Abstract
This chapter gives the Renaissance and rationalist philosophers of the 16th and 17th century have the word. The Renaissance is generally characterised by the belief that human reason can provide insight in the organisation of the world. The world was still considered God’s creation, but it became increasingly common to view it as machine, which functioning the deity has not interfered with since its creation.
The chapter starts out with an account of the so-called scientific revolution and the break with Aristotelian physics that it represents. The move from a geocentric to a heliocentric worldview becomes analysed in detail. The use of mathematics for describing nature is a central element in this move, and the chapter examines the tying together of explanations of nature and mathematics that took place during this tumultuous time. Infinitesimals challenged mathematical ontology. If mathematics is the “language of nature,” infinitesimals must somehow relate to entities in reality. But as such, they are rather unmanageable, for how can a world that has actual extension be built by units so small that they have no extent? How many infinitesimals have to be added up in order to turn into a natural object?
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Notes
- 1.
See for example Abbud (1962).
- 2.
Brahe had his own description of the organization of the world, a peculiar compromise: Brahe placed the Earth at the centre of the universe with the Sun orbiting it, while the planets orbited the sun. This is some indication of the many different possibilities there were for imagining alternative world pictures!
- 3.
See the Galileo Project (1995a).
- 4.
Presumably, Galilei was not the first to attempt to proceed by the method of measuring. In 1544, the historian Benedetto Varchi referred to experiments proving Aristotle wrong. And in 1576, Giuseppe Moletti (Galilei’s predecessor as leader of the mathematics department of the university in Padua) wrote about how bodies made up of the same material but of different weight, as well as bodies of the same volume but of different material, reached the ground at the same time when released from a given height (See the Galileo Project, 1995b).
- 5.
See Descartes (1993).
- 6.
See, for example Dobbs (1983).
- 7.
The tractate is to be found in Whiteside (1961).
- 8.
See Berkeley (2002).
References
Abbud, F. (1962). The planetary theory of Ibn al-Shatir: Reduction of the geometric models to numerical tables. Isis, 53(4), 492–499. Chicago, IL: The University of Chicago Press.
Berkeley, G. (2002). The analyst. Retrieved from http://www.maths.tcd.ie/pub/HistMath/People/Berkeley/Analyst/Analyst.pdf
Bodin, J. (1945). Method for the easy comprehension of history. New York, NY: Columbia University Press.
Bury, J. B. (1955). The idea of progress: An inquiry into its origin and growth. New York, NY: Dover Publications.
Copernicus, N. (1996). On the revolutions of heavenly spheres. New York, NY: Prometheus Books.
Descartes, R. (1993). Meditations on first philosophy in focus. Edited and with an introduction by Stanley Tweyman. London, UK: Routledge.
Descartes, R. (1998). The world and other writings. Cambridge, UK: Cambridge University Press.
Dobbs, B. J. T. (1983). The foundations of Newton’s alchemy. Cambridge, UK: Cambridge University Press.
Foscarini, P. A. (1991). Letter of opinion over the Pythagorean and Copernican opinion concerning the mobility of the earth and the stability of the sun. In R. J. Blackwell (Ed.), Galileo, Bellarmine, and the Bible (pp. 217–251). Notre Dame, IN: University of Notre Dame Press.
Galilei, G. (1957). The assayer. In G. Galilei (Ed.), Discoveries and opinions of Galileo (pp. 229–281). New York, NY: Anchor Books.
Galilei, G. (2001). Dialogue concerning the two chief world systems: Ptolemaic and Copernican. New York, NY: The Modern Library.
Galileo Project. (1995a). Johannes Kepler. Retrieved from http://galileo.rice.edu/sci/kepler.html
Galileo Project. (1995b). On motion. Retrieved from http://galileo.rice.edu/sci/theories/on_motion.html
Kepler, J. (1596). Mysterium cosmographicum (The sacred mystery of the cosmos). Retrieved from http://www.e-rara.ch/doi/10.3931/e-rara-445
Kepler, J. (2008). The harmony of the world. London, UK: Forgotten Books.
Kepler, J. (2014). New world encyclopedia. Retrieved from http://www.newworldencyclopedia.org/entry/Johannes_Kepler
Newton, I. (1999). The principia: Mathematical principles of natural philosophy. Berkeley, CA: University of California Press.
Whiteside, D. T. (1961). Patterns of mathematical thought in the later Seventeenth Century. Arch Hist Exact Sci, 1(3), 179–388.
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Ravn, O., Skovsmose, O. (2019). Mathematics in Nature. In: Connecting Humans to Equations . History of Mathematics Education. Springer, Cham. https://doi.org/10.1007/978-3-030-01337-0_2
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