I think you ought to read, 1984. Winston Smith did believe that 2+2=5. To insist he did not is to beg the question.

You wrote that beliefs have to be acquired in a reasonable or appropriate way. A case in which a belief is not acquired in a reasonable or appropriate way is a counterexample.

But being caused to believe by being given a serum, or by being frightened into belief is not acquiring a belief in a reasonable or appropriate way.
Therefore, both are counterexamples. QED

A case in which a belief is not acquired in such a way entails that the belief is not present.

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Then to say that something is a belief only if it is acquired in such a way is a blatant tautology, since if it is not so acquired, then it is not a belief. Tautologies are empty, and give no information. They are just "definitional". But in fact, people have all kinds of beliefs that are acquired in ways that are not acquired in the way you define them as being acquired on pain of their not being beliefs.

I heard of a child fearing to touch anything made of satin because she believed it was made of "Satan", and she believed it because she heard her mother say it was made of satin, and thought her mother said, "Satan". Are you telling me the child did not believe the material was made of "Satan"?

It's not a tautology. Acquiring is not the same thing as believing what is required. Look at the schema again. Look at examples of what tautologies are, again, and understand just what tautology means.

Yes, the child would not believe the material is Satan. But that's not because of the belief formation condition. I'd likely say such a proposition is unthinkable.

You make it seem like you have a problem with the formation condition, but your arguments have all been directed at the thinkability condition.

I'm not sure what's going on, but you're making a lot of mistakes and misapplying weighty terms (like "tautology"). It doesn't seem to be that you're actually coming to understand anything. Are you actually agreeing with me and understanding at each step along the way? Or are you just ignoring my arguments because you have new complaints to make? It doesn't seem like you're learning or in the business of learning.

The child does not believe the material is made of Satan? Then why is she frightened?
You seem to be in "the grip of a theory".

Suppose we change the statement slightly and say the child (through mishearing) believes the material is controlled by Satan or has associations with Satan, and will therefore cause her harm. This seems to rectify the category mistake. Does this 'belief' now meet (a) the thinkability condition, (b) the belief formation condition?

Suppose we change the statement slightly and say the child (through mishearing) believes the material is controlled by Satan or has associations with Satan, and will therefore cause her harm. This seems to rectify the category mistake. Does this 'belief' now meet (a) the thinkability condition, (b) the belief formation condition?

And what of Winston Smith of Orwell's 1984? Can he believe that 2+2=5, or are we to believe that is impossible because Nerdfiles tells us it is, although Orwell tell us he did believe that?

In any case why cannot I believe a category mistake? Suppose I claim to bellieve that the number three is purple. Why can't I believe that?

Your normative principle is a problem of knowledge similar to the Gettier problems, that is true belief without proper justification.

Belief can be belief no matter how it is justified or formed, and it seems that you are relying on anecdotal evidence that I doesn't make sense to me to support its inclusion.

An example of belief that was not formed up to your standards would be the belief in a lie by someone with assumed authority.

You have stated that it is not the proposition that is believed, but the other's acceptance of the proposition that is believed.

That is a misunderstanding of the Gettier problem.

Gettier problems presume justified true belief. It's not that the justification is improper. It's simply that we cannot say the person has knowledge. The whole point of the Gettier problem is to find a fourth condition for knowledge not to determine the best definition of justification.

However, some epistemologists try to show that a better account of justification resolves the Gettier problem but that is not what Gettier's conclusion calls for. It calls for a fourth condition. Gettier presumes that JTB is insufficient not that justification is lacking, for he presumes that the examples have adequate justification.

Looking for a fourth condition will supplement the belief, justification and truth conditions, not replace them or undermine them.

"Belief can be belief" is like "War is war"; it's tautologies. That much should be clear. I'm not sure how a tautology will confute any claim.

Where have I stated this? You can certainly believe things based on lies. Though likely the belief will be false, or more likely your knowledge will be shaky.

What? S believes that P. The proposition is believed. I'm not sure how this can get confused. It seems straightforward and clear.

I have provided argument. I'm doing more that just saying it.

