Chapter 8: Mathematics and Philosophy: A Semiotic and Historical Perspective
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Published:2015
Michael Otte, 2015. "Mathematics and Philosophy: A Semiotic and Historical Perspective", Refractions of Mathematics Education: Festschrift for Eva Jablonka, Christer Bergsten, Bharath Sriraman
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The importance of philosophy to mathematics education results not least from the fact that the concept of “explanation” is central to our educational practices and aims. Without content, mathematics could not fruitfully be organized and pursued at school as a primarily professional topic or as a mere language. Mathematical education has, like other subjects, also contributed to a common search for clarity on fundamental issues and to the formation of the person; such that philosophical formation seems as important as logical exactness or mathematical literacy.
When Cardinal Bellarmino notified Galileo of a forthcoming decree of the church, condemning the Copernican doctrine of helocentrism and ordering him to abandon it as an explanation of the world, he used an argument saying that mathematicians always used to argue hypothetically or ex suppositione only:
First, I say it seems to me that your Reverence and Signor Galileo act prudently when you content yourselves with speaking hypothetically and not absolutely,… For to say that the assumptions that the Earth moves and the Sun stands still saves all the celestial appearances better than do eccentrics and epicycles is to speak with excellent good sense…. Such a manner of speaking suffices for a mathematician…. To demonstrate that the appearances are saved by assuming the sun at the centre and the earth in the heavens is not the same thing as to demonstrate that in fact the sun is in the centre and the earth is in the heavens. (Bellarmino, 1615)
