Marriages of Mathematics and Physics: A Challenge for Biology

Download Edit this record How to cite View on PhilPapers
The human attempts to access, measure and organize physical phenomena have led to a manifold construction of mathematical and physical spaces. We will survey the evolution of geometries from Euclid to the Algebraic Geometry of the 20th century. The role of Persian/Arabic Algebra in this transition and its Western symbolic development is emphasized. In this relation, we will also discuss changes in the ontological attitudes toward mathematics and its applications. Historically, the encounter of geometric and algebraic perspectives enriched the mathematical practices and their foundations. Yet, the collapse of Euclidean certitudes, of over 2300 years, and the crisis in the mathematical analysis of the 19th century, led to the exclusion of “geometric judgments” from the foundations of Mathematics. After the success and the limits of the logico-formal analysis, it is necessary to broaden our foundational tools and re-examine the interactions with natural sciences. In particular, the way the geometric and algebraic approaches organize knowledge is analyzed as a cross-disciplinary and cross-cultural issue and will be examined in Mathematical Physics and Biology. We finally discuss how the current notions of mathematical (phase) “space” should be revisited for the purposes of life sciences.
PhilPapers/Archive ID
Revision history
Archival date: 2018-08-23
View upload history
References found in this work BETA
I. The Panda's Thumb.Gould, Stephen Jay
Naturalizing Phenomenology: Issues in Contemporary Phenomenology and Cognitive Science.Petitot, Jean; Varela, Francisco; Pachoud, Bernard & Roy, Jean-Michel (eds.)

View all 13 references / Add more references

Citations of this work BETA

Add more citations

Added to PP index

Total views
568 ( #4,823 of 42,370 )

Recent downloads (6 months)
105 ( #4,491 of 42,370 )

How can I increase my downloads?

Downloads since first upload
This graph includes both downloads from PhilArchive and clicks to external links.