What is Atheism? II

0. Introduction

Recently I wrote a blog post about different ways of thinking about the definition of the terms ‘atheism’ and ‘atheist’. I was interested in the relation between belief and degrees of belief. Does lacking a belief mean lacking all degree of belief? To me, it seemed like the answer was ‘no’; one can lack a belief that p, yet still have some small degree of belief that p. That was how I describe my own internal doxastic state with regards to the proposition that no gods exist. I don’t feel like it is correct to say that I believe that no gods exist, but I have a small degree of belief that they don’t.

Part of my reasoning behind why I am only slightly in one direction rather than the other is because it is a proposition in metaphysics, and this seems like the most one can ever really have about such propositions. For example, it seems at least conceptually possible that there exists some god who is entirely unverifiable, some sort of deist god who never intervenes in the world and has left no trace of his existence for us to find. How could I ever know if such a god existed? Obviously, I couldn’t. But this type of god would also be the sort of thing that I couldn’t get any information about at all, either for or against. For this type of thing, there couldn’t be any evidence, and so one can never be confident that it doesn’t exist. So while I have an intuition or feeling that they probably don’t exist, it is not strong – after all, I don’t think that I know what the world is like at the most fundamental lever, so I don’t place much weight in what my pre-theoretical intuitions about that sort of thing say. They do lead me in one direction, but only slightly. That’s my view anyway. (An interventionist god who cares about human suffering seems far less likely to me than this epistemologically inaccessible god, and I would have a far lower degree of belief in such a personal god).

So I would say that my degree of belief that there are no gods is more than 0.5, but not much more. It seems to me that this doesn’t qualify as a strong enough belief for saying “I believe that there are no gods”. To me, saying that requires a higher degree of belief than I have. It is a declaration of a certain level of commitment to something to say “I believe that p”, and while it is not saying that you are utterly convinced that p, it is saying more than that you are minimally convinced; belief means something like ‘somewhat convinced’. I’m not sure that there is a precise numerical value which is the cut-off point between non-belief and belief; certainly not for all possible circumstances anyway. However, I just feel like my degree of belief is not strong enough to qualify in this context.

This is just like a situation where you may feel quite sure that a given person has not enough hair to count as hirsute, even though you are not sure whether there really is a precise number of hairs that one has to have in order to count as hirsute, or if so what that number of hairs is. Yet you just feel quite sure that this amount of hair isn’t enough. That’s how I feel about the god proposition.

Before getting to that point though, I spent some time explaining how there is some controversy about the definition of ‘atheist’, and this caused a bit of discussion on the comments below my past blog post on this – quite a lot longer than the actual article itself (and is still continuing as I write this), where people continued to discuss how they saw the right and wrong ways to define ‘atheist’.

My main point in the first section of that post was actually to argue that what seemed like a significant discussion between the atheist and theist is actually just a trivial definitional exercise on which nothing of any significance hangs. By this, I mean that it doesn’t matter if people disagree about whether someone should be called an atheist, a lacktheist or a hard-atheist, etc. The doxastic stance that the person holds, and any burden of evidence that comes with it, is what is actually important, and it remains the same regardless of what definition is used for the terms involved. We should just agree on a definition at the start of the argument and then move on into the interesting stuff.

Here I want to make that point as clearly as possible. So I will visualise a set of related positions – not a comprehensive list, but a reasonably thorough and precise list – so that we can see clearly what the different definitional positions are. I also want to express how this area is actually surprisingly rich from a logical point of view, and the various combinations of positions makes for an interesting enough landscape to categorise as a purely academic exercise. However, once we have a good grasp of the different definitions we could plausibly have in mind (the ‘landscape’), we can see how a particular person’s view gets classified. As we shall see, on some views I am an atheist, on some I am an agnostic atheist. The ability to translate between the different schemes considered provides the potential for more than just an academic classification exercise. It suggests the ability to help people stop talking past one another by providing a precise translation manual. All too often people hold different but not clearly articulated ideas about what it means to be an ‘atheist’ or ‘agnostic’ when they are in discussion and hopefully by setting out the landscape clearly we can be of some help here.

