Justifying universal and existence statements

My post on how we should implement the Year of Reason by asking religious people why they believe in god provoked quite a spirited back-and-forth in the comments section.

In the post, I said that there was no substantive reason that religious people could give in response to the question “Why do you believe in god?” and I categorized the likely things they would say under the headings Argument From Personal Incredulity, Argument From Wishful Thinking, and Argument From Vague Feelings. I endorsed Sigmund Freud’s assertion that religion was a form of mass delusion since so many people believed in something for which there was no credible evidence whatsoever.

Commenter Lucas took exception to my post and critiqued it saying that I should not make statements such as that “There is no sense in believing in something for which there is no evidence” without substantiating them. He said that he himself did believe in god because he had “studied the evidence” and found it to be “extremely convincing”.

This is where the discussion in the comments took an interesting and somewhat surprising turn. I asked for an example of the convincing evidence that he had that did not fit under the three umbrella headings that I had given. But Lucas resolutely refused to do so, saying that that was a detour, and that I was using it as an excuse to avoid addressing his challenge to my lack of substantiation.

This post seeks to clarify what seems to be a basic misunderstanding between us about where the burden of proof lies and what kinds of statements need evidence in support of them and what kinds of statements are justified by the absence of evidence against them.

To begin, let me repeat what I said in an even earlier post.

As mathematician John Allen Paulos argues in his book Irreligion: A mathematician explains why the arguments for god just don’t add up (2008), basic logic requires that existence claims and universal claims be treated differently.

Existence claims can be proved but not disproved. “No matter how absurd the existence claim (there exists a dog who speaks English out of its rear end), we cannot look everywhere and check everything in order to assert with absolute confidence that there’s no entity having the property.” (Paulos, p. 42) But all the person making the existence claim needs to do to prove it is to produce just one specimen. So the burden of proof is on the person making the existence claim, and in the absence of such proof, it is perfectly logical to deny the validity of the claim.

On the other hand, universal claims can be disproved but not proved. For example, the claim that all swans are white can be disproved by producing just one black swan. But no one can prove the universal claim since we can never say we have checked each and every swan. So the burden of proof is on the person denying the universal claim and in the absence of such proof, it is perfectly logical to assume the validity of the universal claim.

My statement that “There is no evidence for god” is a universal statement whose justification depends on the lack of a counter-example, and so according to the rules of logic, the burden of proof is on the person who challenges it to provide that counter-example. Equivalently, the statement by someone that he or she has convincing evidence for the existence of god that does not fall under the three categories that I provided is an existence statement, and again the burden of proof is on that person to provide an example, not on me to show that he or she has no such evidence.

But if we accept to Lucas’s rules of logic, it seems like I cannot even make a claim such as that “there does not exist any dog that can speak English out of its rear end” unless I can provide citations from peer-reviewed journals that assert that the authors have checked every dog (or at least an extensive number of them) and found this statement to be true.

But of course that is absurd. The reason we can confidently make such a statement and expect them to be believed even in the absence of controlled studies is because we apply the commonly accepted rules of logic, not Lucas’s rules. I have never personally encountered a dog that can speak out of its rear end and base my statement on the confidence that if anyone in the world had such a dog, it would be an event of such enormous significance that it would be publicized widely and known by everyone. So the absence of a counter-example is, by itself, sufficient to justify the statement.

Of course, someone could claim that I should still not say this because there may be a dog somewhere that can speak out of its rear end but that the owner is keeping it secret and that I do not know for sure that this is not the case. But no one would credit such a statement until the dog is actually produced. This is because the statement that such a dog exists is an existence statement, and the burden of proof is on that person to provide the evidence. It reminds of the claim by the Raelians in December 2002 that they had cloned a human being and would produce the baby later. While this generated a blizzard of publicity, when no baby was forthcoming, people rightly concluded that the whole thing was a hoax.

The point is that there are many statements that all of us can and do routinely make that are perfectly justifiable and accepted as such even if they are generalized from our personal experience of just a few cases, provided the negation of such statements would be extraordinary. These rules of logic are so commonplace and so basic that people may not even consciously realize that they are using them.

So I can confidently say that no cows have seven legs, although I have personally seen only a few cows, noticed that none of them had seven legs, but have not done an exhaustive literature search to see if anyone else had found one. This is because my statement that there does not exist a cow with seven legs is a universal statement. Someone who says I am wrong has to produce such a cow.

This is why I can make the statement that the stated reasons for the beliefs of religious people (except for people like Pat Robertson who have a direct line to god) will fall into the three categories: Argument From Personal Incredulity, Argument From Wishful Thinking, or Argument From Vague Feelings. My statement is a universal statement, based on all the reasons that have been given to me over a long time discussing these issues with thoughtful people, and similar to the ones about the absence of seven-legged cows or rear-end talking dogs. Its validity has to be challenged by providing a counter-example.

