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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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"?
On the submission for your 2 + 2 Substack post, you write:
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?
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 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.
This was after I linked to them saying it:
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?
How does this imply that his definitions are "wrong" when they are not flipped?
Where do I say that?
No, I believe in this particular case they would understand that "assume" in this context means "take for granted", but that doesn't contradict the notion that they have zero doubts in their minds. They have zero doubts in their mind because most people don't see there's any doubt to be had.
No.
No. In my substack article I said: "Why insist on 100% certainty?". My point and the objective of my point are two different things.
Because the fact that it can happen doesn't mean it's likely to happen.
Not everyone follows Bayes' theorem.
And if it's true that under Bayes the probability of an event doesn't get updated if the prior is 1, regardless of the result. Then that proves Bayes is a poor heuristic for a belief system.
Yes, I was. So I believe the dictionaries saying those things are wrong.
The links you provided showed one dictionary saying those things, therefore if I believe those dictionaries saying those things are wrong, I believe that one dictionary saying those things is wrong.
I explained that in the very next sentence.
You literally said: «since most people here were under the impression that by an "assumption" you meant a "strong supposition"».
In your view, is having doubt the result of a conscious consideration of whether one may be wrong? Or can one have doubt even before considering the matter?
How does this property prove that Bayes' theorem is a poor heuristic? Since most people can change their minds given enough evidence, a Bayesian would infer that it's rare (if even possible) for someone's prior probability to be exactly 1 in real life. What is the issue with the Bayesian statement that hardly anyone holds a prior probability of exactly 1?
The links point to both dictionaries in question, not just one.
Under my own notion, that I use in everyday life, "to assume" is not stronger than "to suppose", so my question still stands. How is the opposite statement being correct under your definitions relevant to his statement about his own definitions being "wrong" per se? What bearing do your definitions have on the intrinsic correctness of his definitions?
First, I attributed that to "most people here", not myself. Second, I was talking about their impression of your meaning of an "assumption", not their own prior notions of an "assumption". Personally, my prior notion places no relative strength between an "assumption" and a "supposition"; I would not hazard to guess how strong others' prior notions of an "assumption" are without asking them.
Both. Some people can have doubt immediately, other people do not doubt unless they are asked to consider their doubt level. And most people increase their level of doubt once they are asked to put skin in the game, for example with a bet.
I completely disagree with that statement. Most people cannot change their minds regardless of the evidence. In fact in the other discussion I'm having on this site of late the person is obviously holding a
p=1(zero room for doubt).And only one of them is saying those things.
That is what we are talking about: it's your view that most people ascribe the meaning of
X, if a person ascribes the meaning opposite ofX, that is opposite to your view.Perhaps they assign their belief a probability different than 1, but they don't consider your evidence very strong. But I can't say for certain, since I haven't seen the discussion in question. How do you know that your evidence is so strong that they would change their mind if they had any room for doubt?
Any term X has several possible meanings. When one says the term X, one generally has a particular meaning in mind. And when one hears the term X, one must determine which meaning the speaker is using, if one wishes to correctly understand what point is being made. Usually, one infers this from the surrounding text, alongside one's knowledge of which meanings are often used by other speakers in a similar context. But one can simultaneously infer one meaning in one speaker's words, infer another meaning in another speaker's words, and use an entirely different meaning in one's own words.
When you say that we should not "assume" something, it is my understanding that you mean that we should not think that something is true with zero possible doubt. It is also my understanding that you do not mean that we should never suppose something strongly with little evidence.
What I allege is that most people, when attempting to determine your meaning of "assume", do not rule out the latter meaning. And since most speakers, in most of their speech and writing, include the possibility of doubt in their meaning of "assume", most people are likely to incorrectly infer that you probably include the possibility of doubt in your meaning of "assume".
Therefore, when they determine your meaning of "not assume", they are likely to infer that you mean something closer to "not suppose something strongly with little evidence" than "not think that something is true with zero possible doubt". (It isn't relevant here whether they think either of "assume" or "suppose" is somewhat stronger than the other: what matters is that there exist certain states of mind including some level of doubt, and they incorrectly infer that by saying we should "not assume" things you mean that we should not hold any of those states of mind.)
I'm not saying that most people are unable to understand your terminology, or that your terminology is inherently wrong. I'm saying that most people aren't very familiar with your terms, and they're likely to infer meanings that are overly inclusive. This makes the inferred negations of your terms (e.g., "not assume") overly exclusive, which makes most people miss your point. Thus my original request that you clarify your terminology upfront.
No, it has absolutely nothing to do with my evidence. The claim is 100% false, regardless of the evidence.
He literally said there was no possibility of
Xbeing true: "Do you accept the possibility that X may be true?" "No".You are forgetting the context of this subthread. In thus subthread we are not talking about what I mean, we are talking about the definition that one random stranger gave you, which I claimed goes contrary to your claim.
You claimed: «most people here were under the impression that by an "assumption" you meant a "strong supposition"».
