Richard Joyce explicitly structures his argument as an inference to the best explanation: the complete non-moral genealogy is advanced as the more parsimonious hypothesis, placing the evidential burden on the realist to show moral facts played a causal role.

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Genealogy (philosophical)(as used in history of philosophy): A historical tracing of how an idea, concept, or problem developed and changed over time through different thinkers and traditions.
Moral realist / realism(referring to those who believe morality is real): The philosophical position that moral facts actually exist independently—that something like 'stealing is wrong' is genuinely true, not just an opinion.
Non-moral genealogy(the alternative explanation being proposed): An explanation for how our moral beliefs developed without needing to assume that actual moral facts or truths exist—suggesting morality comes from evolution, psychology, or culture instead.
Parsimonious hypothesis(describing the genealogy as more parsimonious): An explanation that accomplishes its goal using the fewest assumptions or extra ideas; basically, a simpler explanation is preferred unless proven otherwise.

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