:death:

Where have I equivocated over the term reason? Don't tell me what equivocation involves - I know what it involves. Locate where I have done so. (you can't, can you?)

We're in disagreement for all sorts of reasons...

...not all sorts of people. Moron. — creativesoul

Er, what? Are you calling me a moron?

You are equivocating the term "reason" because you are using it in more than one sense in the same argument. This can be easily proven by means of substitution. The same practice will also clearly show that Reason is not a person.

Oh look! There it is directly above! — creativesoul

What the hell are you on about? Do it. Show the equivocation. Stop playing for time while you desperately look up the different meanings of the term 'reason'.

What's the difference between an explanatory reason and a normative reason? Come on know it all - what's the difference?

I don't like the wording here. It doesn't make any sense to say that some state-of-affairs is a truth-maker, as if some state-of-affairs makes some other state-of-affairs called the "truth". Which state-of-affairs are we talking about when using our knowledge - the state-of-affairs that made the truth, or the state-of-affairs that is the truth? Claims don't bear truth if they are wrong.

All you have done is state what makes truth and what bears the truth, but haven't explained what the truth is and how it is made by some state-of-affairs or carried in a claim. — Harry Hindu

In the Alice/rain hypothetical, the state of affairs is that the window is being hosed with water (i.e., it is not raining). When Alice looks out the window, she forms the belief that it is raining.

Her belief represents a state of affairs that has not obtained. Thus her belief is false. However if it were raining (i.e., if that state of affairs had obtained), then her belief would have been true.

That defines the ordinary meaning (or use) of our truth terms.

The standard model for knowledge is JTB. Since Alice's belief is false, she does not have knowledge. If it were raining, she would have had knowledge (since her belief would have been true and also justified by her looking out the window).

That defines the ordinary meaning (or use) of our knowledge terms.

Note that the logic of the use of those terms is demonstrated in that hypothetical. They are, in effect, formal models where claims are satisfied in particular scenarios (and not in others). Also, the models can themselves be contested, as with the Gettier problem (or with your claim that knowledge can be false).

In reality we're in the position of Alice in the hypothetical. Instead of stipulating a hypothetical world with full knowledge of what claims are true and false in that world, we are instead a part of the world we're seeking to represent. However the logic of the terms defined above apply in exactly the same way. That is, if we were in Alice's situation and formed the same belief, our belief would also be false and we wouldn't have knowledge.

If we can't have proof that one's knowledge is actually true, then it is illogical to say "truth" is a property of knowledge. — Harry Hindu

No. See above. If Alice's belief were true (i.e., if it were raining), then she would have had knowledge. Yet the justification for her belief (that she looked out the window) did not amount to a proof.

What is "proof"? — Harry Hindu

A proof is a guarantee of the truth of one's claim.

It seems to me that we can only ever talk about our knowledge, not the actual state-of-affairs. If we say, "I don't know if it is raining", then we're still talking about the state of our knowledge. — Harry Hindu

In that case yes, but if we say, "It is raining" and it is raining, then we are talking about the actual state of affairs.

Her belief represents a state of affairs that has not obtained. Thus her belief is false. However if it were raining (i.e., if that state of affairs had obtained), then her belief would have been true. — Andrew M

So truth is a state-of-affairs where one's claims accurately represent some other state-of-affairs.

Now you just need knowledge of this state-of-affairs called truth in order to make an accurate claim that knowledge entails truth. But you can't because it would require a level or perception that we can never attain - like being the thing you are making a claim about.

No. See above. If Alice's belief were true (i.e., if it were raining), then she would have had knowledge. Yet the justification for her belief (that she looked out the window) did not amount to a proof.

What is "proof"?
— Harry Hindu

A proof is a guarantee of the truth of one's claim. — Andrew M

How do you guarantee the truth of your claim? Isn't this the same as saying that you'd have to know that your claim is true? In order to guarantee the truth of a claim, you'd have to know the actual state-of-affairs, but you don't know if you do, so how can you say that knowledge entails truth? People use "know" and "knowledge" not to claim truth, but to claim justification for their belief. Since we can't have proof that our beliefs are accurate, we only have proof that our beliefs are justified, we don't use these terms as if they bear truth rather than justifications.

In that case yes, but if we say, "It is raining" and it is raining, then we are talking about the actual state of affairs. — Andrew M

What if we're brains in vats? How do you know your not a brain in a vat, or hallucinating when you say "It is raining."?

