Pages Menu
Categories Menu

Posted by on Aug 20, 2013 in philosophy, secularism, skepticism | 34 comments

Why the famous atheism vs agnosticism chart is wrong

[UPDATE - see end of this post]

The dreaded debate
This tumblr popped up in my newsfeed yesterday. It encapsulates the most common conversation between two types of non-religious people in the last couple of decades. I have had or been audience to such an exchange, the dreaded “atheism vs agnosticism” discussion, dozens of times.  It usually goes like this. Self-described atheists says that if you lack belief you are an atheist, period. Self-described agnostic says that nothing can ever be known for sure, so really the atheists are agnostic and should identify as such. This gets resolved, apparently to the general satisfaction of nonbelievers, with the following chart which concludes both parties are right because “knowledge” and “belief” are separate.

Belief Chart, Christmas edition.

Belief Chart, Christmas edition.

Even Richard Dawkins recaps this discussion and its conclusion in The God Delusion. It seems like a coup for agnostics because the chart puts confident atheists on the same footing as fundamentalist Christians and, as in the tumblr, attempts to claim all reasonable people as agnostics. On the upside the atheist does still get to claim the agnostic disbeliever, so there’s a little win for everyone. The only problem is that its cheating. The chart doesn’t make sense, and its fundamental claim about the separable categories of belief and knowledge is completely wrong.

Brass tactsPunnett Square
The basic logic of the chart, and any chart like it, is that the columns represent a property and each column a different (in this case opposite) form of that property. Same for the rows. In this case the columns specify a belief property and the rows a knowledge property. It’s just like those Punnett squares from high school about what color the peas are going to be →

Notice that each gene (allele), denoted by Y or y gets distributed across its row or column and that the meaning is precisely the same across the column or row.

Now let’s simplify the atheism vs agnosticism chart. Let’s say that,
K = Knows X
~K = Does not know X
B = Believes in X
~B = Does not believe in X
X = god exists (but X could be any proposition, does not matter)

Replicating the format of the chart above, we get:

Belief grid

Now let’s have a look. The atheism/agnosticism chart above says in the top left quadrant “100% certain there is a God or Gods”. In the simplified language of my chart, the quadrant contains “knows X, believes X”. So far, so good. The bottom row seems right, too. The agnostic theist does not know, but believes and the agnostic atheist claims neither knowledge nor belief. The top right, aka the strong atheist quadrant reads “Knows X, does not believe X” and as stated, X = “God exists”. So, “knows God exists.” Huh. That’s not quite right, that should be the atheist. That’s not even the biggest problem.  There is no single proposition where this chart works and makes sense.

That’s because it’s cheating by inverting the proposition in at least one term without any justification. In this case, X has to be traded for ~X. It’s the only quadrant where that is done. Why?

You can wrestle with it a few different ways, mucking about with the X’s K’s and B’s, but you’re always going to be fudging exactly one term for it to make sense. The reason for this is the incoherence of a quadrant which will necessarily read “I know X, but I do not believe X”. This is a nonsensical statement. Something must be believed to be known.

Note that there are only three possible locations for any proposition, not four.

Note that there are only three possible locations for any proposition, not four.

If all items that are knowledge always subsume at least one belief, then knowledge and belief can’t be unrelated features like temperate and height, but are instead more like gradations of a single feature which we might describe as “how compelling is the rationale for accepting X”.

I would assert that the chart is sociologically useful, while being epistemologically incoherent. Belief and knowledge are meaningful in that context: I can have very good reasons to think something is true that I can’t prove to anybody, such as the contents of my own thoughts or the fact that I was holding a pen 10 seconds ago. I can never prove that to anyone. It can’t be knowledge per se. But surely, to me, it is a justified, true belief. It would be absurd to demand that I ignore the empirical evidence on the grounds of nonreplicability (many accepted bits of knowledge are one-of events that can’t be replicated empirically).

