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From axiomatic systems to the Dogmatic gene and beyond
Enka Blanchard1, Giuseppe Longo2
1Digitrust Consortium, Loria, Université de Lorraine, Nancy, France.
Positivistic views in mathematics and biology, focusing on formalism and gene-centric models, obscured the historical creation of meaning. Reconsidering history is crucial for understanding both fields.
Area of Science:
- Philosophy of Mathematics
- Philosophy of Biology
- Epistemology
Background:
- Early 20th-century mathematics was dominated by positivistic views, confusing rigor with formalism.
- Similar positivistic, gene-centric views later emerged in molecular biology, emphasizing DNA sequences.
- Both fields disregarded the historical development of meaning and the limits of formal approaches.
Purpose of the Study:
- To analyze the historical confusion between mathematical rigor and formalism.
- To draw parallels between the limitations of formalist mathematics and gene-centric biology.
- To propose an epistemology of mathematics and biology that incorporates the historical creation of sense.
Main Methods:
- Case studies examining the historical development of mathematical concepts.
- Analogical reasoning comparing formalist mathematics with genocentric biology.
- Conceptual analysis of epistemology and the role of history in scientific knowledge.
Main Results:
- Formalism in mathematics, while clarifying praxes, obscured the historical creation of mathematical meaning.
- Genocentric biology's focus on DNA sequences mirrored mathematical formalism's limitations.
- The historical creation of sense is essential for understanding mathematical and biological knowledge.
Conclusions:
- Reconstructing the history of science is vital for a robust epistemology.
- Understanding biological evolution requires considering changing phase spaces and rare events.
- A renewed relationship with the biological environment necessitates analyzing evolutionary processes.
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