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Why cannot matter be infinitely divisible, according to Plato?

Thanks in advance!

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    In the Timaeus, Plato depicts the elemental substances as made up of regular solids, the faces of which are indivisible. The basic reasoning was that when things changed state, elements were created out of or destroyed into something smaller than the minimal constituents of an element.
    – user9166
    Nov 28 '16 at 23:52
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    Go here: classics.mit.edu/Plato/timaeus.html and search for 'triangles'
    – user9166
    Nov 29 '16 at 0:00
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    I am not sure about Plato but the earliest Greek philosophers like Heraclitus believed all matter is made up of few elements like fire , air and water . This was developed as metaphysics . After Plato ,Democritus developed a theory of atomism - which introduces the concept of atoms and void as a constituent of every naturally occurring thing
    – shrey
    Dec 1 '16 at 5:08
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    @shrey Hi. Democritus did not live after Plato. He was a contemporary of Plato's, and older than Plato. Dec 1 '16 at 23:25
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    @RamTobolski my mistake
    – shrey
    Dec 2 '16 at 3:59
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Eventually, dividing something into smaller and smaller parts causes the thing to lose its emergent properties (i.e., its inherent characteristics that we can observe in it and use to describe it). For example, dividing a cell into subcellular components will cause the cell to lose its emergent properties (e.g., self-replication, RNA translation, homeostasis, metabolism, etc.). Plato specifically refered to further dividing atoms into smaller and smaller parts: an element is defined by the number of protons in its nucleus; if we further divide an atom of Carbon (6 protons), it will lose at least a portion of these protons and become some other type of atom (e.g., maybe now we have two atoms with 3 protons each = Lithium).

Advances in our understanding of science can further assist us in dissecting Plato's point. For instance, Kenneth Wilson, a Nobel Laureate Mathematician/Physicist, defines the correlation length as the smallest amount of something needed for its properties that are apparent in larger amounts to subsist. This conception is analogous to Plato's, although more realistic implications are outlined.

Here is a link to the particular Wilson paper, titled "The renormalization group and the epsilon exapansion": https://pdfs.semanticscholar.org/e372/a0dc3053d0630788bc778dbffd6b4ea5d34b.pdf

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Plato actually believed that the most fundamental components of objects were not particulate in nature. To Plato, such a mechanistic model of the world would fail to produce the order and beauty that we see in the natural world. Rather, he believed that at a base level, the elements had faces which were composed of triangles. So, he did believe in a physical theory which incorporated the idea of indivisible components, but these components were mathematical in nature. This is consistent with the views presented in Timaeus wherein he suggests that the cosmos was created according to a model.

References: https://en.wikipedia.org/wiki/Atomism#Geometry_and_atoms https://plato.stanford.edu/entries/atomism-ancient/#PlatPlat

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