(Apologies for the crazy length question)

Whenever the thorny issue of theism vs. atheism comes up -- especially on the internet -- a further issue always seems to arise concerning what these positions are. (See for example this question) Often somebody will claim that atheism is a belief in the non-existence of gods, and then somebody else will retort that it is merely a lack of belief.[*1] There are subtle distinctions to be made between various formulations, and it strikes me that there is a risk of equivocation when such claims are made. Philosophers should be well placed to make the necessary distinctions.

So, Question 1: What discussion in there in the philosophy literature about varieties of atheism and the like?

Let g be the proposition that there is a god (let's not distinguish between competing religions and the like). For any proposition q, let Bq be the proposition that Sally[*2] believes that q.

Then the following seems like a very natural formulation of atheism:

(Atheism) ~g

i.e. it is the claim that there are no gods.

Then, the claim that Sally is an atheist is simple that she believes (Atheism):

(B-atheism1) B(~g)

That is, atheists believe (Atheism). I.e. they believe that there are no gods. Note (see footnote 1) that this does not require that Sally takes it on a matter of faith that (Atheism) is true, or that she believes it with certainty, or anything like that. It just has to be that she has formed that belief for whatever reason, perhaps by following some scientific principles or whatever. This would also be the standard way to move from a formulation of a view to somebody holding that view. In general y-ians believe y-ianism.

But, it is often remarked: atheism is merely a lack of belief. That is, Sally's being an atheist should be formulated as:

(B-atheism2) ~B(g)

I.e. Sally does not believe that there are gods. So:

Question 2: Is the move from (Atheism) to (B-atheism1) incorrect? Why - what makes atheism different from any other position? Or is the resistance to (B-atheism1) simply a case of taking 'belief' to be more than the catch-all term as philosophers use it?

But, aside from Q2, there is, it seems, a further problem. If Sally is agnostic about the existence of gods, this is naturally formulated as:

(Agnosticism) ~B(g) & ~B(~g)

That is, she doesn't believe that there is a god, and she doesn't believe that there is. She withholds belief. (Again, this would be a natural formulation of agnosticism about any other subject matter.) But then, if (B-atheism2) is the correct formulation of being an atheist, then it follows from agnosticism. That's surely not correct!


So, suppose that (B-atheism2) is at least broadly correct; that is, atheism is merely a lack of belief. Then we need to reformulate (Agnosticism) so that it doesn't entail atheism. I can think of two broad strategies:

Higher order beliefs

Perhap agnosticism is not a doxastic position regarding the existence of gods, but rather a doxastic position regarding belief in the existence of gods. So fore example, a particularly strong form of agnosticism is sometimes suggested according to which it is impossible to know whether there are gods or not. Here are some options. But first, some more notation:

  • B_a p -- a believes that p (a is a person, p a proposition)
  • K_a p -- a knows that p
  • []p -- it is necessary that p

The options:

(Reflexive agnosticism) B_a(~K_a(g) & ~K_a(~g))

I.e. a believes that she neither knows that there is a god nor does she know that there is not a god. Depending on your views about the relationship between belief and knowledge (for example, whether you think Bp→BKp is true in general) this may or may not be compatible with atheism1 or theism.

(Universal agnosticism) B_a( (forall x)(~K_a(g) & ~K_a(~g)) )

I.e. a believes that not only does she not know whether gods exist, but that nobody knows whether gods exist.

(Necessary agnosticism) B_a( [](forall x)(~K_a(g) & ~K_a(~g)) )

I.e. a believes that it is impossible to know whether gods exist.

The advantage of these is that they let you have a formulation of a position (by removing B_a from the beginning), as well as a formulation of holding that position.

So, Question 3: Is agnosticism best formulated as a second-order belief?.

Partial beliefs

The language of full beliefs -- 'a believes that p' and so on -- is a bit crude. Although there's no requirement that such a belief be certain, it doesn't allow for distinction between different degrees of belief. Formal epistemologists sometimes talk about credences. These are numbers between 0 and 1 which measure the degree to which somebody believes a proposition (they are often thought of as probabilities).

Might we better formulation atheism and agnosticism in terms of credences? (I've heard Dawkins talk about the probability of God existing before. He clearly can't mean objective probabilities -- either God exists or she doesn't -- so it's plausible to interpret him as talking about credences.)

Here's a suggestion. Let Cr(p) denote the credence that Sally has in proposition p. Suppose that Cr(g)=x, then:

  • Sally is an atheist if x is small ( perhaps <0.25)
  • Sally is a theist if x is high (perhaps >0.75)
  • Sally is agnostic if x is somewhere in the middle (perhaps 0.25

The problem with this, is that it still makes atheism a positive belief: it is a belief (of various levels of certainty) that there are no gods. (I'm assuming that Sally's credences obey the laws of probability, so that Cr(~g)=1-Cr(g)

Question 4: Should atheism, theism and agnosticism be formulated in terms of partial beliefs? Is there a way of doing this which allows one to make the distinction between (B-atheism1) and (B-atheism2)?

Final, overarching question

Question 5: How should we formulate atheism and agnosticism?

[*1] The latter is sometimes be accompanied by some strange attitude that 'belief' in anything is a bad thing, which strikes me as a misunderstanding of what people often mean by belief, as involving faith, or lack of evidence, or something like that. For the purposes of my discussion, I mean by 'belief' what I take it most philosophers mean: somebody believes p if they think that p is true, regardless of how they come to form that belief (whether through proof, evidence, gut feeling or whatever). They are prone to assert and assent to p, and to make use of p in their decision making and so on.

