If the formal distinction fails as a coherent ontological category, the asymmetries in predication it was invoked to explain dissolve, removing the motivation for any redefinition.

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Ontological: "Ontological" refers to questions about what actually exists or is real. It's concerned with the fundamental nature of being—asking "What kinds of things are there?" rather than "How do we know about them?" For example, an ontological question might be whether numbers, ideas, or God actually exist as real things, or if they're just human inventions.
Redefinition(what both ethics and science do when they improve their understanding of concepts): Changing or replacing an old definition of something with a new, more accurate or useful one.
asymmetries in predication(the problem that the formal distinction was supposed to solve): Cases where things work differently when we describe one object versus another—for example, we can say 'God is eternal' but maybe not say 'eternality is God' in the same way.
category(Aristotelian usage as discussed in the passage): A predicate, per Aristotle's usage; the term 'predicate' can refer to realities, concepts, or linguistic terms.

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