I teach about and like to study medieval writers. One perennial debate during the Middle Ages was the "problem of universals."
Now I'm not convinced that universals in the Platonic or Aristotelian sense exist (i.e., rednesss itself, circularity, squareness or beauty as such), but let's assume that we can talk meaningfully about universals, whether they're Platonic, Aristotelian, Ockhamist or Abelardian. We might develop a scenario like the following based on modern psychology:
A) Distal stimulus: a diamond
B) Proximal stimulus: the information from the sensory object (e.g., a diamond) that reaches our sensory receptors
C) Neural networks: the brain is able to form varying representations of the distal stimulus
D) These representations constitute what philosophers have called "universals."
See Rod Plotnik's Introduction to Psychology.
In truth, there is no one answer to this question from a neuroscientific perspective but there are theories which try to explain perception and concept-formation (abstraction). Joseph LeDoux has written an interesting work on this subject entitled The Synaptic Self. I am most convinced by his neuroscientific account and Antonio Damasio's explanation of the embodied self.
Of course, one cannot be dogmatic about such matters, but my ultimate goal is to understand what the self is. How does science correlate to what we learn from Scripture? There appears to be evidence that we do not have souls, but are souls (Genesis 2:7; 1 Corinthians 15:45). While no neuroscientific theory has definitively explained the self, I also don't see a need to invoke the soul concept as an explanation for perception or abstraction.