Did you even bother to read the thread? The context of "belief" with which we're focusing has been noted countless times. We clarified this pages ago.

We're looking at propositional-belief and propositional-knowledge. We don't need to look at the conditions under which one might "believe in" the Communist party. We can easily manufacture convincing examples (involving psychology, etc) for why people might be prone to believe in certain objects. This would be unilluminating.

The only category of belief we are concerned with is propositional-belief; belief insofar as it can possibly tend to truth.

Sure thing, sorry you missed it.

This is reiterated throughout the entire thread.

The type of belief we are talking about can be defined as a proposition that can lend to a truth. An example would be: (I believe--) 2+2=4, Hydrogen is an element on the periodic table, Humans breathe through their lungs. Bad examples would be: (I believe--) that shirt is nice, pumpkin pie is good, Ted is a handsome man. They are bad examples because they are out of the realm of 'true' or 'false'; These are preferential-beliefs. "I believe in God", "I believe in the trinity", are also not what we're speaking about - these have nothing to do with reality, there is no knowledge contained. We call these "Blind-beliefs" (I describe this in one of my posts, and so does nerdfiles).

What we're seeking (or at least I think we are) are necessary and sufficient conditions for truth-beliefs (described above and throughout pages 7-10).

I started a list last page trying to detail at least two of the conditions which nerdfiles brought to light.

(1) The belief cannot be a contradiction
(2) The belief has to be thinkable (insofar as reality)

Thus, the meaning of the term "believe" has to be further stipulated before the analysis can be productive. Is that observation somehow dense or ignorant or irrelevant?

(1) The belief cannot be a contradiction
(2) The belief has to be thinkable (insofar as reality)

In the Middle Ages, mathematicians believed that the circle could be squared, and attempted to do it. It was a while before it was proved that a square circle was a contradiction. Therefore, some people believed a contradiction.
I don't know what it means to say that a belief is "thinkable".

One idea I have for a necessary condition for belief is that the content of that belief ("the proposition") be thinkable (as opposed to, say, "X thinks that P"--thinkable seems to presuppose vaguely a normative constraint).
Thus, we cannot believe contradictions.

So, S believes that P only if "P" is thinkable; by contraposition: If P is not thinkable, then S does not believe that P.

This obviously rules out belief in squared-circles (under a literal meanings and normal grammar). More generally, we cannot believe that where the clause following that is an outright (and confirmed) piece of nonsense.

(1) Sam believes that he saw a squared circle yesterday only if "Sam saw a squared circle yesterday" is thinkable.

By our contraposition, the "thinkable"-part is false (and perhaps necessarily false). Therefore, it follows that the "belief"-part is false.

If the conditional statement itself somehow got 'round the material implication of the "belief"-part being false, we'd either need to (a) readdress our rule about thinkability or (b) the conditional statement itself would be vacuously true (ignoring the thinkability constraint), in which case, we'd still need to determine why thinkability is not a reasonable or relevant constraint.

Can you provide a few examples where we'd see an ambiguity in the usage of "belief", considering the aforementioned type of "belief" we're using?

Further, I pointed out that "He/she believes..." is an expression we routinely use to indicate that we think the person in question erroneously takes as knowledge something that we agree is not.

I thought I did that, in the post that listed five propositions. It contained an account of how the expression "I believe..." within the context of "a proposition that can lead to a truth" may have the same range of meanings as "I know..."

My examples comply with the requirements "(1) The belief cannot be a contradiction and (2) The belief has to be thinkable."

I also demonstrated that "I believe..." within the same parameters, may also be used as an expression indicating some admission of some level of doubt.

What I am proposing is that "believe," even with the confines we have agreed upon, can have at least five possible interpretations.

I'm not familiar with these medieval mathematicians. Can you provide a link?

Once I have more information, I'll be able to determine whether or not your example eludes the "thinkability" condition. Or, you can just explain it to us.

Apart from any information, are you saying that it was somehow impossible that anyone should have tried to square the circle?

In an effort to avoid a semantic battle and delve further into this matter, would you be willing to detail exactly the other five possible interpretations you've pondered?

Apart from any information, I haven't a clue what it even means to "Square a circle". After the information you presented, I still don't really understand what was attempted, and to tell you the truth, I'm too lazy to read all 10 pages. Perhaps you can explain in layman's terms to an unintelligent being such as myself?

