I am not arguing that it is not an empty set. Consider it akin to the intersection of the set of natural numbers, and the set of infinities; the fact that it is the empty set is meaningful. It means that by following the rules of simple, additive arithmetic, one cannot reach infinity, and if one does reach infinity, that is a good sign of an error somewhere in the calculation.
Similarly, one should not be absolutely certain if they are updating from finite evidence. Barring omniscience (infinite evidence), one cannot become absolutely/infinitely certain.
What definition of absolute certainty would you propose?
So you are proposing a definition that nothing can satisfy. That doesn’t seem like a useful activity. If you want to say that no belief can stand up to the powers of imagination, sure, I’ll agree with you. However if we want to talk about what people call “absolute certainty” it would be nice to have some agreed-on terms to use in discussing it. Saying “oh, there just ain’t no such animal” doesn’t lead anywhere.
As to what I propose, I believe that definitions serve a purpose and the same thing can be defined differently in different contexts. You want a definition of “absolute certainty” for which purpose and in which context?
You are correct, I have contradicted myself. I failed to mention the possibility of people who are not reasoning perfectly, and in fact are not close, to the point where they can mistakenly arrive at absolute certainty. I am not arguing that their certainty is fake—it is a mental state, after all—but rather that it cannot be reached using proper rational thought.
What you have pointed out to me is that absolute certainty is not, in fact, a useful thing. It is the result of a mistake in the reasoning process. An inept mathematician can add together a large but finite series of natural numbers, and then write down “infinity” after the equals sign, and thereafter goes about believing that the sum of a certain series is infinite.
The sum is not, in fact, infinite; no finite set of finite things can add up to an infinity, just as no finite set of finite pieces of evidence can produce absolute, infinitely strong certainty. But if we use some process other than the “correct” one, as the mathematician’s brain has to somehow output “infinity” from the finite inputs it has been given, we can generate absolute certainty from finite evidence—it simply isn’t correct. It doesn’t correspond to something which is either impossible or inevitable in the real world, just as the inept mathematician’s infinity does not correspond to a real infinity. Rather, they both correspond to beliefs about the real world.
While I do not believe that there are any rationally acquired beliefs which can stand up to the powers of imagination (though I am not absolutely certain of this belief), I do believe that irrational beliefs can. See my above description of the hypothetical young-earther; they may be able to conceive of a circumstance which would falsify their belief (i.e. their god telling them that it isn’t so), but they cannot conceive of that circumstance actually occurring (they are absolutely certain that their god does not contradict himself, which may have its roots in other absolutely certain beliefs or may be simply taken as a given).
the possibility of people who are not reasoning perfectly
:-) As in, like, every single human being...
certainty … cannot be reached using proper rational thought
Yep. Provided you limit “proper rational thought” to Bayesian updating of probabilities this is correct. Well, as long your prior isn’t 1, that is.
I do believe that irrational beliefs can
I’d say that if you don’t require internal consistency from your beliefs then yes, you can have a subjectively certain belief which nothing can shake. If you’re not bothered by contradictions, well then, doublethink is like Barbie—everything is possible with it.
I am not arguing that it is not an empty set. Consider it akin to the intersection of the set of natural numbers, and the set of infinities; the fact that it is the empty set is meaningful. It means that by following the rules of simple, additive arithmetic, one cannot reach infinity, and if one does reach infinity, that is a good sign of an error somewhere in the calculation.
Similarly, one should not be absolutely certain if they are updating from finite evidence. Barring omniscience (infinite evidence), one cannot become absolutely/infinitely certain.
What definition of absolute certainty would you propose?
So you are proposing a definition that nothing can satisfy. That doesn’t seem like a useful activity. If you want to say that no belief can stand up to the powers of imagination, sure, I’ll agree with you. However if we want to talk about what people call “absolute certainty” it would be nice to have some agreed-on terms to use in discussing it. Saying “oh, there just ain’t no such animal” doesn’t lead anywhere.
As to what I propose, I believe that definitions serve a purpose and the same thing can be defined differently in different contexts. You want a definition of “absolute certainty” for which purpose and in which context?
You are correct, I have contradicted myself. I failed to mention the possibility of people who are not reasoning perfectly, and in fact are not close, to the point where they can mistakenly arrive at absolute certainty. I am not arguing that their certainty is fake—it is a mental state, after all—but rather that it cannot be reached using proper rational thought.
What you have pointed out to me is that absolute certainty is not, in fact, a useful thing. It is the result of a mistake in the reasoning process. An inept mathematician can add together a large but finite series of natural numbers, and then write down “infinity” after the equals sign, and thereafter goes about believing that the sum of a certain series is infinite.
The sum is not, in fact, infinite; no finite set of finite things can add up to an infinity, just as no finite set of finite pieces of evidence can produce absolute, infinitely strong certainty. But if we use some process other than the “correct” one, as the mathematician’s brain has to somehow output “infinity” from the finite inputs it has been given, we can generate absolute certainty from finite evidence—it simply isn’t correct. It doesn’t correspond to something which is either impossible or inevitable in the real world, just as the inept mathematician’s infinity does not correspond to a real infinity. Rather, they both correspond to beliefs about the real world.
While I do not believe that there are any rationally acquired beliefs which can stand up to the powers of imagination (though I am not absolutely certain of this belief), I do believe that irrational beliefs can. See my above description of the hypothetical young-earther; they may be able to conceive of a circumstance which would falsify their belief (i.e. their god telling them that it isn’t so), but they cannot conceive of that circumstance actually occurring (they are absolutely certain that their god does not contradict himself, which may have its roots in other absolutely certain beliefs or may be simply taken as a given).
:-) As in, like, every single human being...
Yep. Provided you limit “proper rational thought” to Bayesian updating of probabilities this is correct. Well, as long your prior isn’t 1, that is.
I’d say that if you don’t require internal consistency from your beliefs then yes, you can have a subjectively certain belief which nothing can shake. If you’re not bothered by contradictions, well then, doublethink is like Barbie—everything is possible with it.