In 'a person is at the door', the phrase 'a person' need not identify which person; it is an indefinite description.
By contrast, 'the person we met yesterday' may single out a known person in context.
Grammatical singularity is not the same as logical particularity. The word 'one' does not automatically establish a uniquely identified individual.
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One person versus that person
Universal and Particular — Definitions and Practical Classification
In 'a person is at the door', the phrase 'a person' need not identify which person; it is an indefinite description.
By contrast, 'the person we met yesterday' may single out a known person in context.
Grammatical singularity is not the same as logical particularity. The word 'one' does not automatically establish a uniquely identified individual.