What do you mean by “|A”? It’s well-defined in mathematics, sure, but in real life, surely the furthest you can go is “|experience/perception of evidence for A”.
Also, there’s also the probability that the particular version of logic you’re using is wrong.
What do you mean by “|A”? It’s well-defined in mathematics, sure, but in real life, surely the furthest you can go is “|experience/perception of evidence for A”.
How far you can go depends on what you mean by “go”.
It’s perfectly possible to calculate, say, P(I see the coin come up heads | the coin is flipped once, it is fair, and I see the outcome), and actually much more difficult to calculate P(I see the coin come up heads | I have experience/perception of evidence for the facts that the coin is flipped once, it is fair, and I see the outcome).
“I see” is what I meant by perception/experience of evidence. Whenever I “see” something, there’s always a non-zero chance of my brain deceiving me. The only thing you can really have to base your decisions on is P(I see the coin come up heads | I see/know the coin is flipped once, I know it is fair, and I see the outcome). P(the coin comes up heads|the coin is flipped once, it is fair and I know the outcome) is possible and easy to calculate, but not completely accurate to the world we live in.
What is P(A|A)?
What do you mean by “|A”? It’s well-defined in mathematics, sure, but in real life, surely the furthest you can go is “|experience/perception of evidence for A”.
Also, there’s also the probability that the particular version of logic you’re using is wrong.
How far you can go depends on what you mean by “go”.
It’s perfectly possible to calculate, say, P(I see the coin come up heads | the coin is flipped once, it is fair, and I see the outcome), and actually much more difficult to calculate P(I see the coin come up heads | I have experience/perception of evidence for the facts that the coin is flipped once, it is fair, and I see the outcome).
“I see” is what I meant by perception/experience of evidence. Whenever I “see” something, there’s always a non-zero chance of my brain deceiving me. The only thing you can really have to base your decisions on is P(I see the coin come up heads | I see/know the coin is flipped once, I know it is fair, and I see the outcome). P(the coin comes up heads|the coin is flipped once, it is fair and I know the outcome) is possible and easy to calculate, but not completely accurate to the world we live in.