an author named Chris Hedges has recently published a book which addresses the OP. I can’t locate the name of the book right now. I’ve enjoyed this author’s other books, but this one’s gotten mixed reviews. still it seems to address just what the OP was asking for.
I honestly don’t know how to respond to that. If you disagree that “does not believe” negates “believe”, then I can’t say anything further. Except maybe I could point out that your disagreement means you do not agree. Or that “not” negates. I really don’t know what more to say.
I think that (4) is nonsense. There’s no point in talking about the belief of a bookmark, anymore than one would talk about a coffee cup’s Indy victory. By assigning belief to your bookmark, you are assigning sentience to it as well.
They are different. (1) is of the form B~G, while (2) is of the form ~BG. (1) is a statement of the form “here is what I believe”, while (2) is a statement of the form “here is what I do not believe”.
Taking it out of an existential context might help. Consider a sales clerk who says:
(1) I believe you did not give me enough money.
(2) I do not believe you gave me enough money.
In (1), what you did not do was give. It is about your giving, not about the clerk. In order to assuage the clerk, you must give more. But in (2) what the clerk does not do is believe. Perhaps you can convince him that what you gave was enough, because the statement is about his belief, not your giving.
Well, you said a few different things about (2) so I should have been more specific.
I think that a sentence’s negation of “believe” does not bring it about that the sentence asserts disbelief. In other words, (2) involves a negation of a predicate “believes,” but this negation does not make the sentence assert that John disbelieves. (Unless “disbelieves” just means “lacks belief,” but you seem to be saying otherwise.)
That last sentence is correct: By saying a thing “believes” something, I am implying (or presupposing) that the thing is sentient. If something believes, then it is sentient.
But my bookmark is not sentient. Therefore, it doesn’t believe. (Modus Tollens.)
An argument with a very similar form:
If my bookmark believes there is a God, then my bookmark is sentient.
My bookmark is not sentient.
Therefore, my bookmark does not believe there is a God.
The conclusion appears to follow from a valid argument with true premises. Do you still think the conclusion is not true, but rather, nonsense?
Okay, I see what you mean by that. Do you think (1) or (2) could be true of a person while the other of the pair remains false?
-FrL-
ETA: Related to the second set of comments above, here’s another argument:
If my bookmark does not believe in God, then my bookmark is sentient.
My bookmark is not sentient.
Therefore, my bookmark believes in God.
Here we have a false conclusion of a valid argument–so one of the premises must be false. The second one is clearly true. So the first must be false. It must be that it is possible for my bookmar not to believe in God, while at the same time failing to be sentient. But this is contrary to your claim that sentences like “X does not believe Y” imply that X is sentient.
Interested to see your comments.
Okay. Well, I’m open to using whatever vocabulary you prefer to mean “the opposite of believe”. That’s what negation is: A is the opposite of Not A.
Yes, because a false antecedant always leads to a true conclusion, no matter whether the consequent is true or false. To say that your bookmark does not believe is to state a tautology — that is, belief is a metaphysical impossibility for your bookmark. The question of a person believing, on the other hand, is epistemic in nature. Just because I don’t believe does not mean I am incapable of believing. Your bookmark not only does not believe; it cannot believe. Belief is a nonsense attribute with respect to it.
Yes. ~BG does not contradict B~G.
ETA:
I believe my comments addressed your ETA. 
Let me know if they did not in your view.
The book is I Don’t Believe in Atheists.
Berlinski is a Creationist and a member of the Discovery Institute (the organization behind the ID movement). He also appears in the Expelled movie, advocating ID,
I have read through some of The Devil’s Delusion (I spend a lot of time in bookstores and I am compulsively drawn to books of theistic apologia, so I’ve at least skimmed through a lot of the books purporting to rebut “The New Atheism”) Berlinski employs two main tactics, semantic obfuscation (using lots and lots of scientific sounding language as an attempt to confuse or cow a lay reader into thinking he must really be saying something even if they can’t quite understand it) and God of the Gaps. He dwells incessently onything he thinks science can’t prove, (“Science can’t prove God does not exist,” “Oh yeah, then how did the universe g*get here , then?”), but really offers nothing in the way of positive proof of a deity.
He also goes the Godwin route and blames the Holocaust on Darwin.
You can see Berlinski getting owned by Ken Miller (a Catholic biologist and a leading defender of theistic evolution) in this debate.
“Opposite” in english has only a tangential relationship to negation. The opposite of up is down, but if something is not up, that does not necessarily mean it is down. It might be right in front of you, for example.