  1. Degree of belief

First, let’s consider the scale of belief about some proposition p (which will remain fixed as ‘some god exists’. The scale ranges from 0 for absolute conviction that p is false, to 1 for absolute conviction that p is true, with 0.5 being the middle point:


We can consider, for some agent a which we will keep fixed, that there are various propositions about a‘s beliefs and knowledge claims that we are interested in:

  • Bp      = a believes that p
  • B~p    = a believes that not-p
  • ~Bp    = it is not the case that a believes that p
  • ~B~p  = it is not the case that a believes that not-p
  • Kp       = a knows that p
  • K~p     = a knows that not-p
  • ~Kp     = it is not the case that a knows that p
  • ~K~p   = it is not the case that a knows that not-p

We will track where these propositions go under the belief scale, and then move on to add labels for various positions in as well.

2. Visualisations

Although the pair p and ~p are dichotomous (so that ‘p v ~p‘ is a tautology), this is obviously not the case for Band B~p; it is quite possible for neither of them to be true. Our agent might not believe that Kuala Lumpur is the capital of Malaysia, and might not believe that Kuala Lumpur is not the capital of Malaysia. The same goes for Kand K~p. This leaves room in the middle for a ‘belief-gap’. We will visualise this on our belief scale with a penumbra (or grey area) in which they a neither believes p nor believes that not-p. We could add this to our diagram as a shaded area underneath the section of the range to which it applies:


So in the diagram above, the grey area (the penumbra) extends beyond 0.5 degree of belief to some extent in either direction. This reflects that someone could have a degree of belief which is (say) 0.51 that p but that this would not be enough for it to be true that “believes that p“. For that to be true, a‘s degree of belief has to be greater than this. Precisely how much greater is vague and impossible to give a precise number to. All that we can (or need to) say is that for a to believe that p, their degree of belief has to be greater than the extent of the penumbra.

On either side of the penumbra, we would find the regions in which a holds a positive belief, either that p or that ~p:


We can add in knowledge claims here as well, where as we go along the scale towards 1 (or 0), we get to some (vague and impossible to make precise) point at which a doesn’t just believe that (not-p), but knows that p (not-p):


So our fully annotated diagram of the situation looks like this:


Given what I outlined in the last post on this topic, I sit just to the left of 0.5 on this scale (where p is ‘some god exists’). The green line is me:


It seems like my degree of belief is such that I don’t believe that p and I don’t believe that not-p. All this is rather uncontroversial*. The controversy, what there is of it, comes in when we decide which labels to apply to which position on the scale. We will do this by adding shaded areas to the top of the diagram. The first proposal we will consider (call it View 1) is where a ‘theist’ is someone who believes that p and an ‘atheist’ is someone who believes that not-p, which makes an ‘atheist’ a ‘hard-atheist’:


This has the consequence that theist/atheist is not an exhaustive distinction; it is possible to be in the area not covered by either (which is where I sit on this diagram). I am not an atheist on this picture (I am unclassified on this picture).

We might want to say that there is no such area, and that everyone is either a theist or an atheist. This sort of line has been put to me in the past. The idea is that if you act as if there is no god, then this makes you an atheist. Actions, it might be thought, are binary, in that you either act like you believe in a god (by going to church, praying, etc), or you act as if there is no god (by not going to church, praying, etc). This may make us think that everyone’s actions either make them an atheist or a theist (depending on how plausible we find this reasoning), in which case there should be no gap between the two positions on our scale (call this View 2):


On this view, a theist is not necessarily someone who ‘believes that p‘, but is just someone whose degree of belief that p is greater than their degree of belief that not-p. Similarly for the definition of ‘atheist’. I would count as an atheist on this view, even though I don’t believe that not-p. I count as an atheist just because my degree of belief that p is slightly less than 0.5. The definition of ‘atheist’ on this view is neither the same as ‘hard-atheist’ nor ‘lacktheist’.

As another option (call it View 3), we could think of the theist/atheist distinction as exhaustive, but draw the line between them on the point at which we switch from not believing that p to believing that p. This would make the definition of ‘atheist’ that of the ‘lacktheist’:


On this view, I count as an atheist, and interestingly so would someone whose degree of belief that was on the positive side of 0.5 but still in the penumbra; the sort of person who would say that they have a very weak degree of belief that some god exists, but not enough for them to say ‘I believe that some god exists’. That person would count as an atheist on this view.

We might think that the term ‘agnostic’ comes in here somewhere, and that it should come in to fill the gap between theist and atheist on View 1, like this (call it View 1.1):


On this picture, an atheist is someone who believes that not-p, a theist is someone who believes that p, and an agnostic is someone who does not believe either of p or not-p. On this picture, I come under the agnostic category, and not the atheist category.

