A shared semantic theory that assigns truth conditions referencing abstract objects creates an implicit ontological commitment that cannot be cleanly separated from the semantic thesis itself.

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Ontology(Carnap argues this enterprise is based on a mistake): The philosophical discipline that tries to answer hard questions about what there really is.
Semantic thesis(philosophy of language/logic): A claim about what words, concepts, or statements mean rather than what actually exists in the world.
Truth conditions(used to describe how we determine whether a thought accurately represents reality): The specific circumstances or facts that would make a statement true or false—what has to be the case for a thought to be correct.
abstract objects(The target of Platonist ontological claims): Objects referred to by singular terms in literally true sentences that cannot be paraphrased away; includes mathematical objects (e.g., numbers), propositions, properties, relations, sentence types, possible worlds, logical objects, and fictional objects.

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