Tom Gilson

The Arithmetical Atheism Argument, or, The Magic of Misdirection

“You’re really just about as atheistic as I am,” says the debater to the Christian. “The non-Christian religions believe in maybe fourteen million different gods. You’re atheistic about all those fourteen million. I’m atheistic about fourteen million and one. What’s the big deal difference?”

The question has a certain zing to it. What indeed is the big deal difference? Think of it in percentage terms–what’s one in fourteen million? I call it the Arithmetical Atheism Argument. (If it has another name I’m not aware of it.) I’ve heard this question from at least from at least half a dozen sources, including Dr. Bill Cooke in the Craig-Cooke debate. As I recall, the crowd laughed when he asked it. It’s the kind of cute question that makes people chuckle. Phrased the way it is, it’s rather an interesting puzzler.

Phrased the way it is, that is. It reminds me of another question with a similar zing to it, one that bothered me a bit when I first heard it: “Why does a mirror reverse left-and-right but not up-and-down?” That’s kind of a tough one, you know. How does it know the difference?

The answer to the question is that it’s the wrong question. It misdirects you entirely. My son is an amateur magician, and from him I’ve learned the importance of misdirection in magic tricks: get the audience’s eyes off of what’s really going on, and you can fool them every time.

The mirror question is worded to get your mind off of what’s really going on. Why does a mirror reverse things one way and not another? Well, it doesn’t reverse either way. It doesn’t reverse anything at all! It reflects what it’s shown. Take a book to the mirror, and you’ll undoubtedly see the letters appearing reversed left-and-right; but that’s just because of the way we usually hold books. You could have turned it toward the mirror by flipping it top to bottom instead. Then the letters would be in their perfectly normal left-to-right order, but they would be reversed up-and-down instead.

The atheist’s question here does a similar thing: it misdirects the argument, in two ways. First, there is the misdirection employed in the word “atheistic.” The question tries to get you to nodding your head, agreeing that you’re an atheist about fourteen million different gods. Don’t fall for it; don’t nod your head. If you’re a Christian you are not atheistic about any gods, because you are not atheistic at all. Atheism is not, “I don’t agree with this or that particular idea of God.” It is, “I believe there is no God.” If you accept the premise that your questioner and you are both atheists, only in different degrees, you’re falling for the misdirection: you’re failing to see what’s really going on.

Second, it misdirects through trying to make the question about arithmetic. What, indeed, is the big deal difference in the ratio of one to fourteen million? Well, it’s not a matter of quantity in the first place. Theists view the universe in one way, and atheists another. Theists view it as an intentionally caused creation, the product of a personal mind, having a purpose and goal, an intended reason for existing, and much more of the sort. Atheists accept none of that. This is not a matter of number; it is an absolute difference in what we take to be the essence or quality of what exists.

Here’s a rule of reasoning that applies to the mirror question, the arithmetical argument, and many other similar puzzles, I’m sure, like the famous algebraic proof that 1=2. Count on it: the cuter an argument is, the more likely it is there’s a trick in it, a misdirection. Take a good look at the question: is there something in there leading your mind away from what’s really going on?

The Arithmetical Atheism Argument is a prime example of misdirection.

Commenting Restored

The comment function here has been out of service, possibly causing frustration, for which I apologize. You can comment again now, and it will save and post as it should do. First-time commenters' comments will not appear, however, until approved in moderation.

20 thoughts on “The Arithmetical Atheism Argument, or, The Magic of Misdirection

  1. By your definition you might not be atheistic but you still don’t believe in all those other Gods.

    So the question of why that is still remains. The Atheist claim that there is no more reason to believe in your God then any other.

    Basically it’s just a matter of semantics whether you treat the statement your way or the way it was intended.

    You can find misdirection in many sentences, but that doesn’t mean they are intended to misdirect. In this case it is intended to illuminate and educate.

  2. I don’t think everyone who asks this question has trickery as a prime motivation, Roger, but the words have that effect regardless.

    By your definition you might not be atheistic but you still don’t believe in all those other Gods.

    I’m certainly comfortable with that…

    So the question of why that is still remains. The Atheist claim that there is no more reason to believe in your God then any other.

