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felipec  unbelief  1yr ago (felipec.substack.com)   Edited 1yr ago   2915 thread views

not-guilty is not the same as innocent

felipec.substack.com

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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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.

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.

The definition is circular: it doesn't lead to your interpretation of "to assume" as "to believe true with absolutely zero possible doubt".

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.

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.

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.

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).

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.

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.

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.

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.

There's a big difference in saying "I'm 75% certain X is true", and "I'm certain X is 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.

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.

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.

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.

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.

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.

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.

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.

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:

What is the difference between assuming something and supposing something?

Assuming and supposing are similar in that they both involve accepting something as true without proof. However, "assuming" often carries a connotation of confidently accepting something as true, while "supposing" suggests tentativeness or uncertainty. For example, "I assumed the train would be on time" implies a level of confidence, while "I supposed the train would be on time" implies some level of doubt. So, in general assuming is more of a confident and sure statement, supposing is more of a tentative and uncertain statement.

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:

Alice has a box. Alice assumes that the box only contains a dog. What does Alice think is in the box?

Alice thinks that there is a dog in the box.

Alice hears a meow coming from the box. What does Alice think is in the box now?

Since Alice hears a meow coming from the box, she may now think that there is a cat in the box instead of a dog. Her assumption of only a dog in the box would be challenged by the new information of the meow.

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?

Sure, my point is just that your meaning can't be supported by that definition alone.

I did not claim my meaning was supported by that definition alone.

That particular dictionary says the exact opposite of what you're saying.

That's not what I'm saying, that's what your dictionary is saying. You are proving that the dictionaries disagree, which is what I'm saying.

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.

That is what I'm saying. In one context the word "theory" means something for most people, in another context it means something else.

You can't say the word "assume" means X and only X in all contexts and here's a dictionary that says so, because that's not how language works, not all dictionaries agree, and dictionaries are not perfect.

You can't say that my categorization system is an error, and you can't say only your categorization system should be considered by default, especially when it's not clear that everyone is following it.

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

To me it said: «to "assume" something is to accept it as true without proof of evidence». That to me doesn't include doubt, because it's true a priori: it's just true.

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.

That aligns with my notion of a priori: you don't need evidence for an assumption, it's just true.

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.

He is wrong: it's the other way around.

After several seconds of thought, she replied that she had no clue, then her friend chimed in to say she also had no clue.

That's what I claim many rational people should do in most circumstances.

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.

That isn't true, that's what you are assuming. It could be that you misinterpreted, and I contend that you did.

You contend that it means "strong supposition", yet the first person you asked said nothing like that, and the second person talked about "predetermined knowledge".

Therefore, I have strong evidence

I guess your definition of "strong evidence" and mine are very different.

What evidence do you have that common usage recognizes your hard boundary, so hard that to cross it is to be unambiguously incorrect?

I never claimed such a thing.

You are the one that claimed most people here equate "assume" with "strong supposition", and that that's what common people believe as well. But there's nothing you have provided to substantiate that. Even the testimonies you provided said nothing about "strong supposition", they talked about "before it occurs" and "predetermined knowledge" which very strongly suggests: without proof of evidence.

Either way I don't have to provide evidence because I did not make that claim, you made the claim that my understanding of "assume" is at odds with what most people understand by that word, but the evidence you yourself provided shows otherwise. You are trying to shift the burden of proof. The person that said to assume is to consider something true before it occurs is completely aligned with my notion of considering something true without evidence.

I don't have to show that my notion is shared by everyone, because I did not claim that, all I need to show is that your notion of "strong supposition" is not shared by everyone, and you yourself proved that.

To me it said: «to "assume" something is to accept it as true without proof of evidence». That to me doesn't include doubt, because it's true a priori: it's just true.

So would you say that ChatGPT disagrees with your notion of "assuming" in my example? If not, then how could Alice change her mind from the indirect evidence, if she had zero doubt that there was only a dog in the box?

I don't have to show that my notion is shared by everyone, because I did not claim that, all I need to show is that your notion of "strong supposition" is not shared by everyone, and you yourself proved that.

You're calling people (like the dictionary author, or the second person I questioned) "wrong" when they say that you can "assume" something while still doubting it to some extent. Why are they "wrong", instead of being "right" about their own notion that is distinct from your notion?

So would you say that ChatGPT disagrees with your notion of "assuming" in my example?

No.

If not, then how could Alice change her mind from the indirect evidence, if she had zero doubt that there was only a dog in the box?

First: I think you misinterpreted what ChatGPT said, and second: ChatGPT can seem to disagree in one interaction, and agree in another, it depends on how the question was posed.

