If true numerical sentences admit of nominalistically adequate paraphrases that preserve all empirical content, then ontological commitment to numbers is not mandatory but merely one interpretive choice.

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Paraphrase(using different language to express the same idea): Rewriting or restating something in a different way while keeping the same meaning.
empirical content(Used by Popper to equate informational richness with falsifiability.): The amount of empirical information conveyed by a theory.
interpretive choice(as used in philosophy of interpretation and metaphysics): A decision about how to understand or explain something when multiple reasonable understandings are possible, rather than something forced upon you by logic or evidence.
nominalism / nominalistically adequate(as used in metaphysics and philosophy of mathematics): A philosophical view that rejects the existence of abstract objects like numbers, and only accepts concrete physical things. A 'nominalistically adequate' explanation is one that describes something without requiring you to believe abstract objects are real.

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