Atheism, theism, agnosticism, gnosticism, ignosticism

[Simon Moon]

Belief is a binary mental state. Either one accepts a premise or proposition as being true, or likely true, or they don't accept it as being true. There is no fuzzy middle ground between belief and disbelief. One important thing to note, is the opposite of 'accepting something as being true', is not, saying it is false.

I disagree here. Belief has different levels of confidence associate with it. So, my confidence in the law of conservation of energy is far higher than my confidence that all genetics is based on DNA.
My confidence that dark matter exists is high, but not as high as my confidence in the conservation of energy.
My confidence in the existence of axions is pretty low, but I see them as plausible, just not yet supported by the evidence.
In a similar way, disbelief can also have confidence levels. My disbelief in the Loch Ness monster has a high degree of confidence.
So, part of my disagreement is that I don't see belief as an all-or-nothing thing. It has degrees the confidence level makes a difference if there are conflicts between beliefs.

You are saying that beliefs have different levels of confidence. I completely agree.

But there is still a binary aspect, in that you are either accept those things (conservation of energy, dark matter, DNA based genetics, etc) as being true, or you do not.

It is kind of like a light dimmer. Sure, there are different levels of light output depending on the position of the dimmer. But, there is a point at which there is no light (disbelief), or some light (belief). That point is where the binary state is. There is no middle ground between light and no light.