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ZENODO
Preprint . 2026
License: CC BY
Data sources: ZENODO
ZENODO
Preprint . 2026
License: CC BY
Data sources: Datacite
ZENODO
Preprint . 2026
License: CC BY
Data sources: Datacite
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Beyond Conditional Independence: Why Markov Blankets Cannot Formalise Constitutive Relations, and What Would Be Required

Authors: Papathanasiou, Vassilis;

Beyond Conditional Independence: Why Markov Blankets Cannot Formalise Constitutive Relations, and What Would Be Required

Abstract

The debate over Markov blankets in the Free Energy Principle (FEP) has been framed as an interpretive dispute: are Markov blankets statistical tools (Pearl blankets) or ontological features (Friston blankets) that systems genuinely instantiate? This paper argues that the framing is mistaken. The problem is not interpretive but formal: conditional independence — the mathematical structure that defines a Markov blanket — is constitutionally incapable of encoding constitutive relations, i.e., relations in which the relata are partially constituted by the relation itself. We establish this through three arguments of increasing depth. The Symmetry Argument: conditional independence is symmetric (X ⊥⊥ Y | Z implies Y ⊥⊥ X | Z), while constitutive relations are directed and asymmetric; no property expressible as a conditional independence statement can distinguish a directed constitutive relation from its converse (Theorem 1). The Pre-Individuation Argument: probability theory requires random variables to be individually typed prior to and independently of any joint distribution, while constitutive relations require the type of at least one relatum to depend on the relation; this is a framework-level incompatibility that no refinement of the Markov blanket concept within standard probability theory can overcome (Theorem 2). The Normativity Argument: constitutive relations carry normative structure — facts about whether a relatum is properly or improperly constituted — that probability distributions cannot represent (Theorem 3). Crucially, Theorem 2 is the load-bearing result: it shows the problem is not that the Markov blanket is insufficiently rich but that probability theory's foundational pre-individuation commitment makes constitutive relations inexpressible at the framework level. Addressing this requires a formal framework in which the type of a term is itself a relational judgment — specifically, a Constitutive Type Theory (CTT) extending Simplicial Type Theory with a directed constitutive type-former ⊲. We sketch this extension, show what participation looks like formalised as a typing judgment in CTT, and identify what this allows the FEP to say that it currently cannot. We close by drawing the precise line between Bruineberg et al.'s underdetermination claim and our stronger misrepresentation claim: underdetermination holds that the formalism is neutral between ontological readings; misrepresentation holds that the formalism actively encodes the wrong kind of relation — symmetric where the actual relation is asymmetric and constitutive. CTT is the required extension; building it is the remaining work.

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
0
Average
Average
Average