Direct Inference and Probabilistic Accounts of Induction

Area of Science:

• Philosophy of Science
• Epistemology
• Logic

Background:

• Probabilistic accounts of induction are criticized for failing to adequately explain inductive reasoning.
• Schurz (2019) specifically critiques Bayesian approaches (subjective and objective) that rely on direct inference principles.
• Existing direct inference principles, such as Reichenbach's and Lewis's, face challenges within standard probabilistic frameworks.

Purpose of the Study:

• To evaluate the viability of standard probabilistic approaches to induction, particularly their use of direct inference.
• To demonstrate the limitations of Reichenbach's Principle of the Narrowest Reference Class and Lewis's Principal Principle in standard probabilistic settings.
• To propose and defend a non-standard objective Bayesian account of induction that accommodates direct inference.

Main Methods:

• Critical analysis of Schurz's arguments against probabilistic accounts of induction.
• Examination of the compatibility of direct inference principles (Reichenbach's and Lewis's) with standard probabilism.
• Development and defense of a non-standard objective Bayesian framework for induction.

Main Results:

• Standard probabilistic approaches, relying on direct inference, are shown to be inadequate for explicating the logic of induction.
• Both Reichenbach's Principle of the Narrowest Reference Class and Lewis's Principal Principle present significant difficulties in standard probabilistic models.
• A non-standard objective Bayesian account of induction is presented as a successful alternative, capable of incorporating direct inference.

Conclusions:

• Direct inference principles face significant challenges within standard probabilistic frameworks for induction.
• A non-standard objective Bayesian approach offers a promising and viable alternative for understanding the logic of induction.
• The proposed non-standard account successfully addresses criticisms leveled against probabilistic theories of induction.