Theories are either true or false. The word “tentative” is there as an expression of fallibility. We cannot know if a theory is in fact true: it may contain problems that we do not yet know about. All knowledge is tentative. The word is not intended as a synonym for probability or to convey anything about probabilities.
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.
It is true that knowledge is fallible—but some knowledge is more fallible than others—and if you can’t measure degrees of uncertainty, you will never develop a quantitative treatment of the subject. Philosophers of science realised this long ago—and developed a useful framework for quantifying uncertainty.
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.
There are no degrees of fallibility. We are simply fallible: that’s it. You have no way of knowing if a currently unproblematic theory is wrong, no matter how obvious the theory may seem, it may end up being spectacularly wrong.
I agree that we can quantity the uncertainty of events and that this is useful.
But theories are a different kettle of fish. Popperian epistemology tells us that we don’t need to know anything about the uncertainty of theories for knowledge to grow. Hence, one does not need to quantify the uncertainty of theories in order to write a knowledge creating computer program.
The thing is, we have a beautiful theory of uncertainty that deals with uncertainty over events, uncertainty about hypotheses—uncertainty about all beliefs, in fact—and it works just great.
Sure, we could go back to the dark days before Bayes, and struggle on with a boolean conception of certainty, and it probably wouldn’t be so bad that it would actually prevent knowledge from accumulating...
...but what possible reason would motivate us to take such a retrograde step?
I mean: how do you model equiprobable competing theories in such a framework.
How do you model induction? How do you model confirmation?
The answer seems to be that you don’t—you just deny the very existence of these phenomena!
I hope you can see how that is not a step forwards, from our point of view.
The thing is, we have a beautiful theory of uncertainty that deals with uncertainty over events, uncertainty about hypotheses—uncertainty about all beliefs, in fact—and it works just great.
Really? No exaggeration?
Sure, we could go back to the dark days before Bayes, and struggle on with a
boolean conception of certainty, and it probably wouldn’t be so bad that it would
acutually prevent knowledge from growing...
Popperian epistemology was created in the 20th century, after Bayes, so what do you mean by dark days. Certainty is not the lynchpin of knowledge creation and in fact has nothing to do with it. You completely devalue the role of explanations and criticisms. Who cares about probability when you have a good explanation that has withstood criticism?
...but what possible reason would motivate us to take such a retrograde step?
Popperian philosophy is about problem-solving, explanation and criticism and these things are not in any way retrograde. Bayesian epistemology is rooted in the
old philosophy of justificationism, a philosophy that Popperian epistemology overturned.
I mean: how do you model equiprobable competing theories in such a framework.
What you do is attempt further criticism of these theories and if that doesn’t progress come up with a meta-theory of what to do giving that you have two good candidate theories. It is always possible to come up with such a meta-theory.
How do you model induction? How do you model confirmation?
The answer seems to be that you don’t—you just deny the very existence of these
phenomena!
Popper and others have given explanations—they don’t just deny without reason. Are you familiar with their arguments? There are real problems with the very concepts of induction and confirmation, problems that you seem not to have appreciated.
I hope you can see how that is not a step forwards, from our point of view.
Popper showed that knowledge grows perfectly fine without concepts of uncertainty, induction, and confirmation. Yes, it is counter-intuitive—that is why most people do not get Popper.
Popper and others have given explanations—they don’t just deny without reason. Are you familiar with their arguments? There are real problems with the very concepts of induction and confirmation, problems that you seem not to have appreciated.
Maybe you should present them, rather than playing ‘I can assert my philosopher is great more than you can’.
The author of that link thinks Popper is falsification. I have already explained why that view of Popper is wrong. Have you been paying attention? And does the author of the link realize that the leading exponent of the multiverse is David Deutsch, who also happens to be the best living Popperian?
“Popper’s great and tireless efforts to expunge the word induction from scientific and philosophical discourse has utterly failed. Except for a small but noisy group of British Popperians, induction is just too firmly embedded in the way philosophers of science and even ordinary people talk and think.
Confirming instances underlie our beliefs that the Sun will rise tomorrow, that dropped objects will fall, that water will freeze and boil, and a million other events. It is hard to think of another philosophical battle so decisively lost.”—M.Gardner.
Gardner can be taken as seriously on Popper as he can on the MWI, i.e, not at all.
BTW, the sun does not rise in Murmansk in the middle of winter, live flies that are dropped do not fall, and water can be prevented from freezing in my car radiator by adding anti-freeze.
Carnap had a major influence on me. He persuaded me that all metaphysical questions are “meaningless” in the sense that they cannot be answered empirically or by reason. They can be defended only on emotive grounds. Carnap was an atheist, but I managed to retain my youthful theism in the form of what is called “fideism.” I like to call it “theological positivism,” a play on Carnap’s “logical positivism.
As far as we can tell, universes are not as plentiful as even two blackberries. Surely the conjecture that there is just one universe and its Creator is infinitely simpler and easier to believe than that there are countless billions upon billions of worlds, constantly increasing in number and created by nobody. I can only marvel at the low state to which today’s philosophy of science has fallen
So why the downvote? Gardner doesn’t understand quantum physics and he doesn’t understand epistemology.
