An acquaintance and myself have been arguing about the existence of universals. His argument is that a universal, such as the number two, is an abstract concept, but must be accounted for somehow. He asks where the number two is. (I consider that a nonsense question.) He believes this number two must exist in some nonmaterial realm. If the number two exists, he says, as it does in mathematics, then it must be somewhere. From this he concludes that philosophical naturalism/materialism is incorrect, thus opening up the possibility of the existence of a supreme being.

I have made many posts explaining why I disagree with his ideas, but he refuses to budge on this matter. I cannot reproduce the posts here because it came from a private forum.

Now on to the question of gods. He argues that it is nonsensical to ask for scientific evidence of a god because science deals with the material realm, and he believes the god is non-material (whatever the hell that means). Because science deals with the material realm, it is illogical to search for evidence for or against the existence of a supreme being; rather, that question must be determined by philosophical proofs in much the same way we have mathematical proofs.

What are your thoughts on the problem of universals? Is it nonsensical to look for scientific evidence of a non-material god? Can philosophical proofs "prove" a god's existence?


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How can something that is nonmaterial possibly occupy a space (be somewhere)? Also, there are an infinite amount of numbers, so such a space would also have to be infinite.
James' acquaintance is producing nothing but series of weasel words in the hope of distancing the truths of scientific methodology from interfering with the fairytale dreams of the godbots. cf similar discussions on "Origins".
Why must abstract concepts be 'accounted for' by postulating some non-material realm? Mathematics is the study of formal systems and concepts such as 2 are parts of those formal systems. These formal systems are defined by collections of axioms. But, and this is important, there are different collections of axioms systems. Some collections give different answers than others. They do not handle the question of 'truth' except in a very technical sense. They consider the question of derivability. So, 2+2=4 is a statement that can be proven from certain assumptions. Whether those assumptions hold in 'reality' is a very different question.

Asking where the number 2 is located is, in my mind, very similar to asking where the game of chess resides. The game of chess is, after all, a formal system. The main difference is that the number 2 (and mathematics in general) has been found to be *useful* for understanding the world around us. But that utility is determined by our ability to state questions in the 'real' world mathematically: in other words as statements that some formal system can deal with. Ultimately, the number 2 and the game of chess both exist in the same sense: as ideas in our minds. If our minds are physical, then there is no need to postulate a separate non-physical mode of existence for either.

As for the question of the existence of God, the question comes down to what it means for something to exist. That is determined by how the concept of 'exist' is defined. The problem is that, unlike in mathematics, there are no agreed upon axioms of philosophy. In particular, philosophers seem to think they are actually stating facts when they are usually simply cloaking their prejudices in fancy words. So, via what axioms is your friend trying to prove the existence of a deity? The question of whether those axioms actually hold is a non-trivial aspect of the question and cannot be determined except through testing. In other words, the scientific method.

In answer to your questions: I think that Plato made a huge error in his concept of non-material universals. It is sensible to ask for scientific evidence of a deity. And philosophy can't prove that a chair exists in my room. Why would I trust it to prove there is a deity?
That's very interesting! Thanks, you've given me lots to think about.

Edit button isn't working.

Anyway, the argument is similar to mine in some ways, but much better stated, and with more knowledge about mathematics.
Another thing to ponder is the nature of 'truth' when it comes to mathematical statements. Let's take the 'obvious' 1+1=2 as an example. Why is it true?

Well, your friend might say that if you take one rock and another rock and put them together, then you will have two rocks. OK, but isn't that more of a statement about rocks than anything else? For example, if you take one lump of silly putty and another lump of silly putty and put them together, you will get one lump of silly putty. We don't use that to show that 1+1=1. You can also point out that one proton colliding into another proton will often produce much more than two protons (that is what happens at various particle accelerators, for example). We say that proton number is not conserved.

Your friend might respond by saying that there is twice as much silly putty in the lump, but ask exactly what that means. If he mentions volume, point out that if you take one gallon of water and add to it one gallon of ethanol (drinking alcohol), you will NOT get two gallons from the mixture, but slightly less (the molecules of water and ethanol intermingle more than either separately). So, again, when you talk about 'conservation of volume', you are talking about how to apply math to the real world and it becomes an experimental question whether the formal system and the real world correspond.

As this analysis proceeds, you will find that mathematical truth may or may not relate to truth in the real world. Whether it does, and in what contexts, is a scientific question, not a philosophical one. This can be related to his overall argument by pointing out that abstract ideas do not have to correspond to the real world and it is a question of science when they do. In particular, whatever axioms your friend proposes to use to prove the existence of God have to be checked to see if they actually are true in the real world.
The statement "1 + 1 = 2" seems to be tautological. Are all mathematical truths tautological?
Perhaps it 'looks' tautological, but it is rather complicated to identify exactly what the statement is saying and why it is true. For example, Russell and Whitehead were not able to prove it in their first volume attempting to reduce math to logic (out of three volumes: Principia Mathematica). Furthermore, their proof would not be seen as valid today. So the issue is rather more complicated than it looks at first glance.

I think the answer to your question depends rather strongly on what sorts of reasoning are considered tautological. Even defining the number 1 is non-trivial.
The universe mustn't necessarily have an immaterial realm at all, maybe all there is is the material world we can study. He also didn't consider that which we find material might both me material and immaterial, ie, some form of monism here. Sciences such as Psychology and Neuroscience support this claim, as we know that the immaterial such as the mind is wired to a material body (the brain).
How can a person assume that there is a immaterial realm? I think your acquaintance is using cop out answers to prove his point. Counter evidence isn't evidence. If you use "unproof" in everyday life you will be insanely irrational.
Thanks for the replies. The discussion with him continues and has strayed from the original topic about universals (where he brought up mathematics), mainly because I have already given him many reasons to doubt his claims, but he continues to claim that he has demonstrated beyond doubt that universals like 2 necessarily indicate a nonmaterial realm.

So when the discussion went on to a god, I asked him about creation and why a creator god who intervenes to create something would not leave evidence. Then he just goes on to say that his god is outside time and thus must always be creating -- yet another cop out, his way of weaseling out of providing any evidence.

Discussions with people on these things will just go on forever because they always come up with a cop out and convoluted reasoning without ever really answering any questions.

I think you are right: most people will bow to the creeds to get the social aspects of religion, the comfort, the ritual. Some people will go on to find some of those same things in a religion like Unitarian Universalism, but I think most people seek a religion that gives more assurance, more tradition, more answers.

As for Christians believing in evolution, I don't think many of them really understand what they are saying. I've heard many Christians say they believe in evolution, yet they don't know what natural selection is and tend to believe that a god directed the course of evolution. Understanding the process of evolution would actually imply the opposite: that we are not designed.





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