First, it is not a mistake to personify Reason. I have now provided - it feels like about 100 times - an argument that demonstrates Reason is a person. There are prescriptions of Reason; only a person can issue a prescription; therefore Reason is a person. — Bartricks

There are prescriptions of shit; only a person can issue a prescription; therefore shit is a person.

There are prescriptions of shit; only a person can issue a prescription; therefore shit is a person. — creativesoul

Er, no there aren't. I mean, what's a 'prescription of shit'? Have you been hitting the home brew again? (But on a positive note, that argument was valid. It's just it was rubbish, due to the first premise being false/incoherent).

Feigning ignorance of form...

Which person is Reason anyway?

:lol:

A proof is a guarantee of the truth of one's claim.
— Andrew M

How do you guarantee the truth of your claim? — Harry Hindu

You don't. Knowledge doesn't require proof. It requires that one's belief is both justified (a standard that is lower than proof) and true.

In that case yes, but if we say, "It is raining" and it is raining, then we are talking about the actual state of affairs.
— Andrew M

What if we're brains in vats? How do you know your not a brain in a vat, or hallucinating when you say "It is raining."? — Harry Hindu

Ordinarily the model is applied to the natural world of everyday experience (where we can point to what we mean by rain), not a supposed brain-in-vat world. So that renders the first question inapplicable (at least for ordinary claims). For the second, the question of knowing that it is raining is just whether your belief is justified and true. You don't need proof that all the things that could go wrong didn't go wrong (though, per Gettier, it does need to be the case that things didn't go wrong in ways that undermine the claim - i.e., that one was hallucinating would preclude the claim from being knowledge).

A proof is a guarantee of the truth of one's claim.
— Andrew M

How do you guarantee the truth of your claim?
— Harry Hindu

You don't. Knowledge doesn't require proof. It requires that one's belief is both justified (a standard that is lower than proof) and true. — Andrew M

If knowledge requires that one's belief is true, but you don't have any guarantees (proof) that your knowledge it true, then how it is that one can claim they have knowledge if they can't prove to themselves or anyone else they are using the word with, that their knowledge is true? If we have no guarantees that something is the case, then we don't ever know when we possess knowledge in order to use the word. If we can never be sure that what we say is true, then how can we attribute truth as a property of knowledge? "Truth" would be ever-elusive, and we would never know when to use the word, "truth" appropriately because we never have any guarantees (proofs) of what the truth is.

"Truth" would be ever-elusive, and we would never know when to use the word, "truth" appropriately because we never have any guarantees (proofs) of what the truth is. — Harry Hindu

We know when to use the word "truth" when we have a justifiable belief for when to use it and our belief is true.

Note that you keep presuming that one needs a guarantee (proof) in order to know something. But that is an infallibilist definition of knowledge, not the ordinary definition.

So I agree that one can never prove that one has the truth. It doesn't follow that one can never know that one has the truth. That's because the standard for knowledge is an ordinary and pragmatic one, not an infallible and unattainable one.

Now you just need knowledge of this state-of-affairs called truth in order to make an accurate claim that knowledge entails truth. But you can't because it would require a level or perception that we can never attain - like being the thing you are making a claim about. — Harry Hindu

So what can know about string theory and how can we know that? :naughty:

What if we're brains in vats? How do you know your not a brain in a vat, or hallucinating when you say "It is raining."? — Harry Hindu

If we were brains in a vat, what could we know and how could we know it? We experience life with our bodies and without them, we might record and regurgitate facts, but we would know not the meaning of them. Without a body what does time or rain mean?

We know when to use the word "truth" when we have a justifiable belief for when to use it and our belief is true.

Note that you keep presuming that one needs a guarantee (proof) in order to know something. But that is an infallibilist definition of knowledge, not the ordinary definition.

So I agree that one can never prove that one has the truth. It doesn't follow that one can never know that one has the truth. That's because the standard for knowledge is an ordinary and pragmatic one, not an infallible and unattainable one. — Andrew M

No, that's the way you used it in this thread. If we use the word "know" to imply more than just a justification for our belief, but also truth, then we'd need proof that our belief was also true to use the word, "knowledge" correctly. You're trying to have your cake and eat it too.

It is you who has provided an infallibist definition of knowledge by making truth a requirement. My definition is the one that would be the "ordinary" definition, as it allows knowledge to be only about justifications, not truth - of which you need proof the claim is true to say that you are using the term "know" correctly.

It appears that either you are just being inconsistent, or we are talking past each other.

