Problem of Universals and Materialistic Atheism

For some time I have been having a discussion with someone about the problem of universals, and I have a hard time understanding why it is so far fetched or impossible, according to some, to conceive of mathematics, or circles, etc., as concepts without resort to a non-material realm.  Below is a link to a refutation of Materialistic Atheism.  Perhaps others will understand it better than I do.  In any case, I am seeking a better understanding of this issue and whether it is really a threat to the materialistic worldview:

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David Armstrong:
"There is an old, and I think good, distinction between the rational and the empirical sciences. The rational sciences are mathematics and logic. (Here I will just talk about mathematics.) They are dubbed "rational" because they are developed a priori as we philosophers say. That is to say, here is no appeal or at worst a minimal appeal, to experience."

In order not to make it too long, I cut off the start of the above quote from Engels' Anti-Dühring. Her it is:
"As with the basic forms of being, so also with the whole of pure mathematics: Herr Dühring thinks that he can produce it a priori that is, without making use of the experience offered us by the external world, can construct it in his head."

Seems like Herr Dühring is joined by Armstrong here (and by Hegel, if you like).

Doen't look much like materialism at this point...
I have posted a reply to the referenced blog post, saying:

You say "...materialistic atheism assumes that only material existents are real."

Some people, including some "scientists," do extrapolate from the methodological naturalism which is the implicit basis of all experimental science, to say that because there is no physical evidence of a god, no gods exist.

You apparently say these people are wrong to make this assertion, but it is not clear to me which part of their statement you are challenging.

Do you claim that there is physical evidence for some god or gods, which is going undetected or is being deliberately ignored? Or do you claim that a god or gods can exist without producing any physical evidence of their existence?

In the first case, trot it out, the ignored evidence, and let's have a look! Victor Stenger (in God: The Failed Hypothesis) reviews the physical evidence that the existence of gods should produce and shows how it is lacking. What evidence did e.g. Stenger miss?

In the second case, you are asserting that a god or gods could exist as something non-physical -- because, you say, "we know that there is such a thing as mathematics." First, the metaphysical existence of such "universals" as mathematics is firmly denied by several branches of philosophy (Nominalism, etc). But even those (neo-)Platonists who say that Universals exist do not attribute causative power to them. The existence of "squareness" as a Universal does not cause any particular square to exist, etc.

So if you assert that gods could exist as non-physical universals of some kind, you have to concede that it, or they, have no causative power. They can't create or intervene in the world in any way.

That would of course explain why they produce no physical evidence! But it also raises the question: of what use are they?
I might be wrong on this, but I am fairly certain science has its roots in philosophy. Philosophy is a very useful discipline which when done properly is mathematically rigorous. It is allegorical of the scientific method.

As to the linked post, I had a read and it seems fairly easily refuted. The poster is making a few fundemental mistakes in how throws around words like "real".
I'll post a refutation when I get a chance.
I posted a quick refutation of the argument the OP linked to on my blog here



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