If the chart is bunk, who wins at Ath vs Ag?
Like Bob Barker used to say, I’m sorry, you’ve all philosophically overbid. OK, so I’m paraphrasing. The correct representation is a single axis continuum of confidence. Somewhere along that axis are markers that denote, at least psychologically, concepts like true, false, correct, nonsense,bullshit, certain, and yes, knowledge. This observation does not itself say where the lines should be, nor where the God hypothesis falls on that, but drawing my line for you might help you understand why everyone in the Ath vs Ag argument has lost. You might be familiar with the Dawkins Scale of belief. I must give the man credit for at least getting the type of representation right.

Dawkins ScaleBut still, not a valid representation. (With all due respect to the Dawkins, Peace be upon Him, e pluribus unum). As I explained in a previous post, this chart misleadingly suggests that the epistemological distances between the items 1-7 are comparable. In fairness, Dawkins does try to add nuance with the descriptions, but still the numbering is misleading. Belief space is vast and has to be described exponentially or logarithmically.  Another problem is that Positions one and seven are philosophical fantasies: they do not exist in the real world, not for God belief, not for any belief. The reason we can change our minds, is that all propositions are inabsolute. Scientifically, the notion of “100% sure” is nonexistent. Here is a better scale I created, which I call the Sagan Plausibility Scale.

Sagan Plausibility Scale

LOD = line of demarcation. A fuzzy, approximate area below which concepts are linguistically and psychologically described as “bullshit” or “untrue”. Measurements accurate to within 0.5 millisagans.

Nobody “won” because everyone from the very start thought that it was worthwhile to invent a labeling system and nonsensical chart for one single reason: to point out that a vanishingly unlikely, silly claim fails to be infinitely unlikely. The moment you started thinking absolution was the rightful yardstick for facts or truth claims, you were wrong and wasting your time. That isn’t what true means.

Further reading
Agnosticism is untenable and irrelevant, part 1
Agnosticism is untenable and irrelevant, part 2
Agnosticism is untenable and irrelevant, part 3

—————— UPDATE —————
A kindly Redditor (OK, more belligerent and rude than kindly) told me the object n question is not a chart or table, but a four-quadrant Venn diagram. After a bit of looking I found this similar representation.

Belief Venn Diagram

I expect this is what the “standard” chart is meant to represent, but it has been distorted and abused over the years. I find this representation quite agreeable. Properly understood, the chart is a 4-square version of the above with the superset’s area outside of the 4 visible sets removed. Note some key differences, the bit about “100% certainty”, silly nonsense really, replaced with much more mundane and sensible “Does claim proof exists”. There is no juxtaposition of belief and knowledge because there is no mention of knowledge.

In light of this finding, I was incorrect to expect properties to be distributed across the table because it isn’t a table, but four sets that do not overlap with their opposing set. Such are the dangers in wading into the philosophical waters when you are not a pro.

I do maintain (and this particular diagram supports) that a belief/knowledge dichotomy isn’t necessary or important, and that the set including the agnostic sections are frivolous in practice.

  • Ianos Gnatiuc

    Let’s assume a Dichotomy – theist and non-theists. Non-Theists is translated as a-theists. So, all people can be divided into theist and atheist. Where you got agnostics here?

    • SandyRavage

      False premise. A word’s etymology doesn’t determine it’s meaning. And anyway, the etymology of atheism is actually “atheos”(ungodly)+ism(belief). If you don’t believe this, look up the history of the words theism and theism and you’ll see that the word “atheism” predates them by centuries.

  • riddles

    So because to you the chart makes no sense, it must be the chart that is wrong rather than your understanding of it?

    • Edward Clint

      No. The claim that something does not make sense must be supported by argumentation. I have provided you with my analysis. I stand to be corrected by anyone who can point out where my reasoning is erroneous, or what I might have missed.

      I would welcome that.

      • riddles

        Well in your “simplified” chart, K doesn’t mean the same thing it does in the original one. In yours you turned it into “Knows gods exist” when on the original chart it should be “Claims knowledge on the existence of gods”. Because you changed what K should mean you made it impossible for gnostic atheists to fit on the chart anymore. If you kept K at the same meaning as it was then everything would be fine.