My definition is the one that would be the "ordinary" definition, as it allows knowledge to be only about justifications, not truth - of which you need proof the claim is true to say that you are using the term "know" correctly. — Harry Hindu

OK, let's test our claims. I'll outline the three distinct models for knowledge that we've discussed here (K1, K2 and K3) and what they imply for two distinct hypotheticals (H1 and H2).

(K1) Knowledge requires proof and truth
(K2) Knowledge requires justification and truth
(K3) Knowledge requires justification

Note that the truth condition in K1 is redundant but I'll leave it there for clarity. That is, if there is a proof that it is raining, then it is true that it is raining.

Also, as we have discussed it, justification falls short of proof and so doesn't imply truth. That is, a justified belief can be false.

Finally, I haven't indicated belief (to reduce clutter), but it should be implied for each model.

--

(H1) It is raining. Alice looks out the window and forms the belief that it is raining (since it appears to her to be raining).

Per K1, Alice does not know that it is raining. That's because she lacks proof - she has not definitively ruled out all other possibilities such as water from a hose.

Per K2, Alice knows that it is raining. That's because her belief is justifiable and her belief is true.

Per K3, Alice knows that it is raining. That's because her belief is justifiable.

--

(H2) It is not raining. However Bob is hosing water on the window. Alice looks out the window and forms the belief that it is raining (since it appears to her to be raining).

Per K1, Alice does not know that it is raining. That's because she lacks proof - she has not definitively ruled out all other possibilities such as water from a hose.

Per K2, Alice does not know that it is raining. That's because her belief, while justifiable, is false.

Per K3, Alice knows that it is raining. That's because her belief is justifiable.

--

I'll leave it there for the moment. Do you agree with the above conclusions for each hypothetical?

This summarizes your problem:

Knowledge requires justification and truth — Andrew M

A proof is a guarantee of the truth of one's claim. — Andrew M

How do you guarantee that your claim is true? How do you show that your claim is true for it to qualify as using the term "knowledge" correctly?

You don't. Knowledge doesn't require proof. It requires that one's belief is both justified (a standard that is lower than proof) and true. — Andrew M

But the only way to know it is true is to have proof. Until you do you don't know when to use the word, "know". If you can't prove your claim is true, then you are misusing the term, "know". If you can't ever show that your claim fits one of the requirements of knowledge, then how can you ever use the term?

So, you seem to be saying that knowledge is something that we can never attain because it requires it to be true, but we never know it is true, so how is it that we know when to use the word, "know"?

In H2, K2, who is claiming that Alice does not know it is raining, and what proof do they have that their claim is true?

How do you guarantee that your claim is true? How do you show that your claim is true for it to qualify as using the term "knowledge" correctly? — Harry Hindu

There is no guarantee. Alice can show that her claim is true in H1 by pointing out the window since that is what justifies her belief. She can't show that her claim is true in H2 since her claim is not true in that hypothetical.

But the only way to know it is true is to have proof. — Harry Hindu

You're asserting K1 here and the rest of your questions assume it. Knowledge on K2 and K3 does not require proof. They require justification, which Alice has since her belief was formed by looking out the window. Thus she knows it is true in H1 on K2 without proof. Interestingly, she knows it is true in both H1 and H2 on K3 (again without proof). That's because she can have false knowledge on K3.

In H2, K2, who is claiming that Alice does not know it is raining, and what proof do they have that their claim is true? — Harry Hindu

That it's not raining is the state of affairs stipulated in H2. That's prior to any claims.

That it's not raining is the state of affairs stipulated in H2. That's prior to any claims. — Andrew M

That's strange. It was your claim that it is raining, not some state-of-affairs that it actually was raining. How do I know that you are right, when all you have to show is your justifications. If you can make a claim and assert that that is the state-of-affairs stipulated, then somehow you have gained true access to the world. How did you do that?

How do you guarantee that your claim is true? How do you show that your claim is true for it to qualify as using the term "knowledge" correctly?
— Harry Hindu

There is no guarantee. Alice can show that her claim is true in H1 by pointing out the window since that is what justifies her belief. She can't show that her claim is true in H2 since her claim is not true in that hypothetical. — Andrew M

If there is no guarantee, then you can't know that you ever used the word correctly. There is no way to correct it's use, if you can't guarantee that your use includes the truth.

