Observers can put probabilities on the truth of theories. They can do it—and will do it—if you ask them to set odds and prepare to receive bets. Quantifying uncertainty allows it to be measured and processed.
Scurfield missed his chance here. He should have asked when it becomes the case that those bets must be paid off, and offered the services of a Popper adept to make that kind of decision. Of course, the Popperite doesn’t rule that one theory is true, he rules that the other theory is refuted.
Short time limits don’t mean that agents can’t meaningfully assign probabilities to the truth of scientific theories—they just decrease the chances of the theories being proven wrong within the time limit a bit.
What is a time limit? Do actual bets on this sort of thing in Britain stipulate a time limit? As a Yank, I have no idea how betting ‘markets’ like this like this actually work.
Prediction markets/betting markets like Intrade or Betfair pretty universally set time limits on their bets. (Browse through Intrade sometime.) This does sometimes require changing the bet/prediction though—from ‘the Higgs boson will be found’ to ‘the Higgs boson will be found by 2020’. Not that this is a bad thing, mind you.
Not really. To the extent that we limit attention to theories of the form:
Always(Everywhere(Forall x (P(x)) ) )
we Bayesians can never “cash in” on a bet that the theory is true—at least not using empirical evidence. All we can do is to continue trying to falsify the theory by experiments at more times, at more places, and for more values of x. As Popper prescribes. Our probabilities that the theory is true grow higher and higher, but they grow more and more slowly, and they can never reach unity.
However, both Bayesians and Popper fans can become pretty certain that such a theory is false—even without checking everywhere, everywhen, and forall x. Popper does not have a monopoly on refutations. Or conjectures either, for that matter.
Scurfield missed his chance here. He should have asked when it becomes the case that those bets must be paid off, and offered the services of a Popper adept to make that kind of decision. Of course, the Popperite doesn’t rule that one theory is true, he rules that the other theory is refuted.
Short time limits don’t mean that agents can’t meaningfully assign probabilities to the truth of scientific theories—they just decrease the chances of the theories being proven wrong within the time limit a bit.
What is a time limit? Do actual bets on this sort of thing in Britain stipulate a time limit? As a Yank, I have no idea how betting ‘markets’ like this like this actually work.
Prediction markets/betting markets like Intrade or Betfair pretty universally set time limits on their bets. (Browse through Intrade sometime.) This does sometimes require changing the bet/prediction though—from ‘the Higgs boson will be found’ to ‘the Higgs boson will be found by 2020’. Not that this is a bad thing, mind you.
Do you have an answer to that point-that-should-have-been?
Not really. To the extent that we limit attention to theories of the form:
we Bayesians can never “cash in” on a bet that the theory is true—at least not using empirical evidence. All we can do is to continue trying to falsify the theory by experiments at more times, at more places, and for more values of x. As Popper prescribes. Our probabilities that the theory is true grow higher and higher, but they grow more and more slowly, and they can never reach unity.
However, both Bayesians and Popper fans can become pretty certain that such a theory is false—even without checking everywhere, everywhen, and forall x. Popper does not have a monopoly on refutations. Or conjectures either, for that matter.