Frege's analysis of implicit definition shows that deriving metric notions from projective ones does not reduceontological commitment if projective space itself harbors metric presuppositions.
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implicit definition(Warren (2017) uses implicit definition as a resource to respond to the meta-theoretic regress objection)
A method of defining a term by specifying the rules or axioms governing its use, rather than by explicit statement — invoked as a possible reply to the regress problem for conventionalism.
ontological commitment(Used to derive that literal truth of 'a is F' entails existence of a)
The criterion by which acceptance of a sentence as literally true commits one to the existence of the objects referred to by singular terms in that sentence, provided the sentence cannot be paraphrased away.
presuppositions(Collingwood, An Essay on Metaphysics)
The foundational assumptions or commitments that govern thought within a given domain of inquiry, which Collingwood later identified as the proper subject matter of philosophical (metaphysical) investigation.