Wednesday, March 23, 2011

What Does It Take to Be An Atheist?

Consider some valid theistic arguments and what an atheist must do to deny their soundness.

Argument A - A Necessary Concrete Entity:

(1) Possibly a necessary concrete being exists implies a necessary concrete being exists.
(2) Possibly, a necessary concrete being exists.
(3) Therefore, a necessary concrete being exists.

Assume further that it can be shown that the necessary being is God.

What must the atheist do to deny this argument? (1) is just axiom S5. Therefore they must deny (2). This implies that (a) possibly nothing exists or (b) necessarily, there exists at least one contingent entity. This also implies that all concrete entities are contingent.

Atheist Theorem 1 (AT1): It is not possible that a necessary concrete being exists.
Atheist Theorem 2 (AT2): Either (a) possibly nothing exists or (b) necessarily there exists at least one contingent entity.
Atheist Theorem 3 (AT3): For any concrete entity x, x is contingent.

Disproving AT1, AT2 or AT3 is sufficient for refuting atheism.

Argument B - The Scotistic Cosmological Argument:
(1') Whatever is possible is contingent or necessary.
(2') A first cause is possible.
(3') Therefore, a first cause is contingent or necessary.
(4') Any contingent substance is possibly actualized by another substance.
(5') A first cause is not possibly actualized by another substance.
(6') Therefore a first cause is not contingent.
(7') Therefore, a first a cause is necessary.

What must the atheist do to deny this argument? The atheist can only really deny either (2) or (4).

Atheist Theorem 4 (AT4): Either (a) a first cause is impossible or (b) some contingent substance is not possibly actualized by another.

Hence, disproving this disjunction AT4 is sufficient for refuting atheism. Saying that (b) is false also leads to some interesting consequences about infinite regresses.

Argument C – A Modal Cosmological Argument:
(1*) Every contingent entity possibly has an external cause.
(2*) If the sum total of contingent concrete entities C has an external cause, that cause is necessary.
(3*) C is a contingent concrete entity.
(4*) Possibly, C has an external cause.
(5*) Therefore, possibly there is a necessary cause of C.
(6*) Therefore, there is a necessary cause of C.

What must the atheist deny? All premises seem quite strong. He must then deny (1*).

Atheist Theorem 5 (AT5): For some concrete contingent entity x it is impossible that x is caused.

Disproving AT5 is sufficient for disproving atheism.

Thus far we have Atheist Theorems 1-5:

AT1: It is not possible that a necessary concrete being exists.
AT2: Either (a) possibly nothing exists or (b) necessarily at least one contingent entity exists.
AT3: For any concrete entity x, x is contingent.
AT4: Either (a) a first cause is impossible or (b) some contingent substance is not possibly actualized by another.
AT5: For some concrete contingent entity x it is impossible that x is caused.

Disproving one of these theorems is sufficient for disproving atheism. Showing a contradiction between these beliefs and other atheist beliefs is sufficient for showing atheism as such to be incoherent. To me all of these propositions seem quite implausible in their own right.

7 comments:

Leo Carton Mollica said...

I'm not certain that you have exhausted all the options available to the atheist:

—I'm not sure that (3*) is as obvious as you seem to make it out to be: unless we are to accept all fusions of any objects as concrete entities (which leads to some strange consequences), (3*) does not seem to have an immediate warrant and thus requires argument.
—I'm also suspicious of premise (5') of B: the atheist might object (as Edwards does, if I understand him correctly) that a first cause could be merely accidentally or contingently first, in which case (5') could be plausibly denied. Proof:

1. Possibly, some first cause is merely contingently first. (Atheistic premise)
2. A cause that is merely contingently first is possibly caused by a distinct substance. (Analytically true)
3. If something be caused by a distinct substance, then it is actualised by a distinct substance. (Analytically true)
4. Possibly, some first cause cause is possibly caused by a distinct substance. (1, 2)
5. ♢^n♢p —> ♢p (S5)
6. Possibly, some first cause is caused by a distinct substance. (4, 5)
7. Possibly, some first cause is actualised by a distinct substance. (3, 6)

awatkins69 said...

Hey there Leo.

Well, for (3*), a collection is defined by its members, right? So if you take away a member of it then it ceases to be the same collection. But if the collection is made up of contingent entities then in some possible world one of those entities seizes to exist, and hence in that possible world the collection does not exist, making it contingent.

As for 5' I'm curious as to what you mean by saying that a first cause is accidentally first. It seems evident that if a first cause is a first cause, then it's not possibly caused; otherwise, it's not a first cause. Let me know what you think.

awatkins69 said...

Do you mean that for *this* concrete entity A, in some possible worlds A is the first cause and in others it isn't?

awatkins69 said...

Woah, can't believe I wrote "seizes to exist". :)

Leo Carton Mollica said...

Concerning (3*), my fear is that we have as yet no reason to think of C as a concrete entity at all (I presume you are using "concrete entity" as others might use "concrete object"), and a fortiori a contingent concrete entity. I think it plausible that not every collection of concrete entities is itself a concrete entity (Lewis' trout-turkey, for example), so why should I expect C to be one? I do agree, however, that if C should turn out to be a concrete entity, then it will be a contingent concrete entity.

Yes, I am saying that the atheist might object that a substance A might be a first cause in this world α but not be a first cause in another world W.

Insofar as he affirms the existence of "brute facts," the atheist seems to endorse something like this line of thought, for a brute fact B, which explains a non-brute fact C, is unexplained, and thus terminates a series of explanations, but is the sort of fact that could, in principle, be explained by a further fact A (possibly, there is a fact A such that A explains B), meaning that B is merely contingently a "first explainer," so to speak, which comes very close to being a merely contingently first cause.

(Mind you, I do not believe that a first cause can be accidentally uncaused, but I recognise that an atheist could deny the same and that further argument is required to defend my belief.)

awatkins69 said...

I see what you are saying. You may have a point here; yet you say you don't think that an accidentally uncaused first cause is metaphysically possible. I'm interested in why you think it's not.

This is good because I think I might like to do a little more research into arguments of this general spirit.

I think though that we can still accept AT1-3 follow from an atheist perspective, and I'm still quite inclined to believe that AT5 follows, but we may need to do more work on showing that the sum total is itself contingent and concrete. (BTW does this lead to a Russell-like paradox?)

Leo Carton Mollica said...

I do not think that an accidentally first cause would be possible because a.) anything that can be caused by something distinct from itself is not per se necessary, since if it were per se necessary it would not admit of causal influx; b.) anything that is not per se necessary requires a cause of its existence, since it has no existence of itself; and therefore c.) only the per se necessary can be a first cause.

I've been thinking recently about whether a concrete mereological sum of all concreta is paradoxical, actually. I suspect that it is, since it would appear to have itself as a proper part, which is absurd; however, the idea of a sum of all concreta seems intuitively plausible, which suggests that I am missing something. I think that David Lewis defends a "mereological sum of all concreta" theory, so perhaps I should check him out.