[*2] We could suffix the belief operator to denote beliefs of different agents, but that would overcomplicate things. Let's just stick with one epistemic agent. She may as well be call Sally, but feel free to substitute a name of your choosing.

  • 4
    This isn't a question, this is, as you've noticed yourself, 5 of them. Why not split them, giving people the chance to answer one of them? Also, your headline doesn't fit the content - a question like "What is atheism?" would be closed because you could look it up in every encyclopedia. Also, that's not your question. As it stands, this is too broad.
    – iphigenie
    Jul 1, 2014 at 11:32
  • Well, they all fall under the general question - 'how should we formulate atheism and agnosticism?'. An answer to this general question would, I take it, answer all of them (with the possible exception of the first). So really, it's two questions: 'how to formulate atheism/agnosticism?' (with some suggested broad ways of answering), and a reference request. Such compound questions of the form 'p? And is there a discussion of p in the literature' seem to be sensible. But if it's felt that this should be split up, I can do so.
    – J.P.
    Jul 1, 2014 at 11:37
  • potentially useful figure: i0.wp.com/cx124.justhost.com/~evolvin5/wp-content/uploads/2011/…
    – Dave
    Jul 1, 2014 at 13:40
  • 1
    Its definitely a long question, but interesting; It might be useful to signal in the question heading that you're looking at an 'analytic' understanding of the terms that you are proposing to debate; Jul 1, 2014 at 15:09
  • 2
    I've got similar worries about this as @iphigenie; is there any chance the headline might be a bit more closely aligned with what the body asks? And maybe this is just a lot of terrain to cover in one Q, it might be more optimal to try to separate these out if that's possible?
    – Joseph Weissman
    Jul 5, 2014 at 1:59

2 Answers 2


(Unable to comment yet, sorry)

Whenever the thorny issue of theism vs. atheism comes up -- especially on the internet --

-- you need to be aware that you are speaking in an arena where context is murky at best and nearly every word longer than 3 letters will have multiple meanings & connotations!

This is why, in informal settings, the definition of atheism as 'lack of belief' rather than 'belief in the lack' is important. In a formal, idealized world filled with frictionless spherical cows I'm sure you could logically demonstrate an equivalence between the two statements (after defining 'belief' of course). In many settings, though, the difference between an active and a passive lack-of-belief can be very important.

I would also like to draw attention here to your use of 'Agnosticism'. You are using 'Agnostic' according to its informal/slang usage rather than its formal/actual definition. Agnosticism is defined as:

Agnosticism is the view that the truth values of certain claims ... are unknown or unknowable.

This is a question completely separate from the theist-atheist one. Theism/atheism deals with whether a person has belief in one or more gods or not, gnosticism/agnosticism deals with whether the question of the existence of one or more gods can even be answered. It is entirely possible to be:

  • A gnostic theist, believing in one or more gods because one believes that god(s) are knowable (and probably believes to have received some direct revelation)
  • An agnostic theist, believing in one or more gods despite believing that there is no way to prove the belief correct (for example, many deist-style beliefs, 'I just know', etc.)
  • An agnostic atheist, unconvinced by any claims involving one or more gods and believing that no positive evidence for said god(s) could even be produced
  • A gnostic atheist, believing that the existence of one or more gods CAN be determined and the absence of the evidence for said god(s) weighs heavily in favour of their non-existence.

As an atheist, I have rejected some god-claims on the basis of contradictory evidence (i.e., believing them to be proven false), others on the grounds of being too vague to waste time on. For example:

  • I am an agnostic atheist with respect to non-interventionist concepts of one or more gods, such as in deist claims or formulations of god(s) as some undetectable 'higher power'. If god(s) do not interfere in the mortal sphere their presence is indistinguishable from their absence, and by Occam's Razor get left out of my overall worldview.
  • I am a gnostic atheist with respect to interventionist god concepts, such as Thor, Yahweh and Osiris. Taking the Bible as an example, there are some very explicit predictions/promises made about the power of faith that are not borne out in the real world. That the world isn't filled with D&D-style clerics healing the sick, raising the dead, smiting their (god's) foes, etc, is direct evidence against the positive claims for those specific gods.

So now I'll wind back to your core question #5:

Question 5: How should we formulate atheism and agnosticism?

Sticking with the existing formal definitions, and being clear that those are the terms being used rather than the colloquial terms, seems more than adequate:

Theism is easy enough: Holding one or more beliefs in a god-concept as true.

Atheism is adequately defined by the negation of theism: Not holding any beliefs in a god-concept as true. (i.e., lack of active belief). Note that this includes most people who would self-identify as agnostic (of the 'not sure' variety). As the stigma associated with the label 'Atheist' diminishes, expect to see more self-identified agnostics to change labels.

Gnosticism is believing that we are able to determine truth or falsehood for a given god-claim. Contrasted to

Agnosticism, the negation of gnosticism, and the belief that the given god-claim is unprovable or unknowable.

When using words it's best to make sure that everybody's using the same meanings, and to recognize that specific fields have specific jargon with very well-defined meanings. Whether it's law, physics, sociology or literature there will be core words that differ from their colloquial usage. When engaging in those topics, either use the jargon properly or not at all.

That's my theory, at least. ;)


Theism & atheism deal with what one believes or does not believe. Agnosticism & gnosticism deal with what one claims to know or is knowable. They are two sides of two different coins: belief and knowledge. So there are 4 possible positions:

  • The gnostic theist, who claims to know some deity exists,
  • The agnostic theist, who doesn't claim to know but believes some deity exists,
  • The gnostic atheist, who claims to know 1 or more deities don't exist,
  • The agnostic atheist, who doesn't claim to know (may believe it can't be known), and doesn't believe a deity exists.

This should clear things up.

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