Are Abstract Thoughts Just Patterns in Our Brains?

Atheist computer scientist Jeffrey Shallit and I have been having a discussion about the nature of our abstract thoughts. Are they material things in our brain, or are they immaterial?

Shallit thinks they are material:

[Abstract thoughts are] patterns in brains, of course. If you weren't so stuck in medieval philosophy, even you could have figured that one out... [p]attern is the differential arrangement of matter...

Shallit is right about some kinds thoughts, and wrong about others. We have...