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LIT-945: Unscrambling the omelette of causation and inference: The framework of causal-inferential theories

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Properties5
StatusActive — read 2026-10-14 (NOTE-737) in part, not in full: the sections that characterise generalized noncontextuality and Leibnizianity (§§V, VI, VIII, IX) were read closely, §II–IV and the proofs in Appendices C–G were not, so the NOTE is Skimmed. Worth reading as the current statement of what a generalized-noncontextuality no-go denies: a classical realist representation that preserves inferential equivalence. It also shows why a prepare-measure scenario, which allows no Bell-like no-go, can still show contextuality. Read it knowing that Leibnizianity implies generalized noncontextuality only in one direction (the converse is Conjecture 1′), that only classical inference is built, that the nonclassical realist theory it aims at is specified by desiderata only, and that it does not discuss the Kochen–Specker or sheaf notions.
Version3
Tagscontextuality, quantum-foundations, causality
Cited as “paper” byNOTE-737 — Schmid, Selby & Spekkens — Unscrambling the omelette of causation and inference
Cited as “source” byTHEORY-011 — Generalized contextuality is strictly broader than Kochen–Specker contextuality: a qubit already has no preparation-noncontextual model, though no Kochen–Specker argument with sharp measurements exists in dimension two, THEORY-231 — Within classical realism, a generalized-noncontextuality no-go refutes Leibnizian representations, not realist representations as such; it rests on a stronger assumption than a Bell-like no-go and so applies where none exists, as in prepare-measure scenarios, but only Leibnizianity implying noncontextuality is proved

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David Schmid, John H. Selby and Robert W. Spekkens (2020), arXiv:2009.03297.

Key takeaways

From the reading, NOTE-737. Read in part; see the NOTE for what was skipped.

  • Inference and influence are kept apart. A causal-inferential theory pairs a causal process theory (laboratory procedures, or functions on classical variables) with Bayesian-Boolean inference. Two processes are inferentially equivalent when they give the same predictions in every causally closed embedding (Definition V.1).
  • Quotienting scrambles them. GPTs and ontological models work up to inferential equivalence. That erases causal structure: a mixture of the two constant bit functions and a mixture of identity and flip are causally opposite, yet inferentially equivalent (§V.C).
  • Leibnizianity. A classical realist representation is Leibnizian if it maps inferentially equivalent processes to inferentially equivalent ones (Definition VI.5). It is a formalisation of Leibniz’s methodological principle, generalised to states of knowledge.
  • Generalized noncontextuality, rehabilitated. It is the same preservation demand on a map into the quotiented realist theory (Definition VIII.2). It holds iff the quotiented operational theory has a classical realist representation (Eq. 214). A quotiented theory is neither contextual nor noncontextual.
  • The implication runs one way. A Leibnizian representation implies a generalized-noncontextual one, so every noncontextuality no-go is a no-go for Leibnizian representations (Eq. 215). The converse is Conjecture 1′.
  • Bell versus noncontextuality. A Bell-like no-go denies every classical realist representation, a weaker assumption. A noncontextuality no-go denies only Leibnizian ones. It applies where no Bell-like constraint exists, as in a prepare-measure scenario (§VIII.C).
  • The way out it proposes. Not abandoning Leibnizianity, but a realist theory whose causation and inference are nonclassical. Five criteria are set for one (§IX.A); none is built.

Standing in the record

Filed on 2026-10-12 from the owner’s papers-feed for QUESTION-067, and read in part on 2026-10-14 in NOTE-737. It gives the question what refuting Spekkens’s notion would commit the record to. Within classical realism, it means giving up Leibnizianity, not realism. That result is filed as THEORY-231. A Bell-type failure would be the stronger result. It also sets two conditions on any pragmatic test. Equivalence must hold over every tester, not only a probe family. And the test must use the unquotiented description, in which equivalent renderings stay distinct. It is the source text for the “Leibnizian methodological principle” that THEORY-011 cites, and it restates the positive-quasiprobability criterion of THEORY-016 (LIT-003). It rehabilitates the definition of LIT-266, which it cites, and does not treat the Kochen–Specker or sheaf notions. A full reading would add the proofs (Appendices E–G) and the construction of the theories in §II–IV.

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