There are 2 unfair coins. One has P(heads)=1/3 and the other P(heads)=2/3. I take one of them, flip twice and it turns heads twice.
Now I believe that the coin chosen was the one with P(heads)=2/3. In fact there are 4⁄5 likelihood of being so. I also believe that flipping again will turn heads again, mostly because I think that I choose the 2⁄3 heads coin (p=8/15). I also admit the possibility of getting heads but being wrong about the chosen coin, but this is much less likely (p=1/15). So I bet on heads.
So I flip it again and it turns heads. I was right. But it turns out that the coin was the other one, the one with P(heads)=1/3 (which I found after a few hundreds flips).
Would you say I was right for the wrong reasons? Well I was certainly surprised to find out I had the wrong coin. Does this apply for the Gettier problem?
Lets go back to the original problem to see that this abstraction is similar. Smith believes “the person who will get the job has ten coins in his pocket”. And he does that mostly because he thinks Jones will get it and has ten coins. But if he is reasonable, he will also admit the possibility of he getting the job and also having ten coins, although with lower probability.
My point here is: at which probability the Gettier problem arises? Would it arises if in the coin problem P(heads) was different?
I think it arises at the point where you did not even consider the alternative. This is a very subjective thing, of course.
If the probability of the actual outcome was really negligible (with a perfect evaluation by the prediction-maker), this should not influence the evaluation of predictions in a significant way. If the probability was significant, it is likely that the prediction-maker considered it. If not, count it as false.
Lets abstract about this:
There are 2 unfair coins. One has P(heads)=1/3 and the other P(heads)=2/3. I take one of them, flip twice and it turns heads twice. Now I believe that the coin chosen was the one with P(heads)=2/3. In fact there are 4⁄5 likelihood of being so. I also believe that flipping again will turn heads again, mostly because I think that I choose the 2⁄3 heads coin (p=8/15). I also admit the possibility of getting heads but being wrong about the chosen coin, but this is much less likely (p=1/15). So I bet on heads. So I flip it again and it turns heads. I was right. But it turns out that the coin was the other one, the one with P(heads)=1/3 (which I found after a few hundreds flips). Would you say I was right for the wrong reasons? Well I was certainly surprised to find out I had the wrong coin. Does this apply for the Gettier problem?
Lets go back to the original problem to see that this abstraction is similar. Smith believes “the person who will get the job has ten coins in his pocket”. And he does that mostly because he thinks Jones will get it and has ten coins. But if he is reasonable, he will also admit the possibility of he getting the job and also having ten coins, although with lower probability.
My point here is: at which probability the Gettier problem arises? Would it arises if in the coin problem P(heads) was different?
I think it arises at the point where you did not even consider the alternative. This is a very subjective thing, of course.
If the probability of the actual outcome was really negligible (with a perfect evaluation by the prediction-maker), this should not influence the evaluation of predictions in a significant way. If the probability was significant, it is likely that the prediction-maker considered it. If not, count it as false.