We could add this version of agnostic (i.e. someone who does not believe either p or not-p) to View 2, to make View 2.1, as follows:


On View 2.1, all agnostics are also either atheists or theists; nobody is just an agnostic. On this view, I am an atheist and an agnostic.

Continuing the series, we could include the agnostic in the diagram and have ‘atheist’ pictured as a lacktheist (View 3), resulting in View 3.1, like this:


On this view, I would count as an atheist and an agnostic. On this view all agnostics are also atheists; there are no pure agnostics or agnostic theists.

However, one might think that the term ‘agnostic’ does not relate to a lack of belief but instead to lack of knowledge; it means that you don’t know if p is true, or if not-p is true. If that were the case (View 1.2), we would want to draw the agnostic area as follows:


On this view, there are ‘pure’ agnostics (and I would be one), but there are also agnostic atheists and agnostic theists (in contrast to View 1.1).

If we add this notion of agnosticism to Veiw 2, then we get View 2.2:


In this view, everyone is either an atheist or a theist (there are no pure agnostics) and there can be both agnostic atheists and agnostic theists. This only differs from View 1.1 in that the definition of agnostic is tied to knowledge, not belief.

Lastly, for completeness, I will consider View 3.2, which combines this agnosticism with the lacktheism of View 3:


On this view, an atheist is a lacktheist, and there can be agnostic atheists and agnostic theists. I am an agnostic atheist on this view.

Here are all 9 of the views for comparison:


3. Logical relationships

We have 9 views outlined above (View 1, 1.1 & 1.2; View 2, 2.1 & 2.3; and View 3, 3.1 & 3.2), but what are the relationships and differences between them? Here is an incomplete table showing some of the various properties of the different views and how they differ from one another:


Each view is unique in some respect or another. The difference between View 1.1 and View 1.2 (for example) is just whether agnostic means not believing either way that p or not knowing either way that p. This difference decides whether there are agnostic atheists/theists or not.

According to that summary, I am an there are two views according to which I am antheist, one according to which I am an agnostic, four according to which  I am agnostic atheist, with one where I am not classified. It is noteworthy how many different classifications one and the same doxastic attitude can come under. No wonder there is often confusion as to the usage of the terms involved.

4. Motivations

What we have is a landscape of different definitions and their various combinations. These are just the combinations I could see as being remotely justified. Each combination has something which backs it up conceptually.

  • There seem to be decent reasons for thinking about atheism and theism as being dependent on believing p and on believing not-p, which is the characteristic of View 1, 1.1 and 1.2.
  • However, the idea that belief is tied to action, and is thus binary, gives rise to the motivation for View 2, 2.1 and 2.2.
  • Then again, the definition of atheism as ‘lacktheism’ is clearly very popular among contemporary atheists, and this motivates View 3, 3.1 and 3.2.
  • There also seems to be some intuitive support for the idea that agnosticism simply fills in the space between atheism and theism, such that everyone is either an atheist, and agnostic or a theist (with no overlap), which informs View 1.1.
  • While this view of agnosticism seems fairly intuitive here, there is also something to be said for modelling agnosticism as relating to knowledge. Thomas Huxley, the person who coined the term ‘agnostic’, seems to have this association in mind when he said the following:

Agnosticism is of the essence of science, whether ancient or modern. It simply means that a man shall not say he knows or believes that which he has no scientific grounds for professing to know or believe.

Thus, there is a sort of exigetical support for the idea that agnosticism is epistemic rather than doxastic (i.e. about knowledge rather than just belief). If that is motivational for you, then you may be drawn to thinking of agnosticism as in View 1.2, 2.2 and 3.2.

5. Conclusion

It seems like a simple question, so often gone over, but so rarely gone over methodically:

What does ‘atheist’ mean?

But it has a surprisingly large number of potential, plausible-looking combinations of positions on the table. The benefit of classifying the various possible logical combinations is that we can translate between people’s usages. Here’s how:

First, one needs to assess internally what their level of belief is in the proposition being considered. Decide as best you can what your degree of belief is. Next also try to decide what you think (roughly) the thresholds are for belief and knowledge. Test yourself. For example, if you feel quite confident that you believe that p, do you also feel like you know that p? If not, then you believe without knowledge, and so you are in the middle section, etc.

