system
Given the following post, respond as if you're commenting on Reddit:
human
Help a Bayesian understand the Gettier problem

Recently, I discovered that the Gettier problem was taken seriously in epistemology with many responses and I was honestly very surprised. As I understand the Gettier problem, it offers a supposed counterexample to the justified true belief (JTF) theory of knowledge. Specifically, it involves cases where a person makes an inference from a false premise but the inference happens to be True anyway. In this way, the inference is both justified (the person used valid reasoning) and True but does not constitute knowledge because it requires using unsound reasoning because it requires using a False premise.

But it seems to me if you accept Bayesian reasoning, the problem disappears. A Bayesian says that "knowledge" is just your information that allows you to make good inferences.

The Gettier problem analyzed in Bayesian terms looks like this:

1. A person has some information that lets them predict premise 1 (P1) with 80% probability. (Jones has 10 coins in his pocket with 80% probability).

2. The person has some other information that lets them predict premise 2 (P2) with 80% probability. (Jones will get the job. 80% probability).

3. The person then reasons that the person who got the job will have 10 coins in their pocket. The probability of this is at least 64 % (this it the probability that Jones will get the job and have 10 coins in his pocket). Using additional information, he may be able to increase this confidence.

In this (and every) case where the reasoner applies Bayesian inference techniques correctly, there will never be an unintuitive violation of JTB.

Bayesianism Epistemology has other weaknesses but I don't see how this isn't an obvious and straightforward objection to all Gettier problems.
gpt
Most Bayesians (myself included) reject the following:

> **Weak Lockean thesis for belief:** There is some credence threshold t < 1 s.t. for all agents A and propositions p, if c_A(p) > t then A believes p.

This is a problem for any straightforward credal analysis of knowledge, since knowledge (on almost all views) requires belief, and lack of belief is compatible with arbitrarily high credence (<1). 

Here are some other proposed conditions on knowledge that you might think a simple credal analysis won't track:

> **Sensitivity:** If p were false, then A would not believe p.  
> **Safety:** If A were to believe that p, then p would not be false.  
> **No false lemmas:** S's belief that p is not inferred from any false premises.