The term relates to supporting Plato's ideas, not just liking his work generally. As a Platonist, she subscribes to the belief in a realm of ideal forms.
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Academic Term
Most often used in academic or philosophical discussions, less in casual talk. His thesis showcases his stance as a modern Platonist.
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Specific Philosophy
Understand that it relates specifically to Plato's philosophy, not ancient Greek philosophy as a whole. She wrote a paper comparing Aristotelians and Platonists.