Source
De Haro & Butterfield (2025), LIT-199 (The Philosophy and Physics of Duality, OUP), read in full in NOTE-178 from the arXiv manuscript (2508.01616v1). Page numbers are printed ones. The Part II derivations were read for their claims, not checked line by line.
What was actually shown
The framework (§3.1, §12.1.2). A duality is an isomorphism between the model roots (states, quantities, dynamics) of two models of a common core, which must itself be a bare theory, a triple ⟨S, Q, D⟩. Duals are physically equivalent iff (A) they are duals and (B) their interpretation maps commute with the duality, i1 = i2∘d. Kramers–Wannier is the worked case of duals that are not physically equivalent: the heat bath is an external standard of temperature.
Underdetermination (§13.4). “Strictly speaking, we do not find any genuine cases of under-determination” (p. 459). In the examples, theoretically inequivalent duals turn out empirically inequivalent, as the Kramers–Wannier temperatures do. For a hypothetical genuine case (§13.2.3, pp. 444–450), each dual entails the common core (M1 ⊨ T, M2 ⊨ T) while contradicting the other on specific structure (M1 ⊨ ¬M2), so the cautious realist commits to T. That makes the underdetermination “benign”, not absent.
Structural realism (§13.2.4, pp. 450–454). The evidence “does not vindicate a structural realist view” (p. 454). Three arguments are given against Matsubara’s and Dawid’s structural readings: the hole-argument analogy, that a referential, intensional semantics for bare theories goes beyond what a structural realist would say, and that common cores are rich:
- bosonization’s contains both bosonic and fermionic states;
- the electric–magnetic one contains a Faraday-type tensor, with “purely electric” a relational fact;
- T-duality’s has momentum and winding as non-independent properties.
What could have come out otherwise. A theoretically inequivalent pair of duals could have proved empirically equivalent, and a common core could have been too thin to interpret. In the examples neither happened.
What this does not say
- That underdetermination never arises. The verdict is over the book’s examples. Underdetermination “as usually stated is too strong”, and the antirealist must show that empirically equivalent rivals lack a compatible common core (pp. 459–460, 528).
- That the cautious realist always has something to commit to. The entailment argument needs an interpreted common core. Not every common core is rich enough to be a theory, and the Schema is restricted to cases where it is.
- That the rich-core verdict covers the cases structural realists cite. For gauge–gravity duality the common core is “only a class of asymptotic operators and a conformal class of … metrics” (p. 70). Whether Dawid’s “virtually empty” worry returns there is open.
- That the physics is settled. Montonen–Olive has “very good evidence” but no proof, and “the main string dualities remain unproven” (p. 353). The Schema is illustrated “if gauge-gravity duality is true”.
- That isomorphism is the only defensible equivalence criterion. The authors argue against categorical and definitional equivalence and “never saw a convincing case against” isomorphism, but that rests on the stipulated principle of univocality and on theories formulated in set theory (p. 393).
Connections
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THEORY-687 (Le Bihan & Read, LIT-113) reaches the opposite verdict on the common core, but for empirically equivalent duals read naively, a weaker notion than the isomorphism used here. The two are not rivals: each states its condition.
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Le Bihan & Read, LIT-113, define duality by empirical equivalence alone and set structural realism aside. The book eliminates two of their six options by the entailment argument.
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Corfield, LIT-115, treats duality category-theoretically; the book judges categorical equivalence “too weak”.
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THEORY-034 and THEORY-038 concern which structural realisms survive Chakravartty’s dilemma and whether category theory supports radical OSR. This account removes one motivation those positions have been given, dualities, and leaves their other arguments untouched. Wallace (LIT-151) and Ladyman (LIT-045, LIT-184) are cited by the book.
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French (THEORY-594) argues that inequivalent representations of one theory help structural realism. That is a different phenomenon from duality, and the two accounts do not conflict.
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The book’s account of emergence is THEORY-459.