I agree that there is a threshold that I will feel subjectively after which I will believe in it. I just don’t think there is such a thing as a partial belief before that threshold occurs. Observing just one or even a few red balls doesn’t make you “partially believe” that most of it is red especially if there are thousands of them. The concept of partial belief seems incoherent for mainly one reason: either most of the balls are red or they are not. As such, I fail to see how this contradicts the attitude that belief should ideally be binary.

@thinkingman Really, so let's say the threshold is N red balls. When you have just observed N-1 red balls, you don't believe at all that the majority of balls are red. You don't even suspect it. Then on the N'th ball you suddenly completely believe the majority of balls are red, with no doubt at all. Going from not even any suspicion to utter undoubted confidence upon seeing just one additional ball. Does that really make sense to you? Oh, and what specifically is N for you?

There is no specific threshold at which you “should” believe in your example. It comes down to intuition and preference. Similarly, there is no specific “degree of belief” you should have after seeing some balls. These are normative questions that don’t have a correct answer. The problem you seem to be pointing out with a binary belief system exists in a graded degree of belief system as well, except that in the latter case, it doesn’t even map to reality. This is because reality is as a matter of fact binary. As mentioned before, most of the balls are either red or they are not.

@thinkingman I didn't ask you a normative question about what threshold "should" cause you to believe. Interpreting that way is only an excuse to avoid answering. I asked you about your actual threshold, N, at which point your belief suddenly switches from total absence of belief to total undoubted belief. Could it be 47? 46 red balls are not enough to have even a suspicion, but 47 is completely sufficient to dispel all doubt?

I don’t know what the threshold is. I don’t need to. But I can say that given thousands of balls, it’s probably not a few. And I can say that observing 300 straight red balls would give me full confidence. But at no point will I have partial belief, or rather, does it make sense to have partial belief. This is because reality isn’t partial. A partial “belief” isn’t really a belief. It’s arguably unfalsifiable. If you are 60% sure that something is true, you can claim that you were correct even when you’re wrong

@thinkingman So 299 won't give you any confidence at all and 300 will give you full confidence. Doesn't something strike you as a little off about that? A little contrary to intuition?

Let us continue this discussion in chat.

Having any sort of hard rule seems off since belief is ultimately just a feeling. The point that I’m making is that there is no correct answer for BOTH a binary and a graded belief system. An analogy I would use is morality. One person may find something completely wrong or right. Another person might find it questionably right, or “partially” right. They both seem on the face of it unintuitive. However, unlike the moral case, the things we have beliefs of are usually either true or false. There’s NO in between. So why bother having a “partial” belief in anything?

@thinkingman "Partial belief" is uncertainty. For the box of balls, you start off being uncertain, and then you become more certain as you get more supporting evidence. Similarly, contrary evidence can make you less certain. On the one side is "I'm sure this is true". On the other side is "I'm sure this is false". In the middle is "I'm not sure whether this is true or false".

@thinkingman One can apply math and statistics to this setup. Null hypothesis is that the majority of balls are red, alternative hypothesis is that a majority of balls is not red. For any number N of independent samples coming up red one can compute a p-value which is generally interpreted as a convidence in your null hypothesis. This number increases gradually with N and one can compute at what specific N it crosses 50% convidence or any other specific convidence bound.

The evidence that there is a majority of red balls in a box is available when we know a majority of red balls has been pulled from the box. One less ball is not evidence (weak or strong) that there is a majority of red balls. It is only evidence that there is - at the time of counting - one less than a majority of red balls. If another red ball is extracted, and we know we now have a majority, then it has become evident that there is a majority of red balls.

Is there are reason you're using "most" instead of "all" here? I feel it just complicates the argument (you now have a separate threshold for the percentage of balls that counts as "most"), when "all" would work just as well.

@HolyBlackCat If I said "all" then thinkingman might decide to say he'd never conclude all are red no matter how many red balls are shown, because he doesn't know if he's seen them all. That objection is less plausible if the question is just whether most are red.

@NotThatGuy If you’re not sure about something, it usually means you suspend belief and don’t take a position on it. Otherwise, we usually believe in things or don’t believe in things. The concept of believing in X “more” confidently than Y seems useless for the main reason that it is unfalsifiable. I do not believe in unfalsifiable claims.

