George Boolos argued that Hume's Principle carries unacceptable ontological commitments by generating an object for every concept, including concepts with infinite extensions, yielding a domain of numbers co-extensive with the concept hierarchy.

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Concept hierarchy(The structure of different concepts that Boolos related to numbers): A structured organization of concepts arranged in levels, where some concepts are broader or more general than others; similar to how 'animal' is more general than 'dog.'
Extension (of a concept)(Refers to what the concept applies to): The set of all individual things that fit under a particular concept; for example, the extension of 'dogs' includes every dog that exists.
George Boolos(as the philosopher who challenged Hume's Principle's status): An American philosopher and logician (1940–1996) who wrote influential papers about mathematical logic, philosophy of mathematics, and what counts as truly logical versus empirical truths.
Hume's Principle(Philosophy of mathematics, neo-logicism): A principle codifying the condition under which two concepts are equinumerous, namely when the number of objects falling under each concept is identical

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