        This is how you can have a gnostic atheist where they do not believe gods exist and they claim to know about the gods existence (in this case, that they do not exist). K should not be Knows a God Exists/Does not Know a God Exists since that doesn’t match what the original chart was saying.

        • Edward Clint

          To entertain your perspective I would have to accept that the phrase a person might utter “I am 100% certain that no God exists” is meaningfully different from the phrase “I know there is no God” in discussions about God.

          If someone asked if cigarettes can cause cancer and I said “I am 100% certain that cigarettes can cause cancer.” How likely is it that the asker would correct me, saying, “No, I didn’t ask about how sure you are. I asked if you *know*?” Nobody would issue such a correction. And if they wouldn’t, then the terms are not meaningfully different in the context of discussions people have about belief in God.

          • riddles

            I’d say the likelihood of a person correcting you in the cigarette example is a bit more likely than I would have thought before considering you are right now pretty much doing the same thing regarding the 100%/know wording.

            While they are technically different, in this situation they mean the same thing. When a person says they know there is or isn’t a god, they are basically saying they are 100% of it.

            Though I’m not sure what this has to do with what I said, seems like meaningless picking at semantics to me.

          • Edward Clint

            I don’t know what you mean by that, but unless you wish to argue people would commonly correct such a reply, I will assume concession on the point.

            “When a person says they know there is or isn’t a god, they are basically saying they are 100% of it.”

            Good, we agree. But you also said, “…on the original chart [K] should be “Claims knowledge on the existence of gods” instead of “knows god exists”. But the square is clearly labeled in the chart “100% certain there is no god or gods”. Since you said just now that means the same as when a person says they know there isn’t a god, the chart must be specifying that the person knows there is no god and I did not, in fact, change its meaning.

          • riddles

            Okay, seems this boils down to you misunderstanding what the “100% certain there is no god or gods” bit means. That means that they know/are 100% on the existence of gods, in this case, that they do not exist. Where B is Belief and K is Knowledge/Certainty, K is a modifier of B in this situation. If a person believes there is a god, K means they know/are 100% there is one. If a person does not believe in a god, K means they know/are 100% there isn’t one.

            Do you get it now? K means they Know/are 100% about the existence of a god be it that they do or do not exist, it does not mean they Know/are 100% that the god exists or they do not Know/are 100%

            If this doesn’t work with your chart, that’s because your chart format is either incapable of explaining it or you need to tidy it up. With the original chart it works fine where one axis is whether a person believes or not and the other is whether they know for certain.

            Think of B as believing a god exists, b as not believing a god exists. K as knowing about the existence of a god and k as not knowing about the existence of a god. Your typical theist would be BK as they believe there is a god and say they know that the god exists. Your typical atheist would be bk where they do not believe a god exists and don’t claim to know they they do not. A gnostic atheist would be bK where they do not believe a god exists but say they know there is no god.

            Like I said, K/k here works as a modifier of B/b.

          • Edward Clint

            I can’t help but wonder what could possibly be meant by “you chart format is either incapable of explaining it to you or you need to tidy it up”.

            Can the format of a chart explain things? The chart is not mine to “tidy up” because it is not mine at all. I wrote this essay to criticize it for what it is, not for what it might be after repairs.

            You say that K is a modifier of B. Please explain what precisely is modified, and what the modified substrate is before and after modification. My understanding is that at the outset, B = “believes in God” and ~B = “does not believe in God”. K, according to you, adds to this 100% certainty about. This does not in any sense modify B or ~B. It remains identical to what it was before. K does serve to modify something, but it isn’t B.

            But your basic argument here (like qbsmd’s below) is that there are two propositions instead of one, as I have demonstrated one proposition (X = god exists) does not work. The two X’s are then X and ~X and ~X is arbitrarily the right column and X the left. This also does not salvage the chart, although it makes it coherent. Why not?

