(Let me just add to what TheOtherKawoomba already said)
This is an infinity, and therefore I have an infinity of beliefs. Is that wrong?
If that were so, then “I believe the sky is blue” would mean “I have an infinity of beliefs about the sky, namely that it is blue, so it also is “not blue+1/nth the distance to the next color” (then vary the n).
A student writing down “x>2” would have stated an infinity of beliefs about the answer. Does that seem like a sensible definition of belief? Say I picked one out of your infinite beliefs about the car’s weight. Where is it located in your brain? Which synapses encode it? It would have to be the same ones also encoding an infinity of other beliefs about the car’s weight. Does that make sense? I plead the Chewbacca defense.
There’s another problem if you consider all the implications as if they were your beliefs, even if you’ve not explicitly followed the implication. Propositions in math simply follow from axioms, i.e. are implications of some basic beliefs. Yet for some of those their truth value is famously not yet known. If you held all beliefs which were logically implied by stated beliefs to also be your beliefs just the same, you’d face a conundrum—you’d be uncertain about such famous—yet unknown—propositions. Yet that uncertainty isn’t in the territory—either the proposition is implied by the axioms or it isn’t. Yet you couldn’t build the “beliefs implied by this belief”. So would you just follow “trivial” implications such as in your example? You’d still need to evaluate them, and it is that simple fact of having to evaluate whether an implication actually is one, or even if 99 is actually smaller than 100 - however trivial it seems—that is the basis for the new (derived) belief, the reason you cannot automatically follow an infinity of implications simultaneously. Since you cannot evaluate an infinity of numbers, you cannot hold an infinity of beliefs.
Agreed. Edit: I don’t think the one claim means the other, but I do agree that the one (in this case) implies the other. Do you believe that the sky’s being blue excludes its being (at the same time and in the same respect) red?
A student writing down “x>2” would have stated an infinity of beliefs about the answer.
Well, the student could be said to believe an infinity of things about the answer, not that the student has stated such an infinity. We agree that to state (or explicitly think about) an infinity of beliefs would be impossible.
Where is it located in your brain?
In response to Dave (the other one), I distinguished beliefs on my view into occurrent beliefs (those beliefs that do or have corresponded to some neural process) and extrapolated beliefs (those beliefs, barring any new information, my brain could predictably arrive at from occurrent beliefs). I am saying that I should be said to believe right now both all of my occurrent beliefs and all my extrapolated beliefs, and that my extrapolated beliefs are infinite. My extrapolated beliefs have no place in my brain, but they’re safely in the bounds of logic+physics.
I plead the Chewbacca defense.
I...haven’t heard that one.
There’s another problem if you consider all the implications as if they were your beliefs, even if you’ve not explicitly followed the implication.
I don’t think this, I agree that this would lead to absurd results.
(Let me just add to what TheOtherKawoomba already said)
If that were so, then “I believe the sky is blue” would mean “I have an infinity of beliefs about the sky, namely that it is blue, so it also is “not blue+1/nth the distance to the next color” (then vary the n).
A student writing down “x>2” would have stated an infinity of beliefs about the answer. Does that seem like a sensible definition of belief? Say I picked one out of your infinite beliefs about the car’s weight. Where is it located in your brain? Which synapses encode it? It would have to be the same ones also encoding an infinity of other beliefs about the car’s weight. Does that make sense? I plead the Chewbacca defense.
There’s another problem if you consider all the implications as if they were your beliefs, even if you’ve not explicitly followed the implication. Propositions in math simply follow from axioms, i.e. are implications of some basic beliefs. Yet for some of those their truth value is famously not yet known. If you held all beliefs which were logically implied by stated beliefs to also be your beliefs just the same, you’d face a conundrum—you’d be uncertain about such famous—yet unknown—propositions. Yet that uncertainty isn’t in the territory—either the proposition is implied by the axioms or it isn’t. Yet you couldn’t build the “beliefs implied by this belief”. So would you just follow “trivial” implications such as in your example? You’d still need to evaluate them, and it is that simple fact of having to evaluate whether an implication actually is one, or even if 99 is actually smaller than 100 - however trivial it seems—that is the basis for the new (derived) belief, the reason you cannot automatically follow an infinity of implications simultaneously. Since you cannot evaluate an infinity of numbers, you cannot hold an infinity of beliefs.
Agreed. Edit: I don’t think the one claim means the other, but I do agree that the one (in this case) implies the other. Do you believe that the sky’s being blue excludes its being (at the same time and in the same respect) red?
Well, the student could be said to believe an infinity of things about the answer, not that the student has stated such an infinity. We agree that to state (or explicitly think about) an infinity of beliefs would be impossible.
In response to Dave (the other one), I distinguished beliefs on my view into occurrent beliefs (those beliefs that do or have corresponded to some neural process) and extrapolated beliefs (those beliefs, barring any new information, my brain could predictably arrive at from occurrent beliefs). I am saying that I should be said to believe right now both all of my occurrent beliefs and all my extrapolated beliefs, and that my extrapolated beliefs are infinite. My extrapolated beliefs have no place in my brain, but they’re safely in the bounds of logic+physics.
I...haven’t heard that one.
I don’t think this, I agree that this would lead to absurd results.