In this subthread
Xis "strong supposition", it's your view that most people's definition of "assumption" is "strong supposition", you provided different examples of people you asked, and one of them gave you the exact opposite: that "supposition" was a "strong assumption". This is the opposite of what you claimed most people were under the impression of.You keep forgetting the context of the claims you are making.
By X I suppose you refer to the statement "2 + 2 = 4 is not unequivocally true". Perhaps by the statement "it is possible that X is true" (which I'll call Y), you meant that "there exists a meaning of the statement X which is true". However, I believe he interpreted Y as something to the effect of, "Given the meaning M which I would ordinarily assign to the statement X, there exists a context in which M is true." It is entirely possible that the proposition he means by Y is unequivocally false, even though the proposition you mean by Y is unequivocally true: that is, he misinterpreted what you meant by Y.
In particular, it is my understanding that when you say X, you mean, "There exists a meaning of the statement '2 + 2 = 4' which is false." You demonstrate this in your original post, so that provides an example of a meaning of X which is true. But I believe that his meaning M of X is something to the effect of, "Given the meaning M´ which I would ordinarily assign to the statement '2 + 2 = 4' (i.e., a proposition about the integers or a compatible exension thereof), there exists a context in which M´ is false." Since the proposition "2 + 2 = 4" about the integers can be trivially proven true, he believes with certainty that M´ is unequivocally true, thus M is unequivocally false, thus "it is impossible that X is true" (by his own meaning).
(In fact, I still wouldn't say that his belief that M is false has probability 1, but it is about as close to 1 as it can get. It's just that to convince him that M is true, you'd need an even more trivial mathematical proof of ¬M´ which he can understand, and he believes with probability as-close-to-1-as-possible that such a counterproof does not exist, since otherwise his life is a lie and basically all of his reasoning is compromised.)
So be it. I'll grant that my claim there was made based on a hasty impression of the other comments, and I do not actually know for sure whether or not most people on this site inferred a meaning of your words precisely compatible with my earlier statement. But I did not make that claim for its own sake, but instead in service of my original argument. (In fact, most of what I've been saying has been intended to relate to my original argument, not to that particular claim. But I have not been at all clear about that; my apologies.)
Having thought about it a bit more, I'll defend a weaker position, which I believe is still sufficient for my original argument. Most people in general, when they hear someone say that a person "assumes" something, infer (in the absence of evidence otherwise) that what is most likely meant is that the person's state of mind about that thing lies within a particular set S, and S includes some states of mind where the person still has a bit of doubt about that thing.
Thus, most people would infer that if someone says a person "doesn't assume" something, they infer that they most likely mean that the person does not harbor any state of mind within S, and consequently, the person does not harbor any of the states of mind that are within S but include a level of doubt.
Would you say that by "not making assumptions", you specifically mean "not thinking things are true with zero possible doubt"? Because if so, then everyone whose inferred set S includes states of mind with nonzero doubt would have misinterpreted the message of your post, if they had not already found evidence of your actual meaning. Thus my real claim, that most people "aren't going to learn anything from your claims if you use your terminology without explaining it upfront" (which is an exaggeration: I mean that most people, just looking at your explanations in your post, are unlikely to learn what you apparently want them to learn).
As the user in question, I can clear this up: Although I didn't make this clear at the time*, I was referring to the statement "2+2=/=4 (mod 4)" (which was @felipec 's argument in favor of "2 + 2 = 4 is not unequivocally true").
This is a plain mathematical statement which I disproved (I didn't publish the formal proof because I wasn't challenged on the informal rebuttal). I consider mathematical proof adequate justification for certainty.
*Perhaps this led to confusion, I might revisit the thread with that in mind.
Notably, this is not the case, the argument in the original post was flawed and the example does not demonstrate what it was supposed to. I had pointed this out in another comment thread and referred to it.
Regardless of what
Xis, you stated that if it's related to mathematics, there was 0% chance of you interpreting it wrong or your conclusion being wrong.More options
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No, it's a meta argument.
Xcould be anything. The user arguedXis false regardless of any interpretation if it's about math.I disagree this is the case, but let's run with your notion.
Are you saying that "doesn't assume" doesn't include any level of doubt? If so, that doesn't fit with what most people think. And if "doesn't assume" includes a level of doubt, then that's contrary to your notion that
Sincludes a level of doubt, because then clearlyS'should not include a level of doubt.The level of doubt is a separate issue. When you wake up do you assume the air is safe to breathe? Clearly close to 100% of the days you wake up you don't even think about that question, if someone were to ask you "are you 100% certain the air is safe to breathe" you might ponder the question and come to the conclusion that you are not 100% sure, but that's only after you have pondered the question.
A rock doesn't have a level of doubt, neither does an unconscious person. This can be considered a failure to adopt any doxastic attitude, but the same applies to a person who has not considered the question, which includes you most days you wake up regarding the question of air safety. Most days you just take for granted that the air is safe, thus most days you assume the air is safe, and don't even consider any level of doubt.
If they don't learn anything it's because they assume (as take for granted) that I'm saying something that I'm not, and they are not willing to consider the possibility that they might be wrong.
(see how my definition of "assume" is actually useful, whereas yours is not as much)
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