I bombarded ChatGPT with questions about the matter, and everything aligned to my notion, for example "If Alice believes claim X is true with zero doubt, can she change her mind?" it answered "Yes", which is obvious to me. Alice believes claim X with zero doubt in one moment, but then receive evidence contradicting that belief (which was assumed in the first place), why wouldn't she change her mind?

But to be crystal clear I asked this killer question:

If Alice believes claim X is true with zero doubt, but then finds out indirect evidence that claim X may not be true and changes her mind, can it be said that Alice no longer assumes claim X is true?

If Alice believes claim X is true with zero doubt, but then finds out indirect evidence that claim X may not be true and changes her mind, it can be said that Alice no longer assumes claim X is true. An assumption is something taken for granted without being verified, whereas a belief is something considered to be true based on evidence and reasoning. When new evidence comes up, it's important to evaluate it and adjust one's beliefs and assumptions accordingly. In this case, Alice's belief was based on a zero doubt, but when new evidence came up, she changed her mind, which indicates that she no longer takes claim X as a given, and it is no longer an assumption. It's important to note that changing one's mind or updating beliefs and assumptions is a natural and healthy process, and it's a sign of a rational and open-minded individual.

How does this not align precisely to my notion? I didn't even use the term "assume" throughout the question, I used it only to verify the outcome.

You're calling people (like the dictionary author, or the second person I questioned) "wrong" when they say that you can "assume" something while still doubting it to some extent.

No, I said: if a dictionary says that to believe something is to assume it, then I believe it's wrong. I did not say the dictionary is wrong, I said that I believe it is wrong.

This is completely different from linking "assume" to doubt.

First, to make sure I'm not putting more words into your mouth: Would you say that most people outside of here would agree that when one assumes something, one cannot have any level of doubt about it?

I bombarded ChatGPT with questions about the matter, and everything aligned to my notion, for example "If Alice believes claim X is true with zero doubt, can she change her mind?" it answered "Yes", which is obvious to me.

That's not at all obvious to me. As it turns out, your notion of "believe with zero doubt" is very likely different than mine! So that I understand what your notion is: If, at a given point in time, Alice believes with zero possible doubt that the box contains nothing but a dog, then does she also believe with zero possible doubt that she will never receive unequivocal evidence otherwise? If so, does she believe there is a 0% chance that she will receive unequivocal evidence otherwise?

Alice believes claim X with zero doubt in one moment, but then receive evidence contradicting that belief (which was assumed in the first place), why wouldn't she change her mind?

The evidence doesn't unequivocally contradict her belief: it could be the case that the box contains only a dog, but she misheard where the meow came from, or the dog is able to make a meowing sound. If she was previously absolutely certain that a dog is in the box, then why wouldn't she adopt one of the alternative hypotheses compatible with both her assumption and the evidence?

How does this not align precisely to my notion? I didn't even use the term "assume" throughout the question, I used it only to verify the outcome.

By my prior notion of "believe with zero doubt", your prompt is vacuous, since it is impossible that "Alice believes claim X is true with zero doubt" but also "changes her mind", since if she can change her mind, then she didn't actually have zero doubt. Under that notion, ChatGPT is logically permitted to output whatever it wants, since it is not consistently capable of detecting absurdities in its input.

But more practically speaking, to ChatGPT, "zero doubt" or "absolute certainty" can be far from absolute:

Alice has a box. Alice believes with absolutely zero doubt that the box contains only a dog. Then, Alice hears a meow coming from the box. Might she now believe that a cat is in the box?

Yes, if Alice hears a meow coming from the box, it would likely cause her to question her belief that only a dog is in the box and she may now believe that a cat is also in the box. The sound of a meow would be strong evidence that contradicts her previous belief that only a dog is in the box, and would likely lead her to update her belief.

Then did Alice truly have absolutely zero doubt in her previous belief?

It is difficult to say for certain without more information about Alice's thought process and the context of the situation. However, it is possible that Alice did not truly have absolutely zero doubt in her previous belief that the box contained only a dog. In general, it is difficult for anyone to be completely certain about anything, and it is possible that Alice had some level of uncertainty or doubt about her belief, even if she did not explicitly acknowledge it.

If Alice did truly have absolutely zero doubt in her previous belief, then how could strong but inconclusive evidence have caused her to question her belief?

If Alice truly had absolutely zero doubt in her previous belief that the box contained only a dog, then it would be unlikely for her to change her belief based on the sound of a meow alone, as it would not be strong enough evidence to overcome her absolute certainty. In this scenario, other evidences or logical reasoning would have to be provided in order to change her belief.

It's important to note that the concept of "absolute certainty" or "absolutely zero doubt" is a theoretical concept, and it's very rare in real-life scenarios, most of the time people have some level of uncertainty. Even in the case where Alice is convinced that only a dog is in the box, a sudden meow would cause her to question this belief, as it is not consistent with her previous belief, and would lead her to investigate and gather more information about the situation.

