Roughly speaking, I’ve heard the following argument a few times recently:
1. I have thought a lot about religion and God.
2. After careful consideration, I don’t care whether or not God exists.
3. If it were remotely likely that God exists, I would care.
4. Therefore, God most likely does not exist.
Wondering what people think of this ‘argument’? In particular, does 1) add anything to the argument? Does it have any force whatsoever? Is 3) the place to press?
I don’t think it an overstatement to say that the concept of the infinite plays a key role in the philosophy of religion. There are at least two senses in which ‘infinite’ is used. First, ‘infinite’ is often used to mean maximal, as in God’s infinite power, knowledge, and goodness. Second, many arguments in the philosophy of religion discuss ‘infinite number’ or ‘infinitely many’. It is this second sense of the infinite that I focus on in this post. Here are two recent examples of this second sense of the infinite, from Prosblogion, with select quotes (and links to the full posts):
Jack loves Jill and Jill hates Jack. They both go to heaven. Do they meet?
Story: Immortal Ike was born, has lived an infinite number of days,
and is alive today.
Question 1: Is this story logically possible?
Question 2: If so, what is the structure of Ike’s days?
I suggest that the answers are: 1) yes, and 2) the structure of an infinite number in a nonstandard model of arithmetic, which looks a bit like:
| | | | | … …| | | | | | … ….| | | | |
Note that everyday, except for the first, needs a yesterday; everyday, except for the last, needs a tomorrow — ruling out such answers as omega + 1.
But interestingly, over a number of informal conversations, many people answer “no” to 1). I have yet to see a knock down argument. Is there such?
Many people believe that there is: 1) no greatest number, 2) no greatest possible world, and 3) a greatest being (person, agent). The reason many people believe 1 and 2 is that there seems to be procedures to take a number (or world) and return a larger (or better) one. For any number (cardinal), take the powerset to get a larger number. For any world, stick some happy people in a far off corner to get a better world. (Of course, there is far from universal agreement on this second point.) The question arises: Is there any way to take a being, and return a better one?
One way is to try and link beings with the worlds they create. The idea would be that a being who creates a surpassable world is a surpassable being. This line of thought gives rise to a whole body of literature, some quite recent. Going in a different direction, here is another way that any being might be surpassable. Let us imagine that some virtues, e.g. courage, are traits wherein one wants to be at the mean that lies between extremes. We might imagine that ‘courage-level’ runs along a continuum from 0 (totally cowardly) to 1 (totally rash). Then, speaking loosely, somewhere in the middle is best. But, is it clear that any specific point is best? That is, what if the function, F, from courage-level (which runs from 0 to 1) to the value or goodness of the being goes as follows: F(x) = x for x in [0, 0.5] and F(x) = 1.01 – x for x in (0.5, 1]. Then there is no greatest being, as for any being, there is a better one. There is no greatest being, as beings get better as they approach 0.5 from the right on courage-level.
If there is an optimal point on a trait, call that trait ‘closed’. If there is not an optimal point on a trait (for any level a being takes on the trait, there is a better level), as in the courage example above, call that trait ‘open’. The question is, are all traits are closed? Or, what is the best argument to the conclusion that all traits are closed? In the absence of an argument regarding open and closed traits, the principle of indifference might suggest that courage is open with 50% probability and closed with 50% probability.
(One way to respond is to argue along these lines: certain traits/properties are fundamental (e.g., power, knowledge, freedom, goodness), these traits take maximal levels (individually and together), all other traits follow logically from these, and thus all traits take optimal levels and so are closed. Is there a relatively simple and convincing argument along these lines? Also, are there other ways to argue that all traits are closed? In particular, and thinking of approaching the question from a non-theistic angle, am I missing some sort of simple argument or reason as to why all traits are closed?)