User:Shapeyness/sandbox/History of philosophy of mathematics

Whilst the use of mathematics for practical affairs can be traced back to the Ancient Egyptians and Mesopotamians, mathematics as an abstract discipline in the Western world arose in Ancient Greece with figures such as Thales of Miletus and Pythagoras of Samos. Amongst the first philosophies of mathematics came from the Pythagoreans, who believed that "everything is number" and that all things are ordered according to whole numbers and their ratios.

The Pythagorean idea that numbers lay behind the objects of the perceived world as a more fundamental reality inspired Plato (c. 427–347 BCE) and his theory of forms. Plato split reality into a constantly-changing world of perceptions and an eternal world consisting of immutable forms and numbers, which he thought all people experience before they are born. For Plato, learning mathematics was actually a process of remembering the world of the forms, of unlocking knowledge that is already innately known (anamnesis). Plato's student, Aristotle (c. 384–322 BCE), agreed in the existence of mathematical forms, but denied that they were separate from the world of physical objects. He thought, instead, that mathematical objects such as surfaces and points existed within physical objects, and that they only appeared not to because mathematicians generalize beyond specific cases and can ignore that surfaces are physical.

Pythagoreanism and Platonism influenced a number of thinkers in early Islamic philosophy due to the translation of Greek works of mathematics into Arabic as early as the 9th century CE. However, these views became unpopular following criticisms from the philosopher and polymath Avicenna. ...

References

Sources

• Felgner, Ulrich (2023). Philosophy of Mathematics in Antiquity and in Modern Times. Birkhäuser. ISBN 978-3-031-27303-2.
• Herrmann, Dietmar (2022). Ancient Mathematics: History of Mathematics in Ancient Greece and Hellenism. Springer-Verlag. ISBN 978-3-662-66493-3.
• Marcus, Russell; McEvoy, Mark, eds. (2016). An Historical Introduction to the Philosophy of Mathematics: A Reader. Bloomsbury Academic. ISBN 978-1-4725-2534-5.
• Stillwell, John (2019). A Concise History of Mathematics for Philosophers. Cambridge Elements in the Philosophy of Mathematics. Cambridge University Press. ISBN 978-1-108-45623-4.