Aquinas's own doctrine of participation, which Mann invokes, distinguishes between a thing participating in a form and a thing being identical to that form—participation presupposes non-identity.

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Aquinas: Thomas Aquinas was a medieval Italian priest and philosopher (1225-1274) who became one of the most influential thinkers in Western history. He attempted to show that Christian faith and human reason are compatible, arguing that we can use logic and observation to understand God and the natural world. His ideas deeply shaped Catholic theology and continue to influence how religious and secular institutions think about ethics, knowledge, and the relationship between science and belief.
Mann(as the philosopher whose argument is being evaluated): A contemporary philosopher who has written about how properties (qualities or characteristics) exist and relate to objects; in this context, he's proposing a theory that the statement is critiquing.
Non-Identity(Used to establish that each newly introduced form of likeness (L2, L3, ...) is distinct from its predecessors): The principle that a form is numerically distinct from the particulars (or other forms) that partake of it
doctrine of participation(as Aquinas's main theory being explained)

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