    The reason I don’t believe in those other gods is because I believe in the one God. Suppose I’m talking business with someone on the phone–someone I’ve never met face to face–and we decide to meet at the coffee shop. I show up and someone greets me, and mentions our phone conversation. I don’t have to go check with everyone else there and see if they’ll also know about that conversation. One positive is sufficient to rule out all the others.

    Of course I wouldn’t assume the first man I saw there was the one. I would want some confirmation of identity, for which the mention that phone conversation would suffice in this case.

    I don’t need to worry about whether Vishnu might be God, if I am reliably convinced that the God of the Bible is God.

    That belief can also be checked. I’m convinced that “the atheist claim that there is no more reasons to believe in your God than any other” is just not true. I don’t want to start enumerating the reasons here, because that has been the main content of my 3 1/2 years of blogging. If you want to know some of what I have said, I suggest the Beauty of God’s Way series (linked from here) as a starting point for you.

  3. Tom:

    Roger’s error is similar to the alleged claim (by atheists) that we are per se atheists when born because we don’t then believe in God, and hence atheists claim the “default position” for human knowledge (or lack thereof) of God. The error springs from the defintion atheist’s employ about themselves: a person who has no faith in God. (You’ve read, I’m sure, the silly assertions by atheists: “faith is to atheism as hair is to baldness” or “calling atheism a religion is like calling bald a hair color”—talk about mixing categories!) Anyway, the definition is not a good one because it’s based on merely the negation of an accident (rather than properly formulated in terms of a genus and difference): privation of faith in God (like in an infant) doesn’t make an infant an atheist any more than the privation of the color red in a ball makes the ball a goat. (Babies are also born without knowledge of calculus, but that doesn’t mean the baby is not mathematically-inclined.) Negation of a quality (the second accident of real being) doesn’t change the substance under consideration. Atheism is not a lack of belief but a knowing, intentional (and I would add disordered) choice to not believe. Saying something is “not this” says little about that thing.

  4. Tom,

    I don’t need to worry about whether Vishnu might be God, if I am reliably convinced that the God of the Bible is God.

    Very true. Of course, we all should continue to re-evaluate and check our beliefs to see if they hold up. Using your example, if another man comes along and mentions that you both had talked before then you have to dig into the situation so you can learn which man you agreed to meet. You are no longer reliably convinced at that point. Turns out it was a different conversation – he has seen your picture but you’ve never met before.


    Atheism is not a lack of belief but a knowing, intentional (and I would add disordered) choice to not believe.

    Agreed. It is an intentional choice made once the evidence has been evaluated and found to be lacking the power to affirm. It’s like being on a jury and saying the evidence doesn’t add up to a guilty verdict. Anyone who says there is NO evidence for God’s existence is either lying, ignorant of the facts or they’ve defined ‘evidence’ so narrowly that, ironically, it turns out there’s NO evidence for they own existence.

  5. Uh, no. Atheism is simply a lack of belief in God. It doesn’t have to based on evidence or be logically consistant- there are atheists who base their beliefs on faith and the Epicureans had a some problems with their worldview.

    Atheism is simply a lack of belief. A rock, a baby, and I all have it.

    There is no evidece for Gods existance. All the arguments you can profer have logical flaws- argument from ignorance being the most obvious.

    If you don’t like the question, that is your problem. However you insist that each and every one of those possible other Gods does not exist. You take a strong atheism position in respect to those Gods… but not to your own. Why? Remember, each of the followers of those Gods did the same thing you are doing. What makes your religion special?

    At this point Christians start claiming that the New Testament is historically accurate and that it has real miracles- basically lying their ***** off. The Koran and the Tipitaka are both more historically accurate- everyone agrees that the people who wrote them actually exist, while there are those who have made a good case that Jesus never existed.

    Why do Christians insist on making up their own definitions?
    I’m using the broadist definition, as are just about ALL atheists. Atheism as an opposite to theism. Theism takes actual belief- atheism doesn’t.