By the way, for anyone still reading this thread, the “300” number I pointed out wasn’t my threshold. It was just an example of a number that would make me believe that most of the balls are red so @causative’s response was a bit of a strawman. To clarify, I believe that there are only three states of belief that make sense: belief, disbelief, and suspension of belief. This does NOT imply that there is a “correct” threshold from disbelief to belief

If you define weak to be “how many people convince you” then sure @SyntaxJunkie. But as we both know, that is not a good metric. There are more people convinced of Christianity being true than atheism. Does that mean Christianity has stronger evidence than atheism? As mentioned before, at the risk of repeating myself, reality is binary. As such, it is best to have beliefs that atleast try to match that.

@thinkingman Confidence in a claim is not a claim, so falsifiability does not apply. If you see someone driving a car, and they say "look at my new car", you may reasonably believe they own the car. If you see proof of ownership in their name, or you see them still driving the car a year from now, that should make you more confident about that (and that they didn't just rent, borrow or steal it and lie about owning it).

I'm willing to bet you apply this type of thinking on a daily basis, because that's a pretty fundamental part of living life.

@NotThatGuy The question is not about whether or not we apply this kind of thinking in our daily lives. I am certain that many of us do. Even I myself may feel “more” confident in thinking that the person owns the car.

The question moreso is whether we are “justified” in doing so. And here is where things get tricky. The more I think about it, the more I think it is reasonable to adopt one of three attitudes at every moment: belief, disbelief, or suspension. In your example specifically, if it is my friend, I would believe him from the beginning, since I would see no reason for him to lie

The additional reasons would simply function more as evidence of my expectations being right, rather that an “increase” in confidence. An analogy I would use is perhaps my belief in my mother loving me. If she says “I love you” an additional ten times over the next few weeks, it isn’t really increasing my confidence in her loving me. It’s just fitting in with my earlier belief that she does love me

Perhaps a better analogy would be asking whether seeing more and more pictures is increasing your confidence that the earth is a sphere. Is it? I doubt this. Probability didn’t exist as a concept until the 1600s and yet our beliefs still functioned. In almost all cases where we have significant shifts in our beliefs, it is usually when it is moving from a state of belief to disbelief or from a suspension of belief to belief or vice versa.

The fine grained belief system just over complicates matters in my eyes

@thinkingman You seem to be trying to turn confidence into a belief in and of itself, which just isn't what it is. Confidence is (or should be) just a function of how much justification/evidence there is for a belief. To say you have low confidence is just to say you don't have much evidence and it wouldn't take much evidence to move you to suspension of belief or disbelief.

It would take a massive amount of evidence to counter all the evidence we have that the Earth is a globe (to the point that we consider it essentially impossible for such evidence to exist), so that equals to high confidence. Since you already have high confidence, you can't get much more confident (we also have lots of photographic evidence already, so even more photos wouldn't do much, whereas some other types of evidence may increase confidence further).

If it wouldn't take much evidence to move you to suspension of belief or disbelief, it would make sense to not base too much on that belief. If someone you don't know that well asks you to drive their car to somewhere (possibly over a border) as a favour, it would be perfectly rational to decline in case it isn't actual their car and the risk of being implicated in a crime doesn't outweigh the benefit to you (assuming you don't decline for other reasons).

@thinkingman We may not have formalized probability mathematically until the 1600s, but we've always had the concepts of suspicions and doubts and uncertainties. Brains naturally represent partial degrees of belief, because brains evolved in an environment of partial information, and modeling uncertainty is the most evolutionary successful way to deal with this.

As a natural example, consider a primitive hunter deciding where to find the best game. He has to weigh his experience hunting in different places, taking into account also sightings of animals he didn't kill and indirect evidence like spoor and tracks. In the end he gets a gut feeling that one hunting ground might be better than another. But he doesn't know for sure, and he's open to trying the other place if the first place disappoints him.

@thinkingman A fine grained belief system may complicate matters, but matters are complicated, so we're just accurately representing that.

@causative Contrary to what you are trying to imply, having a lack of a notion of probability is proof that beliefs when needed do NOT need to be fine grained. No one argued that doubt doesn’t exist or didn’t exist. Of course it did. But that can be modeled as a simple suspension of belief. Lastly, cavemen had to make quick decisions in times of uncertainty.

Who do you think performed better? The caveman who had an all out belief in his decision or the caveman who had a “reasonable but not certain” belief?

I don’t see how most of what you said in your first statement directly disagrees with what I said so I’ll focus on your next statement @NotThatGuy. My issue is your notion of “correct”. The reality is that there is no correct. You cannot get an ought from an is

A simple question that can demonstrate this is by using the very same example of the car you used. I have two questions for you. A) what should your confidence level be when coming across a stranger saying “look at my car” in him owning it? And how should this be represented?

