There’s probably a misunderstanding. I’m sorry I haven’t explained it more clear.
I meant that even if it’s just “a different set of assumptions” (from the mathematical point of view), it still may count as a different type of thinking if:
Your assumptions are different from the usual ones often enough.
You describe the world differently.
Your reasoning method is based on seeking different kinds of patterns in the world. You believe that such patterns are more informative.
This should count as a different epistemology. This is what I meant by “context”: it’s not about any particular example, it’s about the epistemology.
But maybe this difference in epistemology does lead to a difference in math eventually.
This updates you toward there being less marble collections greater than 1⁄100n, because your estimate for the mean collection size has risen. Had you drawn two collections of size ~1/90 n, this would have updated you towards a higher estimate for the number of collections larger than the first.
This seems accurate: a little bit of smartness increases the probability, a lot of smartness decreases the probability.
There’s probably a misunderstanding. I’m sorry I haven’t explained it more clear.
I meant that even if it’s just “a different set of assumptions” (from the mathematical point of view), it still may count as a different type of thinking if:
Your assumptions are different from the usual ones often enough.
You describe the world differently.
Your reasoning method is based on seeking different kinds of patterns in the world. You believe that such patterns are more informative.
This should count as a different epistemology. This is what I meant by “context”: it’s not about any particular example, it’s about the epistemology.
But maybe this difference in epistemology does lead to a difference in math eventually.
This seems accurate: a little bit of smartness increases the probability, a lot of smartness decreases the probability.