Theories are either true or false. The word “tentative” is there as an expression of fallibility. We cannot know if a theory is in fact true: it may contain problems that we do not yet know about. All knowledge is tentative. The word is not intended as a synonym for probability or to convey anything about probabilities.
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.
It is true that knowledge is fallible—but some knowledge is more fallible than others—and if you can’t measure degrees of uncertainty, you will never develop a quantitative treatment of the subject. Philosophers of science realised this long ago—and developed a useful framework for quantifying uncertainty.
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.
There are no degrees of fallibility. We are simply fallible: that’s it. You have no way of knowing if a currently unproblematic theory is wrong, no matter how obvious the theory may seem, it may end up being spectacularly wrong.
I agree that we can quantity the uncertainty of events and that this is useful.
But theories are a different kettle of fish. Popperian epistemology tells us that we don’t need to know anything about the uncertainty of theories for knowledge to grow. Hence, one does not need to quantify the uncertainty of theories in order to write a knowledge creating computer program.
The thing is, we have a beautiful theory of uncertainty that deals with uncertainty over events, uncertainty about hypotheses—uncertainty about all beliefs, in fact—and it works just great.
Sure, we could go back to the dark days before Bayes, and struggle on with a boolean conception of certainty, and it probably wouldn’t be so bad that it would actually prevent knowledge from accumulating...
...but what possible reason would motivate us to take such a retrograde step?
I mean: how do you model equiprobable competing theories in such a framework.
How do you model induction? How do you model confirmation?
The answer seems to be that you don’t—you just deny the very existence of these phenomena!
I hope you can see how that is not a step forwards, from our point of view.
The thing is, we have a beautiful theory of uncertainty that deals with uncertainty over events, uncertainty about hypotheses—uncertainty about all beliefs, in fact—and it works just great.
Really? No exaggeration?
Popperian epistemology was created in the 20th century, after Bayes, so what do you mean by dark days. Certainty is not the lynchpin of knowledge creation and in fact has nothing to do with it. You completely devalue the role of explanations and criticisms. Who cares about probability when you have a good explanation that has withstood criticism?
Popperian philosophy is about problem-solving, explanation and criticism and these things are not in any way retrograde. Bayesian epistemology is rooted in the old philosophy of justificationism, a philosophy that Popperian epistemology overturned.
What you do is attempt further criticism of these theories and if that doesn’t progress come up with a meta-theory of what to do giving that you have two good candidate theories. It is always possible to come up with such a meta-theory.
Popper and others have given explanations—they don’t just deny without reason. Are you familiar with their arguments? There are real problems with the very concepts of induction and confirmation, problems that you seem not to have appreciated.
Popper showed that knowledge grows perfectly fine without concepts of uncertainty, induction, and confirmation. Yes, it is counter-intuitive—that is why most people do not get Popper.
Maybe you should present them, rather than playing ‘I can assert my philosopher is great more than you can’.
Bayesian scientific methods becoming more mainstream is a relatively modern phenomenon. See:
“Do we need to change the definition of science?”
http://postbiota.org/pipermail/tt/2008-May/002997.html
...for a recent overview.
The author of that link thinks Popper is falsification. I have already explained why that view of Popper is wrong. Have you been paying attention? And does the author of the link realize that the leading exponent of the multiverse is David Deutsch, who also happens to be the best living Popperian?
“Popper’s great and tireless efforts to expunge the word induction from scientific and philosophical discourse has utterly failed. Except for a small but noisy group of British Popperians, induction is just too firmly embedded in the way philosophers of science and even ordinary people talk and think.
Confirming instances underlie our beliefs that the Sun will rise tomorrow, that dropped objects will fall, that water will freeze and boil, and a million other events. It is hard to think of another philosophical battle so decisively lost.”—M.Gardner.
http://www.stephenjaygould.org/ctrl/gardner_popper.html
Gardner can be taken as seriously on Popper as he can on the MWI, i.e, not at all.
BTW, the sun does not rise in Murmansk in the middle of winter, live flies that are dropped do not fall, and water can be prevented from freezing in my car radiator by adding anti-freeze.
Edit: Here are some quotes from Gardner:
http://www.csicop.org/si/show/mind_at_play_an_interview_with_martin_gardner/
Carnap had a major influence on me. He persuaded me that all metaphysical questions are “meaningless” in the sense that they cannot be answered empirically or by reason. They can be defended only on emotive grounds. Carnap was an atheist, but I managed to retain my youthful theism in the form of what is called “fideism.” I like to call it “theological positivism,” a play on Carnap’s “logical positivism.
http://www.csicop.org/si/show/multiverses_and_blackberries/
As far as we can tell, universes are not as plentiful as even two blackberries. Surely the conjecture that there is just one universe and its Creator is infinitely simpler and easier to believe than that there are countless billions upon billions of worlds, constantly increasing in number and created by nobody. I can only marvel at the low state to which today’s philosophy of science has fallen
So why the downvote? Gardner doesn’t understand quantum physics and he doesn’t understand epistemology.