“The opposite of believe” is an ambiguous expression. However, “The negation of ‘X believes Y’” is (in the context of discourse about logic) perfectly clear. “The negation of ‘X believes Y’” is a description referring to a statement “It is not the case that X believes Y.” Now under what circumstances is it true that “it is not the case that X believes Y”? Here’s one such circumstance: When X believes “Not-Y” and X is rational. Here’s another such circumstance: When X has no belief whatsoever about Y. Both of these are circumstances in which it is not the case that X believes Y.
When someone says “I don’t believe X” they could mean either “I believe not-X” or “I lack a belief that X.” “I don’t believe X,” as a sentence of ordinary English, is in that way ambiguous. But you seem to be arguing that “I don’t believe X” actually means the speaker believes not-X. That’s not right. “I don’t believe X” is ambiguous in ordinary English, and is clear if interpreted literally or logically. When interpreted literally or logically, it means “It is no the case that I believe X,” and as I showed above, this latter sentence can be true both in the case that I believe not-X (and am rational) and in the case that I lack any belief concerning X at all.
Is it a tautology, or is it nonsense? You’ve made both claims, but they are not compatible.
So, what I’m trying to prod you for is an example. 
But of course it’s easy to give an example where it is true of someone that ~BG and not true that B~G. But if you’re saying (1) means B~G and (2) means ~BG, then now the challenge is to say how either (2) or (3’) could be true of someone while the other of the pair remains false, where (3’) is your modified version of (3):
3’. John does not have a belief that there is a God.
-FrL-
Who’s the guy giving the final closing remarks in the next segment of that video? He looks and talks like William F. Buckley.
-FrL-
That was, indeed, the late William F. Buckley. It was a debate on PBS’ “Firing Line” More info here.
Wow. I suppose my expository skills need serious work, since I’m definitely not saying that. In fact, I’m saying the opposite — that “I don’t believe X” does not mean “I believe not-X”. I wrote them out separately, assigned them symbols, and talked about them in quite some detail. If I’m coming across to you the way you say, then I’m a terrible writer.
At any rate, the whole point of contextualizing the statements with epistemic logic was to remove the ambiguities and equivocations, as I stated early on. I do not disagree with your assertions that English can be vague. That’s why I broke things down the way I did — to explain to you what I meant by those things. To come back now and say, yeah but the English representing those things is vague is pretty much to ignore the whole process of breaking them down.
Well, it’s a tautology in the sense that it gives no new information, like “a bachelor is an unmarried man”. It is nonsense because it assigns to a paper clip or whatever it was the attribute of sentience. That’s what I was pointing out when I drew the distinction between an epistemic claim and a metaphysical claim. To say that your paper clip does not believe something is vague because it is incomplete. Again, it cannot believe anything and so assigning a belief attribute is meaningless. It is also redundant. It does not believe because it cannot believe, just as a bachelor is not married because he cannot be married.
Actually, I did give examples. ~BG -> I do not believe (~B) that God exists (G). B~G -> I do believe (B) that God does not exist (~G). They do not contradict because one statement negates the modal (B) while the other negates the term (G). The modals contradict and the terms contradict, but the joined statements do not.
For another nonexistential example, consider ~RS and R~S, where R is red and S is a shirt. So we have a shirt that is not red and something that is red but is not a shirt. They do not contradict because the latter item might be red pants. I can have both a red shirt and red pants.
accidental double post here
My interlocutor’s failure to explain is identical with my failure to understand.
In any case, I now think the crux of this rests on the distinction between (2) and (3’). In your last post you addressed the difference between (1) and (2) but I was actually asking about (2) and (3’). In abstract form:
(2A): X does not believe that Y
(3A): X does not have a belief that Y.
Do 2A and 3A mean the same thing or different things? And can either of the two be true while the other remains false?
I can understand how one might say they mean different things. I am having trouble seeing how either could be true while the other remains false, however, and this tends to lead me to think they mean the same thing after all.
-FrL-
I"ll take your word on all that…I haven’t read any of these books (on either side), so as I said, I can’t personally vouch. Although it may still help the OP, I don’t know.
I do find your info strange, though, in light of one thing…on the radio, he said he wasn’t particularly religious. I assumed he meant he was kind of like me…like, not an atheist, believes in God but not super devout. But he must be a lot more “religious” than I am if he’s a creationist.
I see what you mean here. Just a point of order: A single sentence really can’t be both tautological and nonsensical. That it is tautological implies that it makes sense.