B) how should your confidence level change when finding out he has ownership papers? What is the “true”/“correct” answer? If you can’t come up with one, then you must admit that this is ultimately a normative question. Believe it or not, it is analogous to asking “is it moral to kill two strangers vs. your mother if you had to pick one”

The only difference between deciding when or how you should represent belief vs. the moral question is that there is an ultimate correct answer to what the belief is ABOUT but not with morality

Is it a matter of fact that the person either owns the car or doesn’t. It is not (arguably) a matter of fact as to which of the two kinds of people should be killed if one had to choose. However, there is no matter of fact when it comes to belief representation. I just choose to represent it in a way that tries its best to accurately map to reality

It is*!

@thinkingman I never used the word "correct". I wasn't trying to get an ought from an is. So I'm not sure which part of what I said you're disagreeing with there, and in the rest of your reply.

@thinkingman The hunter is not performing a "simple suspension of belief" about where the best game is. He's got an idea of where they might be, and that's where he'll go to hunt, but if the results disappoint him he will also easily change his mind, because he has no conviction about it, because the evidence (about where the best game is) isn't strong enough.

@thinkingman if the hunter was totally uncertain and suspended all belief, then he wouldn't be able to decide where to hunt between several reasonable alternatives. On the other hand if the hunter was totally certain where the best hunting is, but not correct about it, then he'd remain there trying to hunt game for a long time, even if the results are unfavorable. Both methods are inferior to the method of going to where you think the best game are, but being willing to change your mind.

There's no advantage to having total irrational certainty in something. Even if you're right, your behavior isn't going to be different from someone who just has a high degree of confidence. The only difference is that the latter person is more willing to change their mind when evidence starts to pile up against them.

You used the word should @NotThatGuy. My apologies. It’s late at night over here

The rest of it still applies. My overall point is that there is nothing in reality that gives you an imperative to believe something. And here’s the trickier part: even if we agree that we should try our best to believe in things that are true, there is STILL no clear cut way to define when or how we should believe in things

This is just semantics at this point @causative. Belief != certainty. Belief just means you believe it. I think it is a whole different kind of mental state. The concept of confidence, in my eyes, isn’t useful in the first place. That’s partially my point. When deciding between A and B, I pick whichever one seems better and I believe in it

Key word “believe in it.” It is not that I think A is more likely than B. It is not that I am more confident in A than B. It is not that the caveman is thinking “I believe A has the best game slightly more than B”

I believe that as a matter of reality, and also as a matter of what I think people “should” do, is that the caveman is simply thinking “I believe A has the best game” and he goes for it. If he’s wrong, he’s wrong

@thinkingman "You used the word should" - you probably should've asked why I used the word "should", rather than assuming it's because of an "is". And I would've said that's on the basis that this would be most conducive to being able to predict what would happen and the consequences of your actions, and thus you can take actions most likely to achieve whatever goal you wish to achieve.

A goal-based "should" is not "an ought from an is" (you can rephrase such a "should" as "this action IS most conducive to achieving that goal").

And we don't all need to agree on that being important. I just need to think so, for it to make sense for me to apply it. If you also think that's important, it would also make sense for you to apply it. If you don't, then you indeed probably won't find this argument compelling.

"My overall point is that there is nothing in reality that gives you an imperative to believe something" - but I still don't really know what this has to do with what I said.

@thinkingman But surely you acknowledge that there is something about the hunter's state of mind that leads him to either (A) be persistent about hunting the same spot despite poor results, maintaining his belief that it is the best spot and he's just been unlucky so far, or (B) accept a few poor results as evidence he should go somewhere else. We might call the difference between (A) and (B) "ease of changing your mind" and abbreviate it EOCYM.

In some situations a high EOCYM is warranted (because the initial evidence that the spot holds the best game was poor) and in some situations a low EOCYM is warranted (because the initial evidence was strong, so it's more likely the recent poor hunting was just bad luck.) Now, if you admit the existence of EOCYM, why not just call it "uncertainty"? Because it certainly acts a lot like uncertainty.

I just think that partial belief doesn’t exist and it is not best modeled as uncertainty. For example, I fully believe that my mother is my actual mother. I also fully believe that the earth is a sphere. In fact, I would bet any amount of money on both @NotThatGuy

This is not to say that there is no difference between those beliefs. If I knew in advance that only one of those beliefs were true, but didn’t know which one, THEN I would bet on the earth being a sphere one. But we don’t live in a world where we apriori know which beliefs are true or false

The common philosophical view is that “confidence” maps to how much money you would bet on for a belief. I don’t think this is the case. I think what’s really going on when we sense a confidence difference is that we imagine what we would bet on if we had to pick ONE of a certain number of beliefs

This would make sense evolutionarily since that is exactly what we had to do. We were not often in situations where we had to bet a certain amount on X and another amount on Y. We were more often in situations where we had to choose BETWEEN X and Y

But beliefs aren’t the latter kind of bets which is why our intuitions go haywire. If I knew in advance that only one of Christianity and the flying teapot being our god was true, and I had to pick one, I would pick Christianity. Does this mean I have stronger confidence in Christianity over the teapot? No.

