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
Only tenuously relevant, but fun to think of in conjunction:
http://www.businessinsider.com/what-is-blue-and-how-do-we-see-color-2015-2