So whenever you tell ChatGPT that Alice has "zero doubt" or "absolute certainty", it may be inferring that you're probably mistaken or exaggerating (since many people exaggerate all the time), and that Alice is strongly but not absolutely convinced. That's my alternative explanation for the output you've posted.

No, I said: if a dictionary says that to believe something is to assume it, then I believe it's wrong. I did not say the dictionary is wrong, I said that I believe it is wrong.

The first time, you indeed said you believe that the dictionaries are wrong. But the second time, you said:

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.

He is wrong: it's the other way around.

How is he "wrong" about his own notion of an assumption?

Would you say that most people outside of here would agree that when one assumes something, one cannot have any level of doubt about it?

No, I believe most people outside of here would agree that when one assumes something it can mean that one doesn't have any level of doubt about it.

If so, does she believe there is a 0% chance that she will receive unequivocal evidence otherwise?

Yes, if that's what she believes, which the word "assume" does not necessarily imply.

If she was previously absolutely certain that a dog is in the box, then why wouldn't she adopt one of the alternative hypotheses compatible with both her assumption and the evidence?

Because she might be attempting to be a rational open-minded individual and actually be seeking the truth.

By my prior notion of "believe with zero doubt", your prompt is vacuous, since it is impossible that "Alice believes claim X is true with zero doubt" but also "changes her mind", since if she can change her mind, then she didn't actually have zero doubt.

It's not impossible because of a fundamental aspect of reality: change.

It's entirely possible for x=1 at t=0, and x=0.8 at t=1.

Under that notion, ChatGPT is logically permitted to output whatever it wants, since it is not consistently capable of detecting absurdities in its input.

The fact that you think it's absurd doesn't mean it is absurd. It is not absurd to me.

So whenever you tell ChatGPT that Alice has "zero doubt" or "absolute certainty", it may be inferring that you're probably mistaken or exaggerating (since many people exaggerate all the time), and that Alice is strongly but not absolutely convinced.

It may, but it's clearly not, since in your interaction it said: "If Alice truly had absolutely zero doubt", and then concluded "it would be unlikely for her to change her belief based". You seem to have a motivated reasoning since you are ignoring what it is saying. It's not impossible for Alice to change her belief, even if she truly had absolutely zero doubt.

The first time, you indeed said you believe that the dictionaries are wrong.

No, I said I believed if they said X, then they would be wrong.

How is he "wrong" about his own notion of an assumption?

Because if you flip the definitions they are entirely correct under my view. Even under your view "assume" is stronger than "suppose", and he is saying the opposite.

No, I believe most people outside of here would agree that when one assumes something it can mean that one doesn't have any level of doubt about it.

If someone reads your words, "Most people assume we are dealing with the standard arithmetic" (from your 2 + 2 post), do you believe that they are likely to understand that you mean, "Most people have zero doubt in their minds that we are dealing with the standard arithmetic"?

Yes, if that's what she believes, which the word "assume" does not necessarily imply.

On the submission for your 2 + 2 Substack post, you write:

Challenging the claim that 2+2 is unequivocally 4 is one of my favorites to get people to reconsider what they think is true with 100% certainty.

Are you saying that "assuming something is true" is different from "thinking something is true with 100% certainty", and that you are making two different points in your Substack post and submission? Or are you saying that one can "think something is true with 100% certainty" without "believing" that it is true?

Because she might be attempting to be a rational open-minded individual and actually be seeking the truth.

Then why does it matter whether or not anyone assumes anything? If people are capable of accepting evidence against what they think is true, regardless of whether they previously had 100% certainty, then why should anyone avoid having 100% certainty?

It's not impossible because of a fundamental aspect of reality: change.

It is impossible by my own prior notion of "believe with zero doubt", which corresponds to assigning the event a Bayesian probability equivalent to 1. By Bayes' theorem, if your prior probability of the event is 1, then your posterior probability of the event given any evidence must also be 1. Therefore, if your posterior probability is something other than 1 (i.e., you have some doubt after receiving the evidence), then your prior probability must not have been 1 (i.e., you must have had some amount of doubt even before receiving the evidence).

I have barely any understanding of your concept of doubt, and this discrepancy appears to have caused a massive disconnect.

No, I said I believed if they said X, then they would be wrong.

This was after I linked to them saying it:

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).

I believe they are. dictionary.com says "believe" is "assume", but Merriam-Webster does not. One of them has to be wrong.

When you said, "I believe they are", were you not referring to the dictionaries being "flat-out wrong to say [those things]"? Or did the links I provided not show them saying those things?

Because if you flip the definitions they are entirely correct under my view.

How does this imply that his definitions are "wrong" when they are not flipped?

Even under your view "assume" is stronger than "suppose"

Where do I say that?

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