When a filtering criterion derives from a source categorically distinct from the filtered items, the theory is foundationally dual, not monist, per Parfit's analysis in Reasons and Persons.

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Derek Parfit(as a philosopher being cited for his theory on personal identity): A highly influential philosopher who argued that personal identity (what makes you 'you' over time) is less important than we think, and that we're not the unified, continuous selves we assume we are.
Filtering criterion(as used in logic and metaphysics): A rule or standard you use to separate things into different groups—like sorting by color or size.
Foundationally dual(as used in metaphysics): A view that reality is built on two completely different kinds of things, rather than one basic kind.
Reasons and Persons(as the source text): A landmark 1984 philosophy book by Derek Parfit that explores how we should live and make decisions, especially when our personal interests conflict with what's best for everyone.

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