02
Part I: GEBChapter 2
Meaning and Form in Mathematics
How symbols acquire meaning through isomorphism. The pq-system.
How do meaningless marks on paper become "truth"? This chapter introduces the pq-system, a tiny formal system that mirrors addition. By showing how the mechanical manipulation of dashes (-) is isomorphic to the mathematical concept of adding numbers, Hofstadter demonstrates that meaning is simply a structural correspondence between a symbol system and the real world.
The pq-System Isomorphism
FORMAL SYSTEM
THEOREM
Valid Theorem!
ISOMORPHIC MEANING
2 + 3 = 5
Arithmetic
"The symbols themselves are meaningless. The meaning comes from the isomorphism between the system and reality."