By adopting second-order logic along with Hume's Principle in an unrestricted form, Wright incurred commitment (as a matter of analyticity) not only to each natural number, seriatim, but also to the cardinal number of any concept whatsoever.
Theories that postulate or prove them need to be supplemented with specific further ontologically committal postulates before incurring commitment to the sort of entities whose broad logical behavior is captured by a single-abstraction identity principle.
Still, it does incur a commitment to the truth of the proposition that there are black swans.
I incur no commitments here about the right analysis of knowledge, if there is one.
On the reading which cannot cancel ontological commitment (as in that reading of 'John thinks about God' which can only be true if there is a God to think about), the premises are question-begging: they incur ontological commitments which non-theists reject.
But there is an influential philosophical tradition that denies this assumption and instead holds that all kinds of quantifiers incur ontological commitments, not just singular first-order ones.[14] The most famous exponent of this tradition is Frege, who claims that second-order quantifiers are committed to concepts, just as singular first-order quantifiers are committed to objects.
If this is right, then incurring a commitment to truth is not sufficient for asserting.
Then the paraphrase does nothing to support the claim that the original sentence can be used without incurring ontological commitment.
If S uses 'green' to mean green, therefore, she becomes a participant in this practice and incurs a commitment to use the term accordingly.
Possessing a concept, grasping it, incurs a commitment to use the concept 'in keeping with its content', in the various propositional attitudes.
