An explosion can be contained by adopting paraconsistent logic, which @Banno likely knows very well. This would maintain the fallibilist spirit of the OP.
The question is ill-formed as is; more data is required.
Since both supposedly know truths, then ‘it’ refers to truths. In this sense, both really knows it.
“Some truths conflict. The earth stands still, revolves about the sun, and runs many another course all at the same time. Yet nothing moves while at rest.”
- Nelson Goodman, Notes on the well-made world (1984)
So, “the earth is in motion” is true in the heliocentric sense, while “the earth is at rest” is true in the geocentric sense. When they are used in their different senses, there is no contradiction.
WHY would just knowing some thing, for certain, cripple anyone’s curiosity.
There are lots of things that ‘we’ can KNOW, with certainty’, and not a single “ounce” of curiosity would be lost nor removed.
Again, another example of ‘confirmation bias’.
Which is more or less exactly what ‘you’ are doing and demonstrating here.
This sounds like ‘those people’ who ‘try to’ claim ‘we cannot know the truth’.
Considering that there are plenty of things that we can know for sure or with certainty, does this Fact, “put holes in your theology of doubt”,
If two human beings are claiming ‘to know’ opposite things are true, then both of them, obviously, do NOT ‘know’.
One can only logically, Accurately, and Correctly claim to ‘know’ something if and when they have the Facts and proof for the claim.
Well, how might a paraconsistent fallibilism work?
The idea is that a theory such as U(x)(Px⊃Qx) is falsified by an observation (Px & ~Qx); It’s a reductio, in that U(x)(Px⊃Qx) and (Px & ~Qx) yield a contradiction…
But if we can have contradictions, then the falsification does not go through.
So, what’s the next step, if we are to have a paraconsistent fallibilism?
Take whatever variable as prior until it’s falsified by additional investigation. Flip a coin if you must.
if you keep A ^ ~A, it never gets falsified.
So flip the coin and take A | ¬A & ¬(A & ¬A). Doesn’t mathematics have an axiom of choice? Well, there’s your problem.
Muddled.
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I’m joking. Paraconsistent logic allows for explosions since the immediate result is taken as true until proven otherwise. Since the explosion is a finite chain, there is no problem and no actual explosion. This is how computers manage to track the messiness of real-world events. Paraconsistent logic is where the conversation goes if we chose to express the original epistemological problem as a logical one.
Certainly. Assuming you’re not using a version of “knowledge” with an impossibly high bar.
This is not a story. It’s a question. There is no author with privileged access to the answer.
If Jones knows there is a lion behind that tree, and Smith knows there is no lion behind that tree, which one of them really knows?
(Smith says it’s just a pile of cardboard boxes. Jones is blind but an expert in lion calls.)
Which one of them really knows the status of the lion?
I’m not sure why you keep insisting on this after I have agreed to it quite clearly. Only one of them can be right, at least in the world of this question.
My puzzle depends on that distinction.
Yes. Stipulated.
But I see you use the word ‘usually’.
Are there cases outside of formal thought systems where you can discern truth from falsity in a way which transcends your personal judgment?
Let’s say you and 99 others have been given every opportunity to investigate the lion.
97, including you, insist there is a lion, but three of the observers disagree.
One is a prophet of God. One believes there is a Universal Force which he can access. And one is a language nerd who argues that this animal is a hybrid… not a true lion.
Who really knows the status of the lion?
I flunked out of algebra, but business math wasn’t so hard.
You are talking my language.
Well, I cannot provide you with a Yes or No to the question, but you are welcome to investigate.
I’m just asking what happens when two people investigate and arrive at contrary knowledge.
Which one of them really knows?
Using the standard definition of “know”, it’s not applicable; the question is indeterminate. Using a more permissive definition, and omitting the trial and error approach I suggested, we might say “both and neither” at once. This takes us into Eastern logic, where mysticism thrives; a place I dare not tread.
So in your conception, it is impossible to know a false thing?
That has not been my experience in the world. I encounter people all the time knowing things which appear false to me.
I mean, I don’t know the things are false, but I feel pretty sure about it, and I often meet people who know opposite things, so it seems like at least one of them must be knowing something false.
Yes… as judged by me, ages.
That’s all I’m saying.
In my estimation you’ve overlooked something in the scenario. I forgot the meanings of the words but “defeasible”, “ampliative” pop up. Perhaps 
this will help
A fairly interesting ‘fact’ (independent of environment) is that water has a critical point at around 22 MPa, 374 C beyond which the difference between a liquid and gas is indistinct. Water has around 14 phases, not just solid, liquid, or gas.
I hope noAxioms won’t mind me quoting his post in a different thread. @noAxioms if you’d like to participate. Good day
Very many people seem to see it that way.
But I don’t. It’s just hard for me to believe that I have direct access to reality itself. I live in a black and silent cave and can only make my best guesses about what’s out there. Some guesses are backed with overwhelming evidence, in my opinion. Such massive evidence that it would be wasteful to go around actively doubting it all day. But if I meet a stranger who claims I am wrong, I will listen, at least for a moment.
And I won’t claim that my knowledge is shared by God. Not any of it. That lion could indeed be an hallucination. I am not privy to a God’s-Eye view.
I’m using a lion behind a tree to give my opponents every possible advantage. But sensory experiences are only a tiny fraction of what humans claim to know, I think, and it is complicated and removed one step by translation into language.
When you say ‘an impossibly high bar’, I’m not sure what you mean.
I am saying that ‘to know’ is a verb. It means we are doing something. But what are we doing when we are knowing? Well, I think we are putting ourselves in a mental state of certainty. We’re making a claim that our internal view is equal to the external universe.
Anyone can do it.
I feel like there are two ways of looking at this. The first being that since we can’t know if reality is actually how we perceive it, then we can never really be certain about anything. Which would mean there is no way to know for certain who is correct in regard to A or Not-A.
However, our perception of reality might be correct for all we know. Meaning there would be an answer one could arrive at with certainty. But there’s no way to know either way.
That leaves the other way to approach this. We use the scientific method to verify something is likely to be true. We then peer-review as a form of quality control to ensure that the data is true. Now this is not perfect either, because if we suddenly discover something new that can change what we believed. However, it’s as close as we can get at any point in time to being certain. So, I’d consider that I might be wrong with A or Not-A, but then I’d make other people check it out and go with the most agreed upon conclusion.
I think for the most part, that in everyday life we are not doubting the things we’ve come to be certain about because we have consensus. And that’s ok, we use our perception of the world to navigate it, even if it isn’t perfect. If someone tells me the Earth is flat, I’m not listening at all. I’m certain it isn’t, even if there’s a tiny chance that it is.
But in more nuanced things like politics and culture, I think we should be more willing to question our beliefs and listen to what opposing views are saying, even if they don’t change our minds.
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