As such they are unchanging and causally inefficacious. They exist in a realm outside of space and time, detached from the physical world or people’s minds. On this account, a particular woman in the sensible world is objectively beautiful by virtue of partaking in the abstract form of beauty. Following Plato’s lead, the mathematical Platonists developed the idea that numbers are abstract objects that are non-spatiotemporal, non-physical, and non-mental. In the fourth century BCE, Plato developed his theory of forms according to which there is a separate realm of ideal immutable forms which are fundamental to reality. They stressed numerical proportions, harmony and order (Thesleff 2013). To the early Pythagoreans number became a sort of cosmic matter, very much like air and water. For example: the female is likened to the number two and the male to the number three. Things “are” number, or “resemble” number. At its deepest level, reality, including music and astronomy, is mathematical. The idea of a close relationship between mathematics and the objective reality is not new: In the late sixth century BCE, the ancient Greek philosopher Pythagoras suggested that numbers are of functional significance in the world (Encyclopedia Britannica 2018, “Pythagoras”).
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