If a form's participation in another form does not require the form to contain parts corresponding to each participated form, then infinite partaking does not entail infinite parts.

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Infinite partaking(as used in this metaphysical argument): The idea that something could endlessly participate in or copy the qualities of multiple Forms without limit.
Infinite parts(as used in this metaphysical argument): The possibility that something could be made up of an endless number of smaller pieces or components.
Participation (or Partaking)(as used in Plato's theory of Forms): When something in the physical world 'participates' in a Form, it means that thing shares in or copies the qualities of that perfect Form—like how a red apple participates in the Form of redness.
The Third Man Argument(The main concept being defined in the passage): A famous logical puzzle that questions Plato's Forms by pointing out that if Forms exist to explain why particular things are similar, you'd need an infinite chain of Forms to explain the Forms themselves.

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