You're asserting K1 here and the rest of your questions assume it. Knowledge on K2 and K3 does not require proof. They require justification, which Alice has since her belief was formed by looking out the window. Thus she knows it is true in H1 on K2 without proof. Interestingly, she knows it is true in both H1 and H2 on K3 (again without proof). That's because she can have false knowledge on K3. — Andrew M

You can prove you have justification, but you can't prove you have truth? What do you have to know in order to use a word correctly? Do you agree that word-use can be picked up and used without really knowing what they mean? For instance, when a toddler hears their parent say "Damn it!" when they get angry, and then copy it, do they really know what they are saying? Is there a difference between using words and understanding what words mean? It seems to me that we can use words that appears to be the correct use, because everyone else uses it that way, but there are cases where mass delusions exist and people use the same words like "I know the Earth is flat" without knowing the truth.

That's strange. It was your claim that it is raining, not some state-of-affairs that it actually was raining. How do I know that you are right, when all you have to show is your justifications. If you can make a claim and assert that that is the state-of-affairs stipulated, then somehow you have gained true access to the world. How did you do that? — Harry Hindu

I didn't. There's a difference between making a claim that it is raining (which I did not do) and presenting a hypothetical within which Alice makes a claim (which I did do).

To ask how I know that Alice exists, for example, or how I know that it is raining is misplaced. We're discussing a hypothetical state-of-affairs that I've stipulated, not an actual state-of-affairs. The premises of the hypothetical are taken as a given or as a basis of agreement (unless there is some reason to take issue with them).

If there is no guarantee, then you can't know that you ever used the word correctly. — Harry Hindu

You're using the word "know" in the sense of K1 again. On K2, you know that you used a word correctly when you have a justified and true belief that you did. You don't need a guarantee, you just need those conditions to be met.

You can prove you have justification, — Harry Hindu

No, you can't prove you have a justification either. Nor did Alice have such a proof in hypotheticals H1 and H2. She hadn't ruled out the possibility, for example, that she was looking at a virtual (VR) window instead. Whether something counts as a justification assumes a particular model for justification, itself contestable. Taking it further, suffering a hallucination may preclude one from having any (or very few) justifiable beliefs at that time.

No claims are provable except within the context of a deductive proof.

Do you agree that word-use can be picked up and used without really knowing what they mean? — Harry Hindu

Yes.

Is there a difference between using words and understanding what words mean? — Harry Hindu

Yes.

It seems to me that we can use words that appears to be the correct use, because everyone else uses it that way, but there are cases where mass delusions exist and people use the same words like "I know the Earth is flat" without knowing the truth. — Harry Hindu

Yes. In those cases, only on K3 would they have knowledge (assuming their claim was justifiable, which is contestable). On K2, they thought they knew that the Earth was flat, but didn't actually know that.

I didn't. There's a difference between making a claim that it is raining (which I did not do) and presenting a hypothetical within which Alice makes a claim (which I did do). — Andrew M

Then your talking about something that no one knows anything about. So how does one get to know it is raining?

You're using the word "know" in the sense of K1 again. On K2, you know that you used a word correctly when you have a justified and true belief that you did. You don't need a guarantee, you just need those conditions to be met. — Andrew M

How can you claim that your belief is true without proof? If you don't need proof that you are using the term correctly, then it seems that thing you don't need proof of isn't a necessary component of "knowledge", or it's not important to know when you're using "know" correctly.

If you can't enforce the rules for the use of the term. "knowledge", then that is to say that there aren't any rules when using the term.

So how does one get to know it is raining? — Harry Hindu

I've presented three models (K1, K2, and K3) that each provide a potential answer. Hypothetical's H1 and H2 demonstrate the consequences of each model for Alice's claim that it is raining.

On model K1, Alice never knows it is raining since proof is unobtainable.

On model K3, Alice knows it is raining whenever her belief that it is raining is justified. The problem is that in H2, she knows it is raining when it is not raining.

On model K2, Alice knows it is raining in H1 but not in H2.

Of those three models, K2 is the best explanation for ordinary usage. It's also the model philosophers generally accept (Gettier aside).

So imagine yourself in Alice's position where it appears to be raining outside. You can't easily distinguish H1 from H2 (nor would all the claim-defeating possibilities like water from a hose even come to mind). But per K2, if you are in H1 your belief meets the conditions for knowledge. If you are in H2, your belief does not.

