Hume's Principle, via Frege's Theorem, actually derives the full Dedekind-infinite sequence of natural numbers, making the number domain as large as any infinite concept-extension.

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Concept-extension(in philosophy of logic): The collection of all things that actually fit a particular idea or category—for example, the concept-extension of 'red things' is everything that is red.
David Hume(as referenced in the statement): An 18th-century Scottish philosopher who argued that our desires and emotions, not reason alone, drive our actions and decisions.
Dedekind-infinite(one of several definitions of infinity being compared): A way of defining something as infinite based on the idea that it can be matched up with a proper part of itself (like how the whole numbers can be matched with just the even numbers).
Frege's Theorem(in logic and mathematics): A mathematical proof showing that you can build all the natural numbers (0, 1, 2, 3...) starting from basic logical rules and Hume's Principle.

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