Philosophy or Math, what is at the heart of all science?

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SUMMARY

The discussion centers on the foundational relationship between philosophy and mathematics in the context of science. It highlights that historically, mathematics and philosophy were intertwined, with figures like Bertrand Russell, Karl Popper, and Ludwig Wittgenstein bridging the two fields. The modern perspective views mathematics as a language for natural sciences, while philosophy offers a framework for discourse and understanding of scientific ideas. Ultimately, both disciplines are essential, with mathematics facilitating observation and experimentation, and philosophy connecting historical and contemporary knowledge.

PREREQUISITES
  • Understanding of basic mathematical concepts and their applications in science.
  • Familiarity with key philosophical figures such as Bertrand Russell and Karl Popper.
  • Knowledge of logic and set theory as foundational elements in both fields.
  • Awareness of the historical context of the relationship between mathematics and philosophy.
NEXT STEPS
  • Research the contributions of Bertrand Russell to both philosophy and mathematics.
  • Explore the role of logic and set theory in modern scientific methodologies.
  • Study the philosophical implications of scientific observation and experimentation.
  • Investigate the historical evolution of the relationship between mathematics and philosophy.
USEFUL FOR

Students of philosophy and mathematics, educators in the sciences, and anyone interested in the interdisciplinary connections between these fields and their impact on scientific inquiry.

AchillesWrathfulLove
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I am wondering which you think is the foundation of all sciences, I have no real understanding of either but I have a general idea of it I think so please offer your opinion!
 
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Not that long ago the two were closely related and a PhD in math was / is a Dr. phil. The point of view of mathematics as a language for the natural sciences is quite modern. Many mathematicians some hundred years ago studied philosophy and mathematics, and often theology and law. The latter for the better perspective to earn a living. They are still closely related when it comes to logic and set theory. And philosophers like Russell, Popper, Wittgenstein were travellers between the subjects - some more and some less.

I think it is harder to separate the two as to answer: both.
 
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The foundation of modern science includes observation and experimentation expressed in mathematics. Philosophy provides a discourse of ideas connecting past and present knowledge.
 
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