence philosophy, and cognitive studies to explain its dual nature as a number and concept of nothingness.
Area of Science:
- Philosophy of Mathematics
- Metaphysics
- Epistemology
Background:
- Zero presents a philosophical paradox: it is a cardinal number yet associated with nothingness.
- Realist philosophies of mathematics struggle to reconcile zero's existence with its conceptual links to non-being.
Purpose of the Study:
- To analyze the epistemology and metaphysics of zero.
- To develop constraints for a satisfactory philosophical account of zero.
- To propose an integrated framework for understanding zero.
Main Methods:
- Analysis of philosophical concepts related to zero.
- Integration of number theory as properties of collections.
- Incorporation of theories on the philosophy of absences.
- Consideration of recent findings in numerical cognition and ontogenetic studies.
Main Results:
- A framework is proposed that reconciles zero's numerical and 'nothingness' aspects.
- The integration of diverse philosophical and scientific perspectives provides a robust account of zero.
- Constraints are developed to guide future philosophical discussions on zero.
Conclusions:
- A satisfactory account of zero is achievable by synthesizing number theory, absence philosophy, and cognitive science.
- This integrated approach addresses the metaphysical and epistemological challenges posed by zero.
- Understanding zero requires acknowledging its role as a property of collections and its cognitive underpinnings.
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