Formal mutual exclusiveness requires categories to be defined over a fixed, well-determined domain of entities, but ontological inquiry cannot presuppose such a domain without circularity.

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Circularity (circular reasoning)(as used in logic and epistemology): A logical problem where you need to assume something is true in order to prove it, making your argument go in circles instead of actually proving anything.
Domain (in logic)(as used in logic and mathematics): The complete collection of all the things you're talking about or considering in a particular discussion—for example, if you're discussing animals, the domain would be all animals.
Formal mutual exclusiveness(as used in logic and philosophy of language): When two categories are set up so that nothing can belong to both of them at the same time—like how something cannot be both entirely red and entirely blue simultaneously.
Ontological inquiry(as what Collingwood later rejected metaphysics from being): An investigation focused on understanding what exists and the nature of existence itself—asking 'what is being?' rather than 'how do we know things?'

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