But I understand the distinctions you’re working with here. I think the best tool to use to understand this kind of thing is the concept of a “presupposition.”
“I have not stopped beating my wife” is a statement that can hardly be uttered without the speaker implying that he has beat his wife in the past. In this sense, the sentence (or anyway its utterance) presupposes that he has beat his wife.
However, the meaning of the sentence strictly speaking does not imply that the speaker was ever a wife beater. All the sentence means, strictly speaking, is that
(A) It is not the case that [the speaker once beat his wife and now does not].
(A) is true even of someone who has never beat his wife. For (A) contains a conjunction under a negation, and so is true if either of the conjuncts is false. One of the conjuncts is false–the speaker has not once beat his wife–and so the whole sentence is true.
(A) is true, and I think (A) has the same meaning as “The speaker has not stopped beating his wife.” It’s just that in almost any context, a person uttering a sentence like “I have not stopped beating my wife” would be inexplicable unless we assume the speaker means us to take it, as a presupposition, that he has in fact beat his wife in the past. (And of course if that presupposition were true, then by saying he has not stopped beating his wife, he would be implying that he beats his wife right now.)
Likewise, in general, utterances like “X does not believe Y” are made inexplicably unless the utterer intends his hearers to take X’s sentience to be a presupposition of the conversation. But X’s sentience is not logically implied by the utterance. The utterance is true (even if made inexplicably*) even if X is not sentient–because non-sentient things don’t believe anything, including Y.
-FrL-
*Note that it’s easier to make “Non-sentient X does not believe Y” explicable as an utterance than it is to make “I have not stopped beating my wife” explicable as an utterance. I can hardly think of a context where the latter could be said by someone who has never beat his wife. But the former is fairly easy to say. If I say “My stapler doesn’t believe in Democracy,” it is my experience that the listener comes to understand my meaning almost immediately–“ah, he means because staplers don’t have beliefs at all!.”
-FrL-
Okay, since you’re so patient, I’ll have a final go. 
The difference, as I said, is that 2A is a statement about what X believes, while 3A is a statement about what X has. If you want to express the opposite of belief — I don’t think you’ve said yet what term you prefer for that — then use 2A. If you want to remove belief from the subject of the assertion, then use 2B.
Since the non-existentials seem to facilitate understanding better, let’s do that here as well. It’s like the difference between (5A) “John does not eat grits” and (5B) “John does not have any grits to eat”. If 3A did have a belief, we do not know what it would be, just as if John had some grits in 5B, we don’t know whether he would eat them. We do know that he would not eat them in 5A even if he had them.
I’m okay with that.
To reply a bit to my own post, you answered the first question in a previous post already. I don’t know if I missed it or just forgot about it, but here it is:
.
Another way to put what I’m saying is as follows. I don’t understand the comment quoted above, and could you please explain. One thing that would help is an example in which either of (2A) or (2B) is true while the other remains false. Otherwise, I am not sure what work you are trying to do using the distinction you’ve made in what I just quoted.
Perhaps a third way to express what I’m saying is as follows. “Believe that X” and “Have a belief that X” appear to me to be synonymous–it appears to me that the one can be substituted for the other (with appropriate grammatical adjustments) without changing the truth or falsehood of the sentence. (Though you might get different presuppositional forces!) Do you think otherwise? If so, why? If not, then what distinction are you trying to make in the passage quoted above, and what work are you trying to do with it?
-FrL-
I would suggest the works of G. K. Chesterton, beginning with Orthodoxy. This book is a very thoughtful, deep, and logical defense of Christianity, with a specific eye towards addressing scientific materialism. Of course it was written almost exactly a century ago, but I still find it to be the best response.
I agree with you that those statements as unary terms are interchangeable. However, the question originally raised was with regard to whether someone believes that something is true (or false) or simply doesn’t have a belief. Your first statement is impossible to arrange in any way to satisfy that request. The second one, however, is done simply by making the term compound and negating the “have”. That allows a person to say that he doesn’t have a belief. It’s not that he believes X and it’s not that he doesn’t believe X. It’s that with respect to X, he has no belief of any kind.
So:
“I don’t believe that God exists” is ambiguous: It might mean speaker believes there is no God, but it also might mean the speaker lacks a belief that God exists. Meanwhile “I don’t have a belief that God exists” more clearly means the latter.
Is that what you’ve been saying, in summary? (Of course you’ve been saying more than this. I’m asking if this is your point.)