In many discussions I'm pulled back to the distinction between not-guilty and innocent as a way to demonstrate how the burden of proof works and what the true default position should be in any given argument. A lot of people seem to not have any problem seeing the distinction, but many intelligent people for some reason don't see it.
In this article I explain why the distinction exists and why it matters, in particular why it matters in real-life scenarios, especially when people try to shift the burden of proof.
Essentially, in my view the universe we are talking about is {uncertain,guilty,innocent}, therefore not-guilty is guilty', which is {uncertain,innocent}. Therefore innocent ⇒ not-guilty, but not-guilty ⇏ innocent.
When O. J. Simpson was acquitted, that doesn’t mean he was found innocent, it means the prosecution could not prove his guilt beyond reasonable doubt. He was found not-guilty, which is not the same as innocent. It very well could be that the jury found the truth of the matter uncertain.
This notion has implications in many real-life scenarios when people want to shift the burden of proof if you reject a claim when it's not substantiated. They wrongly assume you claim their claim is false (equivalent to innocent), when in truth all you are doing is staying in the default position (uncertain).
Rejecting the claim that a god exists is not the same as claim a god doesn't exist: it doesn't require a burden of proof because it's the default position. Agnosticism is the default position. The burden of proof is on the people making the claim.
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I'm not overly familiar with the Bayesian way of thinking, I have seen it expressed very often in The Motte and similar circles, but I don't see why would anyone conclude that this is a valid way of reasoning, especially when it comes to beliefs. I do understand Bayes' theorem, and I understand the concept of updating a probability, what I don't understand is why anyone would jump to conclusions based on that probability.
Let's say through a process of Bayesian updating I arrive to a 83% probability of success, should I jump the gun? That to me is not nearly enough information.
Now let's say that if I "win" I get $100, and if I "lose" I pay $100. Well now I have a bit more information and I would say this bet is in my favor. But if we calculate the odds and adjust the numbers so that if I lose I pay $500, now it turns out that I don't gain anything by participating in this bet, the math doesn't add up:
((5 / 6) * 100) / ((1 / 6) * 500) = 1.Even worse: let's say that if I win I get $100, but if I lose I get a bullet in my brain. I'm literally playing Russian roulette.
83% tells me absolutely nothing.
Real actions in real life are not percentages, they are: do you do it or not? and: how much are you willing to risk?
You can't say I'm 60% certain my wife is faithful, so I'm going to 40% divorce her. Either you believe something, or you don't. Period.
Even worse is the concept of the default position in Bayesian thinking, which as far as I understand it's 50%.
Edit: I mean the probability that the next coin toss is going to land heads is 50%.
So starting off if I don't know if a coin is fair or not, I would assume it is. If I throw the coin 100 times and 50 of those it lands head the final percentage is 50%. If I throw the coin 1,000,000 times and 500,000 of those times it land heads it's still 50%, so I have gained zero information. This does not map to the reality I live in at all.
My pants require at least two numbers to be measured properly, surely I can manage two numbers for a belief. So let's say before I have any evidence I believe a coin is fair
50%±50(no idea), after throwing it a million times I would guess it's about50%±0.01(I'm pretty sure it's fair).So no, I'm not sold on this Bayesian idea of a continuous belief, I can't divorce my wife 40%, or blow my brains 17%. In the real world I have to decide if I roll the dice or not.
No, the probability that the next toss of a coin is going to land heads is 50%, regardless if the results have been 0/0, 50/50, or 500000/500000.
My beliefs are binary. Either I believe in something or I don't. I believe everyone's beliefs are like that. But people who follow Bayesian thinking confuse certainty with belief.
In your view, is "believing" something equivalent to supposing it with 100% certainty (or near-100% certainty)?
I have a strong suspicion that your epistemic terminology is very different from most other people's, and they aren't going to learn anything from your claims if you use your terminology without explaining it upfront. For instance, people may have been far more receptive to your "2 + 2" post if you'd explained what you mean by an "assumption", since most people here were under the impression that by an "assumption" you meant a "strong supposition". So it's hard to tell what you mean by "people who follow Bayesian thinking confuse certainty with belief" if we misunderstand what you mean by "certainty" or "belief". Is a "belief" a kind of "supposition", or is it something else entirely?
No.
How so? I believe the Bayesian notion that you can believe something 60% is what is not shared by most people. Most people either believe something or they don't.
There's a difference between most people and most people "here". My understanding of "assume" is in accordance with many dictionaries, for example: to take as granted or true.
certainty: a quality of being proven to be true
belief: something considered to be true
Something can be 60% proven to be true, it can't be 60% considered true.
And something that is "granted" is "assumed to be true", by the same dictionary. The definition is circular: it doesn't lead to your interpretation of "to assume" as "to believe true with absolutely zero possible doubt".