You just changed the example which is a common tactic from Bayesians. Many of our beliefs are not repeatable experiments. Most of the important ones are not @causative. Even in your original example, I wasn’t guessing whether red is the majority in multiple jars over and over. There was just one jar

@thinkingman No response on EOCYM? Do you acknowledge that a person believing X may have a higher or lower degree of Ease Of Changing Their Mind away from X, depending on how much evidence they currently have for X? And if you acknowledge that, what distinction do you draw, if any, between EOCYM and degree of uncertainty?

@thinkingman Your last set of comments is pretty much exactly what someone might say if they're trying to argue in favour of the idea of confidence of beliefs, so I'm not really sure how you end up concluding the opposite. Rather than concluding that we aren't in the situation you described, someone else might just conclude that what you just described represents confidence. Hypotheticals and analogies are good ways to explain things.

(You obviously won't have any degree of confidence that something is true, if you believe it's false, you'd rather have some degree of confidence in it being false.)

EOCYM isn’t uncertainty as described earlier because we were talking about belief at a particular instance of trying to find the best game. Not as a repeatable experiment. You are referring to norms of action one should take given different scenarios. This is not the same as belief

@causative

Well in the standard conception of degree of belief, it is taken to mean how much money you would bet. But I would bet an infinite amount of money in both Zeus and the Flying Teapot being true. So as per that conception, I have equal confidence! @NotThatGuy And yet, if I knew apriori that one of them were true, I would pick Zeus. Actions one takes during particular designed bets does not imply a difference in confidence of belief. That’s my ultimate point

Sorry I meant in both being false *

This has gotten me to realize something: it seems that the concept of a “strength” of a belief is vacuous in and of itself. It must, like probability, be reduced to an interpretation. In this case, it seems like it depends on how we reduce that definition

If we define A being a stronger belief than B to mean that you would bet more money on A, then in my Christianity example, my belief in it isn’t stronger than the belief in the teapot. If we define A being a stronger belief than B to mean which one you would pick if you HAD to, then I suppose I would have a stronger belief in the teapot being false. This indicates to me that the “strength” of a belief is something that doesn’t actually exist

And is rather just an invented phenomenon to help us imagine different sorts of actions we would take in betting scenarios

@thinkingman You presented one way of thinking of confidence, and dismissed that in favour of a different way of thinking of confidence. In doing so, you haven't rebutted all ideas of confidence of beliefs as much as you've demonstrated one such idea. You may be very sure both are false, but if you'd pick one above the other, that tells me that you're more sure about one than the other.

(Also, would you be willing to bet an infinite amount of money on every single claim having the truth value you believe it to have, on claims where you're not suspending belief? Because if there's even 1 thing that you believe to be true, but you wouldn't bet an infinite amount of money on it being so, that would demonstrate the original way of thinking you were trying to rebut.)

@thinkingman I don't quite understand what distinction you're drawing between EOCYM and uncertainty. Are you saying that uncertainty only applies in repeatable experiments, and EOCYM applies in situations that are not repeatable experiments? (I wouldn't agree that uncertainty only applies in repeatable experiments.)

* When I said "You may be very sure both are false", I was talking about Zeus and the Flying Teapot, not the aforementioned ideas of confidence, in case that wasn't clear.

@notthatguy No it tells you that I would pick A over B in certain scenarios. Anything more is just your assumption. Of course, if you simply define being more sure of A to directly mean trust you would pick it in a certain scenario, then sure. But that just begs the question of why that should be the definition

To answer your second question, it depends on the context. If there is only one bet, but the claim is one of any in which I believe, then yes, I would bet an infinite amount of money. But if the number of bets were equal to my number of beliefs, then no I would not

To directly mean that you would* in my first sentence

@causative. I think we’re complicating things. I think that belief should be represented as belief, disbelief, or suspension of belief (usually when you’re not sure). That is the only kind of uncertainty that makes sense to me. You seem to defend a fine grained 0 to 1 degree of belief. So far, I have seen no reason to prefer yours over mine