            Because the chart is invariably used to prove the point that positions people take are categorized in terms of knowledge and belief. In fact, that is wrong. The chart has no power to demonstrate that either knowledge or belief categorizes people’s positions. The inputs are different, X versus ~X. Because of that, every pair of terms in adjacent squares are incomparable or identical. Does “belief”, the act of believing or disbelieving, separate the theists and atheists? Strangely, per the chart, we can’t conclude that. If we represent belief as B(X) and B(~X), it’s plain to see the two don’t differ in B, they differ in their inputs. The inputs could be anything, and arbitrary choice of inputs would make the terms different no matter whether it was B or ~B.
            What if we think about the term itself instead of the individual B part of it, and represent the term as B and ~B (for believe in god, does not believe in god)? That’s fine for belief, but it breaks the K term. You said that K is a modifier of B. It makes B into “100% certainty” about/of B. But if B = believe in god, the K modifies it to “There is 100% certainty [I] believe in god”. Wrestle with the language and labels all you want, Using Kk/Bb or K~K/B~B will fail every time.

            You can switch models but they all break down. My simplified one in the essay makes a strong atheist that believes in God. Nesting the B and K with a third variable X, as you and qbsmd suggest breaks the B by rendering opposite B’s identical. Getting rid of the X to solve the B problem leads to K being distorted into a claim about the person’s state of believing without asserting they know or are sure about God or any other proposition.

          • Edward Clint

            I’ve added an update to the end of my post. Please take a look.

          • riddles

            Hmm, curious that they would describe it as a Venn diagram like that. Not sure about the connotation that one can be in the agnostic/gnostic circles without being in the other two. It implies that you can neither have a believe in a god(s) and lack one at the same time. I guess I will have to find that guy’s posts to better understand what they are saying here.

            Other than that, nice to see you are open to changing your mind when presented with sufficient reasoning to do so.

          • Edward Clint

            I wondered about the “between” space as well. I suppose that it is possible a person is a (a)theist and has never made any particular claims about proof, Maybe it’s meant to describe a person like a child who could have a belief without understanding or considering proof for that belief. Still an odd situation.

  • qbsmd

    I think the chart works if you translate the propositions as B=”believes at least one god exists” and K=”believes B meets the criteria for ‘knowledge’”.

    But either way, I’m not convinced the philosophy is all that important to the discussion. The term “atheist” has certain negative connotations and some people, for reasons that are closer to political than philosophical, choose to either embrace or reject that label. The philosophical justification they use follows from that choice. I’ve seen people use the terms “tooth-fairy atheist” and “teapot agnostic”, which make it pretty clear that people with identical philosophies are choosing different labels.

    • Stuart Thomas

      I agree, atheist is a flawed term, it assumes that there is something in which to believe and that some people make a choice not to believe. I do not choose not to believe, as there is no evidence on which to base belief. I prefer the term anti-theist, as it doesn’t acknowledge that there is a god to believe in, or not.

      • Severisth

        Anti-theist also carries the connotation that you are actively working against religion. Not all atheists fit that description (though I wish they would!).

      • Edward Clint

        I am curious why you think the word “atheist” carries the assumption anything in particular exists. I feel .. sort of like that, in the sense of, why do we have special words to describe nonsense? It elevates the issue above and beyond what is intellectually warranted, even if it makes sense socially.

        But I don’t think the word itself suggests there is a thing (other than an idea). We could as easily coin the expression asantaist without the implication Santa is real.

    • Edward Clint

      I can not semantically parse your revision of B and K. Put together, (when both are positive) we get “Believes that believing at least one god exists meets the criteria for knowledge”. Which sounds like saying the act of believing in God is knowledge. I’m not trying to be obtuse, this really doesn’t work out.

      • qbsmd

        Okay, I think the goal propositions are
        “x believes a god exists but x is not certain a god exists”
        “x believes no god exists but x is not certain no god exists”
        “x is certain a god exists (and x believes a god exists)” and
        “x is certain no god exists (and x believes no god exists)”

        I guess the easiest way to put the chart together would be to assign G=”a god exists”, B(x,p)=”x believes p”, and K(x,p)=”x is certain that p”.

