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It is not the case that Lange's argument is flawed because it relies on the unacknowledged assumption that a universal sentence explains its instances
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Reasons For
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1.
Lange's argument presupposes that a universal sentence explains its instances
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2.
This assumption is not acknowledged or justified in Lange's argument
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Reasons Against
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Reason against 1 of 2
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1.
Hempel's Deductive-Nomological model explicitly requires that explanations subsume instances under universal laws, making this assumption theoretically loaded.
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2.
Lange's argument structurally mirrors DN explanation by deriving specific outcomes from universal mathematical truths, inheriting DN's undefended subsumption principle.
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3.
Without acknowledging this DN inheritance, Lange's argument smuggles in a contested covering-law framework that Scriven and others have shown requires independent justification.
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Reason against 2 of 2
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1.
Aristotle's Posterior Analytics distinguishes demonstrative knowledge of universals from explanatory knowledge of particulars, showing universal-to-instance inference is non-trivial.
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2.
Even if a universal mathematical truth holds necessarily, its explanatory relevance to a particular instance requires a non-deductive relevance relation that Lange never specifies.
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