In this way, we can get a feel for which region in the bottom part of the diagrams you fit into without too much need to quantify your degree of belief precisely. All you have to do is find which region of the belief scale you fit on. Once you have this in place, you can see how you are classified according to the various views. I did this in this post, and showed my results. So if someone asks me if I’m an atheist, I think my reply will now be ‘I’m an agnostic atheist on most definitions of the key terms, but on some of them I am an atheist’. This qualification doesn’t mean that I am changing my mind about what I believe, or trying to dodge any burden of proof for my claim. All the different views indicate is different ways of describing the same thing. 

There is no such thing as the ‘correct’ definition of what an atheist is. There is no such thing as the ‘correct’ definition of anything. Definitions are all arbitrary. One can use a definition in a way that fits the practices of a language using community, but other than ‘fitting in’ there is nothing else to decide whether a definition is correct or not. So there shouldn’t be a debate about what the definitions mean, from a logical point of view. We should only be interested in what people actually believe, and why.

There may be a larger political issue about the definition of ‘atheist’ due to the idea of an ‘atheist community’, but this is an issue I am not interested in. If I don’t classify as atheist enough for the atheist community, then so be it. I’m not going to change my sincerely held views just to be part of a club, and any club which is defined in terms of belief which requires people to adopt beliefs merely for the purposes of joining seems like an inherently contradictory institution.

It may be that people hold that the definitional game is more significant that I think it is for the following reason. It may be that when one joins a religion (or a new church, etc), that one sort of fits their beliefs to the community. As if someone says to themselves, ‘Now I’m part of the Calvinist community, I better figure out what beliefs I have’. This would make the beliefs follow from the belonging to a group. For all I know, this is how people view beliefs, and are happy to let themselves hold beliefs just because they are told that ‘people like us believe in such and such’. To me though, this gets the direction of travel the wrong way. First you have to have certain beliefs, and it is only because you antecedently do (or do not) hold whatever beliefs you do that you qualify for belonging to a club that is defined by beliefs. So one should say something like ‘I believe in the doctrine of predestination and original sin (etc), so I better figure out which group I belong to’. For me, beliefs come first, and labels (such as ‘Calvinist’ or ‘atheist’) follow after.


*From here on out, I will assume this basic picture to be correct. One could argue that the penumbra could really just apply to the 0.5 point and extend no distance in either direction. Even if you do so, this would still mean that the grey area has some extension. The reader should feel free to imagine the grey area being larger or smaller if  they so wish if they disagree with the extent I have given it above. It should be agreed by all parties that there is some penumbra, even if it only apples to 0.5 and nowhere else.


What is Atheism?

0. Introduction

Atheism may be defined provisionally as the view according to which there are no gods. However, despite this seemingly simple idea, there is a bit of controversy about the more precise meaning of ‘an atheist’. I will spell out some of the issues involved and outline my position.

  1. Atheism and theism

One might like to think of a proposition, p, which is to be understood as follows:

0)           p = ‘Some god exists’

It seems clear that the terms ‘theism’ and ‘atheism’ have some intrinsic relationship to p. One may think that the relationship is of the following sort (where ‘iff’ means ‘if and only if’):

i)            Theism is true      iff     p is true

ii)           Atheism is true    iff     p is false

This means that theism is logically equivalent to the proposition that some god exists, and atheism is logically inequivalent to the proposition that some god exists (it is equivalent to the falsity of ‘some god exists’).

1.1 Atheist and theist

If we accept i) and ii) as the definitions of theism and atheism, then we may move on to the definition of ‘theist‘ and ‘atheist‘. Doing this means bringing the agent, a,  into the definition. The natural way to define these terms is like this:

iii)           a is a theist       iff     a believes that [p is true]

iv)           a is an atheist   iff     a believes that [p is false]

There is a direct symmetry between -ism and -ist on this view. It is a nice and easy to grasp picture. The pattern is that the definiens of iii) and iv) are just those of i) and ii) but with the words ‘a believes that…’ at the start, and that the difference between theism/-ist and atheism/-ist is just that the former has ‘p is true’, and the latter has ‘p is false’. This means that a theist is just someone who believes that theism is true, and an atheist is just someone who believes that atheism is true. Thus, we have the pleasing result that theist is to theism what atheist is to atheism.