So getting back to Lucas’s concerns, I am not even asking that any counter-evidence he produces be convincing because what is convincing to one person may not be convincing to another. All I am asking is that he produce any evidence at all that does not fall under those three categories because I am really curious what form such evidence would take, the same way I would be really curious to see what a rear-end talking dog would look like.

It is his choice whether he wants to provide such evidence.

POST SCRIPT: Why science and religion can never be reconciled

Jerry Coyne, a professor in the Department of Ecology and Evolution at the University of Chicago, has written a terrific review of two new books by scientists trying to reconcile science with religion: Saving Darwin: How to be a Christian and Believe in Evolution by Karl W. Giberson and Only A Theory: Evolution and the Battle for America’s Soul by Kenneth R. Miller.

The review, titled Seeing and Believing: The never-ending attempt to reconcile science and religion, and why it is doomed to fail, contains arguments and conclusions that will be familiar to regular readers of this blog, but it is all in one place and very well-written, well worth reading.


  1. says

    Dr. Singham, do you have a past post wherein you define “evidence”? It will aid my understanding of the full meaning of your statement, “There is no evidence for god.” Thank you!

  2. Bob says

    It seems that there once was a lamb born with seven legs:


    And since lambs, like cows, are mammals it seem reasonable that there have been cows also born with 7 legs.

    In fact this has happened. A seven legged cow does exist:


    So, I have proven you wrong on the cow point.

    Of course, it isn’t as easy to disprove your statement about god.

    To provide an analogy. Imagine there is an ant colony setup in a glass aquarium by a 10 year old boy. The boy found the aquarium, found the dirt, and transplanted the colony. Occasionally he interacts in their life by placing food in the aquarium or rearranging the rocks.

    Now some of these ants are more precocious than the others and they start talking about the nature of existence. One ant argues that there must be existence that is greater than them. The other ants cry that there is no proof for such a statement.

    Now, looking at this scenario from our (human) vantage point we can see the conundrum the ‘believer’ is in. How can an ant prove the existence of a being that is so much higher in functioning and so omnipresent?

    This is the same problem that those who believe in god face.

    That fact that you continue to push this ‘logical’ question is very interesting. It seems that you’ve found a wedge to use against believers. You know they can’t answer the question because of the nature of the subject matter yet you continue to ask the question.

    A person who believes in god can not provide any substantive proof of god’s existence because god (in their paradigm) is omnipresent.

    So now that issue is resolved. There is no need to ask the question again.

    I wonder if I could pose my own universal statement. I say there is no evidence that god does not exist.

    To be clear, I’m not speaking of any god as expressed in any text. Rather, simply a higher being that is responsible for our existence.

  3. says

    One ant argues that there must be existence that is greater than them. The other ants cry that there is no proof for such a statement.

    Why would they say that? They can look up and see the boy delivering food and moving rocks.

  4. says


    The ants wouldn’t see a boy. They would see movement in the ‘skies’ and experience a change in atmosphere. These ants, although precocious, don’t know what a boy is.

  5. says

    “One ant argues that there must be existence that is greater than them. The other ants cry that there is no proof for such a statement.”

    There would be indirect evidence, too. If food suddenly appeared in the aquarium over night, and there was no possible natural explanation (no growing plants), they could hypothesize about a boy putting the food there.

    If, using their best ant-tools, they could find no other explanation for the existence of the aquarium itself (no remains of a previous advanced ant colony that could have built it), or no natural explanation for the lights overhead, or the air in the room, or the dirt… then of course it’s fair to assume it was all put there artificially. In this scenario, it was — by the boy. There’s no other way to connect the dots.

    The problem with this analogy is that in our world, we *DO* have natural explanations for just about everything. There used to be a lot of dots missing, but by building tools (scientific method included) we’ve been steadily filling in the gaps. We have plenty good reason to think we can continue doing so, too, so there’s no point falling back on any form of creationism when there’s so much to explore and explain naturally.

  6. Mark says

    On the other hand, universal claims can be disproved but not proved. For example, the claim that all swans are white can be disproved by producing just one black swan. But no one can prove the universal claim since we can never say we have checked each and every swan.

    Except… since we’re talking math here… by various proof techniques designed to do exactly that, based on generative or defined properties of the objects, such as contradiction or induction?

    Honestly, this is why I hate seeing arguments from math or science applied to debates about whether God exists. Whichever side they come from, they nearly always turn out to be nonsensical pseudo-arguments from people on the low end of the comprehension/application spectrum. This doesn’t even really make all that much sense as a way of framing the debate, as far as I can tell.

