Liu, Chong (2026) Probability-Distribution Determinism: A Logical Reconstruction from Determination Relations to Causal Language. [Preprint]

Text PDD_metaphysics_en_later.pdf Download (203kB)

Abstract

Classical determinism typically construes ``determination'' as ``a single outcome being determined,'' and consequently tends to regard probabilistic phenomena as challenges to determinism. Existing causal theories analyze causal relations respectively in terms of counterfactual dependence, interventional invariance, and structural models; this paper asks the further question of what form is taken by the determination relation presupposed by these analyses. To answer it, the paper proposes Probability-Distribution Determinism (PDD), which defines the general form of ``determination'' as follows: when the full determining conditions obtain, the resultant state of affairs is uniquely determined in the form of a probability distribution. The degenerate distribution in classical determinism, which assigns probability $1$ to one outcome, is not abolished but repositioned as a special case of this more general form.

To avoid mistaking epistemic tools for metaphysical structures, this paper first distinguishes three levels: pure determination relations, physical ontology, and epistemic tools. Under this level distinction, PDD is situated primarily as a determination-relation structure at the metaphysical/logical level. Its theoretical value lies in the fact that this structure can also serve, at the epistemic level, as a regulative framework for understanding the empirical world and provide a conceptual perspective on relation types, background conditions, and causal language in empirical research.

The main contributions of this paper are threefold. First, PDD reconstructs the determined object from a single outcome into a resultant state of affairs expressed as a probability distribution, and on this basis analyzes the atemporality, multiple realizability, and unidirectionality of determination relations, together with the compositional forms of PDD relation networks. In chain structures with sustained probabilistic branching and no reconvergence, increasing logical distance is usually accompanied by dilution in the concentration of distal outcomes, while the complete probability distribution remains uniquely determined by the full determining conditions. Second, the paper distinguishes determination relations from whole-part constitutive relations and explains how conflating the two may produce misleading transitivity and category mismatches in graphical models. Third, it first analyzes how background-condition stability affects the epistemic representation of determination relations, then distinguishes general relations from retrospective explanation and responsibility attribution in terms of epistemic aim, and argues that Simpson's paradox is more accurately described as the conflation, as one determination relation, of relation labels arising under different background conditions.

PDD thereby provides a framework for metaphysical relational analysis and conceptual audit, allowing debates about the nature of causation to be reformulated as analyses of determination-relation structures, background conditions, relation types, and the contextual adaptation of causal language. It does not replace specific methods of causal inference or statistics, but offers a conceptual perspective from which to understand the relational structures presupposed by those methods and the boundaries of their application.

---

Export/Citation:

EndNote | BibTeX | Dublin Core | ASCII/Text Citation (Chicago) | HTML Citation | OpenURL

Social Networking:

Share |

---

Item Type:	Preprint
Creators:	Creators Email ORCID Liu, Chong john.liuchong@gmail.com 0009-0009-8116-1255
Keywords:	Probability-Distribution Determinism (PDD), determination relation, complete background conditions, constitutive relation, contextual adaptation of causal language, Simpson's paradox
Subjects:	General Issues > Scientific Metaphysics General Issues > Causation General Issues > Determinism/Indeterminism General Issues > Explanation
Depositing User:	Mr. Chong Liu
Date Deposited:	08 Jun 2026 18:41
Last Modified:	08 Jun 2026 18:41
Item ID:	29978
Subjects:	General Issues > Scientific Metaphysics General Issues > Causation General Issues > Determinism/Indeterminism General Issues > Explanation
Date:	2026
URI:	https://philsci-archive.pitt.edu/id/eprint/29978

Available Versions of this Item

• Probabilistic Distribution Determinism: A Logical Reconstruction from Determination Relations to Causal Language. (deposited 05 Jun 2026 19:07)
  • Probability-Distribution Determinism: A Logical Reconstruction from Determination Relations to Causal Language. (deposited 08 Jun 2026 18:41) [Currently Displayed]

Monthly Views for the past 3 years

Monthly Downloads for the past 3 years

Plum Analytics

Actions (login required)

View Item