Besides, the dictionary argument can be taken in any direction. Per Dictionary.com, "to assume" is "to take for granted or without proof", "to take for granted" is "to consider as true or real", "to consider" is "to regard as or deem to be true", and "to regard as true" is "to judge true". That leads to the usage of the term by many here, where to make an assumption about something is to make a strong judgment about its nature, while still possibly holding some amount of doubt.
You draw strong boundaries between these epistemic terms. But if common usage recognized your boundaries, then the dictionaries would be flat-out wrong to say that, e.g., to believe something is to assume it, suppose it, or hold it as an opinion (where an opinion is explicitly a belief less strong than positive knowledge). That's why I suspect that your understanding of the terms is not aligned with common usage, since the dictionaries trample all over your boundaries.
Also, I think that "certainty" in a Bayesian context is best treated as a term of art, equivalent to "degree of belief": a measure of one's belief in the likelihood of an event. It's obviously incompatible with the everyday notion of something being certainly true, but just using the term of art in context doesn't mean one is confusing it with the general term. After all, mathematicians can talk about "fields" all the time without confusing them with grassy plains.
Many definitions on all dictionaries are circular. Language is not an easy thing, which is why AI still has not been able to master it.
No, that's not what the definition is saying. "[[[judge true] or deem to be true] as true or real] or without proof". There is no possibility of doubt. It's judged/deemed/considered to be true.
I believe they are. dictionary.com says "believe" is "assume", but Merriam-Webster does not. One of them has to be wrong.
That's the whole reason dictionaries exist: people disagree.
One dictionary does, not all.
BTW. I used ChatGPT and asked it if it saw any difference between "assume" and "suppose", and it 100% said exactly what is my understanding.
There's a big difference in saying "I'm 75% certain
Xis true", and "I'm certainXis 75%". If I believe it's likely that Ukraine launched a missile and not Russia, I'm saying I'm 75% certain that's true, I don't think there's an event which is 75% likely. I believe most people think this way, and it's more rational.Sure, my point is just that your meaning can't be supported by that definition alone. Even if we say that "to assume" is the same as "to take as granted or true", that isn't sufficient to refute my notion that in common usage, neither "to assume" nor "to take as granted or true" necessarily implies zero possible doubt.
That particular dictionary says the exact opposite of what you're saying. To "judge" is "to infer, think, or hold as an opinion; conclude about or assess" (def. 10), and an "opinion" is "a belief or judgment that rests on grounds insufficient to produce complete certainty" (emphasis mine; notice how its author thinks one can be uncertain about a judgment?). So if you want a dictionary to support you on that, you'll have to find another dictionary.
Or perhaps both dictionaries are sometimes correct, sometimes incorrect, and sometimes partially correct, since in real life people can have subtly or obviously different understandings of terms depending on the context. That's the whole thesis of "The Categories Were Made for Man, Not Man for the Categories": nearly all our categories are fuzzy and ill-defined, but they're still useful enough that we talk about them anyway. So in general usage, people don't usually resolve ambiguity by refining their terminology (since hardly anyone else would recognize it), but instead by inserting enough qualifications and explanations that their point hopefully gets across to most of the audience.
I asked ChatGPT the question, and the interpretation it produced is certainly far less strong than your standard of "zero possible doubt" regarding an assumption:
I wouldn't say that being "confident" about something implies that you necessarily have zero possible doubt. But even if you disagree on that, ChatGPT doesn't act on such a strict definition in practice. For instance, it produced the following exchange:
If Alice had absolutely zero doubt that the box contained a dog, then her belief could not be challenged in that way: she'd have to conclude that the dog can meow, or that the meow came from outside the box.
Since I'm not one to trust ChatGPT's output to be representative of anything, I decided to ask some people in real life about it.
First, I asked a friend, "What do you think is the difference between assuming something and supposing something?" He replied that the difference is that you assume something before it occurs, but you suppose it while it's occurring or after it occurs.
I asked the same question to a stranger at the bus stop. He replied that when you assume something, you're not entirely sure whether or not it's true, but when you suppose something, you have some kind of predetermined knowledge that it's true.
Finally, I asked the same question to a stranger in a hallway. After several seconds of thought, she replied that she had no clue, then her friend chimed in to say she also had no clue.
ChatGPT, the dictionaries I've checked, and the ordinary people I've asked all give different definitions of "assume" and "suppose", none of which include your standard of zero possible doubt in order to assume something. Therefore, I have strong evidence to believe that in common usage, the terms have no fixed meaning beyond "to accept as true without proof"; all else is vague connotation that can be overridden by context.
What evidence do you have that common usage recognizes your hard boundary, so hard that to cross it is to be unambiguously incorrect?
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