Your point, however, was that we can believe in contradictions. We're all on the same playing field, yet I feel you're a bit hostile - why in the world was the "are you saying it's somehow impossible" comment directed to me, as if I preached being an enlightened geometer. Understand I am not saying anything is impossible, nor am I even contesting you: I'm here to find the necessary and sufficient conditions. If you don't feel any of these are conditions, I have open arms and would love to hear your contribution.

Perhaps it involves the person *knowing* it's a contradiction at the time of the belief. Can a person believe someone is both dead and alive? Can you cite any other examples in which we knowingly believe a contradiction? Tear it apart, I can't think of any.

I did not say that people knowingly believe a contradiction, although that also is, I think, true. But I suppose lots of people believe contradictions without knowing that what they believe is a contradiction.

Within the context of propositional beliefs, I offered five examples, four of which you allow, denying that "Jesus saves" complies with the criteria, presumably because it has religious overtones. I hereby reinstate it defining "Jesus" as my friend "Jesus Morales" and "saves" as "puts money in the bank." (Hey, I think its important to have a little fun with this kind of stuff).

1. I know for an absolute fact it is true. I personally possess the knowledge.
2. I assume it to be true, my assumption linked to my trust in the source. (May not be materially different from 1).
3. The truth claim, like every truth claim in the world, is, at best, only plausibly true, but I accept it and proceed accordingly.
4. I'm inclined to accept it as true, but I have serious doubts.

5. Finally, while any individual may have any of those four going on, I, as an observer saying "Henry believes the light works" may in fact be signifying, "Henry assumes something that I claim to know is not true." This, I admit, may fall outside of the analysis at hand, being perhaps only an example of two people having different opinions, but it does specifically address the fact that we can use the word within the same parameters to signify some thing different--i.e., erroneous belief.

Let me just clarify the reason "Jesus saves" does not comply is not because it has religious overtones per se. ... The problem is the mysticism, the deviation from reality (as far as I can see these truth-beliefs going).

I believe for the sake of this conversation we are only focusing on #1.

If the individual does not hold personal knowledge of such and such, it does not fit into the type of belief we're focusing.

The other interpretations appear figurative, and although I completely understand they are common in every day speak (hell, I just used one in my first sentence!), I don't feel this involves what we're analyzing here.

PS: NICE, WE NOW HAVE AN AUTO POST JOINER. SCORE!!

That sense of "I believe" is not (as far as I can tell) distinguishable from "I know."

That statement seems to indicate the opposite of the one immediately preceeding it. I am totally confused.

What does that mean?

The type of belief I thought we were speaking of, is supported by personal knowledge. For instance, after witnessing the light is on, "I believe the light is on". There are no doubts - you have empirical knowledge to support your belief.

I need clarification, and I'm just not able to find it...

That seems to me the easiest category of belief that would fit the model we are discussing. They are both justified, but neither is demonstrably true at the point in time.

Can we agree at least on that?

Of course, because justification of p does not imply that p is true, is the justification is non-deductive justification. Indeed, two people, A and B, may have the exactly the same justification for proposition, p at different times, but A know that p, and B not know that p, because p is true at one time, but false at a different time.

But the light example you have given is a Gettier-case example, in which you both have justified belief, and, if on flipping the switch, the light works, then Henry had justified true belief the light would work, but if the light does not work, then you have justified true belief the light would not work, but neither of you knew.

And the reason for this is, as your example shows, Justified true belief are necessary conditions for knowledge, but are not a sufficient conditions for knowledge; which is the point of Gettier's famous objection to the analysis of knowledge as JTB.

This is not a Gettier-case.

Of course, because justification of p does not imply that p is true, is the justification is non-deductive justification.

Indeed, two people, A and B, may have the exactly the same justification for proposition, p at different times, but A know that p, and B not know that p, because p is true at one time, but false at a different time.

But the light example you have given is a Gettier-case example, in which you both have justified belief, and, if on flipping the switch, the light works, then Henry had justified true belief the light would work, but if the light does not work, then you have justified true belief the light would not work, but neither of you knew.

And the reason for this is, as your example shows, Justified true belief are necessary conditions for knowledge, but are not a sufficient conditions for knowledge; which is the point of Gettier's famous objection to the analysis of knowledge as JTB.