Kant famously classified traditional arguments for the existence of a divine being into three categories: ontological, cosmological, and teleological. Very few, if any, philosophers today think that any of these forms of argument is conclusive. However, some philosophers do believe that a cumulative case for the existence of a divine being can be made out from these arguments. Atheist colleagues often respond that "three leaky buckets won't hold water any better than one." However, this reply assumes that the traditional arguments don't show anything at all. Specifically, those who respond this way are often assuming that the arguments are straightforwardly invalid (that is, that they commit formal errors of reasoning).
I myself believe that the traditional arguments can contribute to a cumulative case. I think that a person who has certain background beliefs/information might be perfectly rational in accepting the existence of God on the basis of these arguments alone. However, I am willing to admit that for most people the traditional arguments are insufficient. In short, I only want to make the modest claim that each of the arguments has something positive to contribute to our overall evaluation of the plausibility of theism.
Let us begin with teleological arguments. Nearly everyone agrees that the world appears to have elements of purposiveness. That is, it often seems as if there is some sort of grand plan. This appearance is created by natural beauty, and also by the sophistication of certain natural (especially biological) systems.
Now, in the absence of evidence to the contrary, it is reasonable to believe that things are as they seem. For instance, my stapler looks red. Most philosophers would agree that it is prima facie reasonable to believe that my stapler is red on the basis of its looking that way, unless I have some evidence to the contrary. This is despite the fact that if I were wearing red glasses, or was under red light, or my lens had been dyed red, or I was being deceived by the Cartesian demon, the stapler might look just the same to me. (What it means for the stapler to really be red is, of course, another matter entirely.) These are all more or less extravagant hypotheses, and if I have no evidence that one of them is true, then I should just proceed on the assumption that things are as they appear.
So we arrive at this general maxim: other things being equal, we should assume that things are as they appear.
When combined with the appearance of purposiveness in the natural world, this maxim yields the result that, other things being equal, we ought to assume that there are elements of the natural world which have a purpose. Yet it is hard to see how anything could have a purpose in the absence of one who purposes, and this all men call 'God.'
Now, many atheists implicitly accept this line of argument, but deny that other things are equal. This at least seems to be what is going on with those who claim that primitive people were (or are) reasonable in believing in a divine being, but there is surely no excuse now that modern science has explained everything. Individuals familiar with modern science are in possession of evidence that we are wearing red glasses (so to speak). When posting on the teleological argument a while back, I argued that this line of argument was ineffective.
Teleological arguments show that belief in a divine being is prima facie reasonable. The structure of the argument, as I conceive it, is like this:
Cosmological arguments start from the basic idea that "why is there anything at all?" is a reasonable question to ask. Most people seem to agree with this basic idea.
There are a number of ways of turning this question into an argument for a divine being. Some versions become quite complicated, especially those that allow that the universe might not have a beginning in time. However, if we assume that the universe did have a beginning (since, on the basis of discoveries in physics, most people now believe that it did), we can state the argument quite simply, as I did a couple months ago:
Ontological arguments are trickier. Here's an example of an ontological argument that is at least clearly valid:
Well, a key weakness of teleological and cosmological arguments is that they don't establish anything like a being with the traditional divine attributes. Teleological arguments establish the reasonableness of believing in someone who creates (or at least directs) the world for certain purposes, and cosmological arguments establish the existence of a necessary being. I understand the contribution of ontological arguments to be that they contribute to the unity or coherence of the theistic hypothesis - that is, they show that something like the traditional God is a good candidate for the roles carved out by the previous arguments.
In order to see how this is supposed to work, let's start by examining premise (1). Premise (1) is supposed to be a non-trivial 'analytic' truth. (I put 'analytic' in scare quotes to remain agnostic as to whether there is a non-vague analytic-synthetic distinction.) That is, it is supposed to be the case that the definition of 'divine' implicitly includes necessary existence. One can run the argument above with any adjective whose definition implicitly or explicitly includes necessary existence. However, if premise (2) is to be plausible, we should have some kind of simple definition which entails necessary existence and we should already have reason to believe that something exists which has some of the other properties entailed by the definition. This is basically the project of traditional philosophical theology: give some simple definition like 'pure actuality' (Aristotle) or 'a being greater than which none can be conceived' (Anselm) and try to show that it entails (a) necessary existence, and (b) some collection of attributes we already know something has.
If this project is successful, we can exploit it in two ways. First, if we can show that the simple definition entails that a divine being would have the properties necessary to satisfy the teleological and cosmological arguments (i.e. would have the sorts of purposes we observe, and would be a first cause of the sort of universe we are in), then we will have reason to believe that something fitting that definition exists. It would have the theoretical benefit of unifying the theoretical postulates the two arguments led us to Second, religious believers (who we have mostly left out of our discussion so far) believe on the basis of (alleged) revelation that God has certain attributes - e.g. omnipotence, omniscience, etc. If it can be shown that those properties follow from a simple definition which also entails necessary existence, then this will contribute greatly to the theoretical unity of the theory.
In sum, I believe that (assuming someone can make good on my hand-waving promises of a philosophical theology) these three arguments together help to show that theism is a theory with a high degree of internal coherence which allows one to endorse some independently plausible metaphysical theses. If the atheist merely wants to defend the consistency of her position, all she has to do is deny one of the premises of the cosmological argument (e.g. by saying that the Big Bang is contingent but doesn't need a cause), or argue that some alternative entity (e.g. the universe itself) can be the first cause; neither the teleological argument nor the ontological argument establishes the existence of a divine being. If, however, the atheist wants to show that her theory is superior to the theist's - so that the theist ought rationally adopt it - then, for each argument, she will have to do one of the following:
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