So to answer your question, you get to know it is raining when you are in scenarios like H1, but not when you are in scenarios like H2. If you wish to, you can also do things like go outside to check. The benefit is that you can potentially rule out or discover some H2-like scenarios (though not all), but it also bears the practical cost associated with the checking. The standard for justification is a pragmatic middle-ground between not bothering to look at all (i.e., guessing or believing whatever one wants to believe) and endlessly checking (which will still fall short of proof).

How can you claim that your belief is true without proof? — Harry Hindu

Because it is justifiable to do so - that's the normative rule for when we can make knowledge claims. If we needed proof, no claim could ever be made.

Now that means that we can sometimes inadvertently make false claims. That is, we can use the word "rain" when there is no rain, which would be a misuse. Normatively, that is okay - we're not infallible and we don't hold anyone to that standard. But veridically, we would have made a mistake. If we have made a mistake then it's not knowledge. That's a logical consequence of the model K2 - it doesn't depend on anyone ever discovering the mistake.

If you don't need proof that you are using the term correctly, then it seems that thing you don't need proof of isn't a necessary component of "knowledge", or it's not important to know when you're using "know" correctly. — Harry Hindu

We ultimately want true claims, not false claims. That's why truth is a condition of knowledge. But we also recognize that the possibility of mistakes shouldn't preclude people from making claims at all. It just won't be knowledge if the claim is false.

If you can't enforce the rules for the use of the term. "knowledge", then that is to say that there aren't any rules when using the term. — Harry Hindu

The only way to enforce the rules upfront is either to require proof (per K1), which makes knowledge unattainable, or to allow false claims to count as knowledge (per K3).

What we do instead is to enforce the rules retroactively (per K2). That is, if we discover a misuse it is retroactively corrected. For example, suppose in H2 Alice later discovers that Bob was hosing water on the window. In that case, she recognizes that she didn't know it was raining at the time, she only thought she did.

How can you claim that your belief is true without proof?
— Harry Hindu

Because it is justifiable to do so - that's the normative rule for when we can make knowledge claims. If we needed proof, no claim could ever be made. — Andrew M

Exactly. Which is to say that justification is the only requirement for when someone uses the word, "know".

Now that means that we can sometimes inadvertently make false claims. That is, we can use the word "rain" when there is no rain, which would be a misuse. Normatively, that is okay - we're not infallible and we don't hold anyone to that standard. But veridically, we would have made a mistake. If we have made a mistake then it's not knowledge. That's a logical consequence of the model K2 - it doesn't depend on anyone ever discovering the mistake. — Andrew M

I think we got mixed up again. Are we talking about the state of one's knowledge, or the state of the weather? When the window is being hosed, what is the distinction between, "I know it is raining" and "It is raining."? The latter stems from the prior. You can't say, "It is raining." and say that it is about the weather without having some justification. It would be more like guessing.

If you can't enforce the rules for the use of the term. "knowledge", then that is to say that there aren't any rules when using the term.
— Harry Hindu

The only way to enforce the rules upfront is either to require proof (per K1), which makes knowledge unattainable, or to allow false claims to count as knowledge (per K3).

What we do instead is to enforce the rules retroactively (per K2). That is, if we discover a misuse it is retroactively corrected. For example, suppose in H2 Alice later discovers that Bob was hosing water on the window. In that case, she recognizes that she didn't know it was raining at the time, she only thought she did. — Andrew M

I thought you said that we can't have proof, yet you are now saying that you can have proof retroactively?

If Alice was using the term in the normative way, then she is using it as I have defined it. The veridical use would be your definition. But you have shown that the veridical use refers to something unattainable, while the normative use refers to having justification only. I think we are pretty much in agreement, it's just you haven't realized it yet.

Are we talking about the state of one's knowledge, or the state of the weather? — Harry Hindu

Alice has formed a belief about the state of the weather (in H1 and H2). We are talking about the state of her knowledge (in terms of K1, K2 and K3).

When the window is being hosed, what is the distinction between, "I know it is raining" and "It is raining."? — Harry Hindu

When Alice forms the belief, "It is raining", her belief is about the state of the weather. Per K2, she knows that it is raining in H1 but not in H2.

If Alice further forms the belief, "I know it is raining", her belief is about the state of her knowledge. Per K2, this latter claim is justified in both H1 and H2 but only true in H1. Therefore she knows that she knows it is raining in H1 but not in H2.

The latter stems from the prior. You can't say, "It is raining." and say that it is about the weather without having some justification. It would be more like guessing. — Harry Hindu

That statement is still about the weather even if you are guessing. An unjustified claim can still be true, but it wouldn't be knowledge under models K1, K2 or K3.