Here is a diagram of the logical relations:


If is an atheist in the sense of iv) above, call her a ‘hard atheist‘.

2. Lacktheism

There is another way of characterising what it means to be an atheist, and this departs from the pattern we have established above. On this definition, an atheist is someone who does not believe that p is true:

v)        a is an atheist    iff      not-[believes that p is true]

This definition of atheism is well-represented in public defences of atheism. Atheists commonly claim not to have a positive belief that p is false, i.e. to believe that no god exists, but merely to lack the belief that p is true. When they are doing this, they are advocating v), and someone who does this is a ‘lacktheist’.

3. Does ‘atheist’ mean ‘hard atheist’ or ‘lacktheist’?

There is some controversy about whether ‘atheist’ means ‘hard-atheist’ or ‘lacktheist’. Often, ‘atheists’ self-describe as lacktheists, but this leads to a charge of being ad hoc by the theists. I will explain the controversy and why I think it is logically dissolvable. First, I will outline the argument by theists according to which an ‘atheist’ should be thought of as a ‘hard-atheist’.

It seems like v) (the definition of lacktheist) messes up with the symmetry we had between i) and iii) (theism and theist), and between ii) and iv) (atheism and atheist). The symmetry was that the difference between theism/-ist and atheism/-ist is that the former ascribes truth to p and the latter ascribes falsity to p. With definition v) in place of iv) though, we have switched to talking in terms of the negation of p instead. The diagram would look like this:


So, the theist is someone who believes that theism is true, but (according to v) the atheist isn’t someone who believes that atheism is true, rather they are someone who does not believe that theism is true. This seeming abnormality may be seen as reason to reject v) (lacktheist) in favour of iv) (hard-atheist). Why, we might think, should we break the symmetry? We might just insist that an atheist is to atheism as a theist is to theism. If so, then an ‘atheist’ is a hard atheist, and a lacktheist isn’t an atheist at all. Changing the definition of ‘atheist’ seems unsystematic. In this situation, it is not that atheist is to atheism what theist is to theism, so we have lost our intuitive looking principle.

Added to the feeling of oddity about breaking the symmetry of the definitions, theists may be cynical about the motives of the atheist who argues for v) rather than iv) (the lacktheist). The reason for this cynicism would be that a consequence of using v) is that the defender of it seems to have less burden of proof in an argument than the defender of iv). And a position with lighter burden is easier to defend. So, the theist may suspect the atheist is choosing definition v) over iv) for the sole reason that  it makes her position easier to defend. If that were the only motivation on behalf of the atheist, we might view her decision to do so as ad hoc. In addition, if the approach treats atheist differently from any other similar position, then there could also be the accusation of special pleading as well.

The theist may insist that the situation should, in fact, be a level playing field, where each side (theist and atheist) has the same justificatory burden. The reasoning for this would be something like the following:

  1. If a says “I am a theist”, then is implicitly saying that a believes that p is true.
  2. If a (even implicitly) says “I believe that p is true”, then a has the justificatory burden of the claim “is true”.
  3. Therefore, if a says “I am a theist” then a has the justificatory burden of the claim “p is true”.    (1, 2, hypothetical syllogism)

Thus, claiming to be a theist carries with it the justificatory burden of claiming that it is true that some god exists. These justificatory relations are mirrored with our first definition of an atheist:

  1. If a says “I am an atheist” (and means definition iv), then is implicitly saying that a believes that p is false.
  2. If (even implicitly) says “I believe that p is false”, then a has the justificatory burden of the claim “is false”.
  3. Therefore, if a says “I am an atheist” this means that a has taken on the justificatory burden of the claim “p is false”.   (1, 2, hypothetical syllogism)

Thus, if we use the original definition of ‘atheist’, then the theist and atheist have the same justificatory burden. Surely, to try to change the definition of atheism here would be just to avoid this burden.

And indeed, if says “I am an atheist”, and means definition v), then a has not made an implicit claim about what a believes. Rather, a has made a claim that a does not have a belief that “p is true”. Thus, premise 1 above would be false if we used definition v) for ‘atheist’. This is why, if uses the lacktheist definition of ‘atheist’, that a‘s claim “I am an atheist” does not have the justificatory burden of the claim that “p is false”, and why the burden is avoided.