        Then the chart becomes
        K(x,G)&B(x,G) K(x,~G)&B(x,~G)
        ~K(x,G)&B(x,G) ~K(x,~G)&B(x,~G)
        where the axes are certaintyuncertainty and belief in a god or not.

        • Edward Clint

          Thank you for the detailed explanation qbsmd. One question, why is the agnostic K position ~K(x,G) on the one side and ~K(x,~G)? Functionally about the same, I’d grant.

          You formalize the inversion, but the cost in doing so is that the terms are no longer distributed across rows and columns. This is because half of the chart applies to a different premise than the other half. G and ~G are not interchangeable parts. K and ~K are row definitions. B and ~B are column definitions. G is the premise or else ~G is, but not both without sacrificing the meaning of the rows.

          • qbsmd

            re ~K(x,G) and ~K(x,~G), you could rewrite the table as

            [K(x,G)&~K(x,~G)&B(x,G), K(x,~G)&~K(x,G)&B(x,~G);
            ~K(x,G)&~K(x,~G)&B(x,G), ~K(x,G)&~K(x,~G)&B(x,~G)]

            but does it add anything? I think B(x,p)->~K(x,~p).

            I chose to use G and ~G as column definitions, so every term on the left used G, and on the right ~G. I consider that a feature rather than a bug, because it directly captures the difference between theism and atheism while preserving the original meaning of the table. I could have used B(x,~G)=~B(x,G) to rewrite the table, but then there would have been terms with G and ~G in the same cells, so the column definitions couldn’t be B or G.

          • Edward Clint

            I’ve added an update to the end of the post, please take a look. I think all this is unnecessary, but I thank you kindly for helping me mull this one over.

          • marmot_smith

            I believe a better premise to use to eliminate the inversions is

            x=god’s existence is determined

            strong atheist and strong theist can agree on this hence no inversion

  • William Satire

    To me the “know” didn’t mean “knows god exists”. On theist side it means that. On atheist side it means “knows god doesn’t exist”. That’s 2 panels where it’s flipped which makes sense. Your definition of K is too strict. K equals knows exists / knows doesn’t exist

  • jg29a

    “The correct representation is a single axis continuum of confidence.”

    This strikes me as psychologically naive.

    A person is not a uniform belief state (between 0 and 1) with respect to a certain proposition. Rather, depending upon the current environment and what thoughts, feelings, etc. are being activated, there are typically different, and perhaps wildly different beliefs about the same content that are differentially activated. (Someone may be very anti-racist while voting and very racist while hiring, for example.)

    IMHO, the major problem we face in combating religion is the “Emperor’s New Clothes” phenomenon, i.e. vast numbers of people who believe that a god exists with the parts of their brains connected to their social personae, affiliations, abstract arguments, and so on, but believe that no god exists with the parts of their brains that govern wearing seatbelts or getting medical treatment. These people are not merely in-between; rather, they have both represented in different parts of the brain, differently connected.

    • jg29a

      …which is to say, an “atheist” is really someone who has brought the behavioral consequences of no god existing into the social, discursive realm, rather than just having a background effect on practical life decisions.

    • Edward Clint

      It isn’t a statement about psychology, other than to say it is to do with contents of beliefs. At any one moment or in any one context, how can we characterize a belief or a rather, a person’s disposition on a proposition? That is all I can claim to be trying to address. That is the “representation” I refer to above, as opposed to representing a person and the full spectrum of potential states over time and circumstance.

      • jg29a

        Okay, I can read your point that way, and it’s reasonable. But you’ll also acknowledge, I hope, that this chart is typically used to label *people*. My claim is that supposed “agnostic theists” are usually really theists in the parts of their brain related to answering explicit questions about religious affiliation, and atheists in the parts that govern real-world decision making. Such people, I’d say, are not halfway between atheism and theism on a single continuum — they’re *both* atheist and theist, in separate compartments.

