The problem I have in accepting the concept of synthetic, a priori knowledge is in explaining where it comes from. I can understand that it might be in our genes to acquire such knowledge in early childhood, but our genes are presumably the way they are because that kind of knowledge contributed to the survival of our ancestors.
It comes from grasping abstract objects. E.g., understanding what green is and what red is leads to the knowledge that nothing is completely red and completely green. Understanding what 'lines' are and what 'distance' is leads to the understanding that the shortest path between a pair of points will be a straight line. Etc.
Thanks. I just checked whether there is evidence that people who are born blind can understand the concept of colour. Apparently they can reason about colour without ever having seen it.
I thought all Bayesian accepted that prior probabilities were not determined by Bayes' rule. If thinking you can have any prior is subjectivist Bayesianism, what are the alternatives (presumably objectivist Bayianism)?
Right. "Objective Bayesians" introduce principles that go beyond the Kolmogorov axioms, to constrain prior probabilities. The most popular such principle is probably the Principle of Indifference, whereby if there is no reason to favor a possibility A1 over A2 or vice versa, then the initial P(A1) = P(A2).
This will give me something to ponder about for a good while. Thanks.
The problem I have in accepting the concept of synthetic, a priori knowledge is in explaining where it comes from. I can understand that it might be in our genes to acquire such knowledge in early childhood, but our genes are presumably the way they are because that kind of knowledge contributed to the survival of our ancestors.
It comes from grasping abstract objects. E.g., understanding what green is and what red is leads to the knowledge that nothing is completely red and completely green. Understanding what 'lines' are and what 'distance' is leads to the understanding that the shortest path between a pair of points will be a straight line. Etc.
Thanks. I just checked whether there is evidence that people who are born blind can understand the concept of colour. Apparently they can reason about colour without ever having seen it.
They may be reasoning based on what other people told them.
I expect that is correct. So, could it be argued that they acquire the concept of colour via their hearing senses?
I thought all Bayesian accepted that prior probabilities were not determined by Bayes' rule. If thinking you can have any prior is subjectivist Bayesianism, what are the alternatives (presumably objectivist Bayianism)?
Right. "Objective Bayesians" introduce principles that go beyond the Kolmogorov axioms, to constrain prior probabilities. The most popular such principle is probably the Principle of Indifference, whereby if there is no reason to favor a possibility A1 over A2 or vice versa, then the initial P(A1) = P(A2).
As I explain elsewhere, this approach can be used to solve the problem of induction. (https://fakenous.substack.com/p/explanationist-aid-for-the-theory)
The trick seems to be defining what is “rational” for priori probabilities.