Higher quality version of this:
Do you believe that the planet Mars exists? Of course you do.
Abundant good evidence for Mars' physical existence is to be found. So, even though you have not visited the planet or watched it rise behind Elephant Rock (right), you believe that it exists.
Belief simply signifies the mental state of holding something to be true. Stating belief demonstrates no more than the personal possession of a mental state. Even a passionate or long-held belief is not necessarily a realistic belief. It boggles the mind, but some people believe that the Earth is only 6,000 years old.
Do you believe that electrons exist? I can't show you a photo of an electron. With a rest mass of only 9.109 x 10 -31 kg, you could never see an electron. However, the activities of electrons are detectable as electricity, and you could not be reading this post without the benefit of electricity.
Do you believe that little green men live on Mars? Let's call them Martians. Here's a picture of one.
One could argue that they would have to be green, as are plants, because there is no available energy except for sunlight.
Do you think that you do not have enough evidence to rule Martians in or out? After all, human missions to Mars have not scoured every nook and cranny of the planet.
How could one disprove the postulated existence of something that does not exist?
It is not logically possible to categorically prove that something non-existent does not actually exist. The logical inability of disproof would not indicate that the claim for existence necessarily had any validity. To insist otherwise is illogical. Fallacious arguments from ignorance erroneously insist either that lack of proof must render a claim false, or that lack of disproof must render a claim true.
Lack of proof could result from practical difficulties in obtaining evidence for a true claim, just as lack of disproof could accompany a false claim. The point is that it is illogical to extrapolate from proveability to insistence.
Should atheists respond to demands for proof that deities don't exist? No. To do so is to submit to the theistic fallacy of shifting the burden of proof. The theists make the claim for existence of deities, so it is their burden to provide proof. Their failure to date is not for lack of trying.
Back to the little green fella.
I'll assume that there is no need to send any men in white coats to collect you, because you undoubtedly are not fooled by the picture of the Martian.
No doubt, you realize that someone before me invented the fantasy of Martians, and you further realize that I doctored the image. (Need proof? I admit to doctoring the image twice.)
Since it is known that Mars has no liquid water and almost no atmosphere, not to mention inhospitable surface temperatures, the physical data suggest that Mars could not support such life. Toss the physical data together with your recognition of the fantasy element, and you probably think that you can make a decision concerning Martian ontology.
Since it is logically impossible to prove non-existence, do you think that even though you don't believe, you must be a purist and declare yourself agnostic about Martians?
Agnostic means “cannot be known”.
T.H. Huxley coined the term agnostic to suggest that one should not profess to a belief in something that cannot be proven. (Atheism: Huxley on agnosticism, Huxley And Agnosticism)
Huxley did not use agnostic to suggest that one should believe a non-existence that cannot be disproven.
If you have even a smidgen of belief, then you are a believer and not an agnostic. Even a smidgen of belief is equivalent to Faith in Martians, no matter the evidence. After all, faith is belief despite absence of evidence. Specifically, absence of evidence – or absence of correctly interpreted evidence. Since belief is merely a state of mind, so is faith.
I "don't believe in" versus "I believe not to exist" is the same thing expressed differently, right?
"I don't believe in the existence" is logically equivalent to "I believe in the nonexistence."
A strong conviction that we “know” something does not count as knowledge. The conviction is merely belief passed off as knowledge unless it coincides with reality. We require both logic and unbiased evidence, even that aquired by others, to make any claim to knowledge. Knowledge is defined as having a true belief – accurately holding something to be true, even if you have not personally encountered the reality. (Pulsars exist. I've never met one.)
Circular "evidence" is not unbiased evidence. The Bible tells us God exists. Why do theists believe this? Because they also believe that the Bible is the Word of God. Why do people believe this? After all, the Hypothetical Entity didn't sign it. Theists believe because they are instructed to believe under threat of eternal punishment or loss of eternal rewards. In face of religious repetitis, they cannot conceive of, or entertain, a more realistic explanation for the written recording of myths.
Back to Mars.
Given that conditions on Mars are inhospitable to life and that we know that human imagination is responsible for the concept of Martians, we are quite justified in saying that Martians do not exist. We do not have to never meet a Martian to know that there are no little green men running around Mars, no matter what Disney cartoonists or Hollywood producers would have us believe. The fantasy does sell tickets, though.
See the point?