You’re right that I didn’t clearly describe probability, though; I needed to make it clear that in the denominator you must count everything, however you group it.
Yes; to count everything that can occur when you flip an actual, physical coin, you must first invent the universe. It could also be swallowed by a passing bird, which then blunders into a metal foundry and is built into a new space probe, never landing at all. As a human, you just happen to count a huge number of outcomes together under “heads,” a huge number of outcomes together under “tails,” and a somewhat smaller number of outcomes together under “edge.”
Yes; to count everything that can occur when you flip an actual, physical coin, you must first invent the universe.
In fact, it may be more than merely our universe. The probability assignment actually incorporates doubt about what the precise details of the physics of our universe are. So you may need to invent Kolmogorov complexity and Tegmark’s Ultimate Ensemble before you get to the serious counting.
The problem is that “everything” contains infinitely many possibilities, so putting the number of possibilities in the denominator to calculate the probability doesn’t work.
I’m confused about your assumption.
You’re right that I didn’t clearly describe probability, though; I needed to make it clear that in the denominator you must count everything, however you group it.
When I flip a coin, it can land on heads, tails, or edge; however, the probability that it lands on edge is not 1⁄3.
Yes; to count everything that can occur when you flip an actual, physical coin, you must first invent the universe. It could also be swallowed by a passing bird, which then blunders into a metal foundry and is built into a new space probe, never landing at all. As a human, you just happen to count a huge number of outcomes together under “heads,” a huge number of outcomes together under “tails,” and a somewhat smaller number of outcomes together under “edge.”
In fact, it may be more than merely our universe. The probability assignment actually incorporates doubt about what the precise details of the physics of our universe are. So you may need to invent Kolmogorov complexity and Tegmark’s Ultimate Ensemble before you get to the serious counting.
Even that isn’t enough since it doesn’t incorporate our uncertainty about mathematics.
When I flip a coin, I count some outcomes under “heads”, some outcomes under “tails”, and everything else I ignore and demand we flip the coin again.
The problem is that “everything” contains infinitely many possibilities, so putting the number of possibilities in the denominator to calculate the probability doesn’t work.