Key Arguments

Central Problem: How can credence obey probability laws when there’s no underlying objective probability (especially for logical/mathematical statements)?

Solution: Logical Induction

Introduced by Garrabrant, Benson-Tilsen, Critch, Soares, Taylor (2016).

What It Does:

  • Rigorously formalizes epistemic uncertainty about logical/mathematical statements
  • Assigns probabilistic credences to logical propositions
  • Ensures rational coherence and consistency
  • Generates sequence of credences that become more accurate as evidence accumulates
  • Crucially: Satisfies probability axioms despite no empirical probability

How It Works (Market Analogy):

  • Logical uncertainty = “market”
  • “Traders” = algorithmic strategies/computational heuristics
  • Traders “bet” on logical statements (true/false)
  • As new information emerges (proofs, computations, heuristics), traders update
  • Market credences gradually converge toward accurate beliefs
  • Analogy ensures internal coherence, rational updating

Resolution of Philosophical Tension:

  • Credences must obey probability laws (rational consistency)
  • But logical credences are epistemic, not empirically objective
  • Logical Induction shows how probabilistic consistency maintained without objective probabilities

Result: Rigorous embrace of epistemic probabilities—can assign rational, probabilistic credences even without empirical probabilities

Connection to Framework

Defending Bayes Sequence:

  • Part 5 (Batch 2): Empirical vs logical credence distinction
  • Part 6 (this post): Formal tool for logical credences
  • Part 7 (this batch): Application to theories

Epistemological Foundations:

  • Distinguishes Measure (objective QBU probability) from Credence (subjective epistemic)
  • Logical Induction provides formal basis for credences in non-empirical domains
  • Resolves how credences can be rational without corresponding to physical probabilities

AI Safety Connection:

  • Paper from MIRI (Machine Intelligence Research Institute)
  • Relevant to AI reasoning about logical uncertainty
  • Connects framework to AI alignment community

Evolution Tracking

New Technical Tool:

  • First appearance of Logical Induction in archive
  • Provides formal underpinning for credence theory
  • Borrowed from AI safety research, applied to philosophy

Methodological: Uses technical result from computer science to resolve philosophical problem

Integration: Logical Induction becomes load-bearing concept for defending Bayesianism against Deutsch/Hall critique

Cross-References

Notes

Significance: Imports technical result from AI research to solve philosophical problem. Cross-disciplinary synthesis.

Accessibility: Uses market analogy to explain complex formal concept. Generally readable despite technical content.

AI Safety Bridge: Connects Axio framework to AI alignment community’s work. Suggests shared intellectual ecosystem.

Formal Rigor: Cites actual research paper, engages with technical literature (not just philosophy).