The proposition does not have sense. It is not possible for it to be true. It's not the kind of thing that can be true. It has no truth conditions.[INDENT]I went on and on about this in talking about logical grammar earlier. Merely because you form a grammatical sentence in English, that does not guarantee that it has a sense. "The Communist party is 200 pages long" has no truth conditions. It's not false or true; it is senseless. You wouldn't look for the first page to begin counting, to confirm or falsify its truth. You'd say, "That doesn't make any sense." You cannot believe "The Communist party is 200 pages long."
[/INDENT]It's Aristotle's law of noncontradiction. "One cannot say of something that it is and that it is not in the same respect and at the same time."

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Can you provide a Gettier-like counterexample that doesn't rely on a justification through false premises?

That is quite obviously the problem, if you wish to call it a problem, presented by these cases. No problem extends from JTB, but from equivocation due to the aforementioned ambiguity of the term "justification". What is the point of using justification in the definition of knowledge if it doesn't need to be valid justification.

How close is this to a Gettier counterexample:

I believe all apples are green.
I believe only fruits are green.
Therefore I believe apples are fruit.

Its a true belief, just like in the Gettier counterexamples, and just like in the counterexamples my belief rests on false premises. Yet it hardly seems like there would be any difficulty in dismissing anyone who would call this knowledge because the justification is ludicrous.

My point is that there is no difference between a doctor who injects a serum that causes belief, and an authority that lies to cause belief. It is still belief no matter how substandard the formation is.

But why cannot Winston Smith, or anyone else, believe a contradiction, which is, of course, false, is true. People believed many false beliefs to be true, why can't Winston Smith just because he believes a contradiction to be true?

And why cannot I believe that it is true that the number 3 is purple for the same reason.

"Justification through false premises"? I'm not sure what this means.

Gettier problems work like this: S passes our Justified True Belief definition of knowledge.

So, using our schema, S knows that P because[INDENT]1. S believes that P (it is true that S believes that P),
2. S has justification or evidence for P (it is true that S has
justification or evidence for P), and
3. P is true (it is true that P is true).
[/INDENT]The Gettier problem is supposed to deny the claim that jointly those conditions suffice for S's knowing P.

Not close at all. It's a syllogism. That "only" is doing something suspicious. And "believe" is doing something suspicious too. You're blending implicitly the notion of "observation" and "induction" into a deductive argument.

All Ss are Ps.
All Rs are Ps.
Therefore, Ss are Rs.

All cats are mammals.
All dogs are mammals.
Therefore, all cats are dogs.

This is clearly invalid. But what is your "only" doing? It's implicating some extra-deductive rule or thing.

If any of the premises (the conditions which are necessary) are falsified, then S does not know. Gettier spent the whole paper trying to get us to accept that the premises are not falsifed. Gettier is not resting anything on 'false premises.'

Why? Having a reason to believe is different from being caused to believe.

Here, maybe you will admit this to be valid logic:

All apples are green.
If something is green, it is a fruit.
Therefore all apples are fruit.

To me, the logic seems perfectly valid, yet the premises are false.

Absolute nonsense.

CASE I:

Proposition (e): The man who will get the job has ten coins in his pocket is the proposition in question. It is a true belief.

It is entailed from the conjunctive proposition (d): Jones is the man who will get the job, and Jones has ten coins in his pocket.

Gettier is quite plain when he says:

Let us suppose that Smith sees the entailment from (d) to (e), and accepts (e) on the grounds of (d), for which he has strong evidence. In this case, Smith is clearly justified in believing that (e) is true.

Gettier states that belief in (e)is justified through the reasonable belief in a false premise, as he explicitly states that proposition (d) is false.

Is your language confusing or do you say that belief with cause but not reason can exist?

(d) is irrelevant at that point because Smith is entertaining (e). That (d) is not Smith's justification, so it doesn't matter if it is false.

Gettier's own words:

Let us suppose that Smith sees the entailment from (d) to (e), and accepts (e) on the grounds of (d), for which he has strong evidence. In this case, Smith is clearly justified in believing that (e) is true.

If Smith "accepts (e) on the grounds of (d)," then what would you call (d) and what would Smith's justification be?

I cannot argue with what you have said here, but I'm not sure you answered the question:

Does (d) serve as justification for (e), and is (d) shown to be a false premise?

(e) logically follows from (d). Smith is justified in that he has logical justification applied to or based upon observational/empirical data. So he has compound justification.

(d) is justified by observation. Even if false, it's still justified. We find out it is insufficient justification, perhaps, after we cite the reason why it the proposition in question is false.