ksagan

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Right for the Wrong Reasons

I've been posting this around a lot lately (including on "Gettier in Zombie World"), still looking for a solid response.

I think Bayesian probability actually resolves Gettier problems, completely and (ironically, because Bayesian probability doesn't concern itself with this in the slightest) satisfyingly. Understanding that we only know likelihoods, not facts, is enough.

Situation: I know John had 10 coins in his pocket. I think he got the job. I don't know that Smith had 10 coins in his pocket. Do I "know" that the person who got the job had 10 coins in their pocket?

Classic Gettier Interpretation:

  • Belief-Jones had 10 coins in his pocket
  • Belief-Jones got the job
    • Conclusion-The person who got the job had 10 coins in their pocket

Bayesian Gettier Interpretation(Example numbers used for ease of intuition; minimal significant digits used for ease of calculation):

  • Belief-It's likely (90%) John got the job
  • Belief-It's likely (90%) John had 10 coins in his pocket
    • Conclusion-It's likely (81%) John got the job with 10 coins in his pocket

...and...

  • Belief-It's unlikely (10%) someone other than John got the job
  • Belief-It's possible (50%) a given person had 10 coins in their pocket
    • Conclusion-It's unlikely (5%) that someone other than John got the job with 10 coins in their pocket

...thus...

  • Belief-It's likely (81%) John got the job with 10 coins in his pocket
  • Belief-It's unlikely (5%) that someone other than John got the job with 10 coins in their pocket
    • Conclusion-It's likely (86%) that someone got the job with 10 coins in their pocket
Gettier in Zombie World

I tried, I really tried, to puzzle out what you're saying here, but at this rate, it'll be a lot quicker if someone else just confirms or denies this for me: This is what I came up with, upon reading the Wiki article on Gettier. Is this basically what you're saying?

Situation: I got the job. I believe Jones got the job. I know Jones has 10 coins in his pocket. I have 10 coins in my pocket, but I don't know that. Do I "know" the person who got the job has 10 coins in their pocket?

Classic Gettier Interpretation:

  • Belief-Jones got the job
  • Belief-Jones has 10 coins in his pocket
    • Conclusion-The guy who got the job has 10 coins in his pocket

Bayesian Gettier Interpretation(Example numbers used for ease of intuition; minimal significant digits used for ease of calculation):

  • Belief-Jones probably (90%) got the job
  • Belief-Jones probably (90%) has 10 coins in his pocket
    • Conclusion- The person who got the job probably (81%) has 10 coins in his pocket
  • Belief-Jones might not have gotten the job (10%)
  • Belief-People sometimes have 10 coins in their pocket (50%)
    • Conclusion-Someone other than Jones with 10 coins in their pocket might have gotten the job (5%)
  • Belief-The person who got the job probably (81%) has 10 coins in his pocket
  • Belief-Someone other than Jones with 10 coins in their pocket might have gotten the job (5%)
    • Conclusion-The person who got the job probably (86%) has 10 coins in his pocket

In case it were unclear, I consider the answer to the initial question "Yes".