Friday, November 18, 2016

An Aristotelian picture of set theory

There are some sets we need just because of the fundamental axioms of set theory, whatever these are (ZF? ZFC?). Probably, we could satisfy the fundamental axioms of set theory with a collection of sets that in some sense is countable. But then we need to add some sets because the world is arranged thus and so. For instance, we may need to add a real number representing the exact distance between my thumbs in Planck units. (If the world is describable as a vector in a separable Hilbert space, all we need to add can be encoded as a single real number.) This is a very Aristotelian paper: the sets are an abstraction from the concrete reality of the world.

On this Aristotelian picture, what sets exist might well have been different had I wiggled my thumb. Perhaps, then, some of the non-fundamental axioms of set theory are contingent.


Unknown said...

Hi Dr. Pruss, a friend of mine recommended some smart Christian authors and I found ur blog and was wondering (sorry about the irrelevance to your post) what I should do to believe in God. I want to but I can't find a good reason, other than wanting to. I know there are arguments that no one really knows whether they work or not, so I'm skeptical. One reason I'm unsure about the arguments I've heard for God is that, if an argument worked, why wouldn't everyone believe in God? I don't mean to assume that, if one side is right, everyone would know just seems there are a lot of unsure people, like me, who want to believe but can't. For example, I heard the moral argument, and I'm not really sure I agree. Just because many people agree on morals doesn't mean God set them in our hearts. Couldn't we have just evolved that way?

Then there is the argument that you like, the big bang argument. But I'm so confused: why is Stephen Hawking an atheist if the universe really seems to have come from nothing?

Then my friend explained a "religious experience" argument, which basically says that since everyone believes in similar ideas of God and there's no good evidence against God, we should think he's caused the belief. He compared it to a situation where you're a miner and all 99 of the other workers abandon the mine because they start to think that it will collapse. At first you might think they're crazy, but after seeing that their stories all corroborate, you start to think that you're crazy. I think there's a problem with this argument, though: just because everyone believes something, even if it is a similar belief, doesn't make it true. The situation in real life is very different than the mining analogy.

After that he tried to show me that Jesus rose from the dead, but again: why doesn't everyone believe in Christ if He literally rose from the dead?

I know if there's one argument that works, it's probably "buried" deep inside one side or the other (atheism or Christianity). I suspect that one successful argument is something authenticating about Christianity, and atheists don't naturally go for that so they don't find it--explaining the disparity. But I'm not so sure, yet. I mean, can I really trusts my emotions? How do I know if it's the Holy Spirit saying, "I'm here"?

So...I'm stuck. I really can't approach any arguments confidently because it seems no one takes philosophy for God seriously. Every time I find an argument, there's a youtube video refuting it....I know I shouldn't let other people think for me, but how am I supposed to be intellectually honest and convinced when there's always someone who I wouldn't be able to defend an argument for God against. Also, why aren't Christian philosopher's work more accessible? I wish the Christian academics (especially philosophers) had some kind of internet connections or coordination to develop arguments for the faith and out-do the atheists. It's so specialized that I feel like I'd need a master's degree in the philosophy of religion to be honestly convinced by an argument. ugghhhhhhhhh the God question is so complicated and stressful.

Sorry for how long this is, and please don't worry about answering if you don't have the time.

Unknown said...

also, I was wondering what you think about these arguments and if there is any more evidence for Christianity, thanks!

1. CS Lewis's trilemma
2. Fulfilled prophecy (I can't find any academic who actually cites this, but I would think it would be on the top of their list if it were true)
3. the consciousness argument (is this a "god of the gaps" kind of argument?)
4. the argument about reason (confusing)
5. the argument about the "fine tuning" of the universe
6. the argument about how only God explains everything
7. the argument about the idea of God, and how it shouldn't be a rational concept unless he actually exists.
8. the argument about how orderly the universe is
9. the argument about how the world is mathematically structured
10. the "intentional" argument (extremely confusingšŸ˜…)
11. arguments that infer an Intelligent Source from certain examples of biological complexity (first cell of life, linguistic properties of DNA?)
12. the argument from logical laws (
13. the argument that love and beauty would be arbitrary on atheism, given all the ways the world could have gone (but is it really true that there are other possible worlds?)
14. CS Lewis's argument about how you can't desire something that does not exist, or you can't need something that does not exist (but even if it is true we need God, why is it that there are patients with diseases who need cures that don't exist?)

Are any of these sound? Is there any good argument for God I haven't mentioned? My friend keeps texting me these and they're interesting but I'm still skeptical, and hope to know whether there are philosophers who think they're sound. Thanks again!

Alexander R Pruss said...

These are good questions.

1. "if an argument worked, why wouldn't everyone believe in God": This cuts many ways. Atheists and agnostics give arguments not to believe in God. If those arguments work, why does anyone believe in God? The fact is that arguments just don't convince everyone, even if they are good arguments.

2. Regarding the moral argument, I think the deep question is: Why do our moral conviction match moral reality? If we evolved to have moral beliefs, why did we evolve to have the right moral beliefs rather than the wrong ones?

3. I think Bill Craig has done a lot of good work popularizing arguments for the existence of God. Have a look at some of his online stuff and his debates.

4. That's a pretty big list of arguments. Don't forget the moral one, which comes in two versions: (1) Why are there moral truths? (2) How do we *know* moral truths? And there are also various versions of the ontological argument.

I think an honest assessment should show each of the arguments at least raises the probability that God exists. And then don't forget one more thing: The arguments can be put together. When a hypothesis solves 14+ problems, that's pretty significant evidence for that hypothesis.

Adam said...

Jo F, check out
A great blog by a Christian philosopher, former atheist

Unknown said...


Thanks a ton. Dr. Pruss's essay in the Blackwell reference volume has helped me a lot. My main issue was worrying about whether I was being fooled, or hopelessly radical for believing in many of the advanced formulations of theological arguments. It helps to hear about academics who actually take them seriously. I know there's serious bias towards Christians in colleges today, as well as specialization and the fact that Christians drew out of the colleges they founded to establish their own institutions for Christian-specific academics-- accounting for much of the secularization of academia. In addition to that, atheism has come about through our advances in observational astronomy and the recent atheistic literature of the enlightenment, but both are misguided for assuming God to be something to be found within His creation.

So atheism may very well be adopted at large by intellectuals while not being due to a falsehood of Christianity. It seems that is the case, as I have failed to find something in my study of the sciences that invalidates Christian belief. Beyond that, I learned that the majority of philosophers of religion in Anglo America are Christian, and the supermajority are theists.