    Edited by Siteowner

  6. Well you could turn the whole thing around as a reason for them to give up on atheistic Darwinism: “You’re really as ‘anti-science’ as I am. You don’t believe in epicycles, phlogiston, the lumineferous ether, or spontaneous generation. We just reject one more theory than you do. What’s the big deal?” Devastating!

  7. Then Samuel, I take it that your view of atheism could be stated thus:

    Atheism is a broad category of opinions united strictly by their common rejection of belief in any personal God.

    And that it is incorrect to state it as:

    Atheism is the belief that there is no God.

    I’m not quite sure what the difference is. Maybe you could help me with that.

    And how do you respond to Holopupenko’s prior statement that atheism is a privation of belief, not applicable to rocks and babies? I think that’s a pretty sensible position.

    As to your statement that there is no evidence for God’s existence, I’m going to be gracious and let you clarify before I respond. Did you mean perhaps there is no evidence that you find satisfactory? Or are you saying there is no evidence whatsoever? The way I would answer one of these is different from how I would respond to the other.

    Your charge that Christians are lying–aside from its gross rudeness that remains evident even after I edited it (you’re a guest here, my friend)–is quite inflammatory. Do you mean to tell me you think Christians are intentionally deceiving on this point? There’s an easy answer to this: we aren’t. Maybe I’m wrong on this point or others, but I’m not lying to you. I am quite fully convinced of the things I write.

    “There are those who make a good case that Jesus never existed.” If a good case means an opinion utterly unsupported by historical research or consensus, then I can also make a good case that Napoleon never existed. (Your standards for a good case are altogether too low.)

    The Koran’s historical accuracy is irrelevant, since its historical claims are so minimal. I’m not so versed in the Tipitaka but I think the same would be true of it. So I don’t even know how you could compare their accuracies, or what difference it would make. The point is that the Bible’s historical claims are routinely confirmed by archaeology, by textual criticism, and by the further witness of history. There’s enough there to be able to count on its reliability.

  8. Also, Samuel, “simply a lack of belief” seems like a pretty weak position to take. It seems like a person would be at least as interested in figuring out what they do believe as in making a point about what they don’t.

    Matteo, thanks for that additional thought on how the Arithmetical Argument falls short. Good point.

  9. Samuel said, “Atheism is simply a lack of belief. A rock, a baby, and I all have it.”

    Stand back for a moment and think about how convoluted and reductionist his words are… and note as well the contradiction: according to Samuel, “a lack” is the same thing as to “have.”

    I’ve said it before and I’ll say it again: Atheism, quite literally, leads to disordered thinking.

  10. Regarding mirrors, they don’t reflect left right, they invert front and back. If the coordinate system is x (horizontal) y(vertical) and z perpendicular to the mirror, then the puzzle about left-right up-down is the statement that it appears the mirror distinguishes between the two and treats one differently—i.e., that it treats the x and y axis differently. It does not. It transforms x, y, z to x, y, -z. X and y are treated the same, as our intuition tells us they should be. You essentially see the object from behind, the object being the 2D image of whatever you are looking at. Now if you walk behind something, which is what the mirror is essentially doing for you (in a 2D image sense), what was its left side becomes its right, but what was its top stays its top.

    I think the atheist question is fallacious out of the box. If you believe in just one of only 14,000,001 gods you are not “almost as atheist” as an atheist. An atheist believes in no gods. You are, instead, “as theistic” as the adherents other 14,000,000 religions.

    I do agree, however, that people are born atheists.

  11. David,

    I do agree, however, that people are born atheists.

    People are born ignorant of every conceivable thing so this doesn’t really say much about what it means to be born atheist. From what I gather, there is supposed to be a point to be made when someone says it but I don’t see what it is. I mean, what do you say in response to someone who says “You know, circles are perfectly round” as if there is a point to be made by stating the obvious? *shrug* is about all the response it deserves.

  12. SteveK,

    as if there is a point to be made by stating the obvious? *shrug* is about all the response it deserves.

    On the contrary, it is, in my opinion, a loose summary of Original Sin or Total Depravity. It means that we all are born in rebellion to God. It means that infants also require a savior. It means that, apart from a savior, we will be punished not just for what sins we commit later in life, but even for how we are born. It means there is no “age of accountability.” It is quite a profound statement, in a sense.

