Why Burn Books?
Why would Plato want to burn books? Especially those written by another philosopher?
According to Diogenes, Aristoxenus of Tarentum asserted that Plato would have gladly burned all the works of Democritus. But why?
After all, don't we have Democritus to thank for our modern, atomistic view of the world? Yes, Democritus was an atomist and his ideas that the universe was composed off innumerable "uncuttable" objects serves as the earliest elucidation of a particle-based theory in the West. However, this still doesn't answer why Plato would have been so opposed to his ideas.
Truth be told, evidence suggests that Plato possessed a very different view of the world than most modern scientists. While many moderns just assume that the world is inherently made up of parts, it appears that Plato modeled the Universe from a very different starting point. Rather than assuming that the world was made up of parts, Plato began with the idea of an All-Encompassing Oneness.
Even though it may not be immediately obvious, starting with an Absolute Wholeness naturally gives rise to a very different model of the world than beginning with parts. When viewed in mathematical terms, Plato's perspective is more closely aligned with Geometry, whereas Democritus' model is more consistent with arithmetic.
In classical times, most notably with the Neoplatonists, Geometry and arithmetic were viewed as distinct branches of mathematics. Arithmetic dealt primarily with calculations of discrete amounts of objects, whereas Geometry worked with continuous magnitudes such as time, volume, area, and length.
From what I have been able to find, it appears that Plato viewed the Universe as a series of interrelated continua that could be actively partitioned into pieces through different methods of measurement. This approach is consistent with the continuous magnitudes of length, area, volume, and even time - each of which is measured according to a standard section of itself.
As unusual as it might seem, people measure time with time, volume by volume, area by area, and length by sections of length. From Plato's perspective, every particular "thing" would have been held relative to every "thing" that arose before it - with every particular "thing" being held traceable back to an overarching Whole.
Of course, since everything was contained within this All-Encompassing Wholeness, Plato's perspective naturally gives rises to a Universe that is inherently boundless and limitless - giving rise to a very different concept of Infinity than the partial or incomplete infinity proposed by the particle-based models based off of Democritus' principles.