I dislike this common arguement: "Athiesim is still a belief.".
While that's an interesting side-topic we could discuss, that isn't at all what I said.
I could have very well said. "Sure...you're an athiest. You don't believe in god...but that doesn't mean that you don't like apple pie." "Athiesm" and the subject of "Belief," while they may intersect at some points, are two separate subjects. (Some people, like my father, would disagree. He would say that (provided you're American) Athiest = Non-christian = non-American = no apple pie for you

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I do understand your point though, regarding the definition of "belief" . It is something that I've found quite frustrating as well. Such semantics are a prickly minefield in any philosophical discussion.
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In regards to that, I used to have a roommate who was very religious. When I asked, "how do you know there is a god?" They said "I know it, because I believe it." (They didn't appreciate my comparison to children and Santa Claus, however, nor did they have a rebuttal to the comparison.)
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There are those who use "believe" to mean the same as "know 100%." These same people are those to whom the obvious distinction between "likely" and "certain" are lost. There are both theists and athiests that fall prey to this lack of distinction. "I believe/know science/archaeology as the 100% final word about existence" is as polarized as "I believe/know god's book as the 100% final word about existence." Both are founded upon unwavering blind devotion to an absolute belief.
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Those are extreme ends, however. Many theists and athiests retain a healthy amount of skepticism in varying degrees. Some, like yourself, more than others.
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As Webster would put it, an athiest is "one who believes that there is no deity." In its simplest form, it says something about what you *don't* believe...but it says nothing about what you *do* believe. Anyone identifying as an athiest is essentially stating that they think the entire idea of a deity is bollocks/nonsense. (However, many athiests do tend to turn to science as the core of their belief structure, lacking anything else) If you still retain an openness to the possibility of a deity (however remote), then "athiest" doesn't really fit you.
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"It is perfectly possible to be entirely unbelieving.".
If you mean "It is perfectly possible to think that nothing can be known with 100% certainty", then I'll have to agree. I'm an agnostic...such skepticism is my bread and butter.

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However, if you're trying to tell me that you exist absent of any belief whatsoever, I'll have to strenuously disagree.
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To quite a few athiests, "belief" is a bad word. You can curse up a storm of obscenities without raising an eyebrow, but to say that you "believe" something is considered absolute heresy. To them, athiesm is about "knowing" not about "believing."
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Life, however, isn't so easy...rarely (if ever) will you encounter a subject filled with such absolute certainties.
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Philosophically, everything is built upon belief.
I believe in my existence. (But in what way/ways?)
I believe in my senses. (But to what point?)(Limitations? Deficiencies? Impairments?)
I believe that when others corroborate my observations, those observations become fact.
(Though historically incorrect assumptions have often plagued such 'facts')
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Belief is an interesting topic. You do have beliefs, whether you acknowledge them or not.
Beliefs are the concepts you have enough faith in to act upon. The concepts you base your life around.
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Anyone's core philosophy is all about belief. "Knowledge" is anything you have 100% faith in (The sun will rise again tomorrow) even if you can't prove it until it actually happens again. Society is all about establishing a mutually agreed upon baseline of beliefs to extrapolate further more complex conclusions on. If any core philosophical belief is found to be false (ie. "the world is flat"), the whole house of cards can come tumbling down and must be rebuilt. All knowledge is built upon such beliefs, no matter how small and insignificant those beliefs might seem.
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Before I get carried away on a far-too-lengthy philosophical post, let me just make one simple example.
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When I take an action...of..."I'm going on a picnic tomorrow."
I know that the weather channel says that there is a 30% chance of showers.
I don't know whether it will rain or not. I can choose to believe that it will...or that it won't.
If I believe my chances of sunny weather are good...I will choose to go.
If I believe my chances of rain are too great...I will choose not to go.
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This can be applied to many things...
When I voted for Obama, I did so believing that he would change things for the better. (And while I question that belief every day...I still hope that he will)
When I took the old road to work, I did so believing that traffic would be less. (some days I'm right..some days I'm wrong)
Etc...
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To go through life, believing absolutely nothing...you would probably go crazy, and be able to accomplish nothing. If you don't believe in your own existence, in your senses, in constructed concepts and philosophies, in others, in etc..., questioning everything to the point that nothing means anything anymore...to the point that no actions can be taken because you don't believe one thing over another....it's a difficult way to live...and not very productive. (yes, I've been there. Not a fun place to be.) That doesn't mean things shouldn't be questioned. That doesn't mean that you shouldn't remain flexible and open to other ideas and perspectives. It just means that "belief" is not so inflexible a subject that it cannot be altered when required to.
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You can try to avoid the word "belief" by using "thought" or another word in its place...but that's nothing more than a trick of semantics to try and avoid the dreaded "B-word". "Belief" is a word...a construct...that has been so abused and misused within the religious community that it isn't difficult to see why many who leave those communities choose to shun it. Yet...while understandable...belief itself is an unavoidable part of existence.
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And...getting back to the main topic...these beliefs will form the basis for your arguments about what "rights" someone has. Do you believe that everyone has a right to X? Well...if everyone...then are they all...born as equals? Why? How? "Because in my experience..." "Because I value..." "Because I believe..." etc...