So, the claim could be that the atheist is making an illegitimate switch, from iv) (‘hard atheist’) to v) (‘lacktheist’). It could be seen as illegitimate because definition v) seems to be an otherwise arbitrary breaking of the symmetry of definitions, and seems like it is only justified through the benefit it bestows on the defender of the position (which is the root of the ad hoc complaint). We shouldn’t treat the definition of atheism differently to theism unless there is a good reason to do so  (or it would be special pleading). The atheist seems to have only selfish and illegitimate reasons for identifying as a lacktheist rather than as a hard-atheist.

4. Mirroring

However, one could in fact start the reasoning again slightly differently, and make ‘hard atheist’ look like the deviation from the pattern, and ‘lacktheist’ look like the expected one. This also transfers the charges of ad hoc and special pleading to the theist.

For example, we could stick with definition i), but define atheism as follows:

i)             Theism is true       iff                p is true

vii)           Atheism is true     iff       not-[p is true]

In a classical language, there would be nothing to distinguish between ii) and vii); ‘p is false’ is logically equivalent to ‘not-(p is true)’. Saying that atheism means that “it is not true that there are any gods”, seems just as faithful to the idea of atheism as the claim that it means that “‘there are gods’ is false”. Because they are equivalent, there is nothing one could appeal to logically which could decide in favour of i) rather than vii), and vice versa. Thus, we seem to have no real reason not to start from vii) if we want. And if we do proceed from here, then we can define theism as before, but use v) for the definition of atheism, and it looks like it is obeying the pattern of reasoning employed so far:

iii)           a is a theist       iff                a believes that [p is true]

v)            a is an atheist    iff    not-[believes that [p is true]]

Now the relations between i) and iii), and vii) and v) are just as neat and tidy as they were earlier. Here is a diagram of the logical relations:


As before, the relation between -ism and -ist is just that the -ist definition has ‘a believes that…’ added before ‘p is true’. The relation between theism and theist on the one side and atheism and atheist on the other is just that the atheism/ist side has ‘not-…’ prefixing them. On this view, a theist is to theism what an atheist is to atheism. Note that v) is the definition of a lacktheist.

So, an atheist is ‘naturally’ thought of as a lacktheist if we say that atheism means that it is not true that some gods exist. Given that starting point, it isn’t changing the pattern of definitions to get to lacktheism; instead, it looks as if insisting on hard-atheism would be unsystematic here. One can imagine a theist insisting that an atheist should still be a hard-atheist , but this time the accusation of symmetry-breaking could be levelled at the theist for doing so. Who is being unsystematic, it seems, depends on the starting point taken.

And a theist would have a selfish motive for making this demand too. We cannot ignore the fact that insisting that the atheist breaks the symmetry and uses the definition of ‘hard-atheism’ would remove the justificatory advantage that the atheist would otherwise ‘naturally’ have. However, because ii) and vii) are logically equivalent, there can be no reason to pick one over the other, and so the insistence of the theist to use the hard-atheist definition looks to the atheist as being ad hoc – being done merely for the rhetorical benefit it provides to the theist.

Thus, the two positions mirror each other perfectly. Depending on the definition given for atheism, the definition of atheist as hard-atheist or lacktheist seems unwarranted. The theist judges the atheist as trying to illegitimately lighten their own burden; the atheist judges the theist as trying to illegitimately add to the atheist burden. Whether it makes the atheist’s job harder, or the theist’s job easier, depends on whether atheism means that it is false that some gods exist, or whether it is not that some gods exist is true. And there doesn’t seem like there could be any reason for picking one over the other.

There seemed to be an observation that atheist’s were making an illegitimate move when defining atheist as lacktheist, which was being done just to get an advantage over the theist rhetorically. But if we start at another position, it would seem like the theist is the one trying to shift the burden just for their own advantage. This seems to dissolve the accusations of foul play on either side.

5. Post-definitional thinking

I think that the lesson of all this is just that there is nothing purely logical to appeal to which means that ‘atheist’ should be thought of as ‘hard-atheist’ rather than ‘lacktheist’. Either view is equally defensible, and any choice between them can only be ad hoc. In a sense, as it is a discussion about the nature of definitions, it is rather pointless. And this is hardly surprising.

Instead of worrying about the definition of ‘atheist’, we should rather pay more attention to the nature of the beliefs that a holds. In addition to the basic notion of a simply believing that p, we can talk about the ‘degree of belief’ that a has that p. Let’s say that the degree of belief a has that p is the following:

Da(p) = x, where 0 x ≤ 1.

