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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Notes -
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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