If a single entity possesses both intentional being (which is not accidental inherence) and real accidental being (which is), then Giles' account assigns contradictory modes of existence to the same item without a principled criterion for adjudication.

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Accidental inherence(metaphysics): A property that something has but doesn't need to have to be what it is—like how a cup is white, but a cup could be red and still be a cup.
Contradictory modes of existence(metaphysics/logic): When something is claimed to exist in two completely opposite ways at the same time, which seems impossible and needs explanation.
Giles(as the philosopher whose argument is being discussed): A medieval philosopher (likely Giles of Rome, 13th-14th century) who wrote about how substances and their properties work. He's known for his ideas about what things fundamentally are versus what properties they have.
Intentional being(the other category of existence being discussed): Things that exist because they are in someone's mind or consciousness—like thoughts, dreams, or imagined objects.

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