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.