Does Indexing Really Solve Humphreys’ Paradox?

Julian Vincent Laggner

University of Vienna

According to Humphreys’ paradox (Humphreys 1985), there is a structural tension in the propensity interpretation of probability because propensities are causal and temporally asymmetric, while conditional probability is symmetric within the Kolmogorov framework. In Propensities and Pragmatism (Suárez 2013), Mauricio Suárez rejects the Identity Thesis, proposing the notation “»” to illustrate that the relationship between propensities and their probabilistic manifestations is a sui generis grounding relation, rather than one of conditional probability. He further argues that “Humphreys’ Paradox” should be seen more as “Humphreys’ argument,” because it serves as a general challenge to propensity-based accounts rather than a direct contradiction.

In The Chances of Propensities (Suárez 2018), this evolves into the indexed probability account, which depicts chances as indexed functions (e.g. Prob_Prop(O)). They are removed from the probability space and viewed as metaphysically grounding probability distributions, while remaining categorically distinct. The asymmetry is incorporated into the representation ab initio instead of being derived from conditional structure.

I contend that indexing does not address Humphreys’ argument, rather, it substitutes conditional probability with a grounding relation that maintains the structural asymmetry at the level of system semantics. What results is a re-description instead of a solution: the formal symmetry is eliminated, but the dependence structure is moved into grounding. This means that the fundamental conflict between causal asymmetry and probabilistic structure persists.

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