Mr. Jensen, the problem of universals is usually a heavily obfuscated issue. So, pardon me if my post gets too long because it, since the problem of universals cannot be encountered, without clearing up a few more issues.
We have on one side the contradiction between e.g. the general or
abstract “(being) yellow” vs “yellow things”. Most people would have
difficulties recognizing the issue in everyday terms, contrary to
other classical debates with obvious relation to our time (e.g. the
motion of the Sun and the Earth).
First and foremost we must define what it means for something to be abstract in the sense in which philosophers talk of.
1) Non-spatio temporal, i.e. not in space-time.
2) Causally inefficacious.
3) Non-spatio temporal & causally inefficacous.
4) Incomplete objects.
A murderer is led to the place of execution. For the common populace
he is nothing but a murderer. Ladies perhaps remark that he is a
strong, handsome, interesting man. The populace finds this remark
terrible: What? A murderer handsome? How can one think so wickedly and
call a murderer handsome . . . .
This is abstract thinking: to see nothing in the murderer except the
abstract fact that he is a murderer, and to annul all other human
essence in him with this simple quality.
This last one is owed to, and is with the help of Hegel. A man is a lot of things. A husband, a father, a corporate owner, and a murderer. He is not just a murderer simpliciter. To reduce the man to either one of these things, is known as 'abstraction.' For the man is not just a murderer, but a concrete particular which instantiates all those qualities.
Now, the problem of universals can be approached in many ways. But this is the heart of it. Consider two atoms, they have the same spin and charge. When two things agree in attribute, we naturally ask the next question. How can something which is numerically one, run through numerically distinct entities?
Philosophers use the term "numerically" in contrast with "qualitatively." I was given 5 bottles of coca-cola for the party. It won't make a difference if I use the first bottle, or the fourth one. With regard to the quality of it being a cola, at least, there's no problem, since the first bottle and all the other ones are qualitatively identical. By saying that they are the 'same' I mean to say that they are qualitatively the same. If I say that I want a different one, I'm saying I want a numerically different one. However, it won't make any difference whatsoever, with regard to the property of 'being cola.'
If two things are identical in all their respects, then it follows that they are the same (I am not defending the Principle of Constituent identity or Leibniz's Identity of indiscernibles). If two things are qualitatively identical, then it doesn't follow that they the two things are the same. The problem of universals, then, is to account for the pre-analytic datum of how two things agree with each other in attribute. It is in accounting how a numerically one entity runs through numerically distinct particulars.
Since this is such a complex issue, this issue cannot be reduced to any other issues and must be tackled head-on with as much clarity as needed, so trying to reframe the debate which doesn't capture the essence of what's said above will always miss the mark.
Realists believe that this datum can only be accounted by positing entities known as 'universals,' whereas Nominalists either deny such attribute-agreement obtaining and thus see now need to account for any such anomaly. Simply said, you need a theory of properties to solve the problem, and a realist is one who posits that universals obtain in the world, and the nominalist is one who says that they don't obtain in the world, but only in the mind, or some other sort.