  13. David,
    The statement indeed says something about us all. My comment was more directed toward what the *atheist* thinks the statement says. They are trying to make a point, right?

  14. Heddle and SteveK:

    Consider the following two cases:
         (1) the privation of an accident: all infants are born without a tan.
         (2) the privation of substance: all infants are not born infants.

         The first example is true but says nothing about the nature of the infant. So, when an atheist claims atheism as the “default position” for all humans, it’s only true per accidens (non substantively), not per se. In other words, it’s not in the nature of any infant to be an atheist just like it’s not in the nature of any infant to be born with a tan or to recite a poem immediately upon leaving the womb. What IS in the nature of every human infant is to be born as a “blank slate,” and in this regard to be lacking all knowledge—sensory or intellectual—is not the same thing as saying that an infant is born not believing in God. Again, because the former has to do with what the infant is as substantively (i.e., as a person) while the latter has to do with what an infant is accidentally. (Boethius’ definition of a person as “an individual substance of a rational nature,” which St. Thomas quite nicely defends in ST I:29.) Another way of saying this is: The infant is in an essential state of not knowing or believing, but only in an incidental state of “lack of belief in a diety.”

         The second example is not true, and one immediately senses the sentence is convoluted, contradictory, strange, etc. It is, in fact, nonsense.

         Actually, the above is only an introduction because it’s all a bit trickier than this. Since it is in the nature of a human person to have the capacities of reason and free will, when we reason to obtain knowledge we are perfecting (in the philosophical sense) our natures. (Similarly, we are sinners by nature by virtue of the original sin—it’s “in our blood” so to speak. When we permit God’s grace to operate in us, He doesn’t destroy our nature but perfects it.) At this point I need to introduce an important distinction between attribution and predication.

    Distinguishing “Attributive” from “Predicative” Adjectives

         Consider the following statement: “He is a fat philosopher.” This sentence can be broken down into the following two:
         (1) He is fat.
         (2) He is a philosopher.

         Now consider the following statement: “He is an implicit atheist.” (This works just as well—as it should—with “He is an explicit atheist.”) Try breaking this statement down into two:
         (3) He is implicit.
         (4) He is an atheist.
         Clearly, this doesn’t work so well: one would hesitate to make these two claims because the first of the two begs completion, i.e., “implicit about what?” or “implicit what?” The same sort of thing applies to the following statement: “He is a good philosopher.” This statement also cannot be split up because the first sub-sentence would beg completion: “He is good.” Well, what does that mean: a good (accomplished) piano player, a good (ethical) person, a good (educated and experienced) philosopher, etc., etc.?

         There is an elementary grammatical distinction between attributive and predicative adjectives. “Implicit,” “explicit,” and “good” are attributive adjectives—as are many, many other adjectives: they “stick” to the noun they modify. The only way one can determine what is meant by characterizing someone an “implicit atheist” is to go into what it is to be an atheist. (One does not need to understand that a person is a philosopher in order to understand he is fat.) In other words, the atheism is presupposed, i.e., the atheism is prior to the attribution of “implicit” or “explicit” or whatever, i.e., one must function as an atheist before the attributive adjective “implicit” may be applied. However, to function as an atheist means to have knowledge—even if rudimentary—of what atheism is.

         The punch line? It is impossible to rationally claim a “blank slate” infant (who has no knowledge of atheism… or theism, for that matter) is in the “default position” state of “implicit atheism” when the knowledge of atheism is presupposed. Similar reasoning applies to musicians, philosophers, or baseball players: it is just as incorrect to claim an infant is an “implicit” atheist as it is to claim an infant is an “implicit” piano player or an “implicit” non-Olympic athlete.

         The correct characterization of an infant is that of a “potential” atheist (or musician, non-Olympic athlete, physicist, philosopher, panhandler, sophist, etc.), for this captures the proper understanding of what it means to change from one state to another: a person is a “potential” atheist prior to some acquired to knowledge, while a person is an “actual” atheist once a decision (employing the will) has been taken based on either incomplete or false information obtained.

