I often encounter the argument that “materialism” is false because abstract concepts such as those mathematics exist.
By my understanding, philosophical materialism does not preclude the existence of such abstractions, nor does it entail the position that they are material. Am I wrong about this?
Good question. Not precluding and not entailing seems self-contradictory. I see them as immaterial and don’t see how they can be ‘material’. Calling them a material ‘process’, as in computing, begs the question.
@vjtorley, @jongarvey, @Philosurfer, others?
Yes, excellent question.
I often hear people saying that materialism is false. But nobody ever explains what would be the difference between a world where materialism is true and a world where materialism is false. I’m inclined to doubt that there is any such difference.
Another thing that bothers me – the people who attack materialism seem to be more materialist than I am.
I think we have, except non-Christians can’t experience it: God’s providence and love as evidenced in providence. So no, you won’t be aware of any difference and cannot believe there is any.
One for the real philosophers. But I would say that the existence of mathematics as part of nature is problematic, because it presupposes universals (such as, most obviously, number), which have no reason to exist under materialism.
The best solution I can think of to that is to place mathematics within the human mind only, the universals being abstractions made by people.
But that in itself raises the regress problem of how a materialistic human mind could conceive such universals de novo anyway. But it also creates issues about the apparent universals of patterns within nature, which looks to follow regular immaterial mathematical laws apart from human cognition.
How does the material universe “know” that 2 + 2 of anything in it must equal 4 (an immaterial rule)? I’m not sure how one could go beyond “that’s just the way it is,” which of course could be an equally good answer to any similar question: “Why are there immaterial minds not reducible to matter?” “Well, that’s just the way it is.” Sure, but materialism with ghosts ceases to be materialism.
I don’t consider mathematics to be part of nature, except in the sense that humans are part of nature.
I prefer to describe mathematics in terms of human behavior (particularly the behavior of mathematicians) rather than in term of material things. And that probably makes me a behavioralist rather than a materialist.
But behavior is an abstract idea, so we are still left with the materialism or not question.
This is total nonsense. Please tell me in detail what a non-Christian can’t experience that a Christian can experience. Sound like a lot of Christian BS.
Mathematics is a system of axiomatic premises and logical processes that we find useful. Why we find it useful is an interesting question. I don’t see how invoking the immaterial solves it.
It’s not so abstract. Our whole existence is a matter of behavior (actions).
But providence is an abstract idea, so we are left with the materialism or not question (quoting from @DaleCutler, a few posts above).
…although not any more than behavior, once you’ve seen it in action.
Sets of circumstances as probable as getting all heads on 10,000 coin flips, and infused with personal meaning. You’ve see some of the documentation, but are just in denial that they are anything more than mere coincidence. But how can you not.
Behaviors are not abstract, but the idea of behavior is. Does a piece of metal care that it exhibits ductile or malleable behavior?
If you flip a coin 10,000 times, whatever results you get is exactly as probable as getting them all to land heads.
Think about that,
In the real world, if you get 10,000 heads, you recognize that something else is going on. Think about that, yourself. 
The question really is, why does it exist? Is there a material reason?