Degrees of belief are real numbers between 0 and 1, rather like probabilities. They express your feeling of confidence in a proposition. 0 is maximally uncertain, 1 is maximally certain, and 0.5 is absolute indecision.

It seems to me that the proposition p, that there are any gods, is rather hard to evaluate. I find the idea of a personal loving agent quite unlikely indeed, for various reasons (it seems suspiciously like the sort of thing made up by humans, for one). However, the question of whether there are any gods seems a lot more of a difficult thing to evaluate. Perhaps some kind of being created the universe, but remains utterly divorced from the subsequent comings and goings of the world itself, or perhaps one is fascinated by the comings and goings of radically different forms of life on the other side of the universe than us, etc. These sorts of ideas are interesting, but are almost impossible to say anything about, either for or against. I kind of couldn’t have any good reasons to think that any of these sorts of hypotheses were true rather than false. What would count as evidence for or against? In this situation, my degree of belief that p (i.e. the proposition ‘some god exists’) has got to be around 0.5.

Yet, I do have a sneaking suspicion that there probably aren’t any gods like this. If you put a gun to my head and made me decide, I would opt for the no-gods option. That’s what I think is more likely, and so I my degree of belief that isn’t exactly 0.5. The following is certainly true:

Da(p) < Da(~p)

However, the imbalance seems to me to be very, very slight. I wouldn’t know how to put a precise number on it, but it seems reasonable to think that my degree of belief that ~p is between 0.5 and 0.55.

Now, does this state of mind mean that I believe that p? I certainly believe that there is an almost even probability about whether there are any gods or not, with a very slight imbalance towards no gods. My degree of belief is similarly minimally slanted towards the no-gods position. The question is the relation of these facts to the question of whether I believe that p.

Belief, as opposed to degree of belief, is an all or nothing notion. You either believe p or you don’t. Yet, my degree of belief is a scale. It ranges from 0 (definitely not belief) to 1 (definitely belief), and could be any value in between. How do the two notions relate to one another?

One idea, at one point seemingly advocated by William Lane Craig, is that the relation between belief and degree of belief is as follows:

If it is more plausible that a premiss is, in light of the evidence, true rather than false, then we should believe the premiss.” (taken from: http://www.reasonablefaith.org/apologetics-arguments#ixzz4Kp11AOyR)

The idea could be put as follows:

a believes that p    iff   Da(p) > 0.5

So long as your degree of belief that p is more than 0.5, then you believe that p is true. On this view, saying that you ‘believe that pjust means that your degree of belief is more than 0.5.

One problem with this view is that there seem to be situations in which it sounds wrong to say ‘I believe that p‘, even though they are clearly situations where our degree of belief that p is more than 0.5. Here is one.

Say I have a pack of cards, I thoroughly shuffle it and I take one out. It is the ace of spades. I discard the card, and take another one without looking at it. Let be the proposition that ‘the card is red’. Do I believe r?

The probability that r is true should be calculated as 26:51 (i.e., the remaining number of red cards:the remaining number of cards), or roughly 0.52. Given that I know this, my degree of belief that r is true should be correspondingly 0.52. Any other number would be perverse.

I think that in this situation, though my degree of belief is clearly in favour of red over black (or not-red), I still don’t think it is correct to say that I believe that the card will be red. I am sufficiently hesitant that the phrase ‘I believe that r is true’ would be misleading. It would indicate a higher degree of belief than that.

Perhaps you are thinking that you do believe that the card is red in this situation. Perhaps tilting the degree of belief 2 percentage points towards r is enough for you. If so, then consider the following version of the previous example:

Say I have a million packs of cards, I thoroughly shuffle it (somehow!) and I take one card out. It is the ace of spades. I discard the card, and take another one without looking at it. Let be the proposition that ‘the card is red’. Do I believe r?

This situation is exactly like the previous one, except that the chance that the card is red is slightly closer to being exactly 50:50 than before. The probability would be: 0.50000002. Now, the chance that the card is red is only two millionths of a percentage point more likely than that it won’t be. Do you believe that it is red? If so, then your position is probably that of Craig’s above. Any imbalance in one direction entails belief rather than disbelief.

