Quantifier accounts associate commitment to Ks with the existential claim '∃x Kx', which makes commitment to natural numbers entail commitment to integers — reversing the correct ordering.

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The whole numbers including positive numbers, negative numbers, and zero (like ..., -2, -1, 0, 1, 2, ...).

Natural numbers(mathematics)

The counting numbers: 1, 2, 3, 4, and so on (sometimes including 0, depending on context).

Ontology(Carnap argues this enterprise is based on a mistake)

The philosophical discipline that tries to answer hard questions about what there really is.

Quantifier(in formal logic)

Words in logic that specify how many things you're talking about, like 'all' (universal quantifier) or 'some/at least one' (existential quantifier).

∃x Kx(as used in formal logic notation)

Symbolic shorthand meaning 'there exists at least one thing that is K.' The ∃ symbol means 'there exists' and x is a placeholder for any thing.

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SEP: ontological-commitment

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Once one accepts that a “reality” predicate is needed to characterize ontological commitment, a puzzle about the logic of ontological commitment admits of a natural solution. The puzzle is this (from Fine 2009). Because the natural numbers are included within the integers, an ontological commitment to the integers, it seems, should be a stronger commitment than a commitment to the natural numbers. But quantifier accounts of ontological commitment get this backwards: since commitment to Ks is ass

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