    I agree that if you’re trying to prove that God exists to someone, the burden of proof is on you. But when I’m considering the question of God’s existence (and I personally lean agnostic) I don’t really care whether I can prove it either way to someone else, and I don’t go looking for conclusive ways to do so — it’s a patently ridiculous exercise anyway. My reasons for believing or not believing are my own, as are (or should be) anyone else’s. If you’re not persuaded by my reasons, what do I care?

    Further, when dealing with people who are believers, I think it’s counter-productive to produce logical arguments (granted, somewhat baselessly, that they DO make some kind of internal sense). The fantastic, supernatural, and somewhat anti-logical nature of God is part of the attraction for most people. Saying, “But my view is more logical!” should, properly, get a response of, “Sure. So what?”

    Basically, I really don’t understand why anyone on either side of the debate feels like mathematical or scientific logic is going to be a factor.

  7. says


    The problem with belief is that it has a lot of potential to really get in the way of critical thinking and problem-solving.

    If you’re a member of a cargo cult, why bother planting crops or cultivating disease-resistant strains of the fruits native to your island? If you pray hard enough, god will provide your people with shipping containers full of yummy western prepackaged meals. Right?

    Sure, that’s an extreme example, but even the big religions enact really stupid and backward policies in the name of faith. For catholics, messing up a cracker is worse than genocide. Yeah, that’s exactly the sort of thing we should expend resources to enforce…

  8. Jim D says

    This is going to be a good one I can tell.

    Mark, come on now-have some patience man! Stop being such a kill-joy. If we didn’t argue over stuff like this what would else would we do? Its Ohio in late January for crying out loud (although I guess you might not be in Ohio with this internet thingy and all…). Besides, where is your sense of adventure? Don’t you want to be the one who finally makes Mano see the light? So put your pajamas on backwards and throw some ice cubes in the toilet! I promise it’ll be fun.

    Jim D.

  9. says


    Thanks for the links. Yes, by providing a counter-example of a seven-legged cow, you have proved me wrong about my statement and I would not be justified in making it any more. That is exactly how things are supposed to work.

    Your other universal statement “there is no evidence that god does not exist” would, as you say, require counter-evidence to disprove it. But atheists don’t challenge that statement. We all agree that we cannot disprove the existence of god, especially since believers in god reserve the right to ascribe any and all properties to god, including the ability to evade detection. There is no dispute there.

    The problem is that believers use that agreement to then assert that god exists. This is an existence statement, and then the burden of proof shifts to them to provide evidence. As long as they refrain from that inference, then we are in agreement.

  10. says


    Your question about what constitutes “evidence” is a very interesting one. There is no single, simple answer. It depends on the discipline (the evidence in science is different from that in sociology or from law), it depends on the context, it depends on how unusual the claim is, it depends on whether existence of an effect is claimed or whether some kind of statistical inference is being made.

    Obtaining agreement as to what constitutes legitimate evidence in judging an issue is an important first step. At the very minimum, evidence should be something that goes beyond someone’s personal statement and be something that others can examine critically.

    This is why the god issue is so problematic. Believers tend to appeal to personal experiences as evidence for god while those who are scientific discount them.

  11. says

    I agree on several points…
    I have struggled with this question for quite some time..
    and the best answer I can come up with is..
    I.. Dont.. Know..
    are we alone in this unimaginably HUGE universe,,
    absolutely not..
    were we created by a guy who made the heavens and earth in 7 days and said.
    ‘let there be light’
    maybe there is a god of some sort.. but not the one that religion has created..

  12. Peter LaFond says

    It seems as if there are two arguemtents: does God exists, and what role does religion play in a society- particularly public policy. I for one could care less about a persons religious beliefs or lack thereoff- freedom of thought is paramount. Butwhen thoughts start becoming action, well now the problems begin.

    ie When religion is invoked by someone to support some public policy then that person’s religious beliefs are now no longer protected by the vale of privacy.

    I believe this is why the Founding Fathers wanted religion out of government- they knew religion would not stand up to serious scutiny.

    Rene Decartes almost brought it all down.( how he escaped being burned at the stake is amazing )

    David Hume perhaps the best refuataiton of the Ants as people thing- until we find a second universe and therefore have a control factor that arguement does not work.

    In my humble opinion we need to be students of religion and start practicing the expression ” I just do not know.

  13. says

    Absolutely laFond..
    The really scary thing is that religion is pretty much encrypted.. and if you get the wrong people preaching it.. they bend it and flex it to fit their own agenda..

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