         Heddle: I won’t pursue the “total depravity” thing too far… which is, in the way you’re expressing it, a deep confusion. (If promulgated dogmatically, it is a heresy.) It is a confusion that follows from not carefully distinguishing (1) the role of God’s grace (beyond all that man may do or seek when left to his own faculties, God’s free gift of salvation is due only to acts performed under the influence of a strictly supernatural movement, i.e., there is no way man can save himself (the old Pelegian heresy taught that man can save himself by his own works)) from (2) the role of human nature (as rational beings who participate in that grace through virtuous acts). Again, I won’t pursue this off-topic issue… except to add the similarity you draw to the topic at hand is strained.

  15. Holopupenko,

    Personally I disagree. I think the doctrine of Original Sin and Total Depravity suggests that infants are qualitatively atheists. I don’t see how if you are a Catholic or Reformed you can avoid this.

    Or a better term, perhaps, is unregenerate. So yes, I am treating “unregenerate” and “atheist” as effective synonyms–maybe that is what you are objecting to, in which case I concede the point. The basis for such an objection is that unregenerate includes textbook atheists as well as practitioners of false religion, but the latter hardly applies to infants.

    Of course it doesn’t mean dead babies aren’t saved. It means that if they are saved it for the same reason adults are, they are monergystically regenerated and saved by faith.

    And this is normatively speaking–no doubt some infants are regenerated in the womb, so that some infants are in fact born with saving faith. God will have mercy upon whom he will have mercy.

    I am pretty familiar with the doctrine of Total Depravity. In a nutshell it speaks of unregenerate man’s moral inability to do anything pleasing to God. Or as Augustine split the infinitive, the inability to not sin. That is precisely what I am applying to infants (again normatively.)

    Heddle: I won’t pursue the “total depravity” thing too far… which is, in the way you’re expressing it, a deep confusion. (If promulgated dogmatically, it is a heresy.)

    What is the name of the heresy with which I am flirting?

  16. So yes, I am treating “unregenerate” and “atheist” as effective synonyms–maybe that is what you are objecting to, in which case I concede the point.

    I’m a lot more comfortable with “born unregenerate” than “born atheist,” simply because “atheist” implies having an opinion about God. We are all born outside of proper relationship with God, but it’s hard to call that disbelieving in God at that age, when belief has not really begun to operate at all.

  17. Heddle:

         Re “total depravity,” “unregenerate man’s moral inability to do anything pleasing to God” is a different thing from St. Augustine’s “inability to not sin”… and both beg questions: in the former “anything”? while the latter, does this imply man does nothing but sin? In any event, I’m not going to pursue except to round out the next point: it’s off topic and it’s not in my competency to the level that philosophy is. Apart from that, I must agree with Tom’s discomfort over your explanation, and I think both of us welcome your “synonym” concession.

         Re: heresy, I am not and did not apply the label to you, but I did raise a red warning flag. (“Flirting” is a good word, by the way.) If I understand Calvin correctly, the effect of original sin made our human natures COMPLETELY corrupted in the sense that we can do nothing to attain salvation. Well, that’s wrong: while it is certainly true that without God’s grace we can never be saved, that in no way implies we can’t cooperate with that grace… after all, we must respond with our own fiat. God’s grace moves us toward salvation (which means no action or merit on our part can accomplish that “movement”), but we are free to accept or reject that gift of grace (which means an effort on our part), and all our actions that follow are based on that acceptance or rejection.

         (By the way, that’s why I fear so strongly for the atheist: a rejection of God is a rejection of grace, a direct sin against the First Commandment, and hence the atheist does not permit God to begin perfecting his nature—a nature that is distinguished from all other natures (excluding angels and God, of course) by the capacities of reasoning and free will. If any human decides to “go it on his own” without God’s grace, disaster will ensure sooner or later. I know it sounds very un-PC but why are any of us surprised by the way atheists present their “arguments” on this blog? Argumentation presupposes an intellect, and an intellect that rejects truth and God a priori will not reason correctly, and will hence not provide the will with a “good” as based on truth. Again, that’s a recipe for disaster.)