On the other hand, you may be agreeing with my intuition that asserting belief in these situations is incorrect. If so, then this means that there is some value of degree of belief (say 0.45 – 0.55 or something) in which is is not true that you believe p or disbelieve it (or believe ~p). In this penumbra (or indeterminate area) we lack belief that p, even though we possess a positive degree of belief that p. If you think this, then it cannot be true that ‘a believes that p iff Da(p) < 0.5′.

One may ask what the value is, if not 0.5? What does the value of your degree of belief that have to be in order for it to be true that you believe that p? This, I think, is a complex question. One that is so complex, in fact, that it may be malformed. There may be no answer to it as such. It may be that in certain contexts the threshold is higher than others. Perhaps this varies from person to person, from conversation to conversation, from time to time, etc. Perhaps it varies in a chaotic and untraceable manner. This may be the case, within some sort of range outside of which it doesn’t go. For example, belief is never inappropriate in the case where the agent has a degree of belief which is 0.99, for example. It seems like it also isn’t appropriate in the case where the degree of belief is 0.50000001, etc. When people say ‘I believe that p‘, they are not necessarily reporting to a precise degree of belief (0.65 rather than 0.66, say), but just that they feel that their degree of belief is sufficiently over the threshold (whatever it is). Conversely, when someone says that they believe that ~p, this means that their degree of belief that ~p is sufficiently over the threshold (whatever it is) for ~p. When one is not sufficiently over either threshold, as in the card examples above, one should not say that one believes that p, or that one believes that ~p. One simply lacks beliefs in either direction. This is perfectly compatible with the idea that the degree of belief is believed, and perhaps even known. All that matters is that the degree of belief is extremely close to 0.5.

Thus, I have made a case for my claim to lack belief, which is not ad hoc because it is motivated by a general principle about when to withhold belief either way, and is not special pleading because I apply it to any case that is relevantly similar. I do not believe that any gods exist in the same way as that I do not believe that the card is red. In each case, my degree of belief is very close to 0.5, and that is what makes it inappropriate to affirm in either direction.

5. Conclusion

I think that this characterises my views about theism. I have a degree of belief that theism is false which is marginally over 0.5, but less than enough to indicate positive belief that it is false. Whether that counts as an atheist or not probably depends on your personal choice of definitions. Definitions aside, that is my view.

The problem with Internet atheists

I’ve long been interested in the philosophical problems apparent in much popular Christian apologetics, in particular presuppositional apologetics, but also various other philosophical arguments. Part of the reason for this is simply the presence of bad philosophical arguments, which given my formal philosophical training, I find tempting to expose. But there is also another factor, and that is the smugness, or utter lack of humility, displayed by the people making those bad arguments (Sye Ten, Matt Slick, I’m looking at you). It would be way less inviting to engage with if the proponents of these bad arguments were humble, just playing with an argument or concept to see where it goes, rather than using it like a club to try to hit people over the head with. So it is a mixture of weak arguments and arrogance which annoys me the most.

However, I am increasingly finding this sort of thing on the other side of the divide – on the atheist side of the camp – and this does my head in for precisely the same reasons. Being an atheist (either lacking a belief in a god, or positively believing that there are none) does *not* make you a philosopher, it doesn’t mean you have a good grasp of epistemology, and it does not mean you are correct about anything.  Being able to recite ‘what can be asserted without evidence can be dismissed without evidence’, does *not* make you a philosopher.  Saying that you don’t have a burden of proof just because you are an atheist, is not correct if you have made a claim of any kind. Atheists don’t get a pass. They have to learn the hard way, just like everyone else.

Philosophy, in particular epistemology and logic, are directly relevant to the great debate. It is absolutely fine to talk about these ideas in the absence of formal training. In fact, I think more people should be engaged in precisely these areas and encourage more people to do so. I’m certainly not saying that unless you have a PhD you shouldn’t try to do philosophy. All I’m saying is to remember that philosophy is hard. There is no shallow end of the pool; it’s all deep. Don’t think you are a master Jedi when you barely know one end of a light sabre from the other. Trying to use philosophy like a weapon just to win an argument is going to bite you in the ass if you don’t know what you are doing. Even if you do, it’s still a bad idea.

Philosophy is about exposing the folly of arrogance. Like a grenade, it can go off in your own hands.

There are three ways to avoid this happening: a) don’t bother trying, b) never make a mistake, c) be humble. Always, always, go for the last option.