Classificatory Sorites, Probabilistic Supervenience, and Rule-Making

TL;DR

This paper explores how responses to stimuli in sorites paradoxes are probabilistic rather than deterministic, affecting the formulation of tolerance and connectedness, and discusses the implications for rule-making and classical logic.

Contribution

It introduces a probabilistic framework for supervenience in empirical systems, challenging traditional deterministic views and analyzing the arbitrariness in rule-making within soritical contexts.

Findings

Supervenience of responses can be probabilistic rather than deterministic.

Probabilistic supervenience is stable and reducible to ordinary probabilities.

Arbitrariness in rule-making does not conflict with classical logic.

Abstract

We view sorites in terms of stimuli acting upon a system and evoking this system's responses. Supervenience of responses on stimuli implies that they either lack tolerance (i.e., they change in every vicinity of some of the stimuli), or stimuli are not always connectable by finite chains of stimuli in which successive members are `very similar'. If supervenience does not hold, the properties of tolerance and connectedness cannot be formulated and therefore soritical sequences cannot be constructed. We hypothesize that supervenience in empirical systems (such as people answering questions) is fundamentally probabilistic. The supervenience of probabilities of responses on stimuli is stable, in the sense that `higher-order' probability distributions can always be reduced to `ordinary' ones. In making rules about which stimuli ought to correspond to which responses, the main characterization of choices in soritical situations is their arbitrariness. We argue that arbitrariness poses no problems for classical logic.