Is “lacking belief in X” equivalent to “belief in the nonexistence of X”?

Question

Often I see atheists say they do not have an active belief in the nonexistence of God, only a lack of belief in God.

I see where they are coming from, but I have a suspicion that they're equivalent.

I'd imagine they would not be equivalent under the circumstances that one does not have a concept of X. So it can be said they lack belief in the existence of X. But, if one does have a concept of X, then there seems to be three options: belief in the existence of X, belief in the nonexistence of X, or undecided.

For example, an isolated tribe of people can be said to lack belief in the existence of a toaster because they have no concept of a toaster. But, the moment you explain the concept of a toaster to them, they can either believe in the existence of a toaster, believe in the nonexistence of a toaster, or be undecided on the matter.

Or would the undecided option be "lacking belief"?

The short answer is no, its not; belief and ontology are different ... — Mozibur Ullah, Nov 15 '19 at 16:16
"Undecided" is the closest meaning but sounds too strong, if I tell you right know be were created yesterday by giant tomatoes and we are living the same day again and again with fake memories of our past, you won't believe it but can't say for sure it's not true. I don't think you would describe yourself as "undecided about this theory", but I see what you meant with those 3 states of believing it's true, believing it's false, or undecided, and that's probably what they mean. But undecided can mean you're 99 % sure it's bullshit. — Destal, Nov 15 '19 at 17:35
No, it's not. A belief in something is distinguished from whether that something exists. Likewise, a non-belief in something is distinguished from whether that somthing doesn't exist. — Mozibur Ullah, Nov 15 '19 at 18:01
I think this is kind of just a weakness in our modal structure in English and many other languages. We say "I do not believe this" when we mean "I believe this to be false" because our modal verbs handle negation in a confusing way ("You may not do that" does not mean that you are allowed to avoid doing that, you cannot use the same modal verb to express the negation at all, you need the complementary modal 'should' instead) and we carry that nonsense over onto other verbs that are quasi-modal in nature. — user9166, Nov 15 '19 at 19:36
Possible duplicate of How compatible is atheism with agnosticism? — Conifold, Nov 16 '19 at 0:23

Eliran · Accepted Answer · 2019-11-15 17:45:38Z

I agree with you that in general there are three options regarding believing a statement p: believe p, believe not-p, or be undecided whether p or not-p (this is usually called 'suspending judgment').

Those who are undecided on whether there is a god are usually called agnostics. Those who believe that there is no god are usually called atheists. So in this sense it would be wrong for an atheist to present him or herself as merely lacking a belief regarding god's existence.

I suspect, however, that in some people's minds 'belief' is associated with 'faith', which is why some atheists do not want to describe themselves as 'believing' that there is no god. But we can understand belief in a much more mundane sense. For example, I believe that it's not raining right now where I live, and I believe that there is no beer in the fridge. That doesn't have anything to do with faith or religion. In this mundane sense atheists believe that there is no god.

Perhaps this is a difference between 'believing that' and 'believing in'. It is potentially misleading to describe myself as believing in the nonexistence of beer in the fridge. This makes it seem a matter of faith. But this appearance disappears when I say more simply that I believe that there is no beer in the fridge.