        • Edward Clint

          For practical purposes of discussion, we may then restrict our context to “what do people self-report as when asked about belief”. The point about engaging in epistemological discussion and analysis is to understand belief positions better and to consider their strength (not to understand humans better, exactly).

          But I agree with your point and I have thought as much before. A priest won’t rob the collection plate if he thinks a camera is watching, but he might if there isn’t, even while supposedly knowing an all-powerful judgmental deity is watching everything 24/7. One of these beliefs is a lot more cognitively influential than the other.

          Still, I do not know how to characterize these different kinds of beliefs, and I have found no scientific literature which seeks to.

  • Matt Harrah

    I really like your article, and I also agree that the Dawkins scale is a better measure, for similar reasons to yours. But I do think that the problem with your criticism of the original chart has a potential flaw.

    In the original, only the X-axis has anything to do with the existence of god/s and/or the belief in them. The Y-axis is not about existence at all, but about whether you can be certain about what you believe. And you have both of these axes labeled as such.

    But in your genetics analogy, it seems to me you’ve imputed X-axis semantics onto the Y-axis. The top and bottom row’s K term should be not “Know god/s exist”, but “Know what you believe” if it is to be a true analogy to the original chart. By turning the Y-axis from a statement of certainty of your own beliefs to a statement about the X-axis’ proposition, you’ve altered the original and the analogy breaks down.

    …Which leads me to why I prefer the Dawkins scale. In your Venn diagram, you put knowledge inside beliefs, which I agree with. The Dawkins scale effectively turns the original chart’s Y-axis 90 degrees to be collinear with the X-axis and just acts as an amplifier or measure of degree along the X-axis, which I find to me more satisfying as a representation of the knowledge vs. belief question anyway (to me, knowledge is just what we call beliefs that we have tremendous confidence in).

    Again, I enjoyed your article. Thanks!

  • Matt Harrah

    I really like your article, and I also agree that the Dawkins scale is a better measure, for similar reasons to yours. But I do think that your criticism of the original chart has a potential flaw.

    In the original chart, only the X-axis has anything to do with the existence of god/s and/or the belief in them. The Y-axis is not about existence at all, but about whether you can be certain about your positions on things. And you have both of these axes labeled as such.

    But in your genetics analogy, it seems to me you’ve imputed X-axis semantics onto the Y-axis. The top and bottom row’s K term should be “Know what you believe” (and not “Know god/s exist”) if it is to be a true analogy to the original chart. By turning the Y-axis from a statement of confidence or certainty to a statement about the X-axis’ proposition, you’ve altered the original’s meaning and the analogy breaks down.

    …Which leads me to why I prefer the Dawkins scale. In your Venn diagram, you put knowledge inside beliefs, which I agree with. Knowledge is just what we call beliefs we have great confidence in. The Dawkins scale effectively turns the original chart’s Y-axis 90 degrees to be collinear with the X-axis, and thus acts as an amplifier or measure of degree along the X-axis, which I find to be more satisfying as a representation of this relationship.

    Again, I enjoyed your article. Thanks for sharing it.


  • marmot_smith

    Can you release that Venn diagram to the public by uploading it to Wikipedia and letting us use it on the agnostic article? We have had so many arguments over the diagram for lack of a good one.

    I think the four square chart could be fixed with the premise: ‘x=god’s existence is determined’ so that the knowledgeable theist and atheist both have knowledge of god’s existence and we do not have to use inversion language on any quadrant.

  • MechaVelma

    To be agnostic is to, by default, assume there is a reasonable doubt, supported by evidence on both sides of the argument, in the matter of whether a god exists. Since there is no evidence for the existence of god, the only rational default is to be a gnostic atheist.

  • Brian Sweet

    Except that, once again, one and only one quadrant requires an inversion. In this case the yellow/black overlap should be the intersection of “Doesn’t believe in god(s)” and “Claims proof does not exist” (rather than “Does claim proof exists”). Otherwise, you have the gnostic atheist claiming to prove a negative.