You misunderstand me—I maintain that an obvious unstated condition in the announcement is that there will be a test next week. Under this condition, the student will be surprised by a Wednesday test but not a Friday test, and therefore
p(teacher provides a surprise test) = 1 - x^2
and, if I guess your algorithm correctly,
p(teacher provides a surprise lack of test) = x^2 * (1 - x)
I maintain that an obvious unstated condition in the announcement is that there will be a test next week.
The condition is that there will be a surprise test. If the teacher were to split ‘surprise test’ into two and consider max(p(surprise | p(test) == 100)) then yes, he would find he is somewhat less likely to be making a correct claim.
You misunderstand me
I maintain my previous statement (and math):
The answer to the question ‘Can the teacher fulfill his announcement?’ is ‘Probably’. The answer to the question ‘Is there a 100% chance that the teacher fulfills his announcement?’ is ‘No’.
Something that irritates me with regards to philosophy as it is often practiced is that there is an emphasis on maintaining awe at how deep and counterintuitive a question is rather than extract possible understanding from it, disolve the confusion and move on.
Yes, this question demonstrates how absolute certainty in one thing can preclude uncertainty in some others. Wow. It also demonstrates that one can make self defeating prophecies. Kinda-interesting. But don’t let that stop you from giving the best answer to the question. Given that the teacher has made the prediction and given that he is trying to fulfill his announcement there is a distinct probability that he will be successful. Quit saying ‘wow’, do the math and choose which odds you’ll bet on!
The answer to the question ‘Can the teacher fulfill his announcement?’ is ‘Probably’. The answer to the question ‘Is there a 100% chance that the teacher fulfills his announcement?’ is ‘No’.
You misunderstand me—I maintain that an obvious unstated condition in the announcement is that there will be a test next week. Under this condition, the student will be surprised by a Wednesday test but not a Friday test, and therefore
and, if I guess your algorithm correctly,
[edit: algebra corrected]
The condition is that there will be a surprise test. If the teacher were to split ‘surprise test’ into two and consider max(p(surprise | p(test) == 100)) then yes, he would find he is somewhat less likely to be making a correct claim.
I maintain my previous statement (and math):
Something that irritates me with regards to philosophy as it is often practiced is that there is an emphasis on maintaining awe at how deep and counterintuitive a question is rather than extract possible understanding from it, disolve the confusion and move on.
Yes, this question demonstrates how absolute certainty in one thing can preclude uncertainty in some others. Wow. It also demonstrates that one can make self defeating prophecies. Kinda-interesting. But don’t let that stop you from giving the best answer to the question. Given that the teacher has made the prediction and given that he is trying to fulfill his announcement there is a distinct probability that he will be successful. Quit saying ‘wow’, do the math and choose which odds you’ll bet on!
I never intended to dispute that
only the specific figure 87.5%.
It’s a minor point. Your logic is good.