Faculty Presentation: Hanti Lin
Date & Time
Feb 03, 2017
from
03:10 PM to
06:00 PM
Description
The Cartesian Problem of Induction
The problem of induction is typically discussed with a focus on the skeptical scenarios in which not all ravens are black and an inquirer has hitherto observed many ravens without seeing a counterexample. But there are much worse scenarios, in which not all ravens are black and the inquirer never observes a counterexample throughout her entire life, however long her life might be, as if a Cartesian-like evil demon were always hiding non-black ravens from her. I argue that such Cartesian-like scenarios cause some new and ironic trouble for Bayesian epistemology and learning theory---the two most influential foundations of induction among practicing scientists and, hence, among formal epistemologists. To be more specific, due to such Cartesian-like scenarios, every account of enumerative induction developed so far in Bayesian epistemology or learning theory, if not rendered silent about the issue, turns out to provide reason for siding with the inductive skeptic---for denying that an inquirer who wants to know whether all ravens are black ought to infer inductively at least on some possible occasions in her inquiry. Other accounts of induction (such as Hume's and Popper's) are not helpful either. Call this the Cartesian problem of induction. To solve this problem, I explain how enumerative induction is, in a sense, reliable, and I do so without begging the question---without assuming that the inquirer, or anyone among us, does not live in such a Cartesian-like scenario. The sense of reliability I put to work is obtained by refining a suggestion from Reichenbach and Putnam, called convergence to the truth. In the context of the existing literature, my solution amounts to an improved version of formal learning theory and does Bayesians a favor by giving a partial solution to the problem of the priors.
In this presentation, formal tools (such as partial orders and probabilities) will be used only in a pictorial, accessible way. Rigorous mathematics is left to the paper enclosed.
