(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:
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):
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:
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
(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?.
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.