Defending Bayes, Part 2

Introduction

In our previous discussion, we defended the applicability of Bayes' theorem against criticisms from David Deutsch and Brett Hall, establishing it as the best and only coherent method for aligning subjective Credence with objective Measure. In this post, we aim to provide additional clarity regarding the fundamental nature of empirical uncertainty. We propose a significant reframing: empirical uncertainty is fundamentally about our uncertainty regarding which exact timeline we inhabit within the branching structure comprehensively defined by explanatory knowledge.

Traditional Confusions

There exists a prevalent conceptual confusion when attempting to distinguish between two forms of uncertainty: explanatory uncertainty, which concerns uncertainty about the validity or superiority of explanatory frameworks themselves, and empirical uncertainty, which deals with uncertainty about specific, observable events or outcomes. Frequently, this confusion results in significant misinterpretations of the role and meaning of credence (subjective probability). Many mistakenly view credence as either explanatory in itself or as evidence of a distinct category of knowledge.

Clarifying the Concept: Timeline Uncertainty

To address and resolve this confusion, we present a precise conceptualization: empirical uncertainty should be recognized explicitly as uncertainty regarding our exact position within the branching structure of objectively real timelines defined by explanatory theories. Instead of representing a distinct type of knowledge, credence is best seen as quantifying our uncertainty about which particular timeline we currently occupy within a comprehensively defined set of possible timelines.

This perspective clarifies that credence does not create new explanatory knowledge. Instead, it is a measurement tool designed to quantify uncertainty about facts already implicitly embedded within explanatory frameworks. Each empirical question—whether historical, predictive, or observational—is effectively reduced to identifying our precise timeline within the broader explanatory structure.

Explanatory Knowledge vs. Timeline Uncertainty

The essential distinction between explanatory knowledge and timeline uncertainty can now be articulated more clearly:

• Explanatory Knowledge: This represents comprehensive knowledge that provides robust explanations for why and how branching occurs at each decision point or quantum event. It fully describes and explains the complete branching structure—the collection of all objectively real timelines arising from fundamental events and conditions.

• Timeline Uncertainty (Empirical Uncertainty): This form of uncertainty specifically pertains to our uncertainty about which particular timeline we inhabit at a given moment. It quantifies our subjective assessment of how likely it is, given all available evidence, that we find ourselves in one timeline rather than another. Such uncertainty may pertain equally well to historical events (uncertainty about past conditions), current observations (uncertainty about presently occurring events), or future predictions (uncertainty about future outcomes).

Bayesian Credence as Timeline Localization

In light of this clarified conceptualization, Bayes' theorem emerges as a uniquely powerful and coherent tool for addressing timeline uncertainty. Bayesian methods naturally align subjective uncertainty (credence) with objective probabilities (Measure), enabling us systematically to update and refine our beliefs regarding our exact location within the branching timeline structure. Bayes' theorem thus does not produce explanatory knowledge itself but serves an indispensable pragmatic function—helping localize our uncertainty and thereby improving our decision-making and predictive capacities.

This function clearly positions Bayesian credence as complementary rather than competitive with explanatory knowledge. The Bayesian approach provides a rigorous, coherent, and mathematically precise method for aligning subjective probability assessments with objective reality.

Implications

This reframed perspective on empirical uncertainty offers significant philosophical and practical advantages:

• Philosophical Clarity: It effectively resolves longstanding confusions about the relationship between subjective and objective probabilities, clarifying that subjective probability (credence) quantifies uncertainty about our timeline identity rather than providing explanatory power itself.

• Decision Theory: It greatly enhances conceptual clarity in decision-making contexts, particularly under conditions of uncertainty, by precisely identifying the role and utility of credence. Decisions can now be systematically based on rigorous updates regarding our timeline localization.

• Quantum Foundations: It contributes substantially to the foundations of quantum mechanics by offering an explicit and coherent interpretation of quantum probabilities. Observer uncertainty in quantum measurements becomes clearly interpretable as timeline uncertainty, strengthening the explanatory power and coherence of the QBU framework.

Conclusion

We have provided clarity on a critical conceptual distinction: empirical uncertainty—credence—is fundamentally and precisely timeline uncertainty within an explanatory branching structure. This refined framing provides substantial philosophical and practical clarity, creating a robust foundation for future investigations in epistemology, decision theory, quantum foundations, and beyond. It decisively illustrates the complementary roles of explanatory knowledge (explaining the structure and existence of multiple timelines) and Bayesian credence (quantifying our uncertainty about precisely which timeline we occupy).

Bottom Line: Hall and Deutsch are correct in criticizing Bayesian scientists who mistakenly attach credences directly to explanatory scientific theories. However, they are mistaken to dismiss the practical utility—and indeed the necessity—of employing credences to quantify our uncertainty about precisely which timeline we inhabit within an objectively defined branching structure.