First it means that we cannot ever conclusively prove whether the universe is deterministic (a la Laplace’s Demon) or random. We can still make some strong probabilistic arguments, but a full proof becomes impossible.
0 and 1 are not reachable probabilities. We can’t “conclusively prove” anything. Even with a mathematical proof, there is some chance that there is a really subtle flaw that you didn’t notice, or someone is messing with your mind, or maths is inconsistent.
Is there any difference between a universe with random coins, and one that splits into two parallel worlds, one with heads, the other tails, whenever the coin is tossed. Mathematically, randomness is defined as a measure function over possibilities.
They are not reachable epistemically. The universe could still be deterministic, meaning that everything that happens has probability 1.000. That would be ontological probability, a feature of reality itself, and not provable by armchair argument. The distinction between ontological and epistemic probability has many advantages.
0 and 1 are not reachable probabilities. We can’t “conclusively prove” anything. Even with a mathematical proof, there is some chance that there is a really subtle flaw that you didn’t notice, or someone is messing with your mind, or maths is inconsistent.
Is there any difference between a universe with random coins, and one that splits into two parallel worlds, one with heads, the other tails, whenever the coin is tossed. Mathematically, randomness is defined as a measure function over possibilities.
They are not reachable epistemically. The universe could still be deterministic, meaning that everything that happens has probability 1.000. That would be ontological probability, a feature of reality itself, and not provable by armchair argument. The distinction between ontological and epistemic probability has many advantages.