I thought you said that we can't have proof, yet you are now saying that you can have proof retroactively? — Harry Hindu

No, a revised claim is subject to the same conditions for knowledge as the original claim. Which is to say, there is no proof for the revised claim either.

If Alice was using the term in the normative way, then she is using it as I have defined it. The veridical use would be your definition. But you have shown that the veridical use refers to something unattainable, while the normative use refers to having justification only. I think we are pretty much in agreement, it's just you haven't realized it yet. — Harry Hindu

The veridical use is attainable - see H1, K2 where Alice has a justified and true belief that it is raining, and therefore has knowledge on that model (K2).

I think we are pretty much in agreement, it's just you haven't realized it yet. — Harry Hindu

Here's a question for you. In H2, suppose that Alice later discovers that Bob was hosing the window with water. Thus she now knows that it wasn't raining earlier.

Did Alice know that it was raining at the earlier time?

Here's a question for you. In H2, suppose that Alice later discovers that Bob was hosing the window with water. Thus she now knows that it wasn't raining earlier.

Did Alice know that it was raining at the earlier time? — Andrew M

How does she know it wasn't raining while Bob was hosing the window? Bob hosing the window isn't justification for it not to have rained earlier.

This goes back to what I said about making objective observations. You seem to be saying that we check our knowledge when we get outside of the thing we are talking about. So, if we know that to really know whether or not is raining is to go outside and look, then looking out the window isn't proper justification for knowing it is raining. If this is the case, then no, Alice didn't know it was, or wasn't raining, because she didn't have proper justification. If all she needs is justification, then yes, Alice knew it was raining and now she knows something different - that it wasn't.

If you want to bring up the possibility of Alice hallucinating while outside, how do you retroactively show she is hallucinating - by asking someone else? How do we know that they aren't hallucinating, or lying? If all you can have are justifications and truth is something elusive, then it stands that the only requirement for knowledge is justification. No one can ever know if Alice used the term, "know" correctly, if truth is a requirement for its correct usage, which is the same as saying it isn't a requirement at all.

How does she know it wasn't raining while Bob was hosing the window? Bob hosing the window isn't justification for it not to have rained earlier. — Harry Hindu

OK. Suppose Bob (who she believes to be honest and reliable) told her that it wasn't raining earlier and that he was hosing water on the window. Thus Alice would justifiably form the belief that it was not raining earlier.

This goes back to what I said about making objective observations. You seem to be saying that we check our knowledge when we get outside of the thing we are talking about. — Harry Hindu

No, there is no proof (or getting outside the thing we are talking about).

So, if we know that to really know whether or not is raining is to go outside and look, then looking out the window isn't proper justification for knowing it is raining. If this is the case, then no, Alice didn't know it was, or wasn't raining, because she didn't have proper justification. — Harry Hindu

Alice never has a "proper" justification if proof is required. That is model K1 (which we both reject). Alice's initial belief that it is raining is justifiable in both H1 and H2.

If all she needs is justification, then yes, Alice knew it was raining and now she knows something different - that it wasn't. — Harry Hindu

OK, that is model K3 (which you seem to accept and I reject). The consequence is that per hypothetical H2, Alice at the earlier time knew that it was raining when it was not.

If you want to bring up the possibility of Alice hallucinating while outside, how do you retroactively show she is hallucinating - by asking someone else? How do we know that they aren't hallucinating, or lying? — Harry Hindu

If you have reason to believe someone is hallucinating then you factor that into your judgment. But, as discussed, any reasons you have will fall short of proof, and there is always the possibility of being mistaken despite your belief being justifiably formed. That's the way it goes sometimes when proof is not obtainable.

If all you can have are justifications and truth is something elusive, then it stands that the only requirement for knowledge is justification. No one can ever know if Alice used the term, "know" correctly, if truth is a requirement for its correct usage, which is the same as saying it isn't a requirement at all. — Harry Hindu

Alice has no proof that she used her words correctly. It doesn't follow that she didn't, in fact, use her words correctly. Which she did in H1 on model K2.

You seem to think that rejecting model K3 means that one therefore requires proof of the truth. That's not the case. Proof is not a requirement for K2, only truth and justification is. Since Alice's belief is both true and justified in H1, it follows that Alice has knowledge in H1 per K2.

A thread worthy of careful revisitation...

Around page ten, it gets interesting...

Mary the super-scientist. If Mary learns something/anything new, the JTB theory of knowledge is (hopelessly) inadequate.