         So, to conclude, it’s not a specific “named” heresy for which I’m raising my flag, it’s the overemphasis on certain things (“inability to do anything” and “nothing but sin”) that can lead to heresy. For example, Calvin’s theory of double predestination, which follows logically from the hyper-emphasis on “anything at all” in the concept of “total depravity,” is heresy. Why is it heresy? Because if who is save and who isn’t is predetermined with no possible place for our participation in accepting grace, then there is no room for a truly free will… and (to put it crudely) we can’t be held responsible. Worse, people will start to reason, quite logically, that if each of our fates is sealed, what difference can any action make—including the action or effort of accepting the grace of salvation?

         P.S. By the term heresy I mean something that is a denial or extraction from an integrated whole. The very word heresy from the Greek means “choice”—implying a choice from a whole and a splitting into factions. Also, please trust me I’m not out to “get at” brothers in Christ—Lord knows what we’re up against outside the Body should humble us all into dealing with theological nuances (albeit important ones) off-line… or perhaps even on the other side of glory. I’m stating my position for clarity… not to pound.

  18. Holopupenko

    No problem–after all Rome placed several anathemas on the doctrines of the reformers at Trent, anathemas which it has never lifted–so in some sense all good Catholics should consider all Reformed Christians as at least borderline heretics.

    You should, however, acquaint yourself more with Calvinism. You seem to accept several of the common caricatures.

    One is that there is no cooperation required. There is in fact full cooperation required. The regeneration (and justification) itself is monergystic. However, cooperation with salvation (work out your salvation…) is commanded.

    Another is that free will is lost. Actually, Calvinism has the most libertine of all models of the free will: namely that you will always choose what you want most, all the time. There is no external negating of the free will in Calvinism. There is no puppet master making you choose. You choose what you want, and what nobody wants prior to regeneration is God (No one seeks God, no not one.)

    The third mistake you make is quite serious: Calvin never taught “double predestination.” Actually he didn’t even teach a great deal on single predestination. At any rate, double predestination is a distortion of Calvinism that teaches that God actively changes the hearts of believers toward himself (true) but double predestination also teaches that God actively changes the hearts of the reprobate away from himself. That’s false, makes God the author of evil, and is not a teaching of Calvinism. Calvinism views “hardening of the heart” as a metaphor for God leaving men to their own nature. He may withdraw common grace, but he is not by divine action making their hearts more evil.

  19. Consider the similar argument:

    There is an infinity of possible x’s that could answer the equation x = 1 + 1. I believe they are all wrong. You insist that your answer is right. I believe that an infinity of answers are wrong; you believe that an infinity minus 1 are wrong. That’s not much of a difference!

    Two (1 + 1) problems here:

    1. The one who makes the argument in effect claims that all answers are of equal probability (or quality), or else the statistical argument would be worthless. How can they know that?

    2. The argument totally falls apart if one item in the solution set happens to be correct. All the probability arguments in the world cannot argue away one right answer. Simply counting a large set of possibilities does not say anything about the probability of any single element in the set.

    In reality, the arithmetical argument for athiesm is either a claim to complete knowledge about all religions (i.e. that all are equally probable) or an argument from laziness (I can’t be bothered to look at them, so I’ll assume they are all equally probable).

Comments are closed.


Subscribe here to receive updates and a free Too Good To Be False preview chapter!

"Engaging… exhilarating.… This might be the most surprising and refreshing book you’ll read this year!" — Lee Strobel

"Too Good To Be False is almost too good to be true!" — Josh McDowell

Purchase Here!

More on the book...

Discussion Policy

By commenting here you agree to abide by this site's discussion policy. Comments support Markdown language for your convenience. Each new commenter's first comment goes into moderation temporarily before appearing on the site. Comments close automatically after 120 days.

Copyright, Permissions, Marketing

Some books reviewed on this blog are attached to my account with Amazon’s affiliate marketing program, and I receive a small percentage of revenue from those sales.

All content copyright © Thomas Gilson as of date of posting except as attributed to other